Can Dwarf Spheroidal Galaxies Host a Central Black Hole?

Abstract We construct mass models of Milky Way dwarf spheroidal galaxies to place constraints on the central black hole 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 the 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>•</mml:mo> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mn>6</mml:mn> </mml:math> . We combine our results with black hole mass measurements and upper limits from the literature to construct a unified M • – σ * relation spanning σ * ∼ 10–300 km s −1 , described by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>•</mml:mo> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>8.32</mml:mn> <mml:mo>+</mml:mo> <mml:mn>4.08</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>log</mml:mi> <mml:mfenced close=")" open="("> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:mn>200</mml:mn> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">km</mml:mi> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mfenced> </mml:math> , with an intrinsic scatter of σ 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 ⊙ for the range σ * ∼ 6–12 km s −1 , in close agreement with the M • – σ * relation within the 95% credible upper limits on the black hole masses derived in this work.