  X-ray and gamma-ray observations can help understand the origin of the
electron and positron signals reported by ATIC, PAMELA, PPB-BETS, and Fermi. It
remains unclear whether the observed high-energy electrons and positrons are
produced by relic particles, or by some astrophysical sources. To distinguish
between the two possibilities, one can compare the electron population in the
local neighborhood with that in the dwarf spheroidal galaxies, which are not
expected to host as many pulsars and other astrophysical sources. This can be
accomplished using X-ray and gamma-ray observations of dwarf spheroidal
galaxies. Assuming the signal detected by Fermi and ATIC comes from dark matter
and using the inferred dark matter profile of the Draco dwarf spheroidal galaxy
as an example, we calculate the photon spectrum produced by electrons via
inverse Compton scattering. Since little is known about the magnetic fields in
dwarf spheroidal galaxies, we consider the propagation of charged particles
with and without diffusion. Extending the analysis of Fermi collaboration for
Draco, we find that for a halo mass ~ 1 billion Solar masses, even in the
absence of diffusion, the gamma-ray signal would be above the upper limits.
This conclusion is subject to uncertainties associated with the halo mass. If
dwarf spheroidal galaxies host local magnetic fields, the diffusion of the
electrons can result in a signal detectable by future X-ray telescopes.
