  Sub-GeV dark matter particles can annihilate or decay producing e^\pm pairs
which upscatter the low-energy photon fields in the Galaxy and generate an
X-ray emission (via the Inverse Compton effect). Using X-ray data from
Xmm-Newton, Integral, NuStar and Suzaku, we derive new constraints on this
class of dark matter (DM). In the annihilation case, our new bounds are the
strongest available for DM masses above 180 MeV, reaching <sigma v> < 10^-28
cm^3/s for m_DM ~ 1 GeV. In the decay case, our bounds are the strongest to
date over a large fraction of the considered mass range, constraining tau >
10^28 s for m_DM ~ 1 GeV and improving by up to 3 orders of magnitude upon
existing limits.
