Can dwarf spheroidal galaxies host a central black hole ?

We construct mass models of Milky Way dwarf spheroidal galaxies to place constraints on the central black hole (BH) masses they can host. We model the galaxies as a three-component system consisting of the stars, dark matter halo, and a central black hole, using the Osipkov–Merritt–Cuddeford class of anisotropic distribution function. The posterior distribution of black hole mass remains flat toward the low-mass end, indicating that the kinematic data places an upper limit on the black hole mass. Our analysis yields a 95% credible upper limit of $\log (M_{\bullet }\mathrm{/}{M}_{\odot })<6$. We combine our results with black hole mass measurements and upper limits from the literature to construct a unified $M_{\bullet }$–${\sigma }_{}$ relation spanning ${\sigma }_{}\sim 10$–$300,\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}$, described by $\log (M_{\bullet })=8.32+4.08,\log ({\sigma }_{}\mathrm{/}200,\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1})$, with an intrinsic scatter of ${\sigma }_{\mathrm{i}\mathrm{n}\mathrm{t}}=0.55$. We compare the inferred limits to models of black hole growth via momentum-driven accretion and stellar capture, which predict black hole masses in the range ${10}^3$–${10}^4,M_{\odot }$ for the range ${\sigma }_{}\sim 6$–$12,\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}$, in close agreement with the $M_{\bullet }$–${\sigma }_{\ast }$ relation within the 95% credible upper limits on the black hole masses derived in this work.