WIMP constraints from black hole low-mass X-ray binaries

The abnormally fast orbital decay observed in the black hole (BH) Low -Mass X-ray binaries (BH-LMXB) A0620-00 and XTE J1118+480 can be explained by the dynamical friction between Dark Matter (DM) and the companion star orbiting around the low -mass BH (<^>, a few M circle dot) of the system. In this case the value of the index gamma sp of the DM spike surrounding the BH can be pinned down with an accuracy of <^>, a few percent, way better than that for much bigger systems such as the super massive BHs (SMBHs) in the Galactic Center or in M87. We have used data from XTE J1118+480 to put bounds on the WIMP annihilation cross section times velocity (sigma v), assuming that DM annihilation is driven by the chi chi - bb over bar annihilation channel and that it proceeds in s -wave. The bounds are driven by the radio synchrotron signal produced by e +/- final states propagating in the magnetic field in the vicinity of the BH. We find that for DM masses mx up to the TeV scale XTE J1118+480 allows to constrain (sigma v) well below the standard value (sigma v)thermal , corresponding to the observed DM relic density in the Universe for a thermal WIMP. On the other hand, for mx greater than or similar to 15 GeV, the bounds from the SMBHs in the GC or in M87 do not reach (sigma v)thermal when the very large uncertainties on the corresponding spike indices are taken into account, in spite of potentially producing much larger DM densities compared to XTE J1118+480. Our bounds for XTE J1118+480 have a mild sensitivity on the effect of spatial diffusion (which implies at most a weakening of the bounds of a factor less than or similar to 6 at large mx). However, diffusion is instrumental in enhancing the sensitivity of the results upon the intensity of the magnetic field. In particular, our bounds rest on the assumption that the magnetic field B reaches the equipartition value Beq. We find that a reduction factor of the magnetic field Beq/B larger than about 14 at low mx , becoming progressively smaller at higher WIMP masses, would be sufficient to relax the XTE J1118+480 bound to the level of other existing bounds. Recent estimates, albeit not conclusive, may suggest values of Beq/B in BH-LMXB systems as large as 20. This implies that the intensity of the magnetic field in BH-LMXB systems represents the major uncertainty in using them as an alternative to heavier BHs to search for WIMPs.