University of Kansas X-Ray Emission in the Solar System

Draft X-Ray Emission from the Terrestrial Magnetosheath by Robertson and Cravens

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

The Model

The following expression, similar to the expression originally applied to comets by Cravens [1997], is used to obtain the EUV and soft X-ray power density in the Earth's geocorona:

(1)

where a contains all the detailed atomic cross sections, transition information, and solar wind heavy ion composition, etc. The neutral geocoronal hydrogen density is denoted by n_H, the solar wind density is n_sw and the average ion-neutral collision speed is denoted as g_average. Cravens et al. [2001] actually used a =1.5 x 10^-15 eV cm², although 6 x 10^-16 was stated. a ~= 6 x 10^-16 eV cm² is probably a better choice for the SWCX efficiency factor, although this is still quite uncertain and depends on solar wind conditions [Schwadron and Cravens, 2000; Kharchenko and Dalgarno, 2000].

The unperturbed upstream solar wind density is assumed to be n_sw0 = 7 cm^-3 and the unperturbed solar wind speed is set at u_sw0 = 400 km/s. As the solar wind crosses the bow shock and enters the magnetosheath, however, the density and speed change drastically. The solar wind density, speed and temperature inside the magnetosheath are predicted by the numerical global hydrodynamic model of Spreiter et al. [1966]. We use the Spreiter contour plots for these parameters inside the magnetosheath. Our spatial grid is crude (D r ~= 0.57 R_E), but is sufficient for this initial exploratory study. Some solar wind plasma also certainly enters the magnetosphere through the cusps [Reiff et al., 1977], but we neglect this effect in our current study. The solar wind density jump across the subsolar bow shock is about a factor of 4. The bulk velocity, however, decreases to about a tenth of the unperturbed velocity just outside the nose of the magnetosphere, and the temperature increases by as much as a factor of 22 in the subsolar region. Spreiter's results were for a solar wind with Mach number 8 and a g of 5/3. A reasonable magnetopause distance for "average" solar wind parameters is 9.5 R_E.

The speed in equation (1) is the average relative speed between ions and neutrals and is calculated as follows. The heavy ion thermal speed is assumed to be the same as the proton thermal speed and is given by:

(2)

and the total relative speed is given by

(3)

T is the temperature, k_B is Boltzmann's constant, m is the proton mass, and u_sw is the bulk flow speed. The geocoronal hydrogen densities used in the model were taken from the Monte Carlo model of Hodges [1994]. The resulting hydrogen densities were tabulated at the end of his paper. We used the results for equinox conditions and for an F_10.7 solar flux of 180. Beyond 12 R_E, the outer boundary of the model, we adopted a 1/R³ radial variation for the hydrogen density.

The X-ray intensity in a given direction is obtained by integrating the volume emission rate from equation (1) over an appropriate path length s.

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Last modified January 21, 2004 Tizby Hunt-Ward tizby@ku.edu