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Gas helps massive black holes find each other
When two galaxies merge, a large fraction of the gas they contain is funnelled into the central regions of the merger. Recent simulations suggests that this gas leads to a much faster coalescence of the massive black hole pair compared to the situation where no gas is present. The gas might also force the spins of the black holes to align.
Snapshot of the gas distribution during a galaxy merger simulation performed by Lucio Mayer and collaborators. The image is 120 kpc across. The galaxies are still in the process of merging with each other, 300 Myr before the MBHs form a binary.
Merging pairs of massive black holes are one of the most exciting sources of gravitational waves for LISA (see, e.g. the article by Marta Volonteri in the LISA newsletter 2006-2). Such massive binaries form when galaxies merge - a process both observed and predicted by models of galaxy evolution within the framework of cold dark matter cosmological models. However, a circular binary consisting of two black holes of one million solar masses each can coalesce through emission of gravitational waves in less than one Hubble time (about 1010 years) only if their separation becomes less than 2x10-3 pc, some 6 orders of magnitude smaller than the galactic scale. The question as to whether the black holes can be brought to such a small separation has attracted considerable theoretical attention in the last decades (see review by Merritt & Milosavljevic 2005).
In most studies, only the influence of the stars of the merged galaxy was considered. Dynamical friction, which is the cumulative effect of a large number of weak 2-body encounters between stars and either of the black holes, can reduce the separation to less than 1 pc. At this point, stars need to interact closely with the massive binary to extract energy from it and tighten it further. In spherical galaxies, these strong 3-body interactions quickly eject all stars in the "loss cone". I.e. stars with orbits elongated enough to come close to the binary. Once the loss cone is evacuated, evolution probably slows down considerably as stars have to have their trajectories perturbed into the loss cone through 2-body relaxation, i.e. numerous encounters with other stars. Careful study of this scenario indicates that, for typical properties of their host galaxies, most massive black hole binaries in the LISA sensitivity window (less massive than 107 Msun) can merge within a few 109 years. These relatively long time scales open the possibility of another galaxy merger taking place before the massive binary has coalesced, leading to an interaction between three massive black holes . This situation can lead to the ejection of the least massive object and to a strong increase in the eccentricity of the remaining binary, causing it to coalesce much faster and, in some cases, with a residual eccentricity detectable by LISA.
However, in the mass range of importance for LISA, a large fraction of the host galaxies contain substantial quantities of gas, a fact likely to change the picture significantly. This situation is more difficult to study theoretically as it requires simulations combining the dynamics of the stars and of the gas. At the time of writing, the state-of-the-art in that field is represented by the work of Mayer et al. (2007, Science 316, 1874, http://uk.arxiv.org/abs/0706.1562) who have performed high-resolution simulations of the merger of two milky-way-like galaxies containing gas and hosting massive black holes. During the galactic merger, in each galaxy, torques due to the other galaxy cause the gas to flow in and form a disk of about 4x108 Msun and a size of a few hundred pc around the massive black hole. A few billion years after the beginning of the interaction, the gaseous disks merge. As a result, the black holes find themselves embedded in a very massive and compact gaseous disk. Dynamical friction against the gas completely dominates the orbital evolution of the massive pair, and this evolution occurs much faster than in the stellar case. The separation decreases from about 40 pc to the resolution limit of a few pc in less than one million years. Such a fast evolution, if it continues at smaller scales (as suggested by simulations of massive black holes in massive gaseous disks, e.g. Escala et al. 2005; Dotti et al. 2006b), might have several consequences for LISA sources.
Clearly, these models indicate that LISA-class massive black holes are unlikely to stall for a significant amount of time. Their coalescence should occur quickly after the core of their host galaxies have merged, which removes the possibility of an interaction with a third massive black hole. The interaction with the gas probably circularises the binary long before it emits gravitational waves at a significant rate. Also, the gas disk is likely to torque the spins of the inspiralling black holes into alignment, through the Bardeen-Petterson effect, as studied by Bogdanovic et al. (2007). This has important implications, both astrophysical and practical. From an astrophysical point of view, the point of interest is that the maximum possible recoil velocity due to anisotropic emission of gravitational waves is significantly reduced. From a practical point of view, the results suggest to concentrate the data-analysis and numerical-relativity efforts on this geometry. Furthermore, a circum-binary disk raises the very exciting possibility of detecting an electro-magnetic afterglow to the gravitational-wave signal (e.g. Milosavljevic & Phinney 2005; Dotti et al. 2006a, see this news item). Finally, a fast inspiral means that the massive binary has less time to eject stars from the central regions of the host galaxy and the massive amount of gas concentrated at small scale is likely to trigger a burst of star formation. All of this suggests that the merged black hole will find itself in a dense stellar environment, where extreme-mass ratio inspirals should be relatively common (on this class of LISA sources, see the review by Amaro-Seoane et al. 2007).
It must be stressed that these recent results are not the last word on the matter. Even the best merger simulations are still lacking in resolution and physical realism, particularly for the treatment of the gas. For instance, Mayer at al. (2007) stress that if the gas is heated by the radiation due to accretion onto the black holes, it will not be able to form a dense central disk and its effect on the massive binary will be negligible.