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 ms.tex ApJ, June 2009, 697, 1861
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%http://adsabs.harvard.edu/abs/2009ApJ...697.1861A

\documentclass[12pt,preprint]{aastex}

\begin{document}
\title{Strong mass segregation around a massive black hole}
\author{Tal Alexander}
\affil{Faculty of Physics, Weizmann Institute of Science, P.O. Box 26, Rehovot
76100, Israel}
\email{tal.alexander@weizmann.ac.il }
\and{}
\author{Clovis Hopman }
\affil{Leiden University, Leiden Observatory, P.O. box 9513, NL-2300 RA
Leiden, The Netherlands}
\email{clovis@strw.leidenuniv.nl}
\begin{abstract}
We show that the mass-segregation solution for the steady state distribution
of stars around a massive black hole (MBH) has two branches: the well-known
weak segregation solution \citep{bah+77}, and a strong segregation
solution, which is analyzed here for the first time. The nature of
the solution depends on the heavy-to-light stellar mass ratio $M_{H}/M_{L}$
and on the unbound population number ratio $N_{H}/N_{L}$, through
the relaxational coupling parameter $\Delta\!=\!4N_{H}M_{H}^{2}\left/\left[N_{L}M_{L}^{2}(3\!+\! M_{H}/M_{L})\right]\ri
ght.$.
When the heavy stars are relatively common ($\Delta\!\gg\!1$), they
scatter frequently on each other. This efficient self-coupling leads
to weak mass segregation, where the stars form $n\!\propto\! r^{-\alpha_{M}}$
mass-dependent cusps near the MBH, with indices $\alpha_{H}\!=\!7/4$
for the heavy stars and $3/2\!<\!\alpha_{L}\!<\!7/4$ for the light
stars (i.e. $\max(\alpha_{H}\!-\!\alpha_{L})\!\simeq\!1/4$). However,
when the heavy stars are relatively rare ($\Delta\!\ll\!1$), they
scatter mostly on light stars, sink to the center by dynamical friction
and settle into a much steeper cusp with $2\!\lesssim\!\alpha_{H}\!\lesssim\!11/4$,
while the light stars form a $3/2\!<\!\alpha_{L}\!<\!7/4$ cusp, resulting
in strong segregation (i.e. $\max(\alpha_{H}\!-\!\alpha_{L})\!\simeq\!1$).
We show that the present-day mass function of evolved stellar populations
with a universal initial mass function (coeval or continuously star
forming) separate into two distinct mass scales, $\sim\!1\,\Mo$ of
main sequence and compact dwarfs, and $\sim\!10\,\Mo$ of stellar
black holes (SBHs), and have $\Delta\!<\!0.1$. We conclude that it
is likely that many relaxed galactic nuclei are strongly segregated.
We review indications of strong segregation in observations of the
Galactic Center and in results of numeric simulations, and briefly
list possible implications of a very high central concentration of
SBHs around a MBH.
\end{abstract}

\keywords{Galaxy: kinematics and dynamics --- stellar dynamics --- black hole
physics}
\end{document}