EVAPORATION OF WIMPS WITH ARBITRARY CROSS-SECTIONS

A formula for the evaporation rate of weakly interacting massive particles (WIMPs) from a star is derived for the case of large optical depth. The evaporation rate may be calculated to within a factor of ∼ 2, which implies an accuracy of ∼ 2% for the corresponding evaporation mass. The formula also gives the correct answer for the case of small optical depth and is thus completely general. In the case of the Sun, the evaporation mass is 3.9 GeV for a cross section per baryon of 10-36 cm2 and 2.3 GeV for a cross section of 10-34 cm2. These cross sections are the approximate range for which WIMPs can solve the solar neutrino problem. For horizontal-branch stars, the corresponding evaporation masses are 5.3 GeV at σHe = 4 × 10-36 cm2 and 2.7 GeV at σHe = 4 × 10-34 cm2. The evaporation-mass curves of the two types of stars are remarkably similar for σHe ≳ 10-35 cm2.