March 21, 2006
Hydrodynamical Simulations of Merging Galaxies with Supermassive Black Holes
by Stelios Kazantzidis
Hydrodynamical Simulations of Merging Galaxies with Supermassive Black Holes
Supermassive black holes (SMBHs) are ubiquitously detected at the centers of most nearby and distant galaxies hosting spheroids. The available data reveal the existence of a remarkably tight correlation between the mass of the central SMBH and the central stellar velocity dispersion of the host galaxy spheroidal component, suggesting a fundamental mechanism connecting the properties of SMBHs with those of their host galaxies. According to the currently popular ''bottom-up'' galaxy formation paradigm, structures in the Universe grow through a complex process of continuous mergers and accretion of smaller systems. Thus, the hierarchical buildup of SMBHs by massive seed black holes present at the center of protogalaxies and the formation of SMBH binaries appear as natural consequences in any hierarchical cosmogony. KICP fellow Stelios Kazantzidis and his collaborators are investigating the coevolution of SMBHs and their host galaxies using supercomputer simulations of galaxy collisions. These numerical simulations provide new insights into how SMBHs form pairs and coalescence, and underscore that the gaseous component of galaxies is the main mode of black hole growth.
<b>Pairing and Coalescence of SMBHs in Galactic Collisions:</b><br /> The dynamical evolution during the interaction of two systems containing central SMBHs can be divided into three main phases: <br />(1) the two black holes sink to the center of the common mass distribution by a process called dynamical friction that slows down the relative motions of the host galactic cores and causes the SMBHs to form a pair once the two galaxies merge;<br />(2) the orbital radius of the SMBH pair shrinks as three-body interactions between the black holes and other components of the galaxies, such as stars and gas, extract energy from the orbit;<br />(3) the black holes come close enough for gravitational radiation to become an efficient mechanism for further angular momentum loss, causing the eventual coalescence of the pair. <br /> It is of primary importance to establish the necessary conditions leading to the merger of two SMBHs since coalescing SMBH binaries constitute the most powerful sources of gravitational wave emission that the <a target='_blank' href='http://lisa.nasa.gov'>Laser Interferometer Space Antenna (LISA)</a> will be able to detect. To gain insight in the physical processes which determine the fate of SMBHs during galactic collisions, Kazantzidis and his collaborators, Lucio Mayer from ETH Zurich, Monica Colpi from the University Milano-Bicocca, Piero Madau from UCSC, Victor P. Debattista and Thomas Quinn from the University of Washington, Ben Moore and Joachim Stadel from the University of Zurich and James Wadsley from McMaster University, performed high-resolution supercomputer simulations of galaxy mergers. The simulations employ the popular astrophysics technique of Smooth Particle Hydrodynamics in which the gaseous component of galaxies is modeled as a collection of discrete particles and include the effects of radiative cooling and star formation. One of the most intriguing findings of this study is that gaseous dissipation facilitates the process of SMBH pairing and merging by increasing the resilience of the interacting galactic cores to tidal disruption. This result supports scenarios of hierarchical build-up of SMBHs, due to collisions and gas accretion, following the merger hierarchy from early times until present. The higher SMBH pairing efficiency reported by Kazantzidis and his collaborators has interesting implications for the probability of observing coalescence events whose gravitational radiation emission would be detectable up to high redshift by LISA. A paper describing these results was published in the April 2005 issue of The Astrophysical Journal. In a complementary study that was presented in the ESO/MPE Conference ''Relativistic Astrophysics and Cosmology: Einstein's Legacy'' and appeared recently on the <a target='_blank' href='http://xxx.lanl.gov/abs/astro-ph/0602029'>Astrophysics abstracts</a>, Mayer, Kazantzidis, Madau, Colpi, Quinn and Wadsley showed that at very small scales the details of SMBH binding are extremely sensitive to gas thermodynamics. The figure presents the relative separation of two black holes as a function of time in merger simulations with different prescriptions for the equation of state (EOS) of the gas which are motivated by both theoretical models and observations of interacting galaxies. The first case (blue line) approximates well the balance between radiative heating and cooling in a galaxy that is forming stars at a prodigious rate (''starburst galaxy''). The second case (red line) pertains to galaxies, known as ''active galactic nuclei'' (AGN), the nucleus of which produces more radiation than the rest of the galaxy and which are thought to harbor SMBHs at their centers. The results of the simulations suggest that the coalescence of the two black holes will occur when the merger remnant is a powerful starburst galaxy, such as an Ultraluminous Infrared Galaxy (ULRIG), rather than an AGN.
<b>Gas Inflows and the Formation of Nuclear Disks in Galaxy Mergers:</b><br />Gas-rich merging galaxies such as ULRIGs are invariably associated with the most powerful starbursts in the Universe. In some cases the remnants of these interactions are known to host an AGN in addition to the starburst. Various observations of colliding galaxies show the ubiquitous presence of massive, central nuclear disk-like structures of gas and stars. These disks have sizes from few hundred parsecs to more than a kiloparsec, and masses that range from few hundred million to more than a billion solar masses. Normal galaxies such as our own Milky Way do not contain such impressive gaseous nuclear disks suggesting that mergers are important in building these nuclear structures. Since many interacting systems host AGNs, it is natural to assume that the large reservoir of gas present in these nuclear disks represents the fuel that feeds the central supermassive black hole and powers the AGN. So far, limited numerical resolution in supercomputer simulations has precluded detailed studies of the origin of such disks. The simulations performed by Kazantzidis and his collaborators allowed for a considerable dynamic range to be resolved in the same calculation: from scales of hundreds of kiloparsecs at which the galaxies begin their cosmic dance to scales of tens of parsecs that correspond to the sizes of nuclear disks. These simulations employ the technique of ''particle splitting'' to greatly improve the resolution of hydrodynamical computations and are among the most expensive calculations ever performed on this topic, using up to 200000 hours of CPU time each at various supercomputer centers around the world. The first results of this endeavor were presented recently on the ESO/MPE Conference ''Relativistic Astrophysics and Cosmology: Einstein's Legacy'' and a journal paper is currently in progress. In particular, Mayer, Kazantzidis, Madau, Colpi, Wadsley and Quinn showed that nuclear disks are produced by strong gas inflows generated by tidal torques during the merger event. These inflows can proceed to scales below 100 parsecs and slow down considerably at a scale of about 50 parsecs, forming a compact disk embedded in a larger disk of a few hundred parsecs in size. The panel illustrates the complexity of dynamical evolution in a typical collision between two equal-mass disk galaxies. The simulation follows dark matter, stars, gas, and supermassive black holes, but only the gas component is visualized. Brighter colors indicate regions of higher gas density and the time corresponding to each snapshot is given by the labels. The first 10 images measure 100 kpc on a side, roughly five times the diameter of the visible part of the Milky Way galaxy. The next five panels represent successive zooms on the central region. The final frame shows the inner 300 pc of the nuclear region at the end of the simulation. During the interaction violent tidal forces tear the galactic disks apart, generating spectacular tidal tails, plumes and prominent bridges of material connecting the two galaxies. The ultimate outcome of a series of increasingly close encounters is the inevitable merger of the disk galaxies into a single structure and the formation of a nuclear disk as shown in the last panel. The simulated nuclear disks have masses of approximately a billion solar masses and exhibit prominent non-axisymmetric features known to produce strong gas inflows. The gas inflows are likely responsible for fueling the central black hole, but even higher resolution will be needed to study this process in detail. Nevertheless, the simulations carried out by Kazantzidis and his collaborators provide the first direct evidence that gas originally in galaxies separated by hundreds of kiloparsecs is collected to parsec scales simply as a result of the dynamics and hydrodynamics involved in the merger process.
<b>Black Hole Mass - Stellar Velocity Dispersion Relation in Interacting Galaxies:</b><br /> The advent of techniques for measuring the masses of supermassive black holes has established various correlations between the mass of a SMBH and the properties of the host galaxy. Recently, a variety of theoretical models have been proposed to explain the origin of the tightest of these correlations, namely the black hole mass-stellar velocity dispersion relation. Kazantzidis, Mayer, Colpi, Madau, Debattista, Wadsley, Quinn, Stadel and Moore investigated the evolution of this relation using the same hydrodynamical numerical simulations of merging galaxies discussed above. The initial galaxy models (stars with error bars) were built in such a way that they followed the observed relation (solid line) and the stellar velocity dispersions of the resulting merger remnants were measured in a way that closely mimics that used by observers for galaxies with spheroids (open triangles with error bars). The results of these simulations (colored points) show that ''dry'' mergers at low redshift (i.e., mergers with little or no gas) tend to move galaxies away from the mean relation (open blue points), suggesting that the role of such mergers is secondary to the evolution of spheroid-dominated galaxies. On the other hand, hydrodynamical mergers that include star formation (solid green points) preserve the black hole mass-stellar velocity dispersion relation and allow the merger remnants to remain along it. These findings suggest that the interplay between strong gas inflows that bridge orders of magnitude in spatial scales and the consumption of gas by star formation is a key ingredient in preserving the observed correlation that is initially established at high redshift.
<b>Visualizations of Galaxy Interactions:</b><br /> Movies of computer simulations illustrating the dynamical evolution of the gas distribution in a merger between two gas-rich disk galaxies. The simulations include the effects of radiative cooling and star formation and demonstrate the formation of extended gas disks in merger remnants. Both visualizations are encoded in the MPEG format and can be downloaded or displayed directly by clicking on the corresponding frames.
The first animation (600x600, 34Mb) corresponds to an equal-mass encounter with both disks lying in the orbital plane, and spinning in the same direction that the galaxies circle each other. Brightness indicate gas density and the counter in the lower left-hand corners shows the time in units of billion years. The frame is centered on the center of the combined system.
The second animation (600x600, 36Mb) shows the interaction between two disk galaxies of unequal masses. Again, brighter colors indicate regions of higher gas density and both galaxies lie in the orbital plane. The frame is now centered on the center of the largest galaxy.
The images and animations displayed on this page may be copied and used strictly for non-profit purposes only, provided that their origin is acknowledged and appropriate credit is provided. Contact Stelios Kazantzidis for permission to use this material for other purposes.