Emission of Doppler-shifted photons from excited energetic
neutral atoms created in the solar wind
A. Czechowski , M. Hilchenbach† and K.C. Hsieh
Space Research Centre, Polish Academy of Sciences, Bartycka 18A, PL 00-716 Warsaw, Poland
†
Max-Planck-Institut für Aeronomie, D-37191 Katlenburg-Lindau, Germany
Physics Department, University of Arizona, Tucson , AZ 85721, U.S.A.
Abstract. The fast-moving protons from the solar wind plasma convert into energetic hydrogen atoms by charge-exchange
with the background hydrogen from the interstellar medium. If created in the excited state, the energetic atoms will emit
photons, with frequency Doppler-shifted away from the resonance frequency range of the background hydrogen. We estimate
the flux and the spectrum of photons from the de-excitation of the H(2p) state of the energetic hydrogen atoms deriving from
the pick-up protons in the solar wind and from the thermal protons in the hot plasma region beyond the solar wind termination
shock. We also discuss the possibility of detection of the photon flux from this source.
INTRODUCTION
lous cosmic ray protons (by oversight, the contribution
from H(2s) state was calculated using one-photon mechanism).
Gruntman [4] considered the emission from the
He (2p) state ions created from the solar wind α particles picking up electrons from the background
atoms. Most of the signal in this case comes from
the inner heliosphere (within 10 A.U.) and would be
useful for imaging the three-dimensional structure of
the solar wind within this distance. The X-ray emission
from heavier species was calculated by Cravens [5].
His calculation was restricted to the region inside the
termination shock: he estimates, however, that the outer
heliosphere could make a comparable contribution.
One of potential methods to observe the distant heliosphere is by means of photons emitted by excited atoms
in this region. This could supplement the other method,
relying on direct observations of the flux of energetic
neutral atoms (Hsieh et al. [1], Czechowski et al. [2]).
Although expected photon flux intensity from this source
is low, for energetic atoms the Doppler shift, by moving
the emission away from the line centre, might increase
the chance to make the signal observable. In addition,
separating the signal from the background may in some
cases be helped by the shape of the spectrum.
In the following we estimate the flux and spectrum of
Ly-α photons originating in two populations of energetic
protons in the solar wind: the pick-up protons in the supersonic solar wind upstream of the termnination shock
and thermal protons in the shocked solar wind. We also
consider the contribution from protons in the supersonic
solar wind upstream of the shock.
Photons are emitted when those energetic protons are
converted into neutral atoms in excited state (H(2p))
by capturing an electron from hydrogen and helium
atoms of the background gas (the H(2s) state decays by
two-photon emission). The momentum exchange during
such reactions is small, so that the neutral atoms preserve approximately the momentum of the original ions.
The Doppler-shifted spectrum of emitted photons reflects
therefore the velocity distributions of energetic proton
populations.
In our previous study (Hilchenbach et al., [3]) we have
considered the analogous contribution from the anoma-
THE MODEL
The parameters of the plasma flow in the heliosphere are
taken from Kausch five component gas-dynamical solution (Fahr et al. [6]), which also provides the pick-up ion
density and the neutral hydrogen flow. We assume that
the ion populations considered: protons in the supersonic
solar wind, hot protons in the shocked solar wind downstream from the shock, and the pick-up protons in the
solar wind upstream, are described by isotropic distributions in the plasma frame. For solar wind protons we
use the Maxwellian with position-dependent temperature
provided by the Kausch solution. For the pick-up proton
velocity distribution we use two alternative forms. One
corresponds to the assumption used in the Kausch model
to derive the pick-up proton pressure: the distribution
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
721
function is assumed to be a velocity independent constant
for the plasma frame pick-up proton speed v ¼ VSW and
zero for v¼ VSW :
fPUI r v¼ 3
nPUI r
3
4π VSW
fPUI r v¼ 0
v
v
¼
¼
VSW (1)
VSW (2)
of the Kausch model:
fPUI r v¼ 3
nPUI rw 32 vmin v¼ VSW 3
8π VSW
(3)
¼
¼
v VSW v vmin (4)
fPUI r v¼ 0
Here w v¼ VSW . We have introduced the cutoff speed
vmin VSW rmin r32 where rmin 5 AU is the characteristic size of the region with low neutral hydrogen density close to the Sun. Our formula is a simplified version
of that of Vasyliunas and Siscoe, corresponding to taking
the neutral background density to be constant in space
for r rmin and zero otherwise.
The other assumption, which is based on the distribution derived by Vasyliunas and Siscoe [7] (see also
Gloeckler et al. [8]) for the isotropized (fast scattering in
the pitch angle) case, is that the distribution for v ¼ VSW
behaves as v¼ VSW 32 . In each case the normalization
factor is chosen to reproduce the pick-up proton density
FIGURE 3. Flux of photons (from the LISM apex direction)
from de-excitation of the H(2p) state of the energetic hydrogen
atoms originating from hot shocked solar wind protons neutralized by charge-exchange with hydrogen (solid line) and helium
(dashed line) atoms of the background gas. ∆λ λ λ0 where
λ0 is the Lyman-α wavelength. The superimposed peaks show
the contribution from thermal protons upstream of the shock.
FIGURE 1. Proton temperature (Kausch model) plotted as a
function of heliocentric distance for two directions: LISM apex
(solid line) and the heliotail (dotted line).
FIGURE 2. Pick up proton density upstream of the termination shock (Kausch model) as a function of heliocentric distance for two directions: LISM apex (solid line) and LISM antiapex (the heliotail, dotted line).
FIGURE 4. As Fig. 3, but for the flux from the anti-apex
direction (heliotail).
722
FIGURE 8.
tail)
FIGURE 5. Flux of photons (from the LISM apex direction)
from de-excitation of the H(2p) state of energetic hydrogen
atoms originating from pick-up protons upstream of the shock
(the distribution function given by Eqs. 1 & 2)
As Fig. 7, but for the anti-apex direction (helio-
We calculate the photon flux from direction n̂ as the
integral along the line-of-sight:
1
dJ
ds d 3 v¼ f r v¼ vrel σH vrel nH (5)
dν
4π
v n̂ σHe vrel nHe δ ν ν0 1 c
FIGURE 6.
tail).
where dJ d ν is the differential flux of photons per unit
area, time, solid angle and frequency, v and v ¼ the proton velocities in the observer and the plasma frame, respectively, vrel the relative speed between the proton and
the background gas, σ H and σHe the cross sections (Barnett [9]) for electron capture by proton from H and He
atoms into the H(2p) state (H H H 2p H ,
H He H 2p He ), and finally, n H , nHe the
number densities of H and He atoms of the background
gas. We have assumed that the emission of photons occurs at the frequency ν 0 in the atom rest frame and that
it can be taken as approximately isotropic in the observer frame. The flux per unit wavelength is given by
dJ d λ cλ 2 dJ d ν .
The model of the heliosphere which we consider is a
simplification. The flow is assumed to be axially symmetric with respect to the LISM apex-antiapex line: consequently, the three-dimensional structure of the heliosphere, in particular the latitudinal variation of the solar wind, is not included. On the other hand, the apexantiapex asymmetry of the heliosphere, including asymmetric shape of the termination shock and the extended
heliotail, is described by the model. We concentrated on
this asymmetry and calculated the photon fluxes from the
apex and the anti-apex directions.
As Fig. 5, but for the anti-apex direction (helio-
FIGURE 7. Flux of photons (from the LISM apex direction)
from de-excitation of the H(2p) state of energetic hydrogen
atoms originating from pick-up protons upstream of the shock
(the distribution function given by Eqs. 3 & 4)
723
DISCUSSION
REFERENCES
The results are shown in Figs. 3-8. For the photons
originating in thermal protons outside the shock (Figs.
3 and 4) the spectra show a shift by about 0.5 angstrem
to higher wavelength, corresponding to outward plasma
flow at the speed of 100 km/s downstream from the
shock. Despite larger size of the source region in the
heliotail (antiapex) direction, the flux of photons from
the heliotail direction is not larger than from the apex.
This is partly due to higher proton temperature in the
forward region (Fig. 1), which also affects the width of
the spectrum, and partly to higher density of the neutral
hydrogen. The sloping part in the center is caused by
the variation in the relative speed between the protons
and target atoms. As the cross sections for the capture
of electron into the H(2p) excited state in the relevant
energy range increase with energy, the emission rate
from the (neutralized) protons moving outward is larger
than from those moving inward. Note also that only the
high energy tail of the proton distribution contributes to
the emission (the cross section below 600 eV is taken to
be zero). The superimposed peaks show the contribution
from thermal protons upstream of the shock.
The photons coming from the pick-up proton population have a spectrum with sharp cutoff at ∆λ 0 and at
∆λ corresponding to twice the solar wind speed. The results are approximately the same for both models of pickup proton distribution function considered by us (Eqs. 1
or 3). The emission from the apex direction (Figs. 5, 7) is
higher than from the heliotail (Figs. 6, 8): this is because
both the pick-up proton (Fig. 2) and the neutral hydrogen density are higher in the forward region. We did not
calculate the contribution from the pick-up ions downstream of the shock (the flux of energetic neutral atoms
from this source is calculated in Czechowski et al. [10]).
In each case the flux intensity is very low (10 5
rayleigh maximum). The contribution from thermal protons inside the shock is much higher (10 3 R) because
the source region in this case includes the region of high
proton density close to the Sun. The spectra originating
in the inner (narrow peak) and the outer heliosphere are
sufficiently different in shape to make their separation
possible in principle. However, except for the contribution from the inner region, the intensity of the signal is
much below the interplanetary background.
1. Hsieh, K.C., Shih, K.L., Jokipii, J.R. and Grzedzielski, S.,
ApJ 393, 756 (1992).
2. Czechowski, A., Fichtner, H., Grzedzielski, S.,
Hilchenbach, M., Hsieh, K.C., Jokipii, J.R., Kausch,
T., Kota, J. and Shaw, A., A&A 368, 622-634 (2001).
3. Hilchenbach, M., Hsieh, K.C. and Czechowski, A., in:
Proceedings of the COSPAR Colloquium on: The Outer
Heliosphere: the New Frontiers, Potsdam 24-28 July 2000,
2001, p.281
4. Gruntman, M., J. Geophys. Res. 106, 8205-8216 (2001).
5. Cravens, T.E., ApJ 532, L153-L156 (2000).
6. Fahr, H.J., Kausch, T. and Scherer, H., A&A 357, 268-282
(2000).
7. Vasyliunas, V.M., Siscoe, G.L., J. Geophys. Res. 81,
1247-1251 (1976).
8. Gloeckler, G., Schwadron, N.A., Fisk, L.A. and Geiss, J.,
GRL 22, 2665-2668 (1995).
9. Barnett, C.F. (Ed.), Atomic Data for Fusion. Collisions of
H, H2, He and Li Atoms and Ions with Atoms and Molecules,
Oak Ridge Natl. Lab. Report, ORNL-6086-V1, Oak Ridge,
Tenn., 1990.
10. Czechowski, A., Fahr, H.J., Lay, G. and Hilchenbach, M.,
A&A 379, 601 (2001).
ACKNOWLEDGMENTS
A.C. acknowledges support from the KBN grant 8 T12E
029 20. A.C. also wishes to thank Max-Planck-Institut
für Aeronomie in Lindau for hospitality.
724