Dr. Tremaine will develop new methods to study stellar systems around black holes at the centers of galaxies, which are much more massive than any individual star. Changes in the stellar orbits can result in X-ray flares as tidally-disrupted stars fall into the black hole, and cause compact objects such as stars or smaller black holes to spiral slowly into the black hole. If a binary star gets too near the black hole, one of its members can be shot out of the galaxy as a hypervelocity star while the other becomes tightly bound to the black hole. The new method will average over the fast motion of each star in its orbit, and represent the tug on each star of all the others with a basis-function expansion of the secular Hamiltonian, representing each star by its orbital elements or action-angle variables. In a further simplification, the angular momentum of each star usually changes much faster than its energy; so the thermodynamic equilibrium of a disk of stars can be explored under the constraint that the orbital energies are frozen. Preliminary work suggests that a disk of stars around a black hole may undergo a 'phase transition' to become lopsided. This new method will be significantly faster than competing approaches, and offer deeper physical insight.
A graduate student will be trained by participating in the research. This work will give deeper insight into the way that the nuclei of galaxies develop around their central black holes, which is one of the fundamental problems of galaxy formation. Dr. Tremaine is co-author of the heavily-cited graduate-level text 'Galactic Dynamics'; a second edition has just been published.
This work is jointly funded by the NSF Division of Astronomical Sciences and NASA's Astrophysics Theory Program.
Astronomers now have strong evidence that massive black holes − up to ten billion times the mass of the Sun − lurk at the centers of galaxies. The broad goal of the research supported by this grant is to investigate the behavior of stars orbiting close to these black holes. These stars are important because (i) studies of their orbits provide the strongest evidence for the existence of these black holes; (ii) stars swallowed by the black hole may contribute significantly to its growth over cosmic time; (iii) disruption of stars by the tidal field of the black hole may produce flares lasting for months to years that signal the presence and properties of the black hole, and feed the accretion disks around black holes that are the engine for quasars. With Andreas Burkert in Münich I have examined the correlation between black-hole mass and the population of star clusters in a sample of a dozen galaxies. We have found, surprisingly, that the cluster population is a remarkably good predictor of black-hole mass. Subsequent independent studies by others have confirmed and strengthened this correlation, though the reason for this black hole-cluster connection remains obscure. Postdoctoral fellow Shane Davis worked with Ari Laor (a sabbatical visitor from the Technion in Israel) to estimate the radiative efficiency − the fraction of the rest-mass energy of fuel consumed by the black hole that is emitted as radiation − in some 80 quasars using sophisticated models that are fit to the quasar spectra. They find radiative efficiencies of about 10%, far higher than in any other known source. This result is consistent with simple theoretical models of accretion from a thin, rotating disk of gas, and with comparisons of the overall number of quasars and the number of residual black holes in nearby galaxies. My collaborators and I have also developed two new numerical tools for the study of stellar orbits around black holes. These studies are hampered by the short orbital periods (e.g., 20 years for the measured stars around the Galaxy's black hole) and long evolution times (up to 10 billion years) found in these systems. Working with Jihad Touma (American University of Beirut), I have developed algorithms for analytically averaging over the short-period orbital motion of these stars and following only the averaged forces between them. The averaging speeds up numerical computations by two or three orders of magnitude and allows us to follow the evolution of stellar systems around black holes for times comparable to their lifetime. Working with M. Jalali (Sharif Institute of Technology), I have devised novel methods based on the engineering technique of finite elements to construct model stellar systems with smooth distributions of stars in position and velocity. We have illustrated the superior performance of our method by constructing equilibrium distribution functions for spherical stellar systems and plan to extend the method to stellar systems around black holes. Observations with the Hubble Space Telescope and other telescopes have shown that the mass of the central black hole is strongly correlated with the velocity dispersion of stars in its host galaxy. Working with Kayhan Gultekin (University of Michigan), I have examined the possibility that the observed relation is biased by an observational selection effect, the difficulty of detecting a small black hole in a galaxy with a large dispersion. In particular, it has been argued that this relation only represents the upper limit to a broad distribution of black-hole masses in galaxies of a given velocity dispersion. We have shown that this hypothesis can be rejected. We also devised a general procedure for incorporating observational selection effects in estimates of the properties of such correlations; reassuringly, this yields the same parameters for the relations as earlier work, although with larger error bars. Postdoctoral fellow Shane Davis has studied the properties of turbulence in accretion disks, believed to be the process that drives gas from the disk into the black hole and thus powers quasars. This work involved the numerical simulation of a patch of an accretion disk to follow the evolution of the turbulence. Recent studies in disks with cylindrical symmetry found that the evolution was strongly dependent on numerical resolution. The strength of the turbulence and its associated stresses decreased with increasing resolution, a problematic result because vigorous turbulence is thought to be necessary for accretion to proceed in many astrophysical systems. Davis and his collaborators showed that the strength of the turbulence and its associated stresses are convergent once stratification − the finite thickness of the disk − is included, alleviating these concerns and pointing the way to productive determinations of the strength of the turbulence and the accretion rate.
