Dynamics of H, D, and heavy Energetic Neutral Atoms (ENA) between the
termination shock and 1 AU is discussed in the context of the forthcoming NASA
SMEX mission IBEX. In particular, effects of the velocity-dependent radiation
pressure on atomic trajectories are considered and ionization losses between TS
and 1 AU are studied. It is shown, among others, that most of the dynamical
effects and ionization losses are induced within a few AU from the Sun, which
translates to the time domain into $\sim 1 - 3$ solar rotations before
detection. This loosens considerably time requirements for tracking the
ionization and radiation pressure history to just prior 3 months. ENA seem
excellent tracers of the processes within the heliospheric interface, with the
transport effects between the termination shock and detector relatively mild
and easy to account for.Comment: submitted to Proceedings of the 5-th IGPP Astrophysics Conference,
  Honolulu HI, March 2006; 6 page

Bzowski, Maciej

Tarnopolski, Slawomir

English

arXiv

Maciej Bzowski

Sławomir Tarnopolski

Crossref

Neutral atom transport from the termination shock to 1 AU

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Neutral atom transport from the termination
shock to 1 AU
Maciej Bzowski∗ and Sławomir Tarnopolski∗
∗Space Research Centre PAS, Bartycka 18A, 00-716 Warsaw, Poland
Abstract. Dynamics of H, D, and heavy Energetic Neutral Atoms (ENA) between the termination
shock and 1 AU is discussed in the context of the forthcoming NASA SMEX mission IBEX. In
particular, effects of the velocity-dependent radiation pressure on atomic trajectories are considered
and ionization losses between TS and 1 AU are studied. It is shown, among others, that most of the
dynamical effects and ionization losses are induced withina few AU from the Sun, which translates
to the time domain into∼ 1− 3 solar rotations before detection. This loosens considerably time
requirements for tracking the ionization and radiation pressure history to just prior 3 months. ENA
seem excellent tracers of the processes within the heliospheric interface, with the transport effects
between the termination shock and detector relatively mildan easy to account for.
INTRODUCTION
This article is a part of reconnaissance for a NASA SMEX mission IBEX ([1]; McCo-
mas et al, this volume). IBEX will be a spin-stabilized Earthsatellite observing Energetic
Neutral Atoms (ENA) in the 0.01 – 6 keV energy band, with sensors l oking perpen-
dicularly to the spin axis directed at the Sun. The prime target of the mission will be
imaging of the heliospheric interface via neutral atoms andthe goal of an individual
observation will be to obtain the kinematic parameters of the locally registered atom be-
yond the termination shock (TS). To that end, understandingthe processes affecting the
atoms between their source region and the detector is needed. In particular, a control on
the modifications of the kinematic parameters of the atoms between the source region
and the detector and a grasp on loss processes underway is necessary.
Since the ENA gas inside TS is collisionless at all energies,then – from Boltzmann
equation – the transport of ENA from TS to the inner heliosphere is governed solely by
dynamic effects and gain and loss processes.
The losses include all known ionization processes operating in the heliosphere: charge
exchange, EUV ionization, and electron impact [2]. For inward-traveling ENA, gains
(considered by IBEX as unwanted background) include chargeexchange between CME,
CIR and pickup ions and all kinds of neutral populations present inside TS, as well as
production of ENA in the plasma environment of the spacecraft (McComas et al., this
volume) and will be neglected.
-200 -100 0 100 200
radial velocity HkmsL
0
0.5
1
1.5
2
ra
d
.
p
re
ss
u
re
HΜ
u
n
it
sL
Radiation pressure for H and D
D, min
D, max
H, min
H, max
1990 1992.5 1995 1997.5 2000 2002.5 2005
time HyrL
1
1.2
1.4
1.6
1.8
2
fl
u
x
HΜ
-
u
n
it
sL
Solar Ly-Α line-integrated flux:
monthly averages
FIGURE 1. Radiation pressure force acting on H and D atoms as function of atomic radial velocity for
solar minimum and maximum conditions, expressed in the units of solar gravity force (“theµ units") and
the net line-integrated solar Lyman-α flux for the past∼ 1.5 solar cycle, also expressed in theµ units.
DYNAMICS OF H AND D ATOMS WITH DOPPLER EFFECT
From dynamical point of view, heliospheric ENA belong to twocategories: sensitive
and insensitive to solar radiation pressure. The sensitiveones include only hydrogen –
the most abundant heliospheric element – and its isotope deut rium. All atoms are, of
course, sensitive to solar gravity.
All neutral atoms in the heliosphere obey the equation of motion in the form:
d2~r/dt2 =−GM (1−µ (vr, I (t)))~r/|~r|3 (1)
wherevr = (d~r/dt) ·~r/|~r| is radial velocity andGM the gravity constant times solar
mass.I (t) is the line-integrated solar Lyman-α flux. For all atoms heavier than D
the radiation pressure factorµ ≡ 0 and the equation of motion reduces to the simple
Keplerian case, with the ideal hyperbolic solution.
The expected range of velocities of heliospheric H and D ENA is∼ 50−1000 km/s.
Beacuse of the geometry of the lines of sight, IBEX is interested only in the inward-
traveling atoms, with velocities in the source region pointing so that at 1 AU they will be
at perihelion. Such atoms are being detected at 0 radial velocity with respect to the Sun,
but cover most of their paths with radial velocities almost equal to their net velocities.
Consequently, if their net velocity is larger than the spectral range of the solar Lyman-α
line, the atoms do not experience any radiation pressure at all all the way except within
a few AU from the Sun, where before detection they reduce their rad al velocities to 0.
Since, however, they are fast, their trajectories will be weakly modified by solar gravity
and hence close to straight lines. On the other hand, slower ENA (whose velocities
remain within the spectral range of the solar line), will be aff cted by radiation pressure,
which acts against solar gravity. Consequently, they also will follow trajectories close to
straight lines, except perhaps within a few AU from the detector.
The behavior of solar Lyman-α line from solar minimum to maximum has been
recently surveyed by [3]. Based on these data it was possibleto fit a general formula
(Tarnopolski, thesis, in preparation):
µ (vr, I) = (a+bI)
(
exp
[
−cv2r
](
d + f exp
[
−gvr −hv
2
r
]
+ j exp
[
k vr −mv
2
r
]))
(2)
which describes the radiation pressure of H or D atoms traveling at radial velocityvr with
respect to the Sun. The formula, shown for H and D and solar minimum and maximum
conditions in the left-hand panel of Fig.1, is parametrizedby the sole parameterI,
which is the line-integrated solar Lyman-α flux, whose variations during the solar cycle
(SOLAR 2000, [4]) are shown in the right-hand panel of Fig.1.
Due to isotope effect, the deuterium resonant Lyman-α frequency is shifted blueward
by ∼ 80 km/s with respect to H. Hence the D atoms are sensitive to a different part of
the solar Lyman-α profile than H atoms and due to the mass difference the radiation
pressure potentially acting on D atoms is additionally reduced two-fold with respect to
H. The two effects combined will yield different dynamics ofthe H and D ENA: while
radiation pressure for H is approximately symmetric with resp ct to 0 radial velocity,
this is not the case for D and the effective radiation pressure acting on the incoming D
atom will be much lower than on a H atom launched from the termination shock with
the same speed (see Fig.1, left-hand panel). Consequently,the dynamic behavior of the
incoming D ENA is expected to be more similar to the behavior of purely-Keplerian
heavy atoms than to that of H atoms.
Results presented in the following part of the paper are based on numerical solutions
of Equ.(1) with theµ factor taken from Equ.(2), evaluated for two fixed values ofI (t),
appropriate for solar minimum and solar maximum. For heavy atoms theµ factor was
set to 0. The atoms were tracked from their perihelions at 1 AUto TS, with velocities
at perihelion ranging from 50 to 400 km/s. Along with the trajectory tracking the
probability of ionization for an assumed ionization rate at1 AU was calculated.
RESULTS
Trajectories and energy
All heliospheric ENA except those from the low end of the IBEXenergy band follow
almost straight line trajectories, with very little velocity change between TS and the
detector at 1 AU. For detection speedsv >∼ 150 km/s there is practically no velocity
change between TS and 1 AU regardless of the species and solaractivity phase (Fig.2).
For v lower than this value, H atoms detected at velocitiesv have TS launch velocities
vT S,H > vT S,D/O, the launch velocities of the heavier species detected at the samev.
Also, usuallyv < vT S,H , while opposite is true forvT S,D/O. Consequently, mean velocity
of the H atoms detected atv is higher than the mean velocities of the heavies and their
travel time is shorter. For example, an O atom detected at 50 km/s needs∼ 22 yr to
arrive at 1AU from the crosswind TS, where it was launched at∼ 26 km/s, while a
H atom detected at the same 50 km/s needs only∼ 12 yr to make the trip and it was
launched at∼ 60 km/s. During solar minimum, even the slowest H ENA travel almost
30 50 70 100 150 200
v at 1 AU HkmsL
30
50
70
100
150
200
v
at
T
S
Hk
m
s
L
H, D & O speed at TS vs speed at 1 AU
O
H, max
H, min
D, max
D, min
25 50 75 100 125 150 175 200
speed at 1 AU HkmsL
0
5
10
15
20
25
30
d
ef
le
ct
io
n
H°
L
Deflection of source position of H, D & O
at TS from LOS direction
O
H, min
H, max
D, min
D, max
FIGURE 2. Change of speed of H, D, O atoms at solar minimum and maximum conditi ns between the
termination shock and 1 AU (left-hand panel) and angular separation between the line of sight (arrival
direction at perihelion) and the source position at the termination shock for H, D, O atoms at solar
minimum and maximum (right-hand panel). The results for O are valid for all heavy atoms.
constant speed, following straight lines in the whole IBEX energy range. This facilitates
assessment of the travel timestT S from TS to 1 AU for given detection speedv, which
can be with good approximation calculated as:
tTS = rT S (θ)/v = 125.74/(1+0.253cosθ)/v (3)
whereθ is offset angle from the nose of TS and fortT S in yr v must be in AU/yr. For the
lowest-energy atoms (∼ 100 km/s) the difference in travel time from the nose and tail
of TS will be about 5 yr, but for typical H ENA at 400 km/s it willbe only 1 year. The
shape of the termination shock was taken from Grzedzielski et al. (this volume).
Mapping of the launch position of H and D atoms at TS for a givend tector pointing
is practically 1 to 1, with the deflection angle at the lower end of the energy band within
∼ 10o (Fig.2, right-hand panel). Heavy atoms (insensitive to radiation pressure) are also
weakly deflected except the slowest ones, which are deflectedup to∼ 30o at 50 km/s.
Deflection of all species drops below 5o for detection speed 100 km/s. This is favorable
for IBEX since it facilitates linking the pointing of detectors to the source region at TS.
Also favorable is the relatively short range of the combinedsolar gravity and solar
radiation pressure acting on H ENA. The effective “collision time” of H/D ENA with
the Sun before detection is only∼ 0.25yr= 3 solar rotations, so the highly fluctuating
solar Lyman-α output will need to be tracked back no longer than this interval.
Ionization
The survival probability of ENA against ionization betweenTS and 1 AU is a function
of the launch and detection speeds and of the ionization rate(assumed here to vary with
2´10-74´10-76´10-78´10-71´10-6
ionization rate Hsec-1L
0.01
0.02
0.05
0.1
0.2
0.5
1
p
ro
b
ab
il
it
y
Survival probability of H and O from TS
50 kms
100 kms
200 kms
0 2´10-74´10-76´10-78´10-71´10-6
ionization rate Hsec-1L
0.05
0.075
0.1
0.125
0.15
0.175
0.2
0.225
ti
m
e
Hy
rL
Ionization time before detection
50, min
50, max
100, min
100, max
200, min
200, max
0 0.5 1 1.5 2
t HyrL
0
0.2
0.4
0.6
0.8
1
w
Ht
L
w
FIGURE 3. Left-hand panel: Survival probability of H (solid lines) and O ENA (broken lines) from
TS to 1 AU as function of the ionization rate at 1 AU for variousdetection speeds. The solid lines
in the left-hand panel correspond to H ENA, the broken lines to heavy atoms (like O); for 200 km/s
the two lines practically coincide. Right-hand panel: timeof effective ionization defined in Equ.(4) for
H at solar minimum and maximum conditions as function of the ionization rate at 1 AU (right-hand
panel) for various detection speeds, indicated in the figure, and for solar minimum (solid) and maximum
conditions(broken). The inset in the right-hand panel shows an example of the course of relative survival
probabilitywrel (t) between TS andr.
heliocentric distance as 1/r2). For the H ENA expected to be observed by IBEX it is
quite large in the whole energy band except at the lowest end:for a H atom detected at
200 km/s even for the highest expected ionization rate 10−6 s−1 1 AU [2] the probability
is as much as 40%, and for the lowest expected rate equal to 10−7 s−1 it is almost
1. For faster H, D, and heavy atoms the survival probability is correspondingly larger,
depending on the ionization rate. On the other hand, the ionization losses will increase
quickly with the decrease of detection speed, as shown in theleft-hand panel of Fig.3.
In the range of detection speeds shown, one expects some “radiation pressure bonus”
in the survival probability for the H atoms (and to some extent for D) compared with
the heavy atoms because of the larger mean speed of H atoms detected at a givenv in
comparison with the mean speed of heavy atoms. This effect issignificant only at the
lowest end of the detection interval. For H, some variationsf the survival probability
with the phase of the solar cycle are expected, but they are not big and probably will be
masked by fluctuations of the actual ionization rate.
Most of the ionization losses occur shortly before detection. Denoting byw1AU the
ionization probability of an atom underway from TS to 1 AU andby w(t) the probability
of ionization at timet before detection, we can define the relative survival probability
wrel (t) and the ionization timeτion as:
wrel (t) = 1−w(t)/w1AU; wrel (τion)≡ 0.8 (4)
and determine the ionization times for different species and detection speeds. Results are
shown in Fig.3 (right-hand panel). The ionization losses suffered by an atom underway
from TS to 1 AU are relatively small almost all the way down, and i crease exponentially
only within few months before detection. The exact value ofτion is a function of
detection speed and ionization rate, but generally one can say that the 80% ionization
losses of all atoms occur within 0.1 – 0.25 yr (∼ 1−3 solar rotations) before detection.
The ionization times differ most for the lowest expected ionization rates and for the
lowest energies at detection; for typical H ENA expected from the inner heliosheath the
ionization time is expected at the level of one solar rotation period. This is favorable for
IBEX operations because it means that interpretation of a signal requires monitoring of
the local ionization rate only∼ 1 month backward in time.
CONCLUSIONS
The aspects of ENA transport from the termination shock to 1 AU in the contexts of the
planned IBEX mission can be summarized as follows.
Both heavy ENA and H and D ENA are excellent tracers of atomic parameters at
and beyond TS. Velocity change between the termination shock and 1 AU becomes
noticeable only below 150 km/s and deflection of the trajectories with respect to the
launch site at TS beyond angular resolution of IBEX instruments for H ENA occurs only
during solar maximum (which will be beyond IBEX nominal mission time) at the lowest
limit of the energy band. Heavy atoms are a little stronger deflected, but the deflections
exceed IBEX resolution only for detection speeds lower than∼ 70 km/s.
Ionization losses between TS and 1 AU should not be a big problem for H ENA
expected from the heliosheath. The survival probability drops down below 10% only for
H ENA traveling at 1 AU slower than 100 km/s. Most of the ionizat on losses will occur
within a month or so before detection and hence should be relativ ly easy to take into
account.
ACKNOWLEDGMENTS
This research was supported by the Polish MSRiT Grant 1P03D 009 27.
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Neutral atom transport from the termination shock to 1 AU

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