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<header>
 <identifier>oai:arXiv.org:1606.07066</identifier>
 <datestamp>2016-06-24</datestamp>
 <setSpec>physics:astro-ph</setSpec>
 <setSpec>physics:gr-qc</setSpec>
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 <arXiv xmlns="http://arxiv.org/OAI/arXiv/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://arxiv.org/OAI/arXiv/ http://arxiv.org/OAI/arXiv.xsd">
 <id>1606.07066</id><created>2016-06-22</created>
 <authors>
 <author>
    <keyname>Saxton</keyname>
    <keyname>Walton</keyname>
    <forenames>Curtis J.</forenames>
    <affiliation>Technion</affiliation>
    <affiliation>DESY</affiliation>
 </author>
 <author>
    <keyname>Younsi</keyname>
    <forenames>Ziri</forenames>
    <affiliation>U.Frankfurt</affiliation>
  </author>
  <author>
    <keyname>Wu</keyname>
    <forenames>Kinwah</forenames>
  </author>
</authors>
<title>Dark matter concentrations in galactic nuclei according to polytropic
  models</title><categories>astro-ph.GA astro-ph.CO astro-ph.HE gr-qc</categories><comments>MNRAS accepted, 24 pages, 12 figures</comments><license>http://arxiv.org/licenses/nonexclusive-distrib/1.0/</license><abstract>  We calculate the radial profiles of galaxies where the nuclear region is
self-gravitating, consisting of self-interacting dark matter (SIDM) with $F$
degrees of freedom. For sufficiently high density this dark matter becomes
collisional, regardless of its behaviour on galaxy scales. Our calculations
show a spike in the central density profile, with properties determined by the
dark matter microphysics, and the densities can reach the `mean density' of a
black hole (from dividing the black-hole mass by the volume enclosed by the
Schwarzschild radius). For a galaxy halo of given compactness
($\chi=2GM/Rc^2$), certain values for the dark matter entropy yield a dense
central object lacking an event horizon. For some soft equations of state of
the SIDM (e.g. $F\ge6$), there are multiple horizonless solutions at given
compactness. Although light propagates around and through a sphere composed of
dark matter, it is gravitationally lensed and redshifted. While some
calculations give non-singular solutions, others yield solutions with a central
singularity. In all cases the density transitions smoothly from the central
body to the dark-matter envelope around it, and to the galaxy's dark matter
halo. We propose that pulsar timing observations will be able to distinguish
between systems with a centrally dense dark matter sphere (for different
equations of state) and conventional galactic nuclei that harbour a
supermassive black hole.
</abstract></arXiv>
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