University of Southern California Dissertations and Theses

Three-dimensional exospheric hydrogen atom distributions obtained from observations of the geocorona in Lyman-alpha

(USC Thesis Other)

Three-dimensional exospheric hydrogen atom distributions obtained from observations of the geocorona in Lyman-alpha

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content

THREE-DIMENSIONAL EXOSPHERIC HYDROGEN ATOM DISTRIBUTIONS
OBTAINED FROM OBSERVATIONS OF THE GEOCORONA IN LYMAN-ALPHA

by
Justin J. Bailey

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ASTRONAUTICAL ENGINEERING)

May 2012

Copyright 2012 Justin J. Bailey

ii

for my wife, Natalie, a bona fide yogini
who at times had to wrap her hands around my head
to keep my brain from falling out

iii
Acknowledgements

My opportunity to contribute in this field was established and supported by many
different people. After finishing with an M.S. in Astronautical Engineering, I walked
into Professor Mike Gruntman’s office hoping to learn more about space physics and
aeronomy. He proceeded to draw the geocorona in assorted colors on a whiteboard, and
it was then that the content of this dissertation was born. Of course, none of this
research would have been possible were it not for his expertise and guidance.
I would like to thank my advisory committee (Professors Daniel Erwin, Joseph
Kunc, W. Kent Tobiska, and Darrell Judge) for their many insightful observations. I am
especially indebted to Dr. Tobiska for numerous opportunities to learn more about the
solar output and how it drives the exosphere, leading to a much more descriptive science
discussion in the relevant sections.
The TWINS science team offered invaluable feedback, most notably during our
collaboration with Professor Hans J. Fahr and Doctors H. Uwe Nass, Jochen Zoennchen,
and the late Guenter Lay at the University of Bonn. I am particularly grateful to my
colleague and friend, Jochen, for initially providing some necessary details about LAD
operations. Also, I very much appreciate that Raluca Ilie at Los Alamos National
Laboratory allowed me to summarize some of her recent work in ring current modeling
to show an example application of exospheric H density distributions.
This work has been financially supported in part by NASA’s TWINS mission. I
would also like to acknowledge the Northrop Grumman fellowship program for funding
my entire graduate education.

iv
Table of Contents

Dedication ii

Acknowledgements iii

Table of Contents iv

List of Tables vi

List of Figures vii

Abstract xix

Chapter 1: Introduction 1

Chapter 2: The Exosphere 9

Chapter 3: Experimental Study of the Exosphere 16
3.1 Obtaining H Densities from Observations of the Geocorona 16
3.2 Solar Output 17
3.3 Photon Scattering by H Atoms 22

Chapter 4: Interplanetary Glow 25

Chapter 5: Lyman- α Detectors (LADs) on NASA’s TWINS Mission 28
5.1 Instrumentation 28
5.2 Observational Coverage 31
5.3 Data Library 46

Chapter 6: Model 50
6.1 Geophysical Coordinate Systems 50
6.1.1 ECI to GEN 53
6.1.2 ECI to GSE 54
6.1.3 ECI to ECE 55
6.2 LAD Line-of-sight Determination 56
6.3 Earth’s Shadow Approximation 65
6.4 3D Representation of Exospheric H Density Distributions 67
6.5 Least Squares Curve Fitting Procedure 72
6.6 Relative Cross Calibration of the LADs 75
6.7 Example Day, 11 June 2008 82
6.7.1 H Density Radial Profile 88

v
6.7.2 H Distribution Asymmetry 89
6.8 Error Analysis 92

Chapter 7: Spatial and Temporal Response of the Exosphere 96
7.1 Seasonal Variation 96
7.2 Geomagnetic Variation 106
7.3 H Densities at Larger Geocentric Distances 115
7.4 TWINS Simplified Operational Exospheric Model for Solar
Minimum Conditions 117
7.5 Example Application, Ring Current Modeling 126

Chapter 8: Conclusions 132

References 135

Appendix: List of Publications 141

vi
List of Tables

Table 1. Prior models of exospheric H density distributions that were
developed under assumptions of being spherically symmetric, or
representative of typical (not actual) solar conditions, or averaged over an
extended period of time. 14

Table 2: Initial and boundary values for the least squares curve fitting
parameters (, ,
,

,

,

); is in cm
-3
and r is in R
E
. 74

Table 3. Parameters of the exospheric H number density distribution
(Equations 53 – 55) obtained using LAD data from TWINS-1 on 11 June
2008 in Geocentric Equatorial Noon (GEN) coordinates; is in cm
-3
and
r is in R
E
. 82

Table 4. Parameters of the exospheric H number density distribution
(Equations 53 – 55) obtained using LAD data from TWINS-1 on 18-22
June 2008 in Geocentric Equatorial Noon (GEN) coordinates; is in
cm
-3
and r is in R
E
. 98

Table 5. Parameters of the simplified operational model for solar
minimum conditions (Equations 53 – 55) obtained using TWINS-1 LAD
data from June to September 2008 in Geocentric Solar Ecliptic (GSE)
coordinates; is in cm
-3
and r is in R
E
. 123

vii
List of Figures

Figure 1. A 1 minute exposure, wavelength range 105 – 160 nm, of the
optically thick region of the geocorona, taken by astronauts on the Apollo
16 mission. The dark limb of Earth’s nightside is seen silhouetted by the
geocoronal Lyman- α glow [Carruthers et al., 1976]. 2

Figure 2. Space-based measurements of the geocorona include a
contribution of scattered solar Lyman- α radiation that comes from
interplanetary H atoms. 3

Figure 3. Atomic hydrogen number density distribution dependence on
distance from the observer (bottom) for the selected line-of-sight
(top); the middle panel shows the geocentric distance for a given point as a
function of . The blue sphere is the Earth, the yellow line and dot is the
direction to the Sun, the gray cylinder is Earth’s shadow, and the black
curve is the spacecraft trajectory. The observer is at 6.7 R
E
;
= 4.4 R
E
. 5

Figure 4. An energetic neutral atom (ENA) is produced when a fast
energetic ion collides in charge exchange with a slow neutral background
atom. The ENA, not bound by Earth’s magnetic field, can then travel
large distances through space with minimal disturbance. 6

Figure 5. Three-dimensional cutaway drawing of Earth’s magnetosphere
showing currents, fields, and plasma regions [Kivelson and Russell, 1995]. 8

Figure 6. The solar output, shown in F10.7 (top), E10.7 (middle), and
S10.7 (bottom) indices, prominently varies over two time scales. First, the
passage of active regions across the solar disk during a solar rotation
period produces irradiance variations over approximately 27 days.
Second, the solar activity cycle generates irradiance variations over
approximately 11 years. Solar Irradiance Platform (SIP) v2.37 historical
irradiances are provided courtesy of W. Kent Tobiska and Space
Environment Technologies, http://www.spacewx.com/solar2000.html. 18

Figure 7. The composite solar Lyman- α flux at 1 AU, available at the
Laboratory for Atmospheric and Space Physics (LASP) website,
http://lasp.colorado.edu/lisird/lya/, that includes the latest Thermosphere
Ionosphere Mesosphere Energetics and Dynamics (TIMED) Solar EUV
Experiment (SEE) and SOlar Radiation and Climate Experiment (SORCE)
SOLar Stellar Irradiance Comparison Experiment (SOLSTICE)
measurements that have been scaled to the Upper Atmosphere Research
Satellite (UARS) reference level as discussed by Woods et al. [2000]. 19

viii
Figure 8. Scattering intensity I as a function of the scattering angle .
The horizontal dashed line, = 1.0, represents isotropic scattering. 23

Figure 9. The observational geometry used to calculate the resonant
scattering angle, , of Lyman- α photons on exospheric H atoms, which
includes the LAD line-of-sight, , a vector from the spacecraft to the Sun,
, and a vector from the point of scattering to the Sun,
. 24

Figure 10. All-sky image of the interplanetary glow observed by the Solar
Wind ANisotropies (SWAN) instrument on 11 June 2008 (available at the
SWAN website, http://sohowww.nascom.nasa.gov/data/summary/swan/),
where the horizontal axis is ecliptic longitude λ and the vertical axis is
ecliptic latitude β. The non-uniformity of the intensity pattern, coded in
false colors with a scale of counts s
-1
, is due to a combination of varying
interplanetary H atom velocities and ionization processes from the Sun.
The dark areas are field of view obstructions by the sunshield and
spacecraft. The white dots that are denser along the plan of the Milky
Way are the emissions of hot stars. 26

Figure 11. Interplanetary glow on 11 June 2008, derived from SWAN
measurements (W. Pryor and R. Gladstone, personal communication,
2011). Green and pink dots are line-of-sight directions for LAD-1 and
LAD-2, respectively. The horizontal axis is ecliptic longitude λ, the
vertical axis is ecliptic latitude β, and the color bar is in rayleighs. 27

Figure 12. Each TWINS instrument, TWINS-1 and TWINS-2, includes
two ENA imagers, two LADs, and environmental sensors (adapted from
the Instrument Specification Document, March 2008). 29

Figure 13. The field of view, Ω, of each LAD, where is the radius and
is the area at a distance along the line-of-sight . 29

Figure 14. Lyman- α photons pass through a collimator followed by an
optical interference filter before being counted by a channel electron
multiplier. 31

ix
Figure 15. (a) Observational geometry of Lyman- α detectors (LAD-1 and
LAD-2) on a Two Wide-angle Imaging Neutral-atom Spectrometers
(TWINS) satellite in a highly elliptical Molniya-type orbit. The TWINS
mission consists of two satellites, flying in similar orbits that are widely
spaced. Both orbits have an apogee of 7.2 R
E
over the Northern
Hemisphere, an inclination of 63.4°, and an orbital period close to half a
day. Variable
is the geocentric distance of an LAD line-of-sight, ,
closest approach to the Earth. Each LAD has a 4° full width half
maximum field of view, pointed at 40° with respect to the rotating
nominally nadir-pointed instrument platform axis. (b) LAD field of view
coverage through the windshield wiper motion of the instrument platform.
The light and dark shaded sections of the circle show the overlapping
directions covered by LAD-1 ( ω
1
) and LAD-2 ( ω
2
), respectively, as the
actuator rotates through the full motion ( Δω = ± 99°). Note that detector
measurements are only available within the limits Δω = ± 90°. The
windshield wiper motion of the instrument platform results in the LAD
fields of view covering a complete circle, centered on the Earth. 33

Figure 16. LAD observational coverage for TWINS-1 on 11 June 2008.
The coordinate system is Earth Centered Inertial (ECI): the x axis points
toward the vernal equinox and the z axis is the celestial pole. The blue
sphere is the Earth, the yellow line and dot show the direction to the Sun,
the shaded cylinder is Earth’s shadow, the black curve is the spacecraft
trajectory, and the green and pink lines represent the line-of-sight vectors
for LAD-1 and LAD-2, respectively. 35

Figure 17. LAD observational coverage for TWINS-1 on 20 June 2008
(summer solstice). The coordinate system is Earth Centered Inertial
(ECI): the x axis points toward the vernal equinox and the z axis is the
celestial pole. The blue sphere is the Earth, the yellow line and dot show
the direction to the Sun, the shaded cylinder is Earth’s shadow, the black
curve is the spacecraft trajectory, and the green and pink lines represent
the line-of-sight vectors for LAD-1 and LAD-2, respectively. 36

Figure 18. LAD observational coverage for TWINS-1 on 20 July 2008.
The coordinate system is Earth Centered Inertial (ECI): the x axis points
toward the vernal equinox and the z axis is the celestial pole. The blue
sphere is the Earth, the yellow line and dot show the direction to the Sun,
the shaded cylinder is Earth’s shadow, the black curve is the spacecraft
trajectory, and the green and pink lines represent the line-of-sight vectors
for LAD-1 and LAD-2, respectively. 37

x
Figure 19. LAD observational coverage for TWINS-1 on 20 August 2008.
The coordinate system is Earth Centered Inertial (ECI): the x axis points
toward the vernal equinox and the z axis is the celestial pole. The blue
sphere is the Earth, the yellow line and dot show the direction to the Sun,
the shaded cylinder is Earth’s shadow, the black curve is the spacecraft
trajectory, and the green and pink lines represent the line-of-sight vectors
for LAD-1 and LAD-2, respectively. 38

Figure 20. LAD observational coverage for TWINS-1 on 21 July 2009.
The coordinate system is Earth Centered Inertial (ECI): the x axis points
toward the vernal equinox and the z axis is the celestial pole. The blue
sphere is the Earth, the yellow line and dot show the direction to the Sun,
the shaded cylinder is Earth’s shadow, the black curve is the spacecraft
trajectory, and the green and pink lines represent the line-of-sight vectors
for LAD-1 and LAD-2, respectively. 39

Figure 21. LAD observational coverage for TWINS-1 on 6 August 2011.
The coordinate system is Earth Centered Inertial (ECI): the x axis points
toward the vernal equinox and the z axis is the celestial pole. The blue
sphere is the Earth, the yellow line and dot show the direction to the Sun,
the shaded cylinder is Earth’s shadow, the black curve is the spacecraft
trajectory, and the green and pink lines represent the line-of-sight vectors
for LAD-1 and LAD-2, respectively. 40

Figure 22. The longitude of the ascending node Ω (black dots), argument
of perigee (blue dots), beta angle (green dots), right ascension of the
Sun
(red dots), and declination of the Sun
(pink dots) for each
orbit of the TWINS-1 satellite in 2008 (top) through 2011 (bottom). The 4
black vertical lines in each year mark vernal equinox, summer solstice,
autumnal equinox, and winter solstice. The yellow shaded regions
highlight when the orbit apogees are on the dayside of the Earth. 44

Figure 23. The longitude of the ascending node Ω (black dots), argument
of perigee (blue dots), beta angle (green dots), right ascension of the
Sun
(red dots), and declination of the Sun
(pink dots) for each
orbit of the TWINS-2 satellite in 2008 (top) through 2011 (bottom). The 4
black vertical lines in each year mark vernal equinox, summer solstice,
autumnal equinox, and winter solstice. The yellow shaded regions
highlight when the orbit apogees are on the dayside of the Earth. 45

xi
Figure 24. The percentage of TWINS-1 LAD measurements from each
day in 2008 (top) through 2011 (bottom) that, based on various
observational geometry and housekeeping criteria, have been classified as
valid for scientific analysis and available for use in obtaining exospheric H
density distributions. Note, data was unavailable for 3 weeks in
September 2009. 48

Figure 25. The percentage of TWINS-2 LAD measurements from each
day in 2008 (top) through 2011 (bottom) that, based on various
observational geometry and housekeeping criteria, have been classified as
valid for scientific analysis and available for use in obtaining exospheric H
density distributions. Note, data was unavailable for 2 weeks in
September 2009. 49

Figure 26. Angles right ascension and declination defined in the Earth
Centered Inertial (ECI) coordinate system. 51

Figure 27. Longitudinal angle θ and co-latitudinal angle ϕ defined in the
Geocentric Equatorial Noon (GEN) coordinate system. 52

Figure 28. The ecliptic longitude λ and ecliptic latitude β defined in the
Earth Centered Ecliptic (ECE) coordinate system. 53

Figure 29. Rotation about the angle right ascension, , required to
transform from ECI to GEN. 53

Figure 30. The transformation from ECI to GSE coordinates includes a
rotation about the ecliptic pole ( ̂
), which is fixed in the ECI system. 54

Figure 31. The rotation about Earth’s obliquity, , required to transform
from ECI to ECE. 56

Figure 32. A side view of the TWINS instrument with the polar ( ̂) and
azimuthal ( ) directions (Instrument Specification Document, March
2008). 57

Figure 33. Top view of the TWINS instrument frame, ̂, , and ̂. The
Toward and Away directions are defined for the ENA sensor heads that
look toward or away from the electronics box. The LADs are named in a
similar respect to be consistent with the ENA sensor head directions. For
example, the LAD sensor head that looks predominately in the direction of
the ENA Toward is termed the LAD Toward, also known as LAD-1
(adapted from the Instrument Specification Document, March 2008). 58

xii
Figure 34. Top view of TWINS showing the rotation about the actuator
angle ω from the instrument frame ( ̂, , ̂) to the actuator frame ( ̂ , ,
̂ ) (adapted from the Instrument Specification Document, March 2008). 59

Figure 35. The LAD boresights are fixed in the actuator frame ( ̂ , ,
̂ ) by a rotation of ±40° about . 60

Figure 36. The observational geometry used to calculate the geocentric
distance of an LAD line-of-sight closest approach to the Earth,
. The
angle is between the LAD line-of-sight, , and the spacecraft position,
/. 61

Figure 37. The Lyman- α intensity in rayleighs observed by both LAD-1
(green dots) and LAD-2 (pink dots) on TWINS-1 for 11 June 2008 versus
the geocentric distance of each line-of-sight closest approach to the Earth,

. 62

Figure 38. The Lyman- α intensity observed by both LAD-1 (green dots)
and LAD-2 (pink dots) on TWINS-1 for 20 June 2008 versus the
geocentric distance of each line-of-sight closest approach to the Earth,

. 63

Figure 39. A sequence of LAD-1 (green) and LAD-2 (pink)
measurements from TWINS-1 on 16 June 2008 that includes a possible
star sighting. The horizontal axis is the sector number for the day and the
vertical axis is the measured Lyman- α intensity in rayleighs. 64

Figure 40. A sky map with the spectral classes of stars in the Southern
Hemisphere. The dotted circle around the polar vector ( ̂) are the lines-of-
sight for LAD-1 (dark blue) and LAD-2 (light blue) for one rotation of the
actuator. 65

Figure 41. The observational geometry used to approximate Earth’s
shadow as a cylinder. The variables and are the spacecraft and Earth
positions, respectively. The variable is the distance along the LAD
line-of-sight, , and the variable is the distance along the antisolar
direction,
, where the minimum distance between the two lines, l,
occurs along the unit vector . 67

xiii
Figure 42. Three-dimensional color plots of the asymmetry introduced for
positive (left) and negative (right) values of each expansion coefficient
with respect to an x axis (gray line) and z axis (black line). Setting a
particular coefficient to zero during the fitting procedure eliminates the
possibility for the corresponding asymmetry in the obtained three-
dimensional H density distribution. 71

Figure 43. LAD-1 (green dots) and LAD-2 (pink dots) measured Lyman-
α intensities at ω = -90°and ω = 90°, respectively, for both TWINS-1
orbits on 6 August 2011. 76

Figure 44. The Lyman- α intensity observed by both LAD-1 (green dots)
and LAD-2 (pink dots) on TWINS-1 for 6 August 2011 versus the
geocentric distance of each line-of-sight closest approach to the Earth,

. 77

Figure 45. LAD-1 (green dots) and LAD-2 (pink dots) measured Lyman-
α intensities at ω = -90°and ω = 90°, respectively, for both TWINS-1
orbits on 6 August 2011; the LAD-1 measurements have been increased
by a factor of 1 / 0.80 = 1.25. 78

Figure 46. The Lyman- α intensity observed by both LAD-1 (green dots)
and LAD-2 (pink dots) on TWINS-1 for 6 August 2011 versus the
geocentric distance of each line-of-sight closest approach to the Earth,

; the LAD-1 measurements have been increased by a factor of 1 / 0.80
= 1.25. 79

Figure 47. The ratio of cross calibration, LAD-1 / LAD-2, for TWINS-1
from 2008 (top) through 2011 (bottom). 80

Figure 48. The ratio of cross calibration, LAD-1 / LAD-2, for TWINS-2
from 2008 (top) through 2011 (bottom). 81

Figure 49. Contour plots of the exospheric H number density distribution
on 11 June 2008: (left) an equatorial (XY plane) cross section and (right) a
meridional (XZ plane) cross section. Also shown are the definitions of the
angles ϕ and θ. Contours are lines of constant neutral hydrogen number
density (cm
-3
); the color bar is for the contour lines; the yellow dot is the
projection of the direction to the Sun (left) and the direction to the Sun
(right); the filled shaded circle represents the region with radius 3 R
E
; and
the grid of shaded concentric circles for r > 3 R
E
, with a 1 R
E
step,
highlights the asymmetry of the distribution. 83

xiv
Figure 50. Exospheric H number density in the obtained 11 June 2008
distribution as a function of angles ϕ and θ for geocentric distances 3 R
E

(top), 6 R
E
(middle), and 8 R
E
(bottom). In the left plots ( θ = 90°), the
angle ϕ = 0° is equatorial noon and the angle ϕ = 90° is dusk. In the right
plots ( ϕ = 0°), the angle θ = 0° is north and the angle θ = 90° is equatorial
noon. 85

Figure 51. Three-dimensional contour plots of the exospheric H number
density distribution on 11 June 2008 for spherical shells at 6 different
geocentric distances from 3 R
E
to 8 R
E
; the gray lines point toward
equatorial noon, the black lines are the celestial pole, the yellow lines are
the direction to the Sun, and the color bars are in cm
-3
. 87

Figure 52. Comparison of different H number density profiles on 11 June
2008 from this work (solid line), Rairden et al. [1986] (circles), Hodges
[1994] at solstice for F10.7 = 80 (crosses), Østgaard et al. [2003] for solar
zenith angle 90° (long dashed line), and Zoennchen et al. [2010] on 11
June 2008 (short dashed line). 89

Figure 53. Exospheric H number density radial dependencies of the 11
June 2008 distribution toward north (solid line), south (long dashed line),
equatorial noon (short dashed line), and equatorial midnight (dotted line). 91

Figure 54. The estimated uncertainty in the obtained 11 June 2008
distribution. The distribution should be restricted to r < 8 R
E
, or used with
appropriate caution for higher geocentric distances. 94

Figure 55. The H number density profile for the obtained 11 June 2008
distribution with error bars to represent the fitting uncertainty. 95

Figure 56. Contour plots of the exospheric H number density distribution
on 18-22 June 2008: (left) an equatorial (XY plane) cross section and
(right) a meridional (XZ plane) cross section. Also shown are the
definitions of the angles ϕ and θ. Contours are lines of constant neutral
hydrogen number density (cm
-3
); the color bar is for the contour lines; the
yellow dot is the projection of the direction to the Sun (left) and the
direction to the Sun (right); the filled shaded circle represents the region
with radius 3 R
E
; and the grid of shaded concentric circles for r > 3 R
E
,
with a 1 R
E
step, highlights the asymmetry of the distribution. 99

xv
Figure 57. Exospheric H number density in the obtained 18-22 June 2008
distribution as a function of angles ϕ and θ for geocentric distances 3 R
E

(top), 6 R
E
(middle), and 8 R
E
(bottom). In the left plots ( θ = 90°), the
angle ϕ = 0° is equatorial noon and the angle ϕ = 90° is dusk. In the right
plots ( ϕ = 0°), the angle θ = 0° is north and the angle θ = 90° is equatorial
noon. 101

Figure 58. Three-dimensional contour plots of the exospheric H number
density distribution on 18-22 June 2008 for spherical shells at 6 different
geocentric distances from 3 R
E
to 8 R
E
; the gray lines point toward
equatorial noon, the black lines are the celestial pole, the yellow lines are
the direction to the Sun, and the color bars are in cm
-3
. 102

Figure 59. Exospheric H number density radial dependencies of the 18-22
June 2008 distribution toward north (solid line), south (long dashed line),
equatorial noon (short dashed line), and equatorial midnight (dotted line). 104

Figure 60. Contour plots of the exospheric H number density distribution
on 18-22 June 2008 (top), 18-22 July 2008 (middle), and 18-22 August
2008 (bottom). The left plots are an equatorial (XY plane) cross section
and the right plots are a meridional (XZ plane) cross section. Also shown
are the definitions of the angles ϕ and θ. Contours are lines of constant
neutral hydrogen number density (cm
-3
); the color bar is for the contour
lines; the yellow dot is the projection of the direction to the Sun (left) and
the direction to the Sun (right); the filled shaded circle represents the
region with radius 3 R
E
; and the grid of shaded concentric circles for r > 3
R
E
, with a 1 R
E
step, highlights the asymmetry of the distribution. 105

Figure 61. The disturbance storm time, Dst, index from 2008 (top)
through 2011 (bottom), available at the World Data Center for
Geomagnetism website, http://wdc.kugi.kyoto-u.ac.jp/, provided by Kyoto
University. 107

Figure 62. The Dst index (top) and number of H atoms between 3 R
E
to 8
R
E
calculated using the obtained density profiles (bottom) from 1 August
2011 to 1 October 2011. The four gray vertical lines in the bottom panel
mark the hour of lowest Dst value for the corresponding magnetic storms. 109

xvi
Figure 63. The Lyman- α intensity observed by both LADs on TWINS-1
for 10 September 2011 versus the geocentric distance of each line-of-sight
closest approach to the Earth,
, color coded on an hourly basis. The
storm sudden commencement occurred on 9 September 2011 at 10:00 PM.
The Dst index began dropping on 10 September 2011 at 1:00 AM, reached
-60 nT at 4:00 AM, and remained low before recovering from -64 nT at
4:00 PM. 110

Figure 64. The Lyman- α intensity observed by both LADs on TWINS-1
for 27 September 2011 versus the geocentric distance of each line-of-sight
closest approach to the Earth,
, color coded on an hourly basis. The
storm sudden commencement occurred on 26 September 2011 at 10:00
PM. The Dst index began dropping on 27 September 2011 at 1:00 AM
and reached -103 nT at 10:00 AM before recovering. 111

Figure 65. The intergral electron flux (electrons cm
-2
s
-1
sr
-1
), averaged in
5 min intervals, with energies ≥ 0.8 MeV (purple and orange curves) and ≥
2 MeV (blue and red curves) from 9 September 2011 to 12 September
2011, data available at the National Oceanic and Atmospheric
Administration (NOAA) Space Weather Prediction Center (SWPC)
website, http://www.swpc.noaa.gov/today.html. 112

Figure 66. The intergral electron flux (electrons cm
-2
s
-1
sr
-1
), averaged in
5 min intervals, with energies ≥ 0.8 MeV (purple and orange curves) and ≥
2 MeV (blue and red curves) from 26 September 2011 to 29 September
2011, data available at the NOAA SWPC website,
http://www.swpc.noaa.gov/today.html. 113

Figure 67. The integral proton flux (protons cm
-2
s
-1
sr
-1
), averaged in 5
minute intervals, for energy thresholds of ≥ 10 MeV (red curves), ≥ 50
MeV (blue curves), and ≥ 100 MeV (green curves) from 9 September
2011 to 12 September 2011, data available at the NOAA SWPC website,
http://www.swpc.noaa.gov/today.html. 114

Figure 68. The integral proton flux (protons cm
-2
s
-1
sr
-1
), averaged in 5
minute intervals, for energy thresholds of ≥ 10 MeV (red curves), ≥ 50
MeV (blue curves), and ≥ 100 MeV (green curves) from 26 September
2011 to 29 September 2011, data available at the NOAA SWPC website,
http://www.swpc.noaa.gov/today.html. 115

Figure 69. The radial dependence of predicted intensity on the position of
a hypothetical observer looking radially away from the Earth. Two
horizontal lines show the range of interplanetary glow intensities for all
directions covered by the LADs on 11 June 2008. 116

xvii
Figure 70. Interplanetary glow on 11 June 2008, derived from SWAN
measurements (Pryor and Gladstone, personal communication, November
2010). The horizontal axis is ecliptic longitude λ, the vertical axis is
ecliptic latitude β, and the color bar is in rayleighs. 118

Figure 71. LAD-1 measured intensities for 11 June 2008 (black), 22-24
July 2008 (blue), 15-17 August 2008 (green), and 1-13 September 2008
(red) versus the geocentric distance of each line-of-sight closest approach
to the Earth,
. 120

Figure 72. LAD-2 measured intensities for 11 June 2008 (black), 22-24
July 2008 (blue), 15-17 August 2008 (green), and 1-13 September 2008
(red) versus the geocentric distance of each line-of-sight closest approach
to the Earth,
. 121

Figure 73. Comparison of different H number density profiles including
segments (A) and (B) of the TWINS simplified operational exospheric
model for solar minimum conditions [Zoennchen et al., 2010] (solid line),
Rairden et al. [1986] (circles), and Østgaard et al. [2003] for solar zenith
angle 90° (long dashed line). 124

Figure 74. Contour plots of the exospheric H number density distribution
for the TWINS simplified operational model for solar minimum
conditions: (left) an ecliptic (XY plane) cross section and (right) a
meridional (XZ plane) cross section. Also shown are the definitions of the
angles ϕ and θ. Contours are lines of constant neutral hydrogen number
density (cm
-3
); the color bar is for the contour lines; the yellow dots are the
direction to the Sun; the filled shaded circle represents the region with
radius 3 R
E
; and the grid of shaded concentric circles for r > 3 R
E
, with a 1
R
E
step, highlights the asymmetry of the distribution. 125

Figure 75. The TWINS mission stereoscopically images features of the
magnetosphere from two satellites in widely spaced Molniya-type orbits,
ideal for imaging ENAs that originate in the ring current (J. Goldstein). 126

xviii
Figure 76. Variation of the charge exchange decay rate of ring current H
+

ions with 88° (top), 60° (middle), and 30° (bottom) equatorial pitch angle,
at a radial distance of 5 R
E
at midnight ( ϕ = 0°, left column) and dawn ( ϕ =
90°, right column) obtained using H density distributions from Rairden et
al. [1986] (black), Hodges [1994] (blue), Østgaard et al. [2003] (red), the
11 June 2008 distribution [Bailey and Gruntman, 2011] (green), and
Zoennchen et al. [2011] (light blue) [Ilie et al., 2011]. 128

Figure 77. TWINS-2 observation of ENA fluxes in the 6 – 18 keV energy
range (top left) and reconstructed ENA images using 5 different H density
distributions: Rairden et al. [1986] (top right), Hodges [1994] (center left),
Østgaard et al. [2003] (center right), Zoennchen et al. [2011] (bottom
left), and the 11 June 2008 distribution [Bailey and Gruntman, 2011]
(bottom right) [Ilie et al., 2011]. 130

xix
Abstract

Exospheric atomic hydrogen (H) resonantly scatters solar Lyman- α (121.567
nm) radiation, observed as the glow of the geocorona. Measurements of scattered solar
photons allow one to probe time-varying three-dimensional distributions of exospheric
H atoms. The Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS) mission
images the magnetosphere in energetic neutral atom (ENA) fluxes and additionally
carries Lyman- α Detectors (LADs) to register line-of-sight intensities of the geocorona.
This work details a process for preparing TWINS data such that LAD measurements can
be used to obtain global H density distributions with three-dimensional asymmetries
above 3 earth radii. Sequences of distributions are presented to investigate the dynamic
exosphere, responding to seasonal variations between a summer solstice and autumnal
equinox, as well as to solar and geomagnetic variations as described by commonly used
indices. The distributions reveal asymmetries from day to night, north to south, and
dawn to dusk. A nightside extension persists that is consistent with the location of a
geotail. A seasonal north-south asymmetry occurs as solar illumination differs between
the summer and winter polar regions. Pole-equator and less pronounced dawn-dusk
asymmetries also appear, possibly due to a coupling effect via charge exchange with the
polar wind and plasmasphere, respectively.
A common phenomenon in geospace occurs as magnetospheric energetic ions
collide with neutral background atoms and produce ENAs that, no longer bound by
Earth’s magnetic field, can travel large distances though space with minimal disturbance
— providing an opportunity for remote detection. Knowledge of the distribution of the

xx
primary neutral partner, exospheric H atoms, is therefore essential for the interpretation
of ENA fluxes and subsequent retrieval of ion densities. An analysis is summarized that
demonstrates the importance of exospheric H density distributions on reconstructing
magnetospheric images in ENA fluxes and obtaining ring current ion densities.
Some of the main findings in this work have been accepted [Ilie et al., 2012] or
are already published [Bailey and Gruntman, 2011; Zoennchen et al., 2011] in various
scientific journals.

1
Chapter 1: Introduction

The most abundant neutral constituent in Earth’s upper exosphere, atomic
hydrogen (H), resonantly scatters solar Lyman- α (121.567 nm) radiation – creating a
phenomenon known as the geocorona. Several space experiments have observed the
geocorona under various conditions. The first geocoronal Lyman- α measurements were
obtained by sounding rocket experiments that started in the late 1950s [e.g., Kupperian
et al., 1959; Donahue, 1966]. In comparison to rocket-born experiments, satellite
missions provided observations over longer time scales. In particular, these longer
duration observations were first recorded by three of the Orbiting Geophysical
Observatory satellites, OGO-3, -4, -5, and -6 [Bertaux and Blamont, 1970; Mange and
Meier, 1970; Thomas, 1970], followed by one of the Orbiting Solar Observatory
satellites, OSO-4 [Thomas and Bohlin, 1972; Bertaux and Blamont, 1973; Meier and
Mange, 1973; Thomas and Anderson, 1976]. The interplanetary spacecraft Mariner 5
observed the dayside geocorona as it departed for Venus [Wallace et al., 1970].
Additionally, images of the geocorona were captured by astronauts using a far-
ultraviolet camera/spectrograph from the lunar surface during the Apollo 16 mission
[Carruthers et al., 1976]. Figure 1 is one such image with the limb of Earth’s nightside
silhouetted by the optically thick region of the geocorona. The spatial distribution over
a large region is captured for a short period (1 minute) of time. A sequence of images
could be used to unambiguously separate spatial and temporal variations.

2

Figure 1. A 1 minute exposure with wavelength range 105 – 160 nm of the optically
thick region of the geocorona, taken by astronauts on the Apollo 16 mission. The dark
limb of Earth’s nightside is seen silhouetted by the geocoronal Lyman- α glow
[Carruthers et al., 1976].

More recent space experiments have been used to reconstruct global H density
distributions over time scales which depend on observational coverage [Rairden et al.
1983, 1986; Østgaard et al., 2003; Zoennchen et al., 2010]. This experimental study
uses Lyman- α Detector (LAD) measurements from the Two Wide-angle Imaging
Neutral-atom Spectrometers (TWINS) mission [McComas et al., 2009] to obtain global
distributions with three-dimensional asymmetries for time periods of a day or five days.
The LADs register line-of-sight intensities of Lyman- α radiation that resonantly scatters
on H atoms of both terrestrial and extraterrestrial origins. The contribution that comes

3
from interplanetary H atoms, called the interplanetary glow, must be approximated and
subtracted out of measurements to obtain exospheric H density distributions.

Figure 2. Space-based measurements of the geocorona include a contribution of
scattered solar Lyman- α radiation that comes from interplanetary H atoms.

The geocorona reveals an exosphere that is asymmetric, including higher
nightside densities, sometimes called the geotail [e.g., Thomas and Bohlin, 1972;
Bertaux and Blamont, 1973; Carruthers et al., 1976; Rairden et al., 1986; Østgaard et
al., 2003; Zoennchen et al., 2010]. This work focuses on geocentric distances r > 3 R
E

(1 R
E
= 6371 km is Earth’s mean radius), where the H densities are low enough to
Exosphere
Interplanetary
Ly- α Background
Solar Lyman- α
40°
40°
Molniya
Orbit
LAD-1
FOV
LAD-2
FOV
TWINS

4
assume optically thin conditions. The uncertainty introduced by assuming optically thin
conditions does not exceed 20% at the minimal geocentric distance of 3 R
E
and
decreases with altitude. Closer to Earth, the denser conditions require a much more
complex essentially radiation transfer treatment [e.g., Thomas, 1963; Meier, 1969; Meier
and Mange, 1970; Anderson and Hord, 1977; Rairden et al., 1986; Bush and
Chakrabarti, 1995; Bishop, 1999] that is beyond the scope of this work. In this single
scattering environment, the observed intensity of scattered Lyman- α radiation is simply
proportional to the integral of the H density over the line-of-sight. The predicted
intensity flux, , as observed by the LADs, in units of rayleigh (R), 1 R = 10
6
/(4 π) phot
cm
-2
s
-1
sr
-1
, is

∗
10

, (1)

where is the local H number density along the line-of-sight ; is a factor that
accounts for the angular dependence of scattered Lyman- α photons; ∗
is the local
(adjusted to the actual heliocentric distance) scattering rate, the g-factor; and
is the
contribution of resonantly scattered Lyman- α radiation that comes from the
extraterrestrial H population, called the interplanetary glow. Figure 3 shows the
predicted H number density along a selected line-of-sight, as an example, allowing one
to see the contributions of various parts of the exosphere. The line-of-sight passes
through the Northern Hemisphere with a maximum H number density of = 175 cm
-3

at a geocentric distance of closest approach to the Earth of
= 4.4 R
E
.

5

Figure 3. Atomic hydrogen number density distribution dependence on distance from
the observer (bottom) for the selected line-of-sight (top); the middle panel shows the
geocentric distance for a given point as a function of . The blue sphere is the Earth, the
yellow line and dot is the direction to the Sun, the gray cylinder is Earth’s shadow, and
the black curve is the spacecraft trajectory. The observer is at 6.7 R
E
;
= 4.4 R
E
.

The interaction between charged and neutral particles is a common phenomenon
in geospace. Energetic ions collide with neutral background atoms and produce

6
energetic neutral atoms (ENAs) that, no longer bound by Earth’s magnetic field, can
travel large distances through space with minimal disturbance (Figure 4), providing an
opportunity for remote detection [Roelof, 1987; Gruntman, 1997].

Figure 4. An energetic neutral atom (ENA) is produced when a fast energetic ion
collides in charge exchange with a slow neutral background atom. The ENA, not bound
by Earth’s magnetic field, can then travel large distances through space with minimal
disturbance.

The most abundant space plasma ion is protons (H
+
). Unlike other space plasma ions
(e.g., He
+
and O
+
), protons cannot be imaged optically and consequently the only
practical way to remotely image populations is with ENAs. Since the primary charge
exchange interaction is between protons and H atoms,

→

, (2)

+
+
Energetic Neutral
Atom (ENA) - Fast
Neutral Hydrogen Atom - Slow
Energetic Ion - Fast

7
knowledge of the H density distribution is essential for the interpretation of ENA fluxes
and subsequent retrieval of ion densities. Furthermore, this charge exchange process is
important to the plasma budget of Earth’s magnetosphere. A coupling effect via charge
exchange exists between the exosphere and the magnetospheric region of least energetic
plasma, the plasmasphere. High densities (~ 10
3
cm
-3
) of cold (~ 1 eV) plasma exist in
approximately the same region of space as the Van Allen radiation belts, terminating at
the plasmapause, which varies from geocentric distances of 4 R
E
to 6 R
E
[Kivelson and
Russell, 1995]. An equatorial cross section of the average shape of the plasmapause
includes a bulge on the duskside, a result of the opposing nature of the convection
(cross-tail) and corotation electric fields [Carpenter, 1970; Chappell et al., 1970;
Carpenter et al., 1993]. The enhanced duskside proton densities can rotate somewhat in
local time due to interaction between the electric ( ) and magnetic ( ) fields,

drift, depending on magnetospheric condition. The principal mechanism by which the
ring current, shown in Figure 5, loses ions following the occurrence of a geomagnetic
storm is charge exchange with exospheric H atoms. The spatial distribution of
exospheric H atoms is therefore essential to understanding the dynamics of certain
magnetospheric processes such as ring current recovery.

8

Figure 5. Three-dimensional cutaway drawing of Earth’s magnetosphere showing
currents, fields, and plasma regions [Kivelson and Russell, 1995].

9
Chapter 2: The Exosphere

The exosphere is the outermost layer of Earth’s neutral atmosphere. The lower
boundary, the exobase, is typically defined as the height above which collisions become
negligible to the motion of particles and is conventionally placed at an altitude of 500
km. The upper boundary can be defined theoretically where the influence of solar
radiation pressure on H atom velocities exceeds that of Earth’s gravitational pull. The
force of solar radiation pressure [Chamberlain and Hunten, 1987],
, on an H atom is

,
(3)

where is Planck’s constant and is the scattering rate of Lyman- α photons at
wavelength = 121.567 nm. The force of Earth’s gravity, , on an H atom is

,
(4)

where is the gravitational constant, is the mass of the Earth, is the mass of an
H atom, and is the geocentric distance. An upper boundary of the exosphere can be
calculated, by setting

,

10

,
(5)

as 28 R
E
to 44 R
E
for the maximum and minimum, respectively, Lyman- α fluxes over
the last 5 solar cycles using the method detailed in Section 3.1 to obtain the scattering
rate, , at 1 AU.
As initially described by Chamberlain [1963], the exosphere is comprised of
three main particle populations, ballistic, escaping, and satellite, moving in Earth’s
gravitational field and influenced by solar radiation pressure. Atoms in ballistic
trajectories rise from the exobase, which is usually assumed to be between 400 and 800
km, depending on solar conditions, and eventually fall back. Atoms with velocities
larger than escape velocities depart from the exobase and leave on hyperbolic
trajectories. Atoms in satellite trajectories have been scattered or injected into closed
orbits by rare elastic collisions or charge exchange, respectively, and do not intersect the
exobase.
Ballistic trajectories dominate in a region immediately above the exobase. As
the density of this population rapidly decreases towards higher altitudes, satellite
particles begin to dominate above where some of the collisions and subsequent orbit
apses occur. Escaping particles are present at all altitudes and at higher altitudes they
are the only terrestrial population that remains. Farther away from Earth, extraterrestrial
hydrogen becomes dominant. This interplanetary population is principally comprised of
inflowing interstellar H atoms from the local interstellar medium (LISM) [e.g., Fahr,

11
1974; Holzer, 1977; Meier, 1977; Thomas, 1978; Bertaux, 1984; Clarke et al., 1998;
Stephan et al., 2001; Quémerais et al., 2003]. It is also possible that energetic neutral
atoms (ENAs) originating in the heliospheric sheath region contribute significantly to
neutral atoms within 1 AU from the Sun [Gruntman and Izmodenov, 2004; Schwadron
and McComas, 2010]. At 1 AU, the extraterrestrial H number density varies between
10
-4
and 10
-2
cm
-3
.
Solar radiative heating largely determines temperature and density at the
exobase, which, in turn, causes a departure from spherical symmetry of the exosphere.
Heating of the upper atmosphere on the dayside, by solar X-ray and extreme ultraviolet
(EUV) radiation, also causes asymmetry. For example, a seasonal north-south
asymmetry occurs as solar illumination differs between the summer and winter polar
regions. In addition, a coupling effect via charge exchange exists between the exosphere
and plasmasphere [e.g., Bishop, 1985; Rairden et al., 1986; Tinsley et al., 1986; Hodges,
1994].
Beyond a few Earth radii, the Keplerian motion of H atoms is also highly
susceptible to an effective pressure caused by the resonant scattering of solar Lyman- α
radiation. This radiation pressure force varied between the extremes of 0.85 and 2.1
times the Sun’s gravitational attraction of H atoms over the last five solar cycles. The
effect of this radiation pressure is rather complex and the details of how it influences the
satellite population is not quantitatively completely understood yet. Some argue that the
satellite population would extend in the antisolar direction, contributing to the geotail
[Bertaux and Blamont, 1973; Bertaux et al., 1995; Østgaard et al., 2003; Zoennchen et

12
al., 2010]. However, this intuitive explanation contradicts the theoretical predictions
made by Chamberlain [1979] and Hodges [1994] who suggested that the geotail was not
enhanced as a result of solar radiation pressure rotating the line of apsides of satellite H
orbits such that the apogees are shifted away from the Sun.
A numerical simulation performed by Bertaux and Blamont [1973] showed that
the number of scattering perturbations necessary to significantly alter the orbital
parameters of particles in the exosphere corresponds to a time longer than the
characteristic time of particles in ballistic and hyperbolic trajectories, but shorter than
the lifetime of particles in satellite orbits — leading to a conclusion that that the geotail
must be enhanced by solar radiation pressure on satellite H atoms. Conversely,
Chamberlain [1979] demonstrated that the global structural “shape” would be
symmetric in the three principal axes but noted that his perturbation technique was
unreliable for trajectories that extend well away from Earth due to the long times spent
near apogee. Chamberlain [1980] speculated that the existence of a geotail may be due
to solar radiation pressure on a loosely bound population of satellite H atoms. The
relevant later work [e.g., Bishop, 1985; Hodges, 1994; Bertaux et al., 1995; Østgaard et
al., 2003; Zoennchen et al., 2010; Bailey and Gruntman, 2011] has yet to definitively
identify the source mechanisms that create the geotail.
More recently, Rairden et al. [1983, 1986] fit a spherically symmetric model to
geocoronal measurements by Dynamics Explorer 1 (DE 1). They also experimentally
confirmed the existence of a geotail.

13
Hodges [1994] used Monte Carlo simulations to obtain asymmetric global H
distributions under solar conditions characterized by F10.7 values representative of a
typical solar cycle. For each used F10.7 value (80, 130, 180, and 230), distributions
were presented for both equinox and solstice. The H concentrations were noticeably
greater at solstice. In addition, his theoretical predictions exhibited an enhancement in
the antisolar direction (geotail) and a secondary enhancement in the solar direction. By
running simulations with and without resonant scattering of solar Lyman- α photons, he
showed that both maxima are related to the effect of solar radiation pressure. He argued
that the presence of two maxima contradicts the notion that solar radiation pressure
simply turns the line of apsides of satellite H orbits such that the apogees are pushed
tailward.
Using the Geocoronal Imager (GEO) on board the Imager for Magnetopause-to-
Aurora Global Exploration (IMAGE) mission, Østgaard et al. [2003] derived H density
profiles that were close to what was reported in Rairden et al. [1986]. However, above
8 R
E
, they found higher densities. They also confirmed the existence of a geotail and
attributed this feature to solar Lyman- α radiation pressure on the satellite population.
A group at the University of Bonn used Lyman- α measurements [Zoennchen et
al., 2010] from the LADs on TWINS to derive asymmetric exospheric H distributions
for the Northern Hemisphere. They applied a conveniently simplified version [Nass et
al., 2006] of the mathematical expansion developed by Hodges [1994] to obtain
distributions in the summer months of 2008. As compared to Hodges [1994] and
Østgaard et al. [2003], the Bonn group found significantly higher day-night asymmetry,

14
showing a much more pronounced geotail. Additionally, the Bonn group observed
much weaker pole-equator asymmetry than Hodges [1994].
Prior models of exospheric H density distributions were usually developed under
assumptions of being spherically symmetric, or representative of typical (not actual)
solar conditions, or averaged over an extended period of time (Table 1). For example,
the Chamberlain [1963] model is spherically symmetric and based entirely on
theoretical predictions. The Rairden et al. [1986] model is spherically symmetric and
averages DE 1 observations over a 4 year period assuming a constant solar Lyman- α
flux at 1 AU of 3.0 × 10
11
ph cm
-2
s
-1
. While the Hodges [1994] model is asymmetric,
its distributions were computationally rather than experimentally derived and are
representative of four F10.7 solar cycle conditions at equinox and solstice. The
Østgaard et al. [2003] model is asymmetric, but due to the specifics of GEO/IMAGE
observational geometry it averages measurements over the time scale of a year.

Table 1. Prior models of exospheric H density distributions that were developed under
assumptions of being spherically symmetric, or representative of typical (not actual)
solar conditions, or averaged over an extended period of time.
Model
Spherically
Symmetric
Solar Output Averaging
Chamberlain, 1963 Yes Indirect Constant
Rairden et al., 1983 Yes Lyman- α 4 years
Hodges, 1994 No F10.7
Solstice and
Equinox
Østgaard et al., 2003 No Lyman- α 1 year

15
This work expands the Bonn model developed by Nass et al. [2006] to describe
the spatial distribution of exospheric H density. Specifically, the modifications include
(1) additional fitting parameters sensitive to possible dawn-dusk asymmetry, (2) an
accurate anisotropic photon scattering function, (3) a photon scattering rate at 1 AU (g-
factor) obtained from independent measurements of the solar Lyman- α, and (4) an
experimentally determined interplanetary glow background derived directly from Solar
Wind Anisotropies (SWAN) measurements on the SOlar and Heliospheric Observatory
(SOHO) mission.

16
Chapter 3: Experimental Study of the Exosphere

The method used to retrieve exospheric H densities relies on measuring the
brightness of the geocorona. The obtained H atom abundance and three-dimensional
asymmetries are therefore directly dependent on the measurement accuracy of both the
geocoronal brightness from the LADs (Section 3.1) and independent observations of the
solar Lyman- α irradiance (Section 3.2). Furthermore, the use of accurate anisotropic
scattering of Lyman- α photons is essential to avoid artifacts in reconstructed
distributions (Section 3.3).

3.1 Obtaining H Densities from Observations of the Geocorona

The transition from the optically thick to optically thin regime in the exosphere is
gradual with increasing geocentric distance. The brightness of the underlying optically
thick region could be as high as 35 kR and its emission would constitute [Østgaard et
al., 2003; Zoennchen et al., 2010], at distances > 3 R
E
, less than 2% of the incident solar
Lyman- α radiation. The exospheric emissions are confined however to a significantly
narrower spectral band than the rather broad solar line. Detailed simulations by Bishop
[1999] show that the altitude-dependent contribution to the glow source function by the
multiply scattered photons would vary, depending on the Sun angle, between 10 – 20%
and 5 – 7% at geocentric distances 3 R
E
and 8 R
E
, respectively. Consequently, the
uncertainties of exospheric number densities would also be of the same order, that is less
than 20% at 3 R
E
and decreasing with increasing geocentric distance.

17
3.2 Solar Output

The solar output in a broad spectral range, from X-rays to ultraviolet, drives the
distribution of atomic hydrogen in the exosphere. Vertical transport of H atoms in the
mesosphere, formed by photodissocation of water vapor and methane [Liu and
Donahue, 1974; Hunten and Strobel, 1974; Hodges, 1994], determines the density and
temperature at the exobase. The global structure of the exosphere thus depends on solar
radiative heating that causes vertical transport and resultant variations at the exobase.
For geocentric distances where TWINS observations are especially sensitive, from 3 R
E

to 8 R
E
, the exosphere is influenced by resonantly scattered solar Lyman- α radiation that
causes an effective pressure; photoionization by solar photons with wavelength λ < 91.1
nm; and coupling via charge exchange with the plasmasphere and polar wind.
The characteristic times of processes that govern atom injection, dynamics, and
losses are different. A few solar indices, namely F10.7, E10.7, and S10.7, are available
to characterize the observational conditions (Figure 6). F10.7 is the solar flux at 10.7 cm
wavelength. E10.7 is the integrated X-ray and EUV flux between 1-105 nm, especially
important for photoionization and heating [Tobiska, 2001]. S10.7 is the integrated EUV
flux between 26-34 nm, dominated by the chromospheric He II line at 30.4 nm and the
coronal Fe XV line at 28.4 nm; it contributes to the thermospheric heating and
expansion [Tobiska et al., 2008] that affects the injection of H atoms into the exosphere.

18

Figure 6. The solar output, shown in F10.7 (top), E10.7 (middle), and S10.7 (bottom)
indices, prominently varies over two time scales. First, the passage of active regions
across the solar disk during a solar rotation period produces irradiance variations over
approximately 27 days. Second, the solar activity cycle generates irradiance variations
over approximately 11 years. Solar Irradiance Platform (SIP) v2.37 historical
irradiances are provided courtesy of W. Kent Tobiska and Space Environment
Technologies, http://www.spacewx.com/solar2000.html.

The bright solar Lyman- α line of hydrogen emission, formed in the
chromosphere and transition region of the solar atmosphere, is an important ultraviolet
source of energy throughout the solar system. Solar Lyman- α radiation penetrates into

19
the mesosphere and deposits energy mainly by molecular oxygen dissociation in the 70
to 100 km region. The photons additionally dissociate water in the mesosphere and
ionize nitric oxide to form the ionospheric D layer that exists between 80 and 110 km
[Woods et al., 2000]. The solar Lyman- α emission is important to this experimental
study for two reasons. First, the LAD count rates are proportional to the solar Lyman- α
flux. Second, an effective pressure caused by scattered solar Lyman- α radiation affects
the dynamics and lifetimes of H atoms in the exosphere.

Figure 7. The composite solar Lyman- α flux at 1 AU, available at the Laboratory for
Atmospheric and Space Physics (LASP) website, http://lasp.colorado.edu/lisird/lya/, that
includes the latest Thermosphere Ionosphere Mesosphere Energetics and Dynamics
(TIMED) Solar EUV Experiment (SEE) and SOlar Radiation and Climate Experiment
(SORCE) SOLar Stellar Irradiance Comparison Experiment (SOLSTICE) measurements
that have been scaled to the Upper Atmosphere Research Satellite (UARS) reference
level as discussed by Woods et al. [2000].

The Lyman- α resonant scattering rate, or g-factor (s
-1
), is determined by the
spectral density at the center of the solar Lyman- α line profile. This spectral density, in
turn, correlates with the total solar Lyman- α line flux. A semi-empirical relationship
between the central spectral, , and (integrated over the whole Lyman- α line profile)

20
sum total, , irradiances in units ph cm
-2
nm
-1
and ph cm
-2
s
-1
, respectively, was defined
by Emerich et al. [2005] as

10

0.64 10

.
0.08,
(6)

using measurements from the Solar Ultraviolet Measurements of Emitted Radiation
(SUMER) spectrometer onboard the SOlar and Helospheric Observatory (SOHO)
mission. For an H atom, the transition probability [Bethe and Salpeter, 1957;
Gruntman, 1989] between the ground state ( = 1, = 0) and the state ( , = 1) is

8 10
∙
2
∙ ∙ 1
3∙ 1

, (7)

where, for = 2,

= 1.872995 × 10
9
s
-1
. The rate at which an H atom will excite to
the state = 2, the g-factor, is then the product of the transition probability,

, and
,

4

8
3 .4745085 1 0

∙ 10

.

.
(8)

21
where is the density of radiation at the angular frequency 2

of Lyman-
alpha ( = 121.567 nm), is the spectral irradiance density from Equation 6, is the
speed of light in vacuum, and is Planck’s constant. The composite solar Lyman- α flux
at 1 AU, available at the Laboratory for Atmospheric and Space Physics (LASP)
website, http://lasp.colorado.edu/lisird/lya/, provides daily values that average the latest
versions of the Thermosphere Ionosphere Mesosphere Energetics and Dynamics
(TIMED) Solar EUV Experiment (SEE) and SOlar Radiation and Climate Experiment
(SORCE) SOLar Stellar Irradiance Comparison Experiment (SOLSTICE)
measurements, scaled to match the Upper Atmosphere Research Satellite (UARS)
reference level as discussed by Woods et al. [2000]. This composite time series is used
to obtain the g-factor in part to be consistent with the interplanetary glow model,
discussed in Chapter 4. It would instead be possible to use the approximately 14 - 15
measurements that are available each day by SEE, which during normal operations
observes the Sun for about 3 minutes every orbit (~ 97 min). The effect of using either
data set results in minimal changes to the obtained exospheric H density distributions,
partially due to the low solar variation that persisted.
The solar Lyman- α flux is used to obtain the g-factor, which at 1 AU varied from
extremes of 1.55 × 10
-3
s
-1
and 3.75 × 10
-3
s
-1
over the last five solar cycles. A scaling
relationship is used to calculate the local g-factor, ∗
, that accounts for deviations from 1
AU during Earth’s orbit around the Sun,

22
∗

1 , (9)

where
is the heliocentric distance. The eccentricity of Earth’s orbit around the Sun
is 0.017, which translates into a ± 1.7% change in the heliocentric distance –
corresponding to a ± 3.5% change in the radiation flux. The actual distance from the
Earth to the Sun is always used when obtaining exospheric H density distributions.

3.3 Photon Scattering by H Atoms

Hydrogen atoms scatter Lyman- α radiation anisotropically. The angular
dependence of the scattered intensity, , obtained by Brandt and Chamberlain
[1959],

1 1
4
2
3
sin
, (10)

is shown in Figure 8. For forward ( = 0°) and backward (180°) scattering, the
probability deviates from the isotropic case by over 15%.

23

Figure 8. Scattering intensity I as a function of the scattering angle . The horizontal
dashed line, = 1.0, represents isotropic scattering.

The angular dependence of scattered Lyman- α photons is always applied when obtaining
exospheric H density distributions. The scattering angle, , is determined using the
relationship

cos

∙

, (11)

where is the LAD line-of-sight vector, is from the spacecraft to the Sun, and
is
from the point of scattering to the Sun as shown in Figure 9.

24

Figure 9. The observational geometry used to calculate the resonant scattering angle, ,
of Lyman- α photons on exospheric H atoms, which includes the LAD line-of-sight, , a
vector from the spacecraft to the Sun, , and a vector from the point of scattering to the
Sun,
.

S

S L
 

L

point of
scattering
spacecraft


25
Chapter 4: Interplanetary Glow

The Sun resides inside a warm, partially ionized, low-density cloud of interstellar
gas. Interstellar H atoms flow into the solar system filling interplanetary space [Fahr,
1974; Holzer, 1977; Meier, 1977; Thomas, 1978; Bertaux, 1984]. Similar to terrestrial
H atoms, interplanetary atoms also resonantly scatter solar Lyman- α photons, producing
the interplanetary glow with typical intensities that vary from 200 to 1000 R depending
on look direction and solar conditions.
The Solar Wind ANisotropies (SWAN) instrument [Bertaux et al., 1995] on the
SOlar and Heliospheric Observatory (SOHO) mission made extensive observations of
the interplanetary glow. Figure 10 shows the observed Lyman- α background for an
example day of 11 June 2008 (available at the SWAN website,
http://sohowww.nascom.nasa.gov/data/summary/swan/).

26

Figure 10. All-sky image of the interplanetary glow observed by the Solar Wind
ANisotropies (SWAN) instrument on 11 June 2008 (available at the SWAN website,
http://sohowww.nascom.nasa.gov/data/summary/swan/), where the horizontal axis is
ecliptic longitude λ and the vertical axis is ecliptic latitude β. The non-uniformity of the
intensity pattern, coded in false colors with a scale of counts s
-1
, is due to a combination
of varying interplanetary H atom velocities and ionization processes from the Sun. The
dark areas are field of view obstructions by the sunshield and spacecraft. The white dots
that are denser along the plan of the Milky Way are the emissions of hot stars.

The LAD measured intensity is the sum of the geocoronal and interplanetary
glow. The contribution of the interplanetary glow must therefore be subtracted from
each LAD measurement to obtain exospheric H densities. This work subtracts the
interplanetary glow using all-sky maps that are derived from SWAN measurements (W.
Pryor and R. Gladstone, personal communication, 2011). Pryor et al. [2012]

27
summarizes the fitting process that accounts for field of view obstructions and stellar
emissions. Figure 11 is one such all-sky map for an example day on 11 June 2008.

Figure 11. Interplanetary glow on 11 June 2008, derived from SWAN measurements
(W. Pryor and R. Gladstone, personal communication, 2011). Green and pink dots are
line-of-sight directions for LAD-1 and LAD-2, respectively. The horizontal axis is
ecliptic longitude λ, the vertical axis is ecliptic latitude β, and the color bar is in
rayleighs.

For all line-of-sight directions covered by the TWINS-1 LADs on 11 June 2008, the
interplanetary glow varied between 860 and 940 R, accounting for 20% — 65% of the
LAD measured intensities. Accuracy of the interplanetary glow predictions is therefore
of critical importance when extracting exospheric H densities from LAD measurements.

28
Chapter 5:
Lyman- α Detectors (LADs) on NASA’s TWINS Mission

The LADs were primarily included on TWINS to contribute to the science
reduction of ENA images by providing time-varying three-dimensional density
distributions , , , . Additionally, the unprecedented observational coverage
provides an opportunity to significantly advance scientific understanding of the physical
processes that drive exospheric H densities.

5.1 Instrumentation

The TWINS mission [McComas et al., 2009] consists of two instruments,
TWINS-1 and TWINS-2, on two separate satellites launched in 2006 and 2008 to
stereoscopically image the magnetosphere in ENA fluxes, which are produced in charge
exchange between magnetospheric energetic ions and exospheric background H atoms.
To derive ion distributions from ENA measurements, knowledge of the exospheric H
density distribution is necessary. Consequently, in addition to ENA imagers, each
TWINS instrument includes a pair of identical Lyman- α detectors, LADs, to register
line-of-sight resonance scattered intensities. LAD data became available since June
2008.

29

Figure 12. Each TWINS instrument, TWINS-1 and TWINS-2, includes two ENA
imagers, two LADs, and environmental sensors (adapted from the Instrument
Specification Document, March 2008).

In each LAD, the incident radiation passes through a collimator followed by an
optical interference filter centered at the wavelength 122 nm with a bandwidth 10 nm
[Nass et al., 2006]. The Lyman- α photons are then counted by a channel electron
multiplier. The recorded photon count rate is proportional to the incident Lyman- α
intensity and the geometric factor.

Figure 13. The field of view, Ω, of each LAD, where is the radius and is the area at
a distance along the line-of-sight .
Lyman- α Detector (LAD)
L
ˆ
2
/ L A   r
 2
A

30
The collimator on each LAD defines an aperture angle of 4° full width at half maximum.
The geometric factor is obtained by first finding the radius, , at a distance along the
line-of-sight, , using a trigonometric relationship,

tan 4°
2
→ tan 2 ° . (12)

The solid angle, Ω, of each LAD field of view is then

Ω
tan
2°
tan
2° 2 1cos 2 ° ,
(13)

and the sensor sensitivity [Nass et al., 2006] is approximately

1 10
4
∙2 1cos 2 ° ∙ 121.6
≅2

,
(14)

where
121.6 is the total quantum efficiency of each detector and 1 R = 1 rayleigh
= 10
6
/(4 π) phot cm
-2
s
-1
sr
-1
. All LADs were calibrated, before the mission start, at the
BESSY Synchrotron in Berlin [Richter et al., 2001]. Typical intensities measured by the
LADs are from 1000 to 10000 R, with corresponding count rates from 2000 to 20000 s
-1
.

31

Figure 14. Lyman- α photons pass through a collimator followed by an optical
interference filter before being counted by a channel electron multiplier.

5.2 Observational Coverage

The TWINS instruments fly on two satellites in widely spaced highly elliptical
Molniya-type orbits, providing observational coverage from very different vantage
points. On each satellite, two LADs, LAD-1 and LAD-2, observe the geocorona for
several hours per orbit, where the orbital period is one half of a sidereal day. The
TWINS instrument is located on a platform that rotates about a nominally nadir-pointed
axis, in a windshield wiper motion, back and forth through overlapping angular limits
Δω = ± 99° with a rotational rate of approximately 3˚ per second (Figure 15). Thus, it
takes approximately 1 minute for LAD-1 and LAD-2, oriented 40° with respect to the
actuator rotation axis, to observe a full circle around the Earth. LAD count rates are
Lyman- α 121.6 nm
∆λ ≈ 12 nm
filter transmission

32
recorded every 0.67 and 1.33 sec, corresponding to Δω = 2° and 4° of platform rotation.
When the platform reaches ω = ± 90°, LAD-1 will point in the same direction as LAD-2
in the opposite orientation, and vice versa, allowing for cross calibration of the sensors.
In general, this observational geometry provides excellent coverage of the Northern
Hemisphere, where the orbit apogees are located, but may be limited in the Southern
Hemisphere.

33

Figure 15. (a) Observational geometry of Lyman- α detectors (LAD-1 and LAD-2) on a
Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS) satellite in a highly
elliptical Molniya-type orbit. The TWINS mission consists of two satellites, flying in
similar orbits that are widely spaced. Both orbits have an apogee of 7.2 R
E
over the
Northern Hemisphere, an inclination of 63.4°, and an orbital period close to half a day.
Variable
is the geocentric distance of an LAD line-of-sight, , closest approach to
the Earth. Each LAD has a 4° full width half maximum field of view, pointed at 40°
with respect to the rotating nominally nadir-pointed instrument platform axis. (b) LAD
field of view coverage through the windshield wiper motion of the instrument platform.
The light and dark shaded sections of the circle show the overlapping directions covered
by LAD-1 ( ω
1
) and LAD-2 ( ω
2
), respectively, as the actuator rotates through the full
motion ( Δω = ± 99°). Note that detector measurements are only available within the
limits Δω = ± 90°. The windshield wiper motion of the instrument platform results in
the LAD fields of view covering a complete circle, centered on the Earth.

34
In total, 26 observational geometry and housekeeping limits are checked before
an LAD measurement is classified as valid for scientific analysis. To avoid the
hazardous environment in the Van Allen radiation belts, all instruments are turned off
below an orbital radius of approximately 4.5 R
E
. During the orbit, the instrument
rotation axis may drift away from nadir. Consequently, the geocentric distance of an
LAD line-of-sight closest approach to the Earth,
, varies from around 2.0 – 6.5 R
E
.
Below 3 R
E
, the geocorona deviates substantially from being optically thin. Thus, those
measurements with
< 3 R
E
are excluded. To mitigate possible solar contamination
[Zoennchen et al., 2010], only those measurements with a detector line-of-sight pointed
at > 90° from the direction to the Sun are used. Additionally, it is required that the line-
of-sight does not pass through Earth’s shadow, approximated by a cylinder (with 1 R
E

radius) in the antisolar direction.
Consider one TWINS satellite in an orbit with typical conditions. The pair of
LADs records around 2 × 8000 = 16000 valid measurements during the orbit. Adequate
observational coverage around the Earth is essential to obtaining exospheric H density
distributions because a global fitting is only sensitive to the observed regions. Figure 16
shows the observational coverage for TWINS-1 on 11 June 2008, as an example.

35

Figure 16. LAD observational coverage for TWINS-1 on 11 June 2008. The coordinate
system is Earth Centered Inertial (ECI): the x axis points toward the vernal equinox and
the z axis is the celestial pole. The blue sphere is the Earth, the yellow line and dot show
the direction to the Sun, the shaded cylinder is Earth’s shadow, the black curve is the
spacecraft trajectory, and the green and pink lines represent the line-of-sight vectors for
LAD-1 and LAD-2, respectively.

The observational coverage on 20 June 2008 (summer solstice) is shown in Figure 17.
The requirement that lines-of-sight be pointed at > 90° eliminates only a small amount
(< 1%) of LAD measurements on 11 June 2008 and 20 June 2008.

36

Figure 17. LAD observational coverage for TWINS-1 on 20 June 2008 (summer
solstice). The coordinate system is Earth Centered Inertial (ECI): the x axis points
toward the vernal equinox and the z axis is the celestial pole. The blue sphere is the
Earth, the yellow line and dot show the direction to the Sun, the shaded cylinder is
Earth’s shadow, the black curve is the spacecraft trajectory, and the green and pink lines
represent the line-of-sight vectors for LAD-1 and LAD-2, respectively.

After 20 June 2008, the favorable observational geometry continues such that all regions
around the Earth are included in the next month or so of TWINS-1 orbits. Figure 18
shows the TWINS-1 coverage on 20 July 2008.

37

Figure 18. LAD observational coverage for TWINS-1 on 20 July 2008. The coordinate
system is Earth Centered Inertial (ECI): the x axis points toward the vernal equinox and
the z axis is the celestial pole. The blue sphere is the Earth, the yellow line and dot show
the direction to the Sun, the shaded cylinder is Earth’s shadow, the black curve is the
spacecraft trajectory, and the green and pink lines represent the line-of-sight vectors for
LAD-1 and LAD-2, respectively.

After 20 July 2008, the orbit orientation with respect to the seasonal position of the Sun
becomes unfavorable such that > 1% of the available LAD measurements must be
excluded for having lines-of-sight pointed at < 90° to the direction of the Sun. For

38
example, by 20 August 2008 the TWINS-1 coverage (Figure 19) excludes 12.5% of the
available LAD measurements to mitigate possible solar contamination.

Figure 19. LAD observational coverage for TWINS-1 on 20 August 2008. The
coordinate system is Earth Centered Inertial (ECI): the x axis points toward the vernal
equinox and the z axis is the celestial pole. The blue sphere is the Earth, the yellow line
and dot show the direction to the Sun, the shaded cylinder is Earth’s shadow, the black
curve is the spacecraft trajectory, and the green and pink lines represent the line-of-sight
vectors for LAD-1 and LAD-2, respectively.

39
The lack of dayside coverage is a persistent feature for the time period after the summer
months of 2008 through 2011. Two additional plots of the observational coverage on 21
July 2009 (Figure 20) and 6 August 2011 (Figure 21) are shown to further visualize the
incomplete coverage.

Figure 20. LAD observational coverage for TWINS-1 on 21 July 2009. The coordinate
system is Earth Centered Inertial (ECI): the x axis points toward the vernal equinox and
the z axis is the celestial pole. The blue sphere is the Earth, the yellow line and dot show
the direction to the Sun, the shaded cylinder is Earth’s shadow, the black curve is the
spacecraft trajectory, and the green and pink lines represent the line-of-sight vectors for
LAD-1 and LAD-2, respectively.

40

Figure 21. LAD observational coverage for TWINS-1 on 6 August 2011. The
coordinate system is Earth Centered Inertial (ECI): the x axis points toward the vernal
equinox and the z axis is the celestial pole. The blue sphere is the Earth, the yellow line
and dot show the direction to the Sun, the shaded cylinder is Earth’s shadow, the black
curve is the spacecraft trajectory, and the green and pink lines represent the line-of-sight
vectors for LAD-1 and LAD-2, respectively.

The incomplete coverage that persists after the summer months of 2008 is a
result of unfavorable observational geometry with respect to the solar direction. A few
orbital elements for both the TWINS-1 and TWINS-2 satellites were calculated to better

41
understand the relationship between the orbit precession and the seasonal position of the
Sun. The orbital angular momentum vector, , was calculated by taking the cross
product,

,
(15)

of the spacecraft position vector, / , and velocity vector, / , for a point
along the orbit. Note, the spacecraft velocity vector is determined by taking the
difference divided by the elapsed time between two consecutive position vectors. A
vector pointing to the ascending node,

,
,0 ,
(16)

where 0, 0, 1 , is needed to obtain the longitude of the ascending node, Ω, with
vernal equinox as the origin of longitude, also known as the right ascension of the
ascending node (RAAN),

Ωcos

| |
.
(17)

If 0 , then Ω2π Ω . Next, the eccentricity vector, , is calculated,

42

| |
| |
∙ | |
,
(18)

where is the standard gravitational parameter of Earth. The argument of perigee, , is
then

cos

∙ | || |
,
(19)

where if 0 , 2π . The beta angle, , between the orbit plane and the
direction to the Sun, is

sin

∙
|
|
,
(20)

where

,

,

is the solar vector. The angles right ascension,
,
and declination,
, of the solar vector,

tan

,
(21)

sin

,
(22)

43
are defined from 0 ⁰ ≤ ≤ 180 ⁰ if
≥ 0, 180 ⁰ ≤ ≤ 360 ⁰ if
≤ 0, and -90 ⁰ ≤ ≤
90 ⁰.
The orbital elements defined above are plotted for each orbit of the TWINS-1
and TWINS-2 satellite in Figure 22 and Figure 23, respectively. The change per orbit
revolution for the longitude of ascending node, ΔΩ, is -0.07° and for the argument of
perigee, Δω, is zero. The beta angle varies by ± 90°, defined for an imaginary
observer at the Sun as positive for counter clockwise and negative for clockwise
rotation. The right ascension,
, and declination,
, of the Sun vary yearly from
0° to 360° and seasonally from ± 23.5°, respectively.
The regions shaded in yellow highlight when orbit apogees are on the dayside of
the Earth. This orientation provides favorable coverage as the nominally nadir-pointed
axis of the instrument is generally looking away from the Sun and the amount of LAD
lines-of-sight excluded for pointing at > 90° to the solar vector is minimal. The ideal
observational conditions would be when the orbit apogee is on the dayside of the Earth,
directly above the solar vector, during summer solstice when the Sun’s declination is
23.5°. The most similar observational geometry to the ideal conditions occurred in the
summer months of 2008.

44

Figure 22. The longitude of the ascending node Ω (black dots), argument of perigee
(blue dots), beta angle (green dots), right ascension of the Sun
(red dots), and
declination of the Sun
(pink dots) for each orbit of the TWINS-1 satellite in 2008
(top) through 2011 (bottom). The 4 black vertical lines in each year mark vernal
equinox, summer solstice, autumnal equinox, and winter solstice. The yellow shaded
regions highlight when the orbit apogees are on the dayside of the Earth.

45

Figure 23. The longitude of the ascending node Ω (black dots), argument of perigee
(blue dots), beta angle (green dots), right ascension of the Sun
(red dots), and
declination of the Sun
(pink dots) for each orbit of the TWINS-2 satellite in 2008
(top) through 2011 (bottom). The 4 black vertical lines in each year mark vernal
equinox, summer solstice, autumnal equinox, and winter solstice. The yellow shaded
regions highlight when the orbit apogees are on the dayside of the Earth.

46
5.3 Data Library

LAD data was routinely downloaded from the TWINS program website
(http://twins.swri.edu/) and processed into a convenient format for scientific analysis.
Each downloaded packet includes four daily text files – telemetry, attitude, ephemeris,
and housekeeping – for each satellite, totaling eight text files. The telemetry, attitude,
and ephemeris data are recorded on Science Packet Time (SPT) that closely but not
exactly matches the housekeeping data on Flight Housekeeping Time (FHT). Each line
of SPT was therefore assigned the closest line (must be within 0.25 s) of FHT and
merged into a single text file.
Various observational geometry and housekeeping limits are checked before an
LAD measurement is classified as valid for scientific analysis and available for use in
obtaining exospheric H density distributions. The observational geometry limits consist
of 3 primary criteria. First, since the geocorona deviates substantially from being
optically thin below a geocentric distance of 3 R
E
, those measurements with a line-of-
sight closest approach to the Earth,
, that is less than 3 R
E
are excluded. Second, to
mitigate possible solar contamination, only those measurements with a detector line-of-
sight pointed at > 90° from the direction to the Sun are used. Third, it is required that
the line-of-sight does not pass through Earth’s shadow, approximated by a cylinder
(with 1 R
E
radius) in the antisolar direction.
The housekeeping limits are primarily associated with verifying nominal
conditions for the actuator motion and LAD high voltage monitor. Additionally, LAD
count rates are recorded for 0.67 and 1.33 sec in each sector, corresponding to Δω = 2°

47
and 4° of actuator rotation. It is required that the 1.33 sec measurement be between a
factor of 1.8 to 2.2 of the corresponding 0.67 sec measurement.
The number of measurements with respect to the total available on each day that
meet all 26 criteria were compiled. Figure 24 and Figure 25 show the percentages for
each LAD on TWINS-1 and TWINS-2, respectively. The actuators on both instruments
stopped rotating smoothly at the start of 2009 due to a faulty command sequence. A fix
was uploaded on 21 July 2009 and the result is noticeable in both Figure 24 and Figure
25 with percentage increases on that day. The performance of the LADs on TWINS-2
degraded shortly thereafter, such that both detectors started recording very low and
unrealistic values. An attempt to correct the problem occurred on 21 March 2011 when
the high voltage commanding for the channel electron multipliers, on both TWINS-1
and TWINS-2, was increased from 199 V to 225 V.
In general, at least 10% of measurements are needed to obtain a global H number
density distribution with three-dimensional asymmetries for any given day. However, a
global fitting is only sensitive to the observed regions and therefore adequate
observational coverage around the Earth is also needed to avoid artifacts in
reconstructed distributions.

48

Figure 24. The percentage of TWINS-1 LAD measurements from each day in 2008
(top) through 2011 (bottom) that, based on various observational geometry and
housekeeping criteria, have been classified as valid for scientific analysis and available
for use in obtaining exospheric H density distributions. Note, data was unavailable for 3
weeks in September 2009.

49

Figure 25. The percentage of TWINS-2 LAD measurements from each day in 2008
(top) through 2011 (bottom) that, based on various observational geometry and
housekeeping criteria, have been classified as valid for scientific analysis and available
for use in obtaining exospheric H density distributions. Note, data was unavailable for 2
weeks in September 2009.

50
Chapter 6: Model

The process of preparing TWINS data such that LAD measurements can be used
to obtain global H density distributions with three-dimensional asymmetries requires
coordinate transformations of the spacecraft position and attitude (Section 6.1 and 6.2)
as well as a routine to approximate Earth’s shadow (Section 6.3). A spherical harmonic
expansion is used for the three-dimensional representation of exospheric H density
distributions (Section 6.4). This expansion contains free parameters that are best fit to
the LAD observational data using a least squares curve fitting (Section 6.5). The results
of a relative cross calibration between LAD-1 and LAD-2 are applied in fittings to
account for any offset in the measured intensities (Section 6.6). Finally, a distribution
for an example day of 11 June 2008 is shown (Section 6.7) with a detailed error analysis
(Section 6.8).

6.1 Geophysical Coordinate Systems

The TWINS program website provides attitude and ephemeris data primarily in
Earth Centered Inertial (ECI) coordinates. This system is geocentric, with the x axis
pointed in the direction of the vernal equinox, the z axis is parallel to Earth’s rotation
axis, and the y axis completes the orthogonal triad. The angles right ascension, , and
declination, , define a spherical coordinate system,

51
tan

,
(23)

sin

,
(24)

where 0 ⁰ ≤ ≤ 180 ⁰ if
≥ 0, 180 ⁰ ≤ ≤ 360 ⁰ if
≤ 0, and -90 ⁰ ≤ ≤ 90 ⁰.

Figure 26. Angles right ascension and declination defined in the Earth Centered
Inertial (ECI) coordinate system.

A solar aligned coordinate system, making one complete rotation with Earth’s
motion around the Sun, is used to obtain global H density distributions because
geocoronal symmetry along the Earth-Sun line is expected. One such system,
Geocentric Equatorial Noon (GEN), has the x axis pointed towards the intersection of
the equator and noon meridian (equatorial noon) and the z axis is the celestial pole; the y
axis completes the orthogonal triad. The longitudinal angle ϕ is measured from the x
ECI
x ˆ
ECI
z ˆ
ECI
y ˆ



52
axis in the XY plane and the co-latitude angle θ is counted from the z axis, such that ϕ =
0˚ and θ = 90˚ points towards equatorial noon.

Figure 27. Longitudinal angle θ and co-latitudinal angle ϕ defined in the Geocentric
Equatorial Noon (GEN) coordinate system.

A second system, Geocentric Solar Ecliptic (GSE), was used to obtain the
TWINS simplified operational exospheric model for solar minimum conditions (Section
7.4) because it is more convenient than GEN for ENA modelers. This system has the x
axis pointed to the Sun, the z axis is the ecliptic pole, and the y axis completes the
orthogonal triad. The longitudinal angle θ and the co-latitudinal angle ϕ are defined in
the same way as for GEN shown in Figure 27.
The Interplanetary glow maps are provided in Earth Centered Ecliptic (ECE)
coordinates, where the x axis is pointed towards the vernal equinox and the z axis is the
ecliptic pole; the y axis completes the orthogonal triad (Figure 28). Ecliptic longitude λ
and ecliptic latitude β are determined in the same way that right ascension and
declination are calculated in ECI coordinates (Equations 23 and 24).
GEN
x ˆ
GEN
y ˆ
GEN
z ˆ



53

Figure 28. The ecliptic longitude λ and ecliptic latitude β defined in the Earth Centered
Ecliptic (ECE) coordinate system.

6.1.1 ECI to GEN

The coordinate transformation from ECI to GEN requires only one rotation to
account for Earth’s motion around the Sun,

Figure 29. Rotation about the angle right ascension, , required to transform from ECI
to GEN.

ECE
x ˆ
ECE
y ˆ
ECE
z ˆ



ECI
y ˆ
ECI
x ˆ
GEN
y ˆ
GEN
x ˆ
GEN ECI
z z ˆ ˆ 


54

cos sin 0
sincos0
00 1

, (25)

where is the right ascension.

6.1.2 ECI to GSE

The direction of the ecliptic pole ( ̂
) is nearly constant in the ECI system,

̂

̂
, (26)

where a constant value is used for Earth’s obliquity, = 23.44°.

Figure 30. The transformation from ECI to GSE coordinates includes a rotation about
the ecliptic pole ( ̂
), which is fixed in the ECI system.

ECLIPTIC
POLE
ECI
z ˆ
ECI
y ˆ


55
The conversion from ECI to GSE coordinates can be expressed in a transformation
matrix [Kivelson and Russell, 1995],

, (27)

where is the solar unit vector, is the direction of the ecliptic pole, and completes
the orthogonal triad,

. (28)

6.1.3 ECI to ECE

The coordinate transformation from ECI to ECE requires only one rotation from
the equatorial to the ecliptic plane about their common x axis,

10 0
0cossin 0sin cos

, (29)

where a constant value is used for Earth’s obliquity, = 23.44°.

56

Figure 31. The rotation about Earth’s obliquity, , required to transform from ECI to
ECE.

6.2 LAD Line-of-sight Determination

Spacecraft pointing is provided as two unit vectors, polar ( ̂) and azimuthal ( ),
and

̂ ̂ (30)

is calculated to complete the orthogonal triad.


ECI
z ˆ
ECI
y ˆ
ECE
z ˆ
ECE
y ˆ
ECE ECI
x x ˆ ˆ 


57

Figure 32. A side view of the TWINS instrument with the polar ( ̂) and azimuthal ( )
directions (Instrument Specification Document, March 2008).

With respect to the instrument frame, ̂, , and ̂, two rotations are required to
determine each LAD line-of-sight unit vector. First, a rotation about the polar vector by
the actuator angle, ω, is performed,

cos sin ̂ , (31)

̂ sin cos ̂ , (32)

such that an actuator frame is defined, which can be expressed in terms of a rotation
matrix,

58
̂ ̂ 10 0
0
0
̂ ̂ . (33)

Figure 33. Top view of the TWINS instrument frame, ̂, , and ̂. The Toward and
Away directions are defined for the ENA sensor heads that look toward or away from
the electronics box. The LADs are named in a similar respect to be consistent with the
ENA sensor head directions. For example, the LAD sensor head that looks
predominately in the direction of the ENA Toward is termed the LAD Toward, also
known as LAD-1 (adapted from the Instrument Specification Document, March 2008).

a ˆ
z ˆ
p ˆ
LAD-2 (Away)
LAD-1 (Toward)

59

Figure 34. Top view of TWINS showing the rotation about the actuator angle ω from
the instrument frame ( ̂, , ̂) to the actuator frame ( ̂ , , ̂ ) (adapted from the
Instrument Specification Document, March 2008).

Second, to obtain the LAD boresight unit vectors, and , a rotation about by
±40° is performed,

c os 40⁰ ̂ sin 40⁰ ̂ , (34)

c os 40⁰ ̂ sin 40⁰ ̂ , (35)

shown in Figure 35.

p p ˆ ˆ 
z ˆ

z ˆ
a ˆ

a ˆ

LAD-2 (Away)
LAD-1 (Toward)


60

Figure 35. The LAD boresights are fixed in the actuator frame ( ̂ , , ̂ ) by a
rotation of ±40° about .

The above transformations (Equations 31 – 35) can be combined into a product of
rotation matrices,

/

̂ ̂ ̂ ̂ ̂ ̂
10 0
0
0

40 °
0
40 °
40 °
0
40 °
.
(36)

The geocentric distance of an LAD line-of-sight closest approach to the Earth,

, is determined in two steps. The angle between the LAD line-of-sight, , and
spacecraft position vector, / , is calculated,

cos

∘ ̂ / , (37)

and finally
40°
2
ˆ
L
1
ˆ
L

a ˆ

p p ˆ ˆ 

z ˆ
40°

61

/ sin . (38)

Figure 36. The observational geometry used to calculate the geocentric distance of an
LAD line-of-sight closest approach to the Earth,
. The angle is between the LAD
line-of-sight, , and the spacecraft position, / .

The variable
, which represents the closest approach to the Earth where H densities
are highest along a typical LAD line-of-sight, opens a way of characterizing the
observed Lyman- α intensities. Figure 37 shows the LAD-1 and LAD-2 measurements
on TWINS-1 for 11 June 2008, as an example. The width of each curve is in part a
result of geocoronal asymmetry over the observed regions.

S/C
LOS
r

L

C S
r
/


62

Figure 37. The Lyman- α intensity in rayleighs observed by both LAD-1 (green dots)
and LAD-2 (pink dots) on TWINS-1 for 11 June 2008 versus the geocentric distance of
each line-of-sight closest approach to the Earth,
.

Figure 38 shows another example of LAD-1 and LAD-2 measurements observed on 20
June 2008.

63

Figure 38. The Lyman- α intensity observed by both LAD-1 (green dots) and LAD-2
(pink dots) on TWINS-1 for 20 June 2008 versus the geocentric distance of each line-of-
sight closest approach to the Earth,
.

The LADs are sensitive to certain classes of stars, specifically O and B, that have
prominent hydrogen emissions in Lyman- α. Consequently, star sightings can be used to
validate detector pointing. An example of this capability was performed using LAD
measurements from TWINS-1 on 16 June 2008. Figure 39 shows that LAD-2

64
repeatedly registered a higher signal at certain times while the actuator was sweeping
back and forth through the windshield wiper motion ( Δω ± 90°).

Figure 39. A sequence of LAD-1 (green) and LAD-2 (pink) measurements from
TWINS-1 on 16 June 2008 that includes a possible star sighting. The horizontal axis is
the sector number for the day and the vertical axis is the measured Lyman- α intensity in
rayleighs.

The brightest star in the constellation Virgo, Spica ( α Virginis), was within the LAD-2
field of view (Figure 40) at the times of increased Lyman- α intensities. Spica has an
apparent magnitude of +0.96 and spectral type of B1.

possible star sighting

65

Figure 40. A sky map with the spectral classes of stars in the Southern Hemisphere.
The dotted circle around the polar vector ( ̂) are the lines-of-sight for LAD-1 (dark blue)
and LAD-2 (light blue) for one rotation of the actuator.

6.3 Earth’s Shadow Approximation

Only LAD lines-of-sight that do not pass through Earth’s shadow, approximated
by a cylinder (with 1 R
E
radius) in the antisolar direction (Figure 41), are used to obtain
exospheric H density distributions. A routine to determine the minimum distance
between two skew lines is used to find the minimum distance from a vector in the
antisolar direction,
, to each LAD line-of-sight, . First, the infinite line distance, l, is
obtained using the relationship

66

, (39)

where is the spacecraft position, is the center of the Earth, ∙
, ∙
,
∙
, ∙ , and ̂ ∙ . If l < 1 R
E
, the location of the minimum distance on
each vector,

,
(40)

,
(41)

must be checked such that 0 and 0 . If both conditions are met, then the line-
of-sight is flagged as passing through Earth’s shadow. The requirement that lines-of-
sight do not pass through earth shadow typically excludes less than 2% of LAD
measurements for any given orbit.

67

Figure 41. The observational geometry used to approximate Earth’s shadow as a
cylinder. The variables and are the spacecraft and Earth positions, respectively.
The variable is the distance along the LAD line-of-sight, , and the variable is the
distance along the antisolar direction,
, where the minimum distance between the two
lines, l, occurs along the unit vector .

6.4 3D Representation of Exospheric H Density Distributions

Hodges [1994] modeled exospheric H number density distributions, , , ,
by a third-order spherical harmonic expansion in the form

, , √ 4
cos

sin
,
(42)
where is the radial function;
and
are the radius-dependent
coefficients of the expansion; and
are the spherical harmonic Legendre functions

L
ˆ
C S
r
/

n ˆ
l
S
ˆ

0
L
0
S
c
S
c
L

68

1
4

(43)

3
4
cos θ
(44)

3
4

(45)

5
4
3
2

1
2

(46)

15
8

(47)

1
4
15
2

(48)

7
4
5
2
cos
3
2

(49)

1
4
21
4
sin 5 cos
1
(50)

69

1
4
105
2

cos
(51)

1
4
35
4

(52)

with excluded imaginary parts. He divided the geocentric distance r into 40 steps, which
resulted in a total of 640 free parameters. Considering only the observational geometry
limit with
> 3 R
E
reduces the number of free parameters to 96. This number of free
parameters is still computationally impractical for a curve fitting procedure. Nass et al.
[2006] suggested important simplifications — the Bonn model — that reduced the
number of free parameters to 12. First, they reduced the order of the expansion, l, from
3 to 2. Second, they approximated the mean density, , by a power law

. (53)

Finally, for
a linear approximation was used

, (54)

and all
were set to zero. Computer simulations [Nass et al., 2006] showed that
the Bonn model was able to conveniently reproduce major features of the Hodges [1994]
model.

70
This work expands the Bonn model in an important way by adding
as
free parameters, using a linear approximation

, (55)

which would open the opportunity to account for dawn-dusk asymmetry in the
distribution, impossible if
= 0. This addition increases the number of free
parameters to 18, compared to 12 in the Bonn model.

71

Figure 42. Three-dimensional color plots of the asymmetry introduced for positive (left)
and negative (right) values of each expansion coefficient with respect to an x axis (gray
line) and z axis (black line). Setting a particular coefficient to zero during the fitting
procedure eliminates the possibility for the corresponding asymmetry in the obtained
three-dimensional H density distribution.

r b a r A
10 10 10
) (  
r b a r A
11 11 11
) (  
r d c r B
11 11 11
) (  
r b a r A
20 20 20
) (  
r b a r A
21 21 21
) (  
r d c r B
21 21 21
) (  
r b a r A
22 22 22
) (  
r d c r B
22 22 22
) (  
r b a r A
30 30 30
) (  
r b a r A
31 31 31
) (  
r d c r B
31 31 31
) (  
r b a r A
32 32 32
) (  
r d c r B
32 32 32
) (  
r b a r A
33 33 33
) (  
r d c r B
33 33 33
) (  

72
6.5 Least Squares Curve Fitting Procedure

A process of forward modeling starts with an analytical expression for the three-
dimensional H number density distribution. This expression contains free parameters
that are best fit to the observational data using a least squares curve fitting. The solution
to the fitting minimizes the sum of squared residuals,

,
(56)

where a residual is the difference between an observed intensity ( ) and corresponding
fitted intensity provided by the model ( ). The Levenberg-Marquardt algorithm
[Levenberg, 1944; Marquardt, 1963; Coleman and Li, 1994, 1996], which interpolates
between the Gauss-Newton algorithm and the method of gradient descent, is used such
that in each iteration step the fitting parameters ,,
,

,

,

are
replaced by new estimates, . To determine , the functions , are
approximated by their linearizations,

, ,
, (57)

where , ⁄ is the gradient of with respect to . The sum of squares
becomes

73
,
,
(58)

or in vector notation,

‖ ‖
. (59)

Taking the derivative with respect to of Equation 59 and setting the result to zero
gives

, (60)

which is the Gauss-Newton algorithm. The Levenberg-Marquardt algorithm introduces
a (non-negative) damping factor, , that is adjusted at each iteration,

, (61)

such that if the reduction in the sum of squares is rapid, a smaller value of is used
bringing the algorithm closer to the Gauss-Newton algorithm. Alternatively, if an
iteration results in minimal reduction, is increased bringing the algorithm closer to the
method of gradient descent. Each component of the gradient is scaled according to the
curvature by replacing the identity matrix, , on the left hand side of Equation 61 with

74
, which results in larger movement along directions where the gradient is
smaller. Formally, the Levenberg-Marquardt algorithm is

. (62)

Table 2 lists the initial and boundary values used in the fitting procedure. Initial
parameter values are selected at the start to be equidistant from the lower and upper
boundaries. The boundary conditions are chosen to far exceed, by a factor of 10, values
that would be expected in obtaining exospheric H number densities.

Table 2: Initial and boundary values for the least squares curve fitting parameters
(, ,
,

,

,

); is in cm
-3
and r is in R
E
.
Parameter Initial Value Lower Bound Upper Bound
10
4
10
3
10
5

-3 -1 -5

,

,

,

0 -10
4
10
4

First, the simple r-dependent spherically symmetric density profile,

, is fit, using the method of nonlinear least squares, with the 16 angular coefficients
(
,

,

,

) set to zero. Second, once and have been obtained, their values
are set and another fit is performed to obtain the angular coefficients.
Next, a new fit for and is conducted using the first pass values for the
angular dependence coefficients. The new values for and are then used in another fit

75
for
,
,
, and
, completing the second pass. The process was tested in an
iterative fashion and one pass is usually sufficient to obtain the coefficients with
accuracies better than 1%. A typical fit consists of around 10000 measurements and
takes between 4 to 6 hours to converge on a solution.

6.6 Relative Cross Calibration of the LADs

As discussed in Section 5.2, each TWINS instrument is located on a platform
that rotates about a nominally nadir-pointed axis, in a windshield wiper motion, back
and forth through overlapping angular limits Δω = ± 99° (Figure 1). When the platform
reaches ω = ± 90°, LAD-1 points in the same direction as LAD-2 in the opposite
orientation, and vice versa, which opens a possibility for cross calibration. This
capability is important to verify that the detectors are operating normally.
The LADs on TWINS-1 registered nearly the same cross calibration signals
through 2008, but eventually LAD-1 started recording systematically lower Lyman- α
intensities than LAD-2 for select time periods. Figure 43 shows LAD-1 ( ω = -90°) and
LAD-2 ( ω = 90°) measurements for both TWINS-1 orbits on 6 August 2011, as an
example.

76

Figure 43. LAD-1 (green dots) and LAD-2 (pink dots) measured Lyman- α intensities at
ω = -90°and ω = 90°, respectively, for both TWINS-1 orbits on 6 August 2011.

The difference between LAD-1 and LAD-2 measured intensities at the cross calibration
orientations on 6 August 2011 is reflected in all measurements from that day, as shown
in Figure 44

77

Figure 44. The Lyman- α intensity observed by both LAD-1 (green dots) and LAD-2
(pink dots) on TWINS-1 for 6 August 2011 versus the geocentric distance of each line-
of-sight closest approach to the Earth,
.

The ratio between LAD-1 to LAD-2 measured intensities at the cross calibration
orientations was calculated to be 0.80 for 6 August 2011. Figure 45 shows LAD-1 ( ω =
-90°) and LAD-2 ( ω = 90°) measurements for both TWINS-1 orbits on 6 August 2011
with LAD-1 intensities that have been increased by a factor of 1 / 0.80 = 1.25.

78

Figure 45. LAD-1 (green dots) and LAD-2 (pink dots) measured Lyman- α intensities at
ω = -90°and ω = 90°, respectively, for both TWINS-1 orbits on 6 August 2011; the
LAD-1 measurements have been increased by a factor of 1 / 0.80 = 1.25.

Applying the cross calibration ratio to all LAD-1 measurements on 6 August 2011
appears to correct a possible offset in all measurements, as shown in Figure 46.

79

Figure 46. The Lyman- α intensity observed by both LAD-1 (green dots) and LAD-2
(pink dots) on TWINS-1 for 6 August 2011 versus the geocentric distance of each line-
of-sight closest approach to the Earth,
; the LAD-1 measurements have been
increased by a factor of 1 / 0.80 = 1.25.

The cross calibration ratio between LAD-1 and LAD-2 for all orbits from the start of
TWINS-1 (Figure 47) and TWINS-2 (Figure 48) operations in 2008 through 2011 was
calculated. The ratio is only near unity in the summer months of 2008 for TWINS-1 and
in September and October of 2008 for TWINS-2. The obtained times series is always
applied when reconstructing exospheric H density distributions.

80

Figure 47. The ratio of cross calibration, LAD-1 / LAD-2, for TWINS-1 from 2008
(top) through 2011 (bottom).

81

Figure 48. The ratio of cross calibration, LAD-1 / LAD-2, for TWINS-2 from 2008
(top) through 2011 (bottom).

82
6.7 Example Day, 11 June 2008

Using LAD data from TWINS-1 on 11 June 2008, a three-dimensional
exospheric H number density distribution was obtained, as an example. The
corresponding parameter values in Equations 53 – 55 are listed in Table 3, where is
in cm
-3
and r is in R
E
.

Table 3. Parameters of the exospheric H number density distribution (Equations 53 –
55) obtained using LAD data from TWINS-1 on 11 June 2008 in Geocentric Equatorial
Noon (GEN) coordinates; is in cm
-3
and r is in R
E
.
Radial and
Angular
Parameters
June to September
2008
8.5886 × 10
3

-2.5446

-4.8992 × 10
-2

-1.1927 × 10
-2

-3.8248 × 10
-1

5.7744 × 10
-2

-4.8547 × 10
-2

-1.3753 × 10
-2

1.5739 × 10
-1

-3.9474 × 10
-2

-6.9198 × 10
-2

2.8973 × 10
-2

2.1922 × 10
-1

-4.5158 × 10
-2

-1.0148 × 10
-1

9.4756 × 10
-3

-8.8242 × 10
-2

2.7003 × 10
-2

83
Figure 49 shows cross sections of the obtained 11 June 2008 distribution. The
left panel shows a contour plot in the equatorial plane; day-night and dawn-dusk
asymmetries are clearly visible. The right panel shows a contour plot in the meridional
Earth-Sun plane, where one can see day-night and north-south asymmetries. For larger
geocentric distances, the inferring of density values becomes more challenging as the
geocentric distance of an LAD line-of-sight closest approach to the Earth,
, where
densities are highest, never exceeds 6.5 R
E
.

Figure 49. Contour plots of the exospheric H number density distribution on 11 June
2008: (left) an equatorial (XY plane) cross section and (right) a meridional (XZ plane)
cross section. Also shown are the definitions of the angles ϕ and θ. Contours are lines
of constant neutral hydrogen number density (cm
-3
); the color bar is for the contour
lines; the yellow dot is the projection of the direction to the Sun (left) and the direction
to the Sun (right); the filled shaded circle represents the region with radius 3 R
E
; and the
grid of shaded concentric circles for r > 3 R
E
, with a 1 R
E
step, highlights the asymmetry
of the distribution.

84
The global distribution exhibits asymmetry in the day-night, dawn-dusk, and
north-south directions. Figure 50 presents the angular variation of the distribution at
geocentric distances 3 R
E
, 6 R
E
, and 8 R
E
. Similar to Figure 49, the left plots show
number densities in the equatorial plane and the right plots in the meridional Earth-Sun
plane.
For lower geocentric distances, the dayside has noticeably higher densities than
the nightside. This dayside maximum can be seen at 3 R
E
(Figure 50, top) with ϕ ≈ 60°
and θ ≈ 155°. A nightside enhancement appears at 6 R
E
(Figure 50, middle) with ϕ ≈
235° and θ ≈ 280°. At 8 R
E
(Figure 50, bottom), this nightside enhancement becomes
almost as pronounced as the dayside maximum. As the geocentric distance increases
beyond 8 R
E
, the nightside densities become increasingly more pronounced than the
dayside densities, consistent with the location of a geotail.
The duskside has noticeably higher densities than the dawnside. This asymmetry
can be seen in the left plots of Figure 49 as, compared to the dawnside with ϕ between
180° and 360°, generally higher densities exist on the duskside with ϕ between 0° and
180°.
The right plots of Figure 49 clearly show that the Southern Hemisphere has
noticeably higher densities than the Northern Hemisphere. This observed asymmetry is
consistent with the Hodges [1994] solstice distributions.
The coverage of the exosphere by LAD observations is incomplete, as
determined by the mission geometry. The obtained asymmetry of the H distribution

85
should be more sensitive to the incomplete coverage than the averaged radial density
profile .

Figure 50. Exospheric H number density in the obtained 11 June 2008 distribution as a
function of angles ϕ and θ for geocentric distances 3 R
E
(top), 6 R
E
(middle), and 8 R
E

(bottom). In the left plots ( θ = 90°), the angle ϕ = 0° is equatorial noon and the angle ϕ
= 90° is dusk. In the right plots ( ϕ = 0°), the angle θ = 0° is north and the angle θ = 90°
is equatorial noon.

86
A visualization technique was developed to further investigate the three-
dimensional asymmetry in the obtained exospheric H number density distribution on 11
June 2008. Figure 51 shows spherical H density contour plots at 6 different geocentric
distances from 3 R
E
to 8 R
E
; the gray lines point toward equatorial noon, the black lines
are the celestial pole, and the yellow lines are the direction to the Sun.
A consistent feature at all geocentric distances is that the Southern Hemisphere
has noticeably higher densities than the Northern Hemisphere. The dayside has higher
densities than the nightside for lower geocentric distances, but the nightside becomes
increasingly more pronounced with increasing geocentric distance up to 8 R
E

87

Figure 51. Three-dimensional contour plots of the exospheric H number density
distribution on 11 June 2008 for spherical shells at 6 different geocentric distances from
3 R
E
to 8 R
E
; the gray lines point toward equatorial noon, the black lines are the celestial
pole, the yellow lines are the direction to the Sun, and the color bars are in cm
-3
.

88
6.7.1 H Density Radial Profile

Figure 52 compares the spherically symmetric radial component, , of the 11
June 2008 distribution to prior models. The density profile is remarkably close to those
obtained by Rairden et al. [1986], Hodges [1994], and Østgaard et al. [2003], with
differences less than 50% between 3 to 8 R
E
.
The conditions of the observation on 11 June 2008 correspond to solar minimum.
The DE 1 measurements used by Rairden et al. [1986] were obtained over a different
phase of the solar cycle, during the solar activity increase from 1981 to 1985. Østgaard
et al. [2003] also reported on a different phase of the solar cycle as they used
GEO/IMAGE measurements near solar maximum from June 2000 to June 2001. In
addition to being solar minimum with an F10.7 value of 66, the observation on 11 June
2008 was seasonally close to summer solstice. Thus, the Hodges [1994] solstice
distribution with an F10.7 value of 80 represents the most similar conditions.
For geocentric distances r > 4.5 R
E
, the Zoennchen et al. [2010] density profile
shows somewhat higher densities than those by Rairden et al. [1986], Hodges [1994],
and Østgaard et al. [2003], as well as in the 11 June 2008 distribution. The higher
densities obtained by the Bonn group were due to much lower approximations for the
interplanetary glow that have since been revised to be consistent with Pryor et al.
[2012].

89

Figure 52. Comparison of different H number density profiles on 11 June 2008 from
this work (solid line), Rairden et al. [1986] (circles), Hodges [1994] at solstice for F10.7
= 80 (crosses), Østgaard et al. [2003] for solar zenith angle 90° (long dashed line), and
Zoennchen et al. [2010] on 11 June 2008 (short dashed line).

6.7.2 H Distribution Asymmetry

The 11 June 2008 distribution shares similar three-dimensional features to those
obtained by Hodges [1994] in that they both exhibit an enhancement in the antisolar
direction (geotail) and an enhancement in the solar direction. Figure 53 shows the

90
density distribution along four radial directions: north, south, equatorial noon, and
equatorial midnight, from 3 to 8 R
E
. While the model used describes number densities
at larger geocentric distances, validating the values beyond 8 R
E
becomes increasingly
difficult. However, it is noted that the densities are consistent with the H densities
inferred from measurements by the Interstellar Boundary Explorer (IBEX) mission
[Fuselier et al., 2010], which carries sensitive ENA detectors. Fuselier et al. [2010]
recently reported an H number density range of 4 – 11 cm
-3
at the subsolar
magnetopause (~ 10 R
E
geocentric distance along the Earth-Sun line).
For geocentric distances r < 6 R
E
, the density profile for equatorial noon is
higher than for equatorial midnight. As the geocentric distance increases, the density
profile for equatorial midnight decreases less rapidly than for equatorial noon until the
former becomes dominant, similar to the asymmetry observed by Østgaard et al. [2003].
This asymmetry is less pronounced than that of Zoennchen et al. [2010].
A north-south asymmetry also exists, such that the H densities are depleted at
higher geocentric distances in the Northern Hemisphere. At 4 R
E
, the southern polar
region has 40% higher densities than in the northern polar region; increasing to 70% at 6
R
E
and 125% at 8 R
E
. This asymmetry is likely caused by the Sun’s position near
summer solstice at this time. The Hodges [1994] solstice distributions exhibit similar
asymmetry. While his solstice distribution for F10.7 = 80 is nearly symmetric at lower
geocentric distances, beyond 4 R
E
densities in the Northern Hemisphere decrease more
rapidly than in the Southern Hemisphere.

91

Figure 53. Exospheric H number density radial dependencies of the 11 June 2008
distribution toward north (solid line), south (long dashed line), equatorial noon (short
dashed line), and equatorial midnight (dotted line).

92
6.8 Error Analysis

The least squares curve fit minimizes the standard deviation,

1

,
(63)

between the observed intensities and the fitted intensities provided by the model,
where is the number of observations and is the number of fitting parameters (
is the degrees of freedom). A rigorous derivation of the uncertainty in the retrieved H
densities is needed to demonstrate the validity of the fitting procedure. An error analysis
adapted from Bevington and Robinson [2003] was performed in two steps. First, the
standard deviation for each model parameter, , was obtained using the relationship

, (64)

where is the standard deviation of each observation and
⁄ is the partial
derivative of the z
th
parameter , ,
,

,

,

of each observation. This
operation is performed such that the covariance matrix, , is determined,

, (65)

93
where is the Jacobian matrix (all 1
st
order partial derivatives). Second, with the
propagated standard deviation of each fitted parameter, the total can be calculated using
the propagation of errors,

… 2

….
(66)

A successful fit predicts the measured intensities to within a standard deviation
of around 125 R, which would be, for example, less than 5% and 10% of typical
intensities at distances < 4 R
E
and < 6 R
E
, respectively. The random Poissonian error for
the range of measured detector counts does not exceed 2%. The estimated uncertainty in
the obtained 11 June 2008 distribution (Figure 54) slowly increases from 7% to 9% from
3 R
E
to 6 R
E
and then rapidly increases up to 25% at 8 R
E
.

94

Figure 54. The estimated uncertainty in the obtained 11 June 2008 distribution. The
distribution should be restricted to r < 8 R
E
, or used with appropriate caution for higher
geocentric distances.

Figure 55 shows the spherically symmetric radial component, , of the 11 June 2008
distribution with error bars plotted at regular intervals along the density profile.

95

Figure 55. The H number density profile for the obtained 11 June 2008 distribution with
error bars to represent the fitting uncertainty.

96
Chapter 7: Spatial and Temporal Response of the Exosphere

The TWINS mission provides unprecedented observational coverage of the
geocorona such that global distributions with three-dimensional asymmetries can be
obtained without having to average over extended periods of time. However, detector
lines-of-sight on the dayside are often pointed at < 90° from the solar direction, due to
the satellite orbit orientation with respect to the seasonal position of the Sun, and must
therefore be excluded to mitigate possible solar contamination – resulting in only partial
coverage around the Earth. Consequently, only selected TWINS-1 observations in the
summer months of 2008 are used for obtaining global distributions.
A sequence of distributions was obtained to study the dynamic exosphere
responding to seasonal variation from a summer solstice to autumnal equinox (Section
7.1). Additionally, since the averaged radial density profile, , should be less
sensitive to the incomplete coverage than asymmetry in the three-dimensional
distributions, a sequence of density profiles for a time period that includes four magnetic
storms has been obtained to investigate the effect of geomagnetic variation (Section 7.2).

7.1 Seasonal Variation

Heating of the upper atmosphere on the dayside, by solar X-ray and EUV
radiation, causes asymmetry of the exosphere. For example, a seasonal north-south
asymmetry occurs as solar illumination differs between the summer and winter polar
regions. A very low solar cycle minimum with minimal 27-day variation (< 5%)

97
persisted, and additionally the geomagnetic conditions were quiet, through the summer
months of 2008. Consequently, three time periods (18-22 June, 18-22 July, and 18-22
August) were chosen to investigate seasonal variation from the summer solstice to
autumnal equinox in 2008. The TWINS-1 observational coverage for 18-22 June 2008
and 18-22 July 2008 was excellent, but for 18-22 August 2008 the dayside is excluded to
mitigate possible solar contamination because lines-of-sight are pointed at < 90° from
the direction to the Sun. The parameter values in Equations 53 – 55 for the 18-22 June
2008 distribution are listed in Table 4, where is in cm
-3
and r is in R
E
.

98
Table 4. Parameters of the exospheric H number density distribution (Equations 53 –
55) obtained using LAD data from TWINS-1 on 18-22 June 2008 in Geocentric
Equatorial Noon (GEN) coordinates; is in cm
-3
and r is in R
E
.
Radial and
Angular
Parameters
18-22 June 2008
1.0505 × 10
4

-2.7418

1.5782 × 10
-2

-1.0551 × 10
-3

-4.2828 × 10
-1

5.1883 × 10
-2

-2.7034 × 10
-2

-5.4775 × 10
-3

2.3120 × 10
-1

-5.3657 × 10
-2

1.2715 × 10
-1

-3.9517 × 10
-2

5.0743 × 10
-2

-8.0776 × 10
-3

-1.9040 × 10
-1

4.2901 × 10
-2

1.0511 × 10
-1

-1.4176 × 10
-2

Figure 56 shows cross sections of the obtained 18-22 June 2008 distribution. The left
panel shows a contour plot in the equatorial plane and the right panel shows a contour
plot in the meridional Earth-Sun plane. The solar-antisolar asymmetry is remarkably
similar to the Hodges [1994] solstice distributions and Carruthers et al. [1976] images.

99

Figure 56. Contour plots of the exospheric H number density distribution on 18-22 June
2008: (left) an equatorial (XY plane) cross section and (right) a meridional (XZ plane)
cross section. Also shown are the definitions of the angles ϕ and θ. Contours are lines
of constant neutral hydrogen number density (cm
-3
); the color bar is for the contour
lines; the yellow dot is the projection of the direction to the Sun (left) and the direction
to the Sun (right); the filled shaded circle represents the region with radius 3 R
E
; and the
grid of shaded concentric circles for r > 3 R
E
, with a 1 R
E
step, highlights the asymmetry
of the distribution.

The global distribution exhibits three-dimensional asymmetries. Figure 57
presents the angular variation of the distribution at geocentric distances 3 R
E
, 6 R
E
, and 8
R
E
. Similar to Figure 56, the left plots show number densities in the equatorial plane
and the right plots in the meridional Earth-Sun plane.
For lower geocentric distances, the dayside has noticeably higher densities than
the nightside. This dayside maximum can be seen at 3 R
E
(Figure 57, top) with ϕ ≈ 45°
and θ between 0° and 155°. A nightside enhancement appears at 6 R
E
(Figure 57,
middle) with ϕ ≈ 180° and θ ≈ 250°. At 8 R
E
(Figure 57, bottom), the nightside

100
enhancement becomes almost as pronounced as the dayside maximum. As the
geocentric distance increases beyond 8 R
E
, the nightside densities become increasingly
more pronounced than the dayside densities, consistent with the location of a geotail.
The dawn-dusk asymmetry is minimal, visible in the left plots of Figure 57 as,
compared to the dawnside with ϕ between 180° and 360°, the same general densities
exist on the duskside with ϕ between 0° and 180°.
The right plots of Figure 57 show that the northern and Southern Hemispheres
have similar densities, but at 6 R
E
and 8 R
E
enhancements in the solar ( θ ≈ 75°) and
antisolar ( θ ≈ 255°) direction are clearly visible. This observed asymmetry is
remarkably consistent with the Hodges [1994] solstice distributions.

101

Figure 57. Exospheric H number density in the obtained 18-22 June 2008 distribution as
a function of angles ϕ and θ for geocentric distances 3 R
E
(top), 6 R
E
(middle), and 8 R
E

(bottom). In the left plots ( θ = 90°), the angle ϕ = 0° is equatorial noon and the angle ϕ
= 90° is dusk. In the right plots ( ϕ = 0°), the angle θ = 0° is north and the angle θ = 90°
is equatorial noon.

Asymmetry in the day-night direction is the dominant feature visible in all the
spherical contour plots shown in Figure 58. As the geocentric distance increases,
asymmetry along the solar-antisolar direction emerges and additionally the pole-equator
asymmetry becomes more pronounced. The dawn-dusk asymmetry is minimal.

102

Figure 58. Three-dimensional contour plots of the exospheric H number density
distribution on 18-22 June 2008 for spherical shells at 6 different geocentric distances
from 3 R
E
to 8 R
E
; the gray lines point toward equatorial noon, the black lines are the
celestial pole, the yellow lines are the direction to the Sun, and the color bars are in cm
-3
.

103
The 18-22 June 2008 distribution shares similar three-dimensional features to
those obtained by Hodges [1994] in that they both exhibit pronounced enhancements in
the antisolar direction (geotail) and in the solar direction. Figure 59 shows the density
distribution along four radial directions, north, south, equatorial noon, and equatorial
midnight, from 3 R
E
to 8 R
E
. For geocentric distances r < 6 R
E
, the density profile for
equatorial noon is higher than for equatorial midnight. As the geocentric distance
increases, the density profile for equatorial midnight decreases less rapidly than for
equatorial noon until the former becomes dominant, similar to the asymmetry observed
by Østgaard et al. [2003]. At 8 R
E
, the density profiles for equatorial noon and
equatorial midnight are significantly higher for north and south.

104

Figure 59. Exospheric H number density radial dependencies of the 18-22 June 2008
distribution toward north (solid line), south (long dashed line), equatorial noon (short
dashed line), and equatorial midnight (dotted line).

The three-dimensional asymmetry on 18-22 June 2008 is compared to two other
distributions obtained using TWINS-1 LAD data on 18-22 July 2008 and 18-22 August
2008 in Figure 60. All three distributions exhibit asymmetry that appears oriented with
respect to the solar-antisolar direction such that there are enhancements on the dayside
and nightside that is remarkably consistent with the spatial variation in the Hodges
[1994] solstice distributions and Carruthers et al. [1976] images.

105

Figure 60. Contour plots of the exospheric H number density distribution on 18-22 June
2008 (top), 18-22 July 2008 (middle), and 18-22 August 2008 (bottom). The left plots
are an equatorial (XY plane) cross section and the right plots are a meridional (XZ plane)
cross section. Also shown are the definitions of the angles ϕ and θ. Contours are lines
of constant neutral hydrogen number density (cm
-3
); the color bar is for the contour
lines; the yellow dot is the projection of the direction to the Sun (left) and the direction
to the Sun (right); the filled shaded circle represents the region with radius 3 R
E
; and the
grid of shaded concentric circles for r > 3 R
E
, with a 1 R
E
step, highlights the asymmetry
of the distribution.

106
7.2 Geomagnetic Variation

A coupling effect via charge exchange exists between the exosphere and
plasmasphere, but the response of the exosphere to geomagnetic variation has yet to be
quantitatively completely understood yet. The disturbance storm time, Dst, index is a
global average of the horizontal component of Earth’s magnetic field at the magnetic
equator used to characterize geomagnetic activity. For a typical magnetic storm, the Dst
briefly rises, corresponding to the initial phase known as the storm sudden
commencement, and then decreases sharply as the ring current intensifies. Once the
interplanetary magnetic field (IMF) turns northward again, the Dst slowly rises back to
quiet time levels near zero as magnetospheric features such as the ring current recover.
The plasmapause is systematically closer to Earth during times of high geomagnetic
activity, recovering gradually, such that the outer plasmasphere is observed to refill over
a period of several days [Carpenter and Park, 1973]. Figure 61 shows hourly Dst
values from 2008 through 2011 (available at the World Data Center for Geomagnetism
website, http://wdc.kugi.kyoto-u.ac.jp/, provided by Kyoto University).

107

Figure 61. The disturbance storm time, Dst, index from 2008 (top) through 2011
(bottom), available at the World Data Center for Geomagnetism website,
http://wdc.kugi.kyoto-u.ac.jp/, provided by Kyoto University.

108
The LADs on TWINS-1 only adequately covered the near-Earth region, such that
global distributions with reliable three-dimensional asymmetries can be obtained, during
the summer months of 2008 when no substantial geomagnetic activity occurred. Since
the averaged radial density profile, , should be less sensitive to the incomplete
coverage than asymmetry in the three-dimensional distributions, a sequence of 55
density profiles has been obtained using TWINS-1 LAD data from August and October
in 2011 because four magnetic storms occurred during this time period (Figure 62, top).
The number of H atoms, , between a geocentric distance of 3 R
E
to 8 R
E
,

4

4

4
3
8

3

,
(67)

was calculated using the and values from each density profile, as a convenient way
of characterizing the exosphere (Figure 62, bottom). Interestingly, single day increases
in from 5% to 15% are noticed at the times of the four magnetic storms on 6 August
2011, 10 September 2011, 18 September 2011, and 27 September 2011.

109

Figure 62. The Dst index (top) and number of H atoms between 3 R
E
to 8 R
E
calculated
using the obtained density profiles (bottom) from 1 August 2011 to 1 October 2011.
The four gray vertical lines in the bottom panel mark the hour of lowest Dst value for
the corresponding magnetic storms.

It is not excluded that some apparent increase in the H atom population could be caused
by increased detector noise due to an enhanced energetic particle environment during
disturbed magnetospheric conditions. Plots of the LAD measurements on 10 September
2011 (Figure 63) and 27 September 2011 (Figure 64) versus each line-of-sight closest
approach distance,
, have been color coded on an hourly basis to investigate the
temporal response. It is anticipated that H densities, and in turn resonantly scattered
Lyman- α intensities, would respond gradually to enhanced geomagnetic activity in
contrast to the expectedly rapid change due to detector noise. One can see that in both
Figure 63 and Figure 64 the observed intensities decrease slowly with time.

110

Figure 63. The Lyman- α intensity observed by both LADs on TWINS-1 for 10
September 2011 versus the geocentric distance of each line-of-sight closest approach to
the Earth,
, color coded on an hourly basis. The storm sudden commencement
occurred on 9 September 2011 at 10:00 PM. The Dst index began dropping on 10
September 2011 at 1:00 AM, reached -60 nT at 4:00 AM, and remained low before
recovering from -64 nT at 4:00 PM.

111

Figure 64. The Lyman- α intensity observed by both LADs on TWINS-1 for 27
September 2011 versus the geocentric distance of each line-of-sight closest approach to
the Earth,
, color coded on an hourly basis. The storm sudden commencement
occurred on 26 September 2011 at 10:00 PM. The Dst index began dropping on 27
September 2011 at 1:00 AM and reached -103 nT at 10:00 AM before recovering.

The electron and proton fluxes at geostationary orbit are measured by two of the
Geostationary Operational Environmental Satellites, GOES-13 and -15, data available at
the National Oceanic and Atmospheric Administration (NOAA) Space Weather
Prediction Center (SWPC) website, http://www.swpc.noaa.gov/today.html. Figure 65

112
and Figure 66 show the electron fluxes from 9-12 September 2011 and 26-29 September
2011, respectively, since the obtained H density variation was most significant for the
storms that occurred during these two time periods. The horizontal dashed line at 1000
electrons cm
-2
s
-1
sr
-1
represents when deep dielectric discharging of > 2 MeV fluxes
(blue and red curves) might potentially occur. The > 2 MeV fluxes only slightly
exceeded the threshold value for brief periods on 9 September 2011 and 27 September
2011.

Figure 65. The intergral electron flux (electrons cm
-2
s
-1
sr
-1
), averaged in 5 min
intervals, with energies ≥ 0.8 MeV (purple and orange curves) and ≥ 2 MeV (blue and
red curves) from 9 September 2011 to 12 September 2011, data available at the National
Oceanic and Atmospheric Administration (NOAA) Space Weather Prediction Center
(SWPC) website, http://www.swpc.noaa.gov/today.html.

113

Figure 66. The intergral electron flux (electrons cm
-2
s
-1
sr
-1
), averaged in 5 min
intervals, with energies ≥ 0.8 MeV (purple and orange curves) and ≥ 2 MeV (blue and
red curves) from 26 September 2011 to 29 September 2011, data available at the NOAA
SWPC website, http://www.swpc.noaa.gov/today.html.

The proton fluxes from GOES-13 are shown for 9-12 September 2011 (Figure 67) and
26-29 September 2011 (Figure 68). The proton event threshold, represented by a
horizontal dashed line at 10 protons cm
-2
s
-1
sr
-1
at ≥ 10 MeV, was only slightly
exceeded on 26 September 2006.
The relatively low levels of charged particle fluxes at geostationary orbit would
likely be similar with respect to the TWINS-1 orbit location. However, a more accurate
assessment should be performed using the environmental sensors on TWINS-1.

114

Figure 67. The integral proton flux (protons cm
-2
s
-1
sr
-1
), averaged in 5 minute
intervals, for energy thresholds of ≥ 10 MeV (red curves), ≥ 50 MeV (blue curves), and
≥ 100 MeV (green curves) from 9 September 2011 to 12 September 2011, data available
at the NOAA SWPC website, http://www.swpc.noaa.gov/today.html.

115

Figure 68. The integral proton flux (protons cm
-2
s
-1
sr
-1
), averaged in 5 minute
intervals, for energy thresholds of ≥ 10 MeV (red curves), ≥ 50 MeV (blue curves), and
≥ 100 MeV (green curves) from 26 September 2011 to 29 September 2011, data
available at the NOAA SWPC website, http://www.swpc.noaa.gov/today.html.

7.3 H Densities at Larger Geocentric Distances

In addition to the propagated fitting error, the obtained exospheric H number
density distribution uncertainty increases for larger geocentric distances as the intensity
of the geocorona is exceeded by that of the interplanetary glow. To illustrate the effect
of this uncertainty, the radial dependence of predicted intensity on the position of a
hypothetical observer looking radially away from the Earth is plotted in Figure 69.

116

Figure 69. The radial dependence of predicted intensity on the position of a hypothetical
observer looking radially away from the Earth. Two horizontal lines show the range of
interplanetary glow intensities for all directions covered by the LADs on 11 June 2008.

For the TWINS-1 LAD observational geometry on 11 June 2008, the
interplanetary glow intensity varied from 560 to 820 R. Thus, for geocentric distances r
> 8 R
E
, the interplanetary glow becomes comparable or dominates the observed
intensities. Consequently, intrinsic uncertainty in the interplanetary glow map, which is
difficult to precisely quantify as the map is obtained by complex reduction of
SWAN/SOHO observations, could make the predictions of exospheric H distributions at
large distances less reliable.

117
7.4 TWINS Simplified Operational Exospheric Model for Solar
Minimum Conditions

As part of a collaborative effort with the Bonn group, published jointly
[Zoennchen et al., 2011], an averaged global H density distribution using LAD
measurements from June to September 2008 was reconstructed since there was nearly
constant solar minimum conditions for this entire three month period. The obtained
distribution is an advancement in contrast to the commonly used Rairden et al. [1986]
and Østgaard et al. [2003] models in that it introduces important asymmetries that
impact the results of extracting ion densities from ENA images through inversion or
forward modeling [e.g., Grimes et al., 2010].
The solar F10.7 index, which correlates to some degree with the solar Lyman- α
radiation output, fluctuated by about ± 2.5% around its average value of ~ 68 × 10
−22
W
m
−2
Hz
−1
. The composite solar Lyman- α flux from LASP varied by ± 2.2% around its
average value of 3.5 × 10
11
photons cm
−2
s
−1
. Consequently, the assumption of stable,
invariant geocoronal and interplanetary H atom resonant scattering conditions was
assumed. The obtained distribution is intended for use only during times of comparable
solar activity.
The interplanetary glow was approximated using a representative all-sky map
(Figure 70) that was derived from SWAN measurements on 11 June 2008 (W. Pryor and
R. Gladstone, personal communication, November 2010).

118

Figure 70. Interplanetary glow on 11 June 2008, derived from SWAN measurements
(Pryor and Gladstone, personal communication, November 2010). The horizontal axis is
ecliptic longitude λ, the vertical axis is ecliptic latitude β, and the color bar is in
rayleighs.

It is assumed that only very small fluctuations of the interplanetary glow occurred from
June to September 2008, associated with changes in the solar activity and additionally
the parallax effect caused by the Earth’s motion around the Sun. To investigate errors
introduced by using a single representative all-sky map for the 3 month time period,
interplanetary glow maps (W. Pryor and R. Gladstone, personal communication,
November 2010) were compared for the first (11 June 2008) and last (13 September
2008) day used in the fitting procedure. The TWINS-1 LAD observed regions differed
by an average of 5.6% of the actual observed intensities.

119
The solar activity conditions were quite stable at an extraordinarily low level
from June to September 2008. TWINS-1 LAD measurements from four different time
periods, 11 June, 22–24 July, 15–17 August, and 1–13 September, in 2008 were used as
a representative data set because using all of the observations would be computationally
impractical for a curve fitting procedure. The same amount of measurements was used
from each of the four sections such that they contribute equally to the fitted solution.
The measured Lyman- α intensities from LAD-1 and LAD-2 are shown in Figure 71 and
Figure 72, respectively, versus the geocentric distance of each line-of-sight closest
approach to the Earth,
. This type of plot, discussed in more detail in Section 6.2, is
used as a convenient way of characterizing measurement sets. The coverage includes
from 3 R
E
to above 6 R
E
by both LAD-1 and LAD-2, which is essential to obtaining
accurate density distributions for this range.

120

Figure 71. LAD-1 measured intensities for 11 June 2008 (black), 22-24 July 2008
(blue), 15-17 August 2008 (green), and 1-13 September 2008 (red) versus the geocentric
distance of each line-of-sight closest approach to the Earth,
.

121

Figure 72. LAD-2 measured intensities for 11 June 2008 (black), 22-24 July 2008
(blue), 15-17 August 2008 (green), and 1-13 September 2008 (red) versus the geocentric
distance of each line-of-sight closest approach to the Earth,
.

Since the geocorona exhibits a transition from optically thick to optically thin
around 3 R
E
[Østgaard et al., 2003; Zoennchen et al., 2010], the distribution is split into
2 segments: (A) for r < 3 R
E
and (B) for r > 3 R
E
. Segment (A) was chosen to be
consistent with segment (B) by having nearly the same H number density of 800 cm
-3
at
the 3 R
E
interface to provide a smooth transition.

122
Segment (A): < 3 R
E

For geocentric distances r < 3 R
E
, no LAD data was used to obtain the H density
distribution because of the optically thick conditions. Instead, a simple r-dependent
density profile was developed, similar to the approach used by Carruthers et al. [1976],
where two coefficients and were best fit,

/ , (68)

to a Chamberlain [1963] distribution with critical satellite altitude 2.5 R
E
, resulting in
numerical values = 70.005 and = 7.5498 between 1000 km altitude and r < 3 R
E
.

Segment (B): > 3 R
E

For geocentric distances r > 3 R
E
, a process of forward modeling fit a simplified
version of the expansion in Equations 42 through 55 to the LAD observational data
using a least squares curve fitting. The simplifications set all
= 0, forcing dawn-
dusk symmetry, and additionally setting
= 0 to minimize ecliptic north-south
asymmetry. Additionally, isotropic scattering of Lyman- α photons on H atoms was
assumed.
The corresponding parameter values in Equations 53 – 55 are listed in Table 3,
where is in cm
-3
and r is in R
E
.

123
Table 5. Parameters of the simplified operational model for solar minimum conditions
(Equations 53 – 55) obtained using TWINS-1 LAD data from June to September 2008 in
Geocentric Solar Ecliptic (GSE) coordinates; is in cm
-3
and r is in R
E
.
Radial and
Angular
Parameters
June to September
2008
2.23647 × 10
4

-2.99318

-3.7311 × 10
-2

1.7820 × 10
-2

-1.85094 × 10
-1

5.0944 × 10
-2

0

0

1.59213 × 10
-1

-3.0911 × 10
-2

0

0

0

0

-1.40919 × 10
-1

3.6105 × 10
-2

0

0

Figure 73 shows that the radial dependence for both segments (A) and (B) on the
dayside and nightside of the obtained distribution. The density profiles are consistent
with but somewhat higher than the average profiles obtained by Østgaard et al. [2003]
and Rairden et al. [1986].

124

Figure 73. Comparison of different H number density profiles including segments (A)
and (B) of the TWINS simplified operational exospheric model for solar minimum
conditions (solid line), Rairden et al. [1986] (circles), and Østgaard et al. [2003] for
solar zenith angle 90° (long dashed line).

The three-dimensional asymmetry, visible in Figure 74, is an advancement from
the commonly used (by ENA modelers) distributions of Rairden et al. [1986] and
Østgaard et al. [2003]. The global distribution is essentially cylindrically symmetric
about the Sun-Earth line, exhibiting an enhancement in the antisolar direction that is
consistent with the location of a geotail. The asymmetry does not, however, reflect

125
spatial and temporal variations that occur over shorter time scales than the selected data
set.

Figure 74. Contour plots of the exospheric H number density distribution for the
TWINS simplified operational model for solar minimum conditions: (left) an ecliptic
(XY plane) cross section and (right) a meridional (XZ plane) cross section. Also shown
are the definitions of the angles ϕ and θ. Contours are lines of constant neutral hydrogen
number density (cm
-3
); the color bar is for the contour lines; the yellow dots are the
direction to the Sun; the filled shaded circle represents the region with radius 3 R
E
; and
the grid of shaded concentric circles for r > 3 R
E
, with a 1 R
E
step, highlights the
asymmetry of the distribution.

The estimated uncertainty in the obtained H density distribution is nearly
constant at 15% to 20% from 3 R
E
to 7 R
E
, but then rapidly increases up to a factor of 2
at 10 R
E
. For lower geocentric distances r < 3 R
E
(within the region of the Chamberlain
[1963]-like density profile), a relative error of 5 – 20% is assumed. It is recommended

126
that the model be restricted to within these ranges or otherwise used with appropriate
caution and error analysis.

7.5 Example Application, Ring Current Modeling

The TWINS mission enables three-dimensional visualization of large scale
structures and dynamics of the magnetosphere. The observational geometry is ideal for
investigation of the ring current, shown in Figure 75, which circles Earth in the
equatorial plane. The ring current is generated by the longitudinal drift of energetic (10
– 200 keV) charged particles trapped on field lines between geocentric distances of 2 R
E

and 7 R
E
.

Figure 75. The TWINS mission stereoscopically images features of the magnetosphere
from two satellites in widely spaced Molniya-type orbits, ideal for imaging ENAs that
originate in the ring current (J. Goldstein).

127
Knowledge of the spatial distribution of exospheric hydrogen atoms limits
accuracy of the reconstruction of ENA fluxes, and subsequently of energetic ion
populations in the ring current. For example, long-term ring current decay is primarily
due to collisions of charged particles with neutral atoms in the upper atmosphere. Ilie et
al. [2011] simulated ion densities in the ring current during a geomagnetic storm that
occurred on 22 July 2009 using five different H density distributions: Rairden et al.
[1986], Hodges [1994], Østgaard et al. [2003], Zoennchen et al. [2011], and the 11 June
2008 distribution from this work. For high energy H
+
ions ( ≥ 100 keV), the H density
distributions each predict similar decay rates of the ring current ions. However, for low
energy ions, the decay rate and location of the ENA enhancements are highly dependent
on the chosen exospheric H density distribution. Figure 76 shows the decay rate as a
function of energy for an H
+
ring current ion at a geocentric distance of 5 R
E
. Hodges
[1994] predicts the highest overall H densities and thus results in the fastest decay rate.
The decay rate predicted using the Zoennchen et al. [2011] distribution is closer to that
of Hodges [1994] than of Rairden et al. [1986], Østgaard et al. [2003], and the 11 June
2008 distribution. The latter 3 have similar H density profiles and thus predict similar
charge exchange decay rates as a function of ring current H
+
energy. The percentage
difference between the 11 June 2008 distribution and Hodges [1994] predicted decay
rates varies from 46% for equatorially mirroring particles to 53% for particles with an
equatorial pitch angle of α = 30°.

128

Figure 76. Variation of the charge exchange decay rate of ring current H
+
ions with 88°
(top), 60° (middle), and 30° (bottom) equatorial pitch angle, at a radial distance of 5 R
E

at midnight ( ϕ = 0°, left column) and dawn ( ϕ = 90°, right column) obtained using H
density distributions from Rairden et al. [1986] (black), Hodges [1994] (blue), Østgaard
et al. [2003] (red), the 11 June 2008 distribution [Bailey and Gruntman, 2011] (green),
and Zoennchen et al. [2011] (light blue) [Ilie et al., 2011].

The reconstructed ENA images rely on a line-of-sight integration of the ENA
flux from the TWINS-2 position to the boundary of the HEIDI simulation domain,

,

,
(69)

where
corresponds to the H
+
ion differential flux from the HEIDI model, , is
the charge exchange cross section of an H
+
ion with an exospheric H atom, and is the
exospheric H number density distribution.

129
Figure 77 shows an ENA image of the 12 keV passband (6 – 18 keV) fluxes
observed by TWINS-2 (top left) as well as reconstructed ENA images calculated from
the Hot Electron Ion Drift Integrator (HEIDI) ion fluxes using the five different H
density distributions. The limb of the Earth and the dipole field lines for geocentric
distances of 4 R
E
and 8 R
E
are shown at four magnetic local times: noon (red lines), dusk
(pink lines), midnight (black lines), and dawn (white lines).

130

Figure 77. TWINS-2 observation of ENA fluxes in the 6 – 18 keV energy range (top
left) and reconstructed ENA images using 5 different H density distributions: Rairden et
al. [1986] (top right), Hodges [1994] (center left), Østgaard et al. [2003] (center right),
Zoennchen et al. [2011] (bottom left), and the 11 June 2008 distribution [Bailey and
Gruntman, 2011] (bottom right) [Ilie et al., 2011].

131
Ilie et al. [2011] concluded that changing the H density distribution used to
obtain can have a significant impact on the reconstruction of ENA fluxes. For
example, the TWINS-2 observation (Figure 77, top left) shows an enhancement in the
midnight-dawn sector and weak ENA fluxes from noon-to-dusk during the 22 July 2009
storm. This spatial variation is only closely reproduced when using the 11 June 2008
distribution, which is an indication that allowing for dawn-dusk asymmetry in
exospheric H density distributions may be essential for the reconstruction of certain
magnetospheric features.

132
Chapter 8: Conclusions

A process for preparing TWINS data such that LAD measurements can be used
to obtain global H density distributions with three-dimensional asymmetries above 3 R
E

has been extensively described. Two considerations must be addressed when using the
presented methodology to obtain distributions for days beyond the summer months of
2008. First, the majority of dayside measurements are excluded for having lines-of-sight
that are pointed at < 90° from the solar direction. Second, the relative cross calibration
ratio between LAD-1 to LAD-2 changes with time.
LAD measurements from TWINS-1 on an example day of 11 June 2008 were
used to obtain a global exospheric H density distribution for geocentric distances from 3
R
E
to 8 R
E
. The radial dependence of the spherically symmetric distribution is in
agreement with the density profiles obtained by Rairden et al. [1986], Hodges [1994],
and Østgaard et al. [2003]. For geocentric distances r > 4.5 R
E
, their density profiles, as
well as the 11 June 2008 distribution, decrease more rapidly than that obtained by
Zoennchen et al. [2010]. The 11 June 2008 distribution confirms the existence of an H
density enhancement on the dayside, a feature previously reported by Tinsley et al.
[1986] and Hodges [1994]. The 11 June 2008 distribution also exhibits an enhancement
on the nightside, consistent with the location of a geotail, in agreement with the day-
night asymmetry described by Østgaard et al. [2003], but less pronounced than reported
by Zoennchen et al. [2010]. Another prominent asymmetry exists in the north-south
direction, with larger densities in the Southern Hemisphere, similar to the Hodges [1994]

133
solstice distributions for similar seasonal conditions. The dawn-dusk asymmetry is less
prominent, but visible with densities slightly higher on the duskside.
A sequence of three global distributions with three-dimensional asymmetries
using LAD data from TWINS-1 on 18-22 June 2008, 18-22 July 2008, and 18-22
August 2008 was obtained to investigate seasonal variations. All three distributions
exhibit asymmetry that appears oriented with respect to the solar-antisolar direction such
that there are enhancements on the dayside and nightside that are remarkably consistent
with the spatial variation in the Hodges [1994] solstice distributions and Carruthers et
al. [1976] images.
A sequence of 55 density profiles was obtained using TWINS-1 LAD data from
August and October in 2011 as a way of investigating a possible response of the
exosphere to geomagnetic variations because four magnetic storms occurred during this
time period. Preliminary results suggest that exospheric H densities increase by 5% to
15% for the time period of a day or less in response to a magnetic storm.
For larger distances, uncertainty in the derived distributions accuracy increases
for two reasons. First, the observational geometry is limited by a geocentric distance for
an LAD line-of-sight closest approach to the Earth,
, that does not exceed 6.5 R
E
.
Second, accurate knowledge of the interplanetary glow becomes increasingly important
as, above 8 R
E
, it dominates the observed intensities.
The obtained asymmetries may be of particular interest to magnetospheric ENA
imaging, which heretofore has largely relied on the spherically symmetric distribution of

134
Rairden et al. [1986]. An operational distribution for solar minimum conditions was
collaboratively developed with the Bonn group and is now available for ENA modelers.
An analysis was summarized that demonstrates the importance of exospheric H
density distributions for reconstructing images in ENA fluxes and obtaining ring current
ion densities. Allowing dawn-dusk asymmetry in exospheric H density distributions
may be essential for the reconstruction of certain magnetospheric features.
The unprecedented observational coverage of the LADs on TWINS opens the
possibility for advancing scientific understanding of exospheric physics, including
source and loss processes as well as more accurate details about the ballistic, orbital, and
escaping populations of H atoms. The current rise to the next solar cycle (~ 11 year)
maximum will offer a unique opportunity to investigate the response of the exosphere to
enhanced solar activity. It is also anticipated that prediction capability for higher
geocentric distances (r > 8 R
E
) will eventually become possible.

135
References

Anderson, D. E., Jr., and C. W. Hord (1977), Multidimensional radiative transfer:
Applications to planetary coronae, Planet. Space Sci., 25, 563-571, doi: 10.1016/0032-
0633(77)90063-0.

Bailey, J., and M. Gruntman, Experimental study of exospheric hydrogen atom
distributions by Lyman-alpha detectors on the TWINS mission (2011), J. Geophys. Res.,
116, A09302, doi: 10.1029/2011JA016531.

Bertaux, J. L., E. Kyrölä, E. Quémerais, R. Pellinen, R. Lallement, W. Schmidt, M.
Berthé, E. Dimarellis, J. P. Goutail, C. Taulemesse, C. Bernard, G. Leppelmeier, T.
Summanen, H. Hannula, H. Huomo, V. Kehlä, S. Korpela, K. Leppälä, E. Strömmer, J.
Torsti, K. Viherkanto, J. F. Hochedez, G. Chretiennot, R. Peyroux, and T. Holzer
(1995), SWAN: A study of solar wind anisotropies on SOHO with Lyman alpha sky
mapping, Solar Phys., 162, 403-439, doi: 10.1007/BF00733435.

Bertaux, J. L. (1984), Helium and hydrogen of the local interstellar medium observed in
the vicinity of the Sun, NASA Conf. Publ., CP 2345, 3-23.

Bertaux, J. L., and J. E. Blamont (1970), OGO-5 measurements of Lyman- α intensity
distribution and linewidth up to 6 earth radii, Space Res., 10, 591-601.

Bertaux, J. L., and J. E. Blamont (1973), Interpretation of OGO 5 Lyman alpha
measurements in the upper geocorona, J. Geophys. Res., 78, 80-91, doi:
10.1029/JA078i001p00080.

Beth, H. A., and E. E. Salpeter (2008), Interaction with radiation, in Quantum
Mechanics of One- and Two-Electron Atoms, 262-263, Dover Publications, New York.

Bevington, P. R., and D. K. Robinson (2003), Error analysis, in Data Reduction and
Error Analysis for the Physical Sciences, pp. 36-50, McGraw-Hill, New York.

Bishop, J. (1985), Geocoronal structure: The effects of solar radiation pressure and the
plasmasphere interaction, J. Geophys. Res., 90, 5235-5245, doi:
10.1029/JA090iA06p05235.

Bishop, J. (1999), Transport of resonant atomic hydrogen emissions in the thermosphere
and geocorona: Model description and applications, J. Quant. Spectrosc. Radiat. Transf.,
61, 473-491, doi: 10.1016/S0022-4073(98)0031-4.

Brandt, J. C., and J. W. Chamberlain (1959), Hydrogen radiation in the night sky,
Astrophys. J., 130, 670-682, doi: 10.1086/146756.

136
Bush, B. C., and S. Chakrabarti (1995), Analysis of Lyman α and He I 584-Å airglow
measurements using a spherical radiative transfer model, J. Geophys. Res., 100, 19609-
19625, doi: 10.1029/95JA01210.

Carpenter, D. L. (1970), Whistler evidence of the dynamic behavior of the duskside
bulge in the plasmasphere, J. Geophys. Res., 75, 3837-3847, doi:
10.1029/JA075i019p03837.

Carpenter, D. L., and C. G. Park (1973), On what ionospheric workers should know
about the plasmapause-plasmasphere, Rev. Geophys., 11, 133-154, doi:
10.1029/RG011i001p00133.

Carpenter, D. L., B. L. Giles, C. R. Chappell, P. M. E. Décréau, R. R. Anderson, A. M.
Persoon, A. J. Smith, Y. Corcuff, and P. Canu (1993), Plasmasphere dynamics in the
duskside bulge region: A new look at an old topic, J. Geophys. Res., 98, 19243-19271,
doi: 10.1029/93JA00922.

Carruthers, G. R., T. Page, and R. R. Meier (1976), Apollo 16 Lyman alpha imagery of
the hydrogen geocorona, J. Geophys. Res., 81, 1664-1672, doi:
10.1029/JA081i010p01664.

Chamberlain, J. W. (1963), Planetary coronae and atmospheric evaporation, Planet.
Space Sci., 11, 901-960, doi: 10.1016/0032-0633(63)90122-3.

Chamberlain, J. W. (1979), Depletion of satellite atoms in a collisionless exosphere by
radiation pressure, Icarus, 39, 286-294, doi: 10.1016/0019-1035(79)90171-4.

Chamberlain, J. W. (1980), Exospheric perturbations by radiation pressure: II. Solution
for orbits in the ecliptic plane, Icarus, 44, 651-656, doi: 10.1016/0019-1035(80)90133-5.

Chamberlain, J. W., and D. M. Hunten, Radiation pressure from solar Lyman-alpha, in
Theory of Planetary Atmospheres, 353-354, Academic Press, New York.

Chappell, C. R., K. K. Harris, and G. W. Sharp (1970), The morphology of the bulge
region of the plasmasphere, J. Geophys. Res., 75, 3848-3861, doi:
10.1029/JA075i019p03848.

Clarke, J. T., R. Lallement, J. L. Bertaux, H. Fahr, E. Quémerais, and H. Scherer (1998),
HST/GHRS observations of the velocity structure of interplanetary hydrogen, Astrophys.
J., 499, 482-488, doi: 10.1086/305628.

Coleman, T. F., and L. Yuying (1994), On the convergence of reflective Newton
methods for large-scale nonlinear minimization subject to bounds, Math. Program., 67,
189-224, doi: 10.1.1.52.997.

137
Coleman, T. F., and L. Yuying (1996), An interior trust region approach for nonlinear
minimization subject to bounds, SIAM J. Optim., 6, 418-445, doi: 10.1137/0806023.

Donahue, T. M. (1966), The problem of atomic hydrogen, Ann. Geophys., 22, 175-188.

Emerich, C., P. Lemaire, J. Vial, W. Curdt, U. Schühle, and K. Wilhelm (2005), A new
relation between the central spectral solar H I Lyman α irradiance and the line irradiance
measured by SUMER/SOHO during the cycle 23, Icarus, 178, 429-433, doi:
10.1016/j.icarus.2005.05.002.

Fahr, H. J. (1974), The extraterrestrial UV-background and the nearby interstellar
medium, Space Sci. Rev., 15, 483-540, doi: 10.1007/BF00178217.

Fuselier, S. A., H. O. Funsten, D. Heirtzler, P. Janzen, H. Kucharek, D. J. McComas, E.
Möbius, T. E. Moore, S. M. Petrinec, D. B. Reisenfeld, N. A. Schwadron, K. J. Trattner,
and P. Wurz (2010), Energetic neutral atoms from the Earth’s subsolar magnetopause,
Geophys. Res. Lett., 37, L13101, doi: 10.1029/2010GL044140.

Grimes, E. W., J. D. Perez, J. Goldstein, D. J. McComas, and P. Valek (2010), Global
observations of ring current dynamics during CIR-driven geomagnetic storms in 2008, J.
Geophys. Res., 115, A11207, doi: 10.1029/2010JA015409.

Gruntman, M. (1997), Energetic neutral atom imaging of space plasmas, Rev. Sci.
Instrum., 68, 3617-3656, doi: 10.1063/1.1148389.

Gruntman, M., and V. Izmodenov (2004), Mass transport in the heliosphere by energetic
neutral atoms, J. Geophys. Res., 109, A12108, doi: 10.1029/2004JA010727.

Hodges, R. R. (1994), Monte Carlo simulation of the terrestrial hydrogen exosphere, J.
Geophys. Res., 99, 23229-23247, doi: 10.1029/94JA02183.

Holzer, T. E. (1977), Neutral hydrogen in interplanetary space, Rev. Geophys., 15, 467-
490, doi: 10.1029/RG015i004p00467.

Hunten, D. M., and D. F. Strobel (1974), Production and escape of terrestrial hydrogen,
J. Atmos. Sci., 31, 305-317, 10.1175/1520-0469(1974)031<0305:PAEOTH>2.0.CO;2.

Ilie, R., R. Skoug, H. Funsten, M. W. Liemohn, J. Bailey, M. Gruntman (2012), The
impact of geocoronal density on ring current development, J. Geophys. Res., accepted.

Kivelson, M. G., and C. T. Russell (1995), The plasmasphere, in Introduction to Space
Physics, 298-300, Cambridge University Press, New York.

138
Kupperian, J. E., Jr., E. T. Byram, T. A. Chubb, and H. Friedman (1959), Far ultraviolet
radiation in the night sky, Planet. Space Sci., 1, 3-6, doi: 10.1016/0032-0633(59)90015-
7.

Levenberg, K., A method for the solution of certain problems in least-squares (1944),
Quart. App. Math., 2, 164-168, doi: 10.1.1.135.865.

Liu, S. C., and T. M. Donahue (1974), The aeronomy of hydrogen in the atmosphere of
the earth, J. Atmos. Sci., 31, 1118-1136, doi: 10.1175/1520-
0469(1974)031<1118:TAOHIT>2.0.CO;2.

Mange, P., and R. Meier (1970), OGO 3 observations of the Lyman alpha intensity and
the hydrogen concentration beyond 5 Re, J. Geophys. Res., 75, 1837-1847, doi:
10.1029/JA075i010p01837.

Marquardt, D. (1963), An algorithm for least-squares estimation of nonlinear
parameters, SIAM J. App. Math., 11, 431-441, doi: 10.1137/0111030.

McComas, D. J., F. Allegrini, J. Baldonado, B. Blake, P. C. Brandt, J. Burch, J.
Clemmons, W. Crain, D. Delapp, R. DeMajistre, D. Everett, H. Fahr, L. Friesen, H.
Funsten, J. Goldstein, M. Gruntman, R. Harbaugh, R. Harper, H. Henkel, C. Holmlund,
G. Lay, D. Mabry, D. Mitchell, U. Nass, C. Pollock, S. Pope, M. Reno, S. Ritzau, E.
Roelof, E. Scime, M. Sivjee, R. Skoug, T. S. Sotirelis, M. Thomsen, C. Urdailes, P.
Valek, K. Viherkanto, S. Weidner, T. Ylikorpi, M. Young, J. Zoennchen (2009), The
Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS) NASA Mission-of-
Opportunity, Space Sci. Rev., 142, 157-231, doi: 10.1007/s11214-008-9467-4.

Meier, R. R. (1969), Balmer alpha and Lyman beta in the hydrogen geocorona, J.
Geophys. Res., 74, 3561-3574, doi: 10.1029/JA074i014p03561.

Meier, R. R.(1977), Some optical and kinetic properties of the nearby interstellar gas,
Astron. Astrophys., 55, 211-219.

Meier, R. R. and P. Mange (1970), Geocoronal hydrogen: An analysis of the Ly- α
airglow observed from OGO-4, Planet. Space Sci., 18, 803-821, doi: 10.1016/0032-
0633(70)90080-2.

Meier, R. R., and P. Mange (1973), Spatial and temporal variations of the Lyman-alpha
airglow and related atomic hydrogen distributions, Planet. Space Sci., 21, 309-327,
doi:.10.1016/0032-0633(73)90030-5.

Nass, H. U., J. H. Zoennchen, G. Lay, and H. J. Fahr (2006), The TWINS-LAD mission:
Observations of terrestrial Lyman- α fluxes, Astrophys. Space Sci. Trans., 2, 27-31, doi:
10.5194/astra-2-27-2006.

139
Østgaard, N., S. B. Mende, H. U. Frey, G. R. Gladstone, and H. Lauche (2003), Neutral
hydrogen density profiles derived from geocoronal imaging, J. Geophys. Res., 108,
1300, doi: 10.1029/2002JA009749.

Pryor, W., G. Holsclaw, W. McClintock, M. Snow, R. Vervack, R. Gladstone, A. Stern,
K. Retherford, and P. Miles (2012), Astron. Astrophys., submitted.

Quémerais, E., J. L. Bertaux, R. Lallement, B. Sandel, and V. Izmodenov (2003),
Voyager 1/UVS Lyman α glow data from 1993 to 2003: Hydrogen distribution in the
upwind outer heliosphere, J. Geophys. Res., 108(A10), 8029, doi:
10.1029/2003JA009871.

Rairden, R. L., L. A. Frank, and J. D. Craven (1983), Geocoronal imaging with
dynamics explorer: A first look, Geophys. Res. Lett., 10, 533-536, doi:
10.1029/GL010i007p00533.

Rairden, R. L., L. A. Frank, and J. D. Craven (1986), Geocoronal imaging with
dynamics explorer, J. Geophys. Res., 91, 13613-13630, doi: 10.1029/JA091iA12p13613.

Richter, M., U. Kroth, R. Thornagel, H. J. Fahr, G. Lay, and H. U. Nass (2001),
Calibration of Lyman- α detectors for the NASA satellites TWINS, Annu. Rep. S15,
BESSY, Berlin.

Roelof, E. C. (1987), Energetic neutral atom image of a storm-time ring current,
Geophys. Res. Lett., 14(6), 652-655, doi:10.1029/GL014i006p00652.

Schwadron, N. A., and D. J. McComas (2010), Pickup ions from energetic neutral
atoms, Astrophys. J., 712, L157-L159, doi: 10.1088/2041-8205/712/2/L157.

Stephan, S. G., S. Chakrabarti, J. Vickers, T. Cook, and D. Cotton (2001), Interplanetary
H Ly α observations from a sounding rocket, Astrophys. J., 559, 491-500, doi:
10.1086/322322.

Thomas, G. E. (1963), Lyman α scattering in the Earth’s hydrogen geocorona, J.
Geophys. Res., 68, 2639-2660, doi: 10.1029/JZ068i009p02639.

Thomas, G. E. (1970), Ultraviolet observations of atomic hydrogen and oxygen from the
OGO satellites, Space Res., 10, 602-607.

Thomas, G. E. (1978), The interstellar wind and its influence on the interplanetary
environment, Annu. Rev. Earth Planet. Sci., 6, 173-204, doi:
10.1146/annurev.ea.06.050178.001133.

140
Thomas, G. E. and D. E. Anderson, Jr. (1976), Global atomic hydrogen density derived
from OGO-6 Lyman alpha measurements, Planet. Space Sci., 24, 303-312, doi:
10.1016/0032-0633(76)90042-8.

Thomas, G. E., and R. C. Bohlin (1972), Lyman-alpha measurements of neutral
hydrogen in the outer geocorona and in interplanetary space, J. Geophys. Res., 77(16),
2752-2761, doi: 10.1029/JA077i016p02752.

Tinsley, B. A., R. R. Hodges, and R. P. Rohrbaugh (1986), Monte Carlo models for the
terrestrial exosphere over a solar cycle, J. Geophys. Res., 91(A12), 13631-13647, doi:
10.1029/JA091iA12p12631.

Tobiska, W. K. (2001), Validating the solar EUV proxy, E10.7, J. Geophys. Res.,
106(A12), 29969-29978, doi: 10.1029/2000JA000210.
Tobiska, W. K., S. D. Bouwer, and B. R. Bowman (2008), The development of new
solar indices for use in thermospheric density modeling, J. Atm. Solar-Terr. Phys., 70,
803-819, doi: 10.1016/j.jastp.2007.11.001

Wallace, L., C. A. Barth, J. B. Pearce, K. K. Kelly, D. E. Anderson, Jr., and W. G. Fastie
(1970), Mariner 5 measurement of the earth’s Lyman alpha emission, J. Geophys. Res.,
75, 3769-3777, doi: 10.1029/JA075i019p03769.

Woods, T. N., W. K. Tobiska, G. J. Rottman, and J. R. Worden (2000), Improved solar
Lyman α irradiance modeling from 1947 through 1999 based on UARS observations, J.
Geophys. Res., 105(A12), 27195-27215, doi: 10.1029/2000JA000051.

Zoennchen, J. H., U. Nass, G. Lay, and H. J. Fahr (2010), 3-D-geocoronal hydrogen
density derived from TWINS Ly- α-data, Ann. Geophys., 28, 1221-1228, doi:
10.5194/angeo-28-1221-2010.

Zoennchen, J. H., J. J. Bailey, U. Nass, M. Gruntman, H. Fahr, and J. Goldstein (2011),
The TWINS exospheric neutral H-density distribution under solar minimum conditions,
Ann. Geophys., 29, 2211-2217, doi: 10.5194/angeo-29-2211-2011.

141
Appendix: List of Publications

Published Articles

Bailey, J., and M. Gruntman, Experimental study of exospheric hydrogen atom
distributions by Lyman-alpha detectors on the TWINS mission (2011), J. Geophys. Res.,
116, A09302, doi: 10.1029/2011JA016531.

Zoennchen, J. H., J. J. Bailey, U. Nass, M. Gruntman, H. Fahr, and J. Goldstein (2011),
The TWINS exospheric neutral H-density distribution under solar minimum conditions,
Ann. Geophys., 29, 2211-2217, doi: 10.5194/angeo-29-2211-2011.

Accepted Articles

Ilie, R., R. Skoug, H. Funsten, M. W. Liemohn, J. Bailey, M. Gruntman (2012), The
impact of geocoronal density on ring current development, J. Geophys. Res., accepted.

It is anticipated that one or two additional articles will be submitted in 2012.

Conferences

American Geophysical Union Fall Meeting
San Francisco, CA
13-17 December 2010

American Geophysical Union Fall Meeting
San Francisco, CA
5-9 December 2011

THEMIS-TWINS Workshop
University of California – Los Angeles, CA
21-25 March 2011

Inner Magnetosphere Coupling II
University of California – Los Angeles, CA
19-22 March 2012

142
Presentations

Invited Monthly Speaker Series
The Aerospace Corporation – El Segundo, CA
3 August 2011

TWINS Science Team Meetings
Southwest Research Institute – San Antonio, TX
9-11 February 2009 and 3-5 February 2010

TWINS Science Team Meetings
Johns Hopkins University Applied Physics Laboratory – Laurel, MD
18-20 August 2009 and 16-18 August 2010

TWINS Weekly Teleconferences
15 July 2010, 10 February 2011, 9 June 2011, and 4 August 2011

Abstract (if available)

Abstract Exospheric atomic hydrogen (H) resonantly scatters solar Lyman-alpha (121.567 nm) radiation, observed as the glow of the geocorona. Measurements of scattered solar photons allow one to probe time-varying three-dimensional distributions of exospheric H atoms. The Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS) mission images the magnetosphere in energetic neutral atom (ENA) fluxes and additionally carries Lyman-alpha Detectors (LADs) to register line-of-sight intensities of the geocorona. This work details a process for preparing TWINS data such that LAD measurements can be used to obtain global H density distributions with three-dimensional asymmetries above 3 earth radii. Sequences of distributions are presented to investigate the dynamic exosphere, responding to seasonal variations between a summer solstice and autumnal equinox, as well as to solar and geomagnetic variations as described by commonly used indices. The distributions reveal asymmetries from day to night, north to south, and dawn to dusk. A nightside extension persists that is consistent with the location of a geotail. A seasonal north-south asymmetry occurs as solar illumination differs between the summer and winter polar regions. Pole-equator and less pronounced dawn-dusk asymmetries also appear, possibly due to a coupling effect via charge exchange with the polar wind and plasmasphere, respectively. ❧ A common phenomenon in geospace occurs as magnetospheric energetic ions collide with neutral background atoms and produce ENAs that, no longer bound by Earth's magnetic field, can travel large distances though space with minimal disturbance — providing an opportunity for remote detection. Knowledge of the distribution of the primary neutral partner, exospheric H atoms, is therefore essential for the interpretation of ENA fluxes and subsequent retrieval of ion densities. An analysis is summarized that demonstrates the importance of exospheric H density distributions on reconstructing magnetospheric images in ENA fluxes and obtaining ring current ion densities. ❧ Some of the main findings in this work have been accepted [Ilie et al., 2012] or are already published [Bailey and Gruntman, 2011

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Laboratory investigations of the near surface plasma field and charging at the lunar terminator

PDF

Study of rarefaction effects in gas flows with particle approaches

PDF

Experimental and numerical investigations of charging interactions of a dusty surface in space plasma

PDF

Interactions of planetary surfaces with space environments and their effects on volatile formation and transport: atomic scale simulations

PDF

Particle-in-cell simulations of kinetic-scale turbulence in the solar wind

PDF

Trajectory mission design and navigation for a space weather forecast

PDF

Revised calibration of a long-term solar extreme ultraviolet irradiance data set

PDF

Three-dimensional kinetic simulations of whistler turbulence in solar wind on parallel supercomputers

PDF

Characterization of space debris from collision events using ballistic coefficient estimation

PDF

Designing an optimal software intensive system acquisition: a game theoretic approach

PDF

Extravehicular activity (EVA) emergency aid for extended planetary surface missions: through-the-spacesuit intravenous (IV) administration

PDF

Reduction of large set data transmission using algorithmically corrected model-based techniques for bandwidth efficiency

PDF

Incorporation of mission scenarios in deep space spacecraft design trades

PDF

Autonomous interplanetary constellation design

PDF

Mission design study of an RTG powered, ion engine equipped interstellar spacecraft

PDF

Increased fidelity space weather data collection using a non-linear CubeSat network

PDF

Quantifying the effect of orbit altitude on mission cost for Earth observation satellites

PDF

Grid-based Vlasov method for kinetic plasma simulations

PDF

Kinetic studies of collisionless mesothermal plasma flow dynamics

PDF

The space environment near the Sun and its effects on Parker Solar Probe spacecraft and FIELDS instrumentation

Asset Metadata

Creator Bailey, Justin J. (author)

Core Title Three-dimensional exospheric hydrogen atom distributions obtained from observations of the geocorona in Lyman-alpha

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Astronautical Engineering

Publication Date 04/24/2012

Defense Date 02/28/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag alpha,atomic,exosphere,geocorona,hydrogen,Lyman,OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Gruntman, Michael (committee chair), Erwin, Daniel A. (committee member), Judge, Darrell (committee member), Kunc, Joseph (committee member), Tobiska, Kent (committee member)

Creator Email jjbailey@usc.edu,justin.j.bailey@alumni.usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-9378

Unique identifier UC11290168

Identifier usctheses-c3-9378 (legacy record id)

Legacy Identifier etd-BaileyJust-629-0.pdf

Dmrecord 9378

Document Type Dissertation

Rights Bailey, Justin J.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA