University of Kansas

X-Ray Emission in the Solar System

 Draft
Temporal Variations of Geocoronal and Heliospheric X-Ray Emission Associated with the Solar Wind Interaction with Neutrals
by Cravens et al.

Image: Jovian soft X-rays from ROSAT; courtesy of J. H. Waite.

3. Heliospheric X-Ray Production by the Solar Wind Charge Exchange Mechanism

As discussed by Cravens [2000], equation (2) can be used to calculate the volume emission rate of X-ray energy (or the production rate of photons if divided by the average photon energy of roughly 200 eV) throughout the heliosphere. The neutral density is the combined interstellar hydrogen and helium density. Interstellar neutral hydrogen has been observed by means of resonantly scattered solar Lyman alpha photons [e.g., Chambers et al., 1970; Johnson, 1972; Bertaux et al., 1996; Judge et al., 1990; Quemerais et al., 1993] or by means of pickup ions produced by the ionization of interstellar neutrals and detected by spacecraft such as Ulysses [cf. Gloeckler, 1996; Mobius et al., 1995]. The unperturbed upstream interstellar H density is ~0.15 cm-3 and the interstellar He density is ~10% of the H density. Hydrogen is depleted in the inner solar system due to photoionization by solar radiation, solar radiation pressure, and charge transfer with solar wind protons. This depletion, or attenuation, is much more severe on the downwind side of the heliospheric cavity than on the upwind side. The depletion of helium is much less severe than for H, and in fact, the He density is thought to exhibit a localized enhancement in the downwind direction due to gravitational focusing [Johnson, 1972; Mobius et al., 1995]. Following Cravens [2000], we use the following very approximate expression for either the H or He density as a function of heliocentric distance r:

nn = nn0 exp(-l/r).(3)
The effective attenuation length l adopted here is l = 5 AU for H (upwind) and l = 1 AU for He. For the downwind direction this attenuation length for H is more like 20 AU than 5 AU, but this simple expression is really not valid. This expression and the l parameter were chosen to give a rough match to the density distributions shown in the literature [i.e., Quemerais et al., 1993]. Furthermore, the H and He attenuation lengths also depend on solar activity [cf. Haberli et al., 1997b]. The two main loss processes that contribute to the attenuation of interstellar helium are photoionization by solar extreme ultraviolet radiation and charge transfer with solar wind alpha particles. Using photoionization frequencies for solar minimum and maximum listed by Schunk and Nagy [2000] and the relevant charge transfer cross section from McDaniel [1964], we estimate a He attenuation coefficient ranging from ~0.5 AU at solar minimum to ~1 AU at solar maximum [also see Rucinski et al., 1996]. At this stage our model can only be considered to be partially quantitative, and the next level of model sophistication will require spatially more realistic interstellar neutral distributions.

The solar wind density and speed as functions of distance r and time are given by

nsw(r,t) = nsw0(t*) (r0/r)2
usw(r,t) = usw0(t*),

with

(4)

where r0 = 1.5 x 1013 cm is 1 AU and nsw0(t*) and usw0(t*) are the solar wind density and speed measured at a heliocentric distance of 1 AU and at time t*, respectively. An average solar wind speed is used in the time delay expression. Equation (3) is valid only out to the termination shock and does not take into account the latitudinal or longitudinal structure of the solar wind. That is, solar wind perturbations (or structures) as they propagate away from the Sun are assumed to be spherically symmetric. This assumption should be somewhat better for solar minimum conditions than for solar maximum conditions, but we adopt it for all the model studies in this paper.

The X-ray intensity I(t) as a function of time and in a given direction is determined by integrating the volume emission rate given by (2) over path length s, starting at Earth and going out to 200 AU. Cravens [2000] assumed a steady state solar wind and carried out the integration analytically for a radial direction starting at 1 AU. Cravens found that the H contribution (upwind) was 4pI = 97 keV cm-2 s-1 and that the He contribution was roughly half that of hydrogen, giving a total value of ~150 keV cm-2 s-1. For this paper, we take our integration path to be northward (relative to the ecliptic plane) rather than radial. Our assumption of spherical symmetry in the solar wind is not too bad for this north-south look direction but would not be so good for directions within the ecliptic plane due to the tendency of solar wind structure to corotate with the Sun (see discussion by Neugebauer et al. [2000]).

Next: 4. Geocoronal X-Ray Production by the Solar Wind Charge Exchange Mechanism

Last modified January 8, 2004
Tizby Hunt-Ward
tizby@ku.edu