Mass Segregation and Transient Formation in Nuclear Stellar Clusters

Abstract Supermassive black holes at the centers of galaxies occasionally disrupt stars or consume stellar-mass black holes (BHs) that wander too close, producing observable electromagnetic or gravitational wave signals. We examine how mass segregation impacts the rates and distributions of such events. Assuming a relaxed stellar cluster, composed of stars and stellar-mass BHs, we show that the tidal disruption rate of massive stars ( m ≳ M ⊙ ) is enhanced relative to their abundance in the stellar population. For stars up to m ≈ 3 M ⊙ , this enhancement is roughly m / M ⊙ and it is driven by segregation within the sphere of influence. Stars with masses m ≳ 3 M ⊙ , if relaxed, are predominantly scattered by more massive stellar-mass BHs, leading to a constant enhancement factor of ≈9, independent of mass. This aligns with observational evidence suggesting an over-representation of massive stars in tidal disruption events. For stellar-mass BHs, we predict an enhancement factor scaling as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>•</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> for plunges and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>•</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> for extreme-mass-ratio inspirals (EMRIs). The power of one-half in both cases reflects the shorter relaxation times of heavier BHs, allowing them to segregate into the sphere of influence from greater distances, thereby increasing their abundance. The additional power in the EMRIs’ rate arises from the tendency of heavier BHs to circularize and sink inward more efficiently. Finally, we estimate the rate of main-sequence star inspirals and find that it favors low-mass stars ( m ≲ M ⊙ ). This seems compatible with the observationally estimated rate of quasiperiodic eruptions.