Multi-messenger constraints on dark matter annihilation into
  electron-positron pairs
  We investigate the production of electrons and positrons in the Milky Way
within the context of dark matter annihilation. Upper limits on the relevant
cross-section are obtained by combining observational data at different
wavelengths (from Haslam, WMAP, and Fermi all-sky intensity maps) with recent
measurements of the electron and positron spectra in the solar neighbourhood by
PAMELA, Fermi, and HESS. We consider synchrotron emission in the radio and
microwave bands, as well as inverse Compton scattering and final-state
radiation at gamma-ray energies. According to our results, the dark matter
annihilation cross-section into electron-positron pairs should not be higher
than the canonical value for a thermal relic if the mass of the dark matter
candidate is smaller than a few GeV. In addition, we also derive a stringent
upper limit on the inner logarithmic slope, alpha, of the density profile of
the Milky Way dark matter halo (alpha < 1 if m_dm < 5 GeV, alpha < 1.3 if m_dm
< 100 GeV and alpha < 1.5 if m_dm < 2 TeV) assuming that cross-section = 3 x
10^(-26) cm^3 s(-1). A logarithmic slope steeper than alpha about 1.5 is hardly
compatible with a thermal relic lighter than about 1 TeV, regardless of the
dominant annihilation channel.
