University of Kansas
X-Ray Emission in the Solar System
(DRAFT)
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University of KansasX-Ray Emission in the Solar System |
(DRAFT)
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Image: Jovian soft X-rays from ROSAT; courtesy of J. H. Waite.
The x-ray intensity observed at Earth is more interesting than the total heliospheric luminosity. The intensity, I, in a given direction is determined by integrating the production rate given by equation (2) over pathlength. Approximating this path as being radial in heliocentric coordinates (not exact since the path should start at the Earth and not at the Sun) and integrating from rmin to rmax, we obtain the following expression:
where b = a nsw0 usw nH0 r0, with radial distances in units of AU. 4 p I has units of eV/cm2/s and l is in units of AU. The last approximation in equation (3) is valid for l >> rmin and l << rmax. Using previously discussed upwind parameters (and a = 3 x 10-8) we find that 4 p I = b / l = 97 keV cm-2 s-1 or I = 7.7 keV cm-2 s-1 sr-1 for the upwind value of l. This is the soft x-ray energy intensity (for H) integrated over photon energies approximately 0.1 keV and higher. The downwind intensity is only about 25% of this. The x-ray intensity for He can be estimated the same way but with nHe0 = 0.1 nH0 and l = 1 AU. The He contribution is roughly half that of hydrogen (upwind), or 3.8 keV cm-2 s-1 sr-1. The total estimated intensity is 11 keV cm-2 s-1 sr-1.
The shapes of the heliospheric and cometary x-ray spectra should be essentially the same. The x-ray spectrum produced by the SWCX mechanism contains hundreds of lines (Kharchenko and Dalgarno 1999; Schwadron and Cravens 1999), and appears to be continuum-like when observed at a low or moderate spectral resolution (Wegmann et al. 1998; Dennerl et al. 1997). Even though it is extremely unlikely that the cometary emission is produced by the electron bremsstrahlung mechanism (Krasnopolsky 1997; Lisse et al. 1996, 1999), Dennerl et al. (1997) were able to fit the spectra of several comets observed by the ROSAT/PSPC for energies in excess of about .09 keV with a bremsstrahlung-type spectrum using "effective" temperatures of about 0.2 keV (e.g., the effective temperature for comet Levy was 0.23 keV). This simple fit is adopted here:
where kT = .23 keV was chosen and E is in units of keV. The integral of (E Iph) over energy from 0.1 keV to infinity must equal the total x-ray intensity, I, found earlier, which permits the constant A to be determined; A = 74 cm-2 s-1 sr-1 for I = 11 keV cm-2 s-1 sr-1.
The function E Iph (units of keV cm-2 s-1 sr-1 keV-1) can be determined from Iph and compared with the all-sky average x-ray intensity from the Wisconsin sky survey of the SXRB (McCammon and Sanders 1990) (see Figure 1). The ROSAT XRB results are in overall agreement with the Wisconsin survey (Snowden et al. 1994, 1995, 1998). Figure 1 suggests that at the lowest energies (.1 keV - .5 keV) the heliospheric source might be able to explain as much as half of the observed SXRB.
Next: Temporal and Spatial Variation of Heliospheric X-Ray Emission
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Tizby Hunt-Ward tizby@ku.edu |