White dwarfs (WDs) are the most promising captors of dark matter (DM) particles in the crests that are expected to build up in the cores of dense stellar clusters. The DM particles could reach sufficient densities in WD cores to liberate energy through self-annihilation. The extinction associated with our Galactic Centre, the most promising region where to look for such effects, makes it impossible to detect the potential associated luminosity of the DM-burning WDs. However, in smaller stellar systems which are close enough to us and not heavily extincted, such as $omega-$Cen, we may be able to detect DM-burning WDs. We investigate the prospects of detection of DM-burning WDs in a stellar cluster harbouring an IMBH, which leads to higher densities of DM at the centre as compared with clusters without one. We calculate the capture rate of WIMPs by a WD around an IMBH and estimate the luminosity that a WD would emit depending on its distance to the center of the cluster. Direct-summation $N-$body simulations of $omega-$Cen yield a non-negligible number of WDs in the range of radii of interest. We apply our assumption to published HST/ACS observations of stars in the center of $omega-$Cen to search for DM burning WDs and, although we are not able to identify any evident candidate because of crowding and incompleteness, we proof that their bunching up at high luminosities would be unique. We predict that DM burning will lead to a truncation of the cooling sequence at the faint end. The detection of DM burning in future observations of dense stellar clusters, such as globular clusters or ultra-compact dwarf galaxies could allow us to probe different models of DM distributions and characteristics such as the DM particle scattering cross section on nucleons. On the other hand, if DM-burning WDs really exist, their number and properties could give hints to the existence of IMBHs.
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