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

Abstract: 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 (of a few $M_\odot$) of the system. In this case the value of the index $\gamma_{\rm sp}$ 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 $\langle \sigma v\rangle$, assuming that DM annihilation is driven by the $b\bar{b}$ annihilation channel and that it proceeds in $s$-wave. The bounds are driven by the radio synchrotron signal produced by $e^\pm$ final states propagating in the magnetic field near the BH. For DM masses $m_\chi$ up to the TeV scale XTE J1118+480 allows to constrain $\langle \sigma v\rangle$ well below $\langle\sigma v\rangle_{\rm thermal}$, corresponding to the observed DM relic density in the Universe for a thermal WIMP. On the other hand, for $m_\chi \gtrsim$ 15 GeV, the bounds from the SMBHs in the GC or in M87 do not reach $\langle\sigma v\rangle_{\rm thermal}$ 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 spatial diffusion, but diffusion enhances the sensitivity of the results upon the intensity of the magnetic field. Taken at face value the bound from XTE J1118+480 on $\langle \sigma v\rangle$ is the most constraining compared to all others for $m_\chi\lesssim$ 1 TeV, unless the intensity of the magnetic field is significantly smaller than its equipartition estimation.