8.1 Interaction with hot gas

Hot gas permeates the interstellar space in galaxies and the intergalactic space in groups of galaxies and galaxy clusters. Virial temperatures range between $6 8 10 - 10 K$ and the hot gas is almost completely ionized. Primordial and secondary sources contribute to the pool of hot has. During the early stages of galaxy formation, intergalactic space contains partially ionized gas inherited from the pregalactic, early universe. Hydrogen recombines at redshifts $z ~ 1000$ and is reionized at redshifts $z ~ 10$ by the radiation emitted by the earliest structures. The partially ionized gas cools within the confining gravitational potential of dark matter halos and filaments. Cold gas accelerates toward the halos’ centers of gravity and is shock-heated to about the virial temperature. Some of the coldest inflowing gas escapes heating by accreting along narrow channels that reach deep inside the primary halo. Cooling times in the halo centers where the gas is the densest are short compared to the dynamical time and thus most of the primordial gas is consumed in starbursts on a dynamical time scale.

Tenuous gas that remains after the cooling time has exceeded the dynamical time in the nascent galaxy might still be plentiful enough to feed a massive black hole growing at an Eddington-limited rate. The residual number density at the radius of influence of the SBH is

$s3kT n ~~ ------ GM /\ ( )0.11 ( ) -1 -3 --M---- ---------/\----------- ~~ 20 cm m 108Mo . 2× 10-23erg cm3 s-1 , (44)$

where $T$ is the virial temperature of the galaxy, $m$ is the average atomic mass in units of the proton mass, $/\$ is the cooling function [30 ], and we have employed the $M$ - $s$ relation (Equation 9

) to relate the virial temperature to the black hole mass. The thermal stability limit could in principle be exceeded if the gas kept at the Compton temperature by a continuum flux from an unobscured AGN [45 ].

This so-called “cooling flow model of quasar fueling” [26 , 160 ] is however plagued by many problems (see [108 ] and references therein). Most of the gas left over from star formation might be blown out by the mechanical feedback associated with the radiative and mechanical output of the accreting massive black hole [200 , 100 , 156 ]. A small amount of angular momentum in the gas results in circularization and settling into an accretion disk. This disk may be susceptible to fragmentation, thereby converting most of the gas mass into stars and effectively cutting off the supply of gas to the SBH [208 ].

The geometry of the flow of a hot, magnetized gas near a binary black hole is unknown. Assuming spherical, non-rotating accretion, the time scale on which the hot gas is captured by the SBH is

$M tcapt =_ --- M 3 ~~ f ----s------ bG2M mmpn ( ) -0.44( ) ~~ 108yr f m -2 --M---- ---------/\----------- , (45) b 108Mo . 2 × 10- 23 erg cm3 s-1$

where $fb ~ 1- 10$ is a numerical factor that depends on the equation of state of the gas.

If a binary black hole is present, gravitational torques from the gas induce decay of the binary’s semi-major axis on approximately the same time scale. This crude estimate is based on an analogy with binary-star interactions: The binary must eject of order its own mass in stars to decay an $e$ -folding in separation. Hot gas torquing the binary might be ejected in an outflow and thus the actual rate at which gas is accreting onto individual binary components might be severely suppressed compared to the accretion expected in an isolated black hole.

Galactic nuclei also contain hot gas produced by secondary sources. For example, observations with the Chandra X-ray Observatory have revealed tenuous ( $n ~~ 10- 100cm - 3$ ), hot ( $T ~~ 1 keV$ ) plasma within a parsec of the $6 ~ 4× 10 Mo .$ Milky Way SBH [7 ]. This plasma is being generated by the numerous massive, evolved stars in the galactic region [66 ] through stellar wind and supernova activity. Since its temperature is higher than the virial, most ( $>$ 99%) of the plasma escapes the neighborhood of the SBH [176 ]. While the hot gas densities in active galaxies might be transiently larger than that at the Galactic center, the tendency of the hot plasma to escape the neighborhood of the SBH reduces the likelihood that large quantities of virialized gas would remain enmeshed with the binary’s orbit long enough to affect its dynamical evolution.

Recently, Escala et al. [41 , 42 ] carried out smoothed particle hydrodynamical (SPH) simulations of binary point masses interacting with a massive, spherical cloud of hot gas initially centered on the binary. Gravitational drag from the gas induces decay in the binary’s orbit. The relevance of spherical, hot initial conditions is contingent on the astrophysical plausibility that a compressed accumulation of hot gas comparable in mass to the SBH can be sustained.