  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.
