Temporal and Spatial Variations of Heliospheric X-Ray
Emissions Associated with Charge Transfer of the Solar
Wind with Interstellar Neutrals
I. P. Robertson1, T. E. Cravens1, and S. Snowden2
1
Dept. of Physics and Astronomy, 1251 Wescoe Hall Dr., University of Kansas, Lawrence, KS 66045, U.S.A.
2
NASA Goddard Spaceflight Center, Greenbelt, MD 20771, U.S.A.
Abstract. X-rays should be generated throughout the heliosphere as a consequence of charge transfer collisions between
heavy solar wind ions and interstellar neutrals. The high charge state solar wind ions resulting from these collisions are left
in highly excited states and emit extreme ultraviolet or soft X-ray photons. X-rays should also be generated because of
charge transfer collisions with neutral hydrogen in the Earth’s geocorona. Originally a simple model was developed in
which both the solar wind and the interstellar neutrals were assumed to be spherically symmetric and time independent. In
our updated results, the hot model of Fahr [1] was used to model spatial variations of interstellar helium and hydrogen. At
the same time a simple model was created to simulate X-ray radiation due to the Earth’s geocorona. With the updated
information, time independent maps of the heliospheric X-ray emission across the sky were created. Measured time
histories of the solar wind proton flux were used in this updated model and the results were compared with “long term
enhancements” in the soft X-ray background measured by the Röentgen satellite (ROSAT) for the same time period.
INTRODUCTION
Originally, the interstellar neutral density was
approximated with a simple mathematical formula.
The model has been improved upon by using Fahr’s
[1] hot model for interstellar neutrals, as described in
the current paper. Time independent maps were
created and time dependent behavior was also
studied.
In 1996 X-ray emission from the comet
Hyakutake was discovered [2]. Cravens [3] proposed
that this emission could be explained by charge
exchange collisions between heavy solar wind ions
and cometary neutrals. The product ion is left in an
excited state and eventually emits a photon in the Xray or EUV region of the spectrum [4]. Cox [5]
suggested that this same process could be applied to
interaction between solar wind ions and interstellar
neutrals, or neutrals in the Earth’s geocorona, and
might be able to explain some of the temporal
variation in the observed soft X-ray background
(SXRB). Dennerl et al. [6] even suggested that this
charge exchange mechanism might be able to explain
the Long Term Enhancement (LTE) part of the
SXRB. Cravens [7] consequently created a simple
model of the heliospheric X-ray emissions and
concluded that about half of the SXRB could be
explained by this mechanism. Robertson et al. [8]
and Cravens [9] slowly increased the complexity of
the model and found a significant correlation between
solar wind proton fluxes and LTE X-ray intensities.
MODEL OF X-RAY PRODUCTION BY
SOLAR WIND CHARGE EXCHANGE
The following equation was used by Cravens [2,
3] and Cravens et al. [9] to calculate the X-ray and
EUV power density:
PX-ray = αnnnswusw(eV cm-3s-1)
(1)
where α contains all the atomic cross sections, the
transition information and solar wind heavy ion
composition. α is different for interstellar helium and
hydrogen and also varies with solar wind speed. For
the time being we have used the same slow solar
wind value of α for both helium and hydrogen,
although the helium value should probably be
somewhat less than the hydrogen value. The value
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
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used is: α ≈ 6×10-16 eV cm2. The solar wind density
is denoted as nsw, and the solar wind speed as usw. The
solar wind density is presently considered to be
spherically symmetric, and its dependence on radial
distance (r) is as follows: nsw = nsw0(ro/r)2, where ro is
1 AU and nsw0 is the solar wind density at 1 AU.
The interstellar neutral density (a combination of
interstellar helium and hydrogen) is denoted as nn .
Originally the helium and hydrogen densities were
approximated by a simple mathematical formula.
Fahr’s hot model has been adopted to better calculate
these densities. In this model gravitational focusing,
ionization losses, and radiation pressure are taken
into account. Due to these factors the neutral
hydrogen density is lower in the downwind direction
from the sun than in the upwind direction. For
helium, however, gravitational focusing produces a
cone of enhanced helium abundance downwind from
the sun near 1 AU. The unperturbed interstellar
hydrogen density is taken to be 0.1 cm-3, and that of
helium to be 0.02 cm-3. Fahr [1] noted that even
though the helium density is initially much smaller
than that of interstellar hydrogen, its density reaches
the same order of magnitude as the hydrogen density
1 AU on the upwind side. On the downwind side the
density can be more than an order of magnitude
larger than the hydrogen density.
The production rate, integrated over a path length
s, starting at Earth and going out to 200 AU, yields
the X-ray intensity. Solar wind ions can also charge
transfer with neutral hydrogen in the Earth’s
geocorona outside the magnetopause and produce Xrays. For the time being, a simple mathematical
formula is used to estimate this geocoronal intensity:
4πIgeo = 5αnswuswnH0RE(10 RE/Rmp)2
(2)
where Rmp ≈ 15 RE is the magnetopause distance from
the Earth in the flanks and nH 0 = 25 cm-3 is a
reference value of the exospheric hydrogen density at
10 RE. The results are in agreement with an estimate
of Cox [5].
TIME INDEPENDENT RESULTS
Figure 1 shows the heliospheric X-ray intensities
in the equatorial plane for a solar wind speed of 400
km/s, a solar wind density with no = 7/cm3, and
neutral densities from Fahr’s hot model. The location
of the Earth is at the vernal equinox, as indicated on
the small insert in the figure. The direction of the
interstellar wind is also indicated with the large
arrow.
FIGURE 1. Time independent variation with ecliptic longitude of heliospheric X-ray intensities for look directions in the
ecliptic plane. See text for details.
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Cravens et al. [9] show a plot for the same time
period, but it was produced without the use of Fahr’s
model. Two cases were considered: the Earth located
in the upwind direction (summer) and the Earth
located in the downwind direction (winter). In both
cases depicted, the look direction is northward from
the ecliptic plane. In Figure 2, the Earth is in the
downwind direction (winter solstice). Because the
Earth is immersed in the helium cone, the dominant
contribution, both in variation as well as intensity, is
from helium. The variation in hydrogen is not
noticeable at this scale. Even though the geocoronal
contribution is minimal, it does contribute to the
variation in total intensity. In Figure 3, the Earth is in
the upwind direction (summer solstice). The
hydrogen contribution is dominant but has very little
variation. More variation can be seen in the helium
contribution and even more in the contribution from
the geocorona. It should be noted that these plots
were generated using identical alphas for the
calculations of the helium as well as the hydrogen
contributions. As noted earlier, that is probably not
the case. It can be noticed, however, that even if the
alpha for helium would be smaller by a factor of 2,
the helium continues to be dominant in the X-ray
variability.
The coordinates used are Earth-centered solar
ecliptic; consequently, zero degrees points towards
the sun (an area blocked out in the graph), -90û points
into the interstellar wind and +90û points towards the
tail. There is little variation in the X-ray intensity
due to charge exchange with interstellar hydrogen.
The contribution due to helium varies much more,
with a significant enhancement near 30û when the
look direction intersects with the “helium cone” due
to gravitational focusing. Note, though, that a more
careful determination of α for helium could reduce
these intensities by as much as a factor of 2.
TIME DEPENDENT RESULTS
Time dependent X-ray intensities were calculated
for fixed look directions. We used solar wind proton
fluxes measured by the IMP-8 spacecraft for the time
period 1996-1998. The day number is the number of
days after January 1, 1996. Once again the solar
wind proton flux is assumed to be spherically
symmetric and the flux decreases as 1/r2. Again
Fahr’s hot model is used to model the interstellar
neutral density. Figures 2 and 3 show the X-ray
intensity due to helium, hydrogen and the Earth’s
geocorona. The total intensity is also plotted.
FIGURE 2. X-ray intensity at Winter Solstice versus time. Earth is located in the downwind direction.
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FIGURE 3. X-ray intensity at Summer Solstice versus time. Earth is located in the upwind direction.
1. A more accurate calculation of α for different
species;
2. A solar wind model which includes latitudinal
variations;
3. An improved model of the geocoronal X-ray
emission.
ROSAT LONG-TERM
ENHANCEMENT DATA
Cravens et al. [9] directly compared ROSAT LTE
1/4 keV data with measured solar wind proton fluxes
for the same time period. Even though no selection
was made with respect to look-direction, a significant
correlation was found with a linear regression
coefficient of R = 0.7. Cravens next plotted the total,
helium and geocoronal intensities versus ROSAT
LTE data and found a strong correspondence between
the modeled X-ray intensity and the LTE data. The
downwind plot with Fahr’s densities shows
considerable more variation than the X-ray intensities
Cravens used and, consequently, would show an even
stronger correspondence between X-ray intensity and
LTE data.
ACKNOWLEDGMENTS
NASA Planetary Atmospheres grant NAG5-4358
and NSF grant ATM-9815574 at the University of
Kansas are acknowledged.
REFERENCES
1. Fahr, H. J., Astron. Astrophys. 14, 263-274 (1971).
2. Lisse, C. M. , et al., Science 274, 205 (1996).
3. Cravens, T. E., Geophys. Res. Lett. 24, 105 (1997).
4. Cravens, T. E., Science 296, 1042-1045 (2002).
5. Cox, D. P., “Modeling the local bubble,” in The Local
Bubble and Beyond, edited by D. Breitschwerdt, M. J.
Freyberg, and J. Trümper, New York, Springer-Verlag,
1998, p. 121.
6. Dennerl, K., Englhauser, J., and Trümper, J., Science
277, 1625 (1997).
7. Cravens, T. E., Astrophys. J. 532, L153 (2000).
8. Robertson, I. P., Cravens, T. E., Snowden, S., and Linde,
T., Space Science Reviews 97, 401-405 (2001).
9. Cravens, T. E., Robertson, I. P., and Snowden, S. L., J.
Geophys. Res. 106, 24,883-24,896 (2001).
CONCLUSIONS
Our improved model of soft X-ray intensities
observed at Earth further supports the suggestion that
LTEs, in the observed soft X-ray background, can be
explained by charge exchange between heavy solar
wind ions and interstellar neutrals.
Further
improvements in the modeling of X-ray intensities
should include:
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