  In this paper, we explore the potential astrophysical signatures of dark
matter (DM) annihilations in ultra-compact dwarf galaxies (UCDs) considering
two of the richest known galaxy clusters within 100 million light-years,
nominally, Virgo and Fornax. Fornax UCD3 is the most luminous known UCD and M59
UCD3 is the most massive known UCD. With the detection of a 3.5 million solar
mass black hole (BH) in Fornax UCD3, we carefully model several dark matter
(DM) enhanced profile scenarios, considering the presence of both a
supermassive black hole (SMBH) and DM. For Fornax UCD3, the comparison of the
stellar and dynamical masses suggests that there is little content of DM in
UCDs. M59 UCD3 did not receive the same attention in simulations as Fornax
UCD3, however deep radio imaging and X-ray observations were performed for M59
UCD3 and can be used to place limits in DM content of these UCDs. We take an
average estimate of dark matter content and used the Salpeter and Kroupa mass
functions. We model Fornax UCD3 and M59 UCD3 to have a DM content that is the
average of these mass functions. We then analyze the constraints for Fornax and
M59 UCD3 coming from $\gamma$-ray and radio sources, considering a dark matter
particle with a mass between 10 and 34 GeV in our simulations. In the absence
of a strong $\gamma$-ray signature, we show that the synchrotron emission from
electrons and positrons produced by DM annihilations can be very sensitive to
indirect DM search. We find that DM parameters can be significantly constrained
at radio frequencies and that the spike profiles play an interesting role in
the deep study of the enhancements of DM & BH interactions in ultra-compact
galaxies.
