Can dwarf spheroidal galaxies host a central black hole ?

TL;DR

The paper investigates whether Milky Way dwarf spheroidal galaxies can host central black holes by constructing three-component dynamical models (stars, dark matter, and a central BH) with an Osipkov–Merritt–Cuddeford anisotropic distribution function and using AGAMA for potential and DF calculations. Using stellar photometric data and line-of-sight velocity dispersions, they derive 95% credible upper limits on BH masses in several dSphs, finding $\log(M_{\bullet}/M_{\odot}) < 5.1$–$6.1$. By combining these upper limits with existing BH mass measurements, they derive a unified $M_{\bullet}-\sigma_{*}$ relation spanning $\sigma_{*} \sim 10$–$300\ \mathrm{km\,s^{-1}}$: $\log(M_{\bullet}) = 8.32 + 4.08\ log(\sigma_{*}/200\,\mathrm{km\,s^{-1}})$ with an intrinsic scatter $\sigma_{\rm int} = 0.55$. The results are consistent with black hole growth via momentum-driven gas accretion and stellar capture, and suggest tidal stripping may explain how present-day dwarfs can host BHs up to the upper limits.

Abstract

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 $\log(M_{\bullet}/M_{\odot}) < 6$. We combine our results with black hole mass measurements and upper limits from the literature to construct a unified $M_{\bullet}$--$σ_{}$ relation spanning $σ_{} \sim 10$--$300,\mathrm{km,s^{-1}}$, described by $\log(M_{\bullet}) = 8.32 + 4.08,\log\left(σ_{}/200,\mathrm{km,s^{-1}}\right)$, with an intrinsic scatter of $σ_{\rm int} = 0.55$. 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 $σ_{} \sim 6$--$12,\mathrm{km,s^{-1}}$, in close agreement with the $M_{\bullet}$--$σ_{*}$ relation within the 95% credible upper limits on the black hole masses derived in this work.

Figures (4)

• Figure 1: Posterior probability distribution corresponding to model parameters of dwarf spheroidal galaxies; Carina, Draco, Fornax, and Leo-1. The dashed blue lines depict the $16^{th}$, $50^{th}$, and $84^{th}$ percentiles of the posterior probability distribution. The posterior distribution for the black hole mass is flat towards the low-mass end and drops off at $95\%$ credible upper limit of $\log(M_{\bullet}/M_\odot) < 6$, as indicated by the vertical magenta line.
• Figure 2: Same as Figure 1, but for the dwarf spheroidal galaxies Leo-2, Sculptor, Sextans, and UM.
• Figure 3: The black line indicates the 50$^{\mathrm{th}}$ percentile, and the red curve represents the $95\%$ credible upper limit of the posterior distribution. The blue shaded region indicates the 16$^{\mathrm{th}}$-84$^{\mathrm{th}}$ percentile range. The green curve represents a model with $M_{\bullet} = 10^{7}\,M_{\odot}$, selected from the MCMC posterior samples.
• Figure 4: A unified $\rm M_{\bullet}$--$\sigma_{*}$ relation spanning stellar velocity dispersions from $\sim 10~\mathrm{km\,s^{-1}}$ to $\sim 300~\mathrm{km\,s^{-1}}$. Blue points represent black hole mass estimates, while yellow arrows denote upper limits, compiled from lutzgendorf2013mvan2016unificationgreene2020intermediate. The red arrows indicate the upper limits obtained in the present work. The green line shows the best-fit regression, and the shaded region indicates $1\sigma$ scatter. Magenta points depict ultra massive black holes $(M_{\bullet}>10^{9}$. Theoretical limits on black hole masses (for our sample range $\sigma_{*} \sim 6{-}12 \,\mathrm{km\,s^{-1}}$) due to accretion, stellar capture, and tidal stripping are also overlaid on the plot for comparison.