In the standard cosmological scenario of structure formation, galaxies assemble through successive mergers of larger and larger systems (see Fig. 1 for images of interacting galaxies). Apart from larger galaxies, this also leads to the formation of pairs of massive black holes, called black hole binaries (see Fig. 2 for an illustration), in their centres. Stars that undergo a close encounter with a black hole binary tend to extract energy and angular momentum from the binary, and are ejected to larger distances, while the orbital separation of the binary shrinks. If enough energy is transferred to the stellar population, the black holes come so close that eventually they merge in a burst of gravitational waves. Calculations of the evolution of black hole binaries generally assume spherically symmetric galaxy models. During mergers, however, strong perturbations are produced, which lead to significant deviations from spherical symmetry and to rotation.

So how do black hole binaries evolve in realistic merger remnants? To answer this question, scientists at the Max Planck Institute for Astrophysics and international collaborators performed a series of numerical simulations of galaxy mergers as well as black hole binaries immersed in rotating merger remnants. In these calculations, the gravitational forces between all pairs of particles in the galaxies are computed and very accurate trajectories are derived.

Simulating the merger of two galaxies using highly accurate numerical methods is an extremely challenging computational task, and required more than one year of uninterrupted computations on the GPU machines at the Max Planck Institute for Astrophysics and on the special purpose GRAPE cluster at the Rochester Institute of Technology (Rochester, USA). The results of these calculations, however, are very interesting.

The evolution of black hole binaries in spherically symmetric galaxies is characterized by a first phase, where the binary separation shrinks, followed by a stalling phase of very slow orbital decay. In contrast, the evolution in realistic merger remnants proceeds to very small separations - separations that are small enough that the emission of gravitational waves becomes dominant and the black holes coalesce to form a single black hole.

Simulations of black hole binaries in rotating systems also show that the eccentricity of the binary evolves, where the nature of this evolution (to a more or less eccentric orbit) depends on the degree of co-rotation in the stellar cusp. As the separation of the two black holes shrinks due to close encounters with stars, the orbit will circularize in time, if a large fraction of stars co-rotate with the binary. However, if most stars move on counter-rotating orbits, the binary becomes more eccentric. The latter effect, which could arise as a result of mergers between galaxies of different mass, has important implications for the possible detection of gravitational waves emitted by coalescing black hole binaries.

In addition, if the angular momentum of the binary is initially misaligned with respect to that of the stellar system, a reorientation of the binary orbital plane occurs. In spherically symmetric models, the orientation of the binary plane suffers only small changes on long timescales due to a kind of random walk process as interacting stars exchange angular momentum with the binary. If, on the other hand, the binary is immersed in a stellar system with net rotation where the angular momentum is misaligned, it tends to realign its orbital plane with the angular momentum of the stars. This reorientation takes place on the same timescale over which the separation shrinks and can be quite significant, with changes as large as 100 degrees.

The realignment of the binary plane seen in the simulations may have significant implications for astrophysical observations. The direction of the spin axis of the single black hole that results from the ultimate merger of the binary is affected by the orientation of the binary plane before coalescence. The spin axis, in turn, determines the orientation of the accretion disk around the remnant black hole and, in radio-loud systems, the direction of the radio jet.

Alessia Gualandris

References:

Alessia Gualandris & David Merritt, "Long-term evolution of massive black hole binaries. IV. Mergers of galaxies with collisionally relaxed nuclei", 2011, ApJ, in press, http://arxiv.org/abs/1107.4095

Alberto Sesana, Alessia Gualandris, Massimo Dotti, "Massive black hole binary eccentricity in rotating stellar systems", 2011, MNRAS, 415L, 35 http://arxiv.org/abs/1105.0670

Alessia Gualandris, Massimo Dotti, Alberto Sesana, "Massive black hole binary plane reorientation in rotating stellar systems", 2011, MNRAS, http://arxiv.org/abs/1109.3707