Milos Milosavljevic

MEASURING DISTANCE AND PROPERTIES OF THE MILKY WAY'S CENTRAL SUPERMASSIVE BLACK HOLE WITH STELLAR ORBITS

We report new precision measurements of the properties of our Galaxys supermassive black hole. Based on astrometric (1995-2007) and radial velocity (RV; 2000-2007) measurements from the W. M. Keck 10m telescopes, a fully unconstrained Keplerian orbit for the short-period star S0-2 provides values for the distance (R_0) of 8.0±0.6 kpc, the enclosed mass (M_(bh)) of 4.1±0.6x10^6 M☉ and the black holes RV, which is consistent with zero with 30 km/s uncertainty. If the black hole is assumed to be at rest with respect to the Galaxy (e. g., has no massive companion to induce motion), we can further constrain the fit, obtaining R_0 = 8.4±0.4kpc and M_(bh) 4.5±0.4x10^6 M☉. More complex models constrain the extended dark mass distribution to be less than 3-4x10^5 M☉ within 0.01 pc, ~100 times higher than predictions from stellar and stellar remnant models. For all models, we identify transient astrometric shifts from source confusion (up to 5 times the astrometric error) and the assumptions regarding the black holes radial motion as previously unrecognized limitations on orbital accuracy and the usefulness of fainter stars. Future astrometric and RV observations will remedy these effects. Our estimates of R_0 and the Galaxys local rotation speed, which it is derived from combining R_0 with the apparent proper motion of Sgr A*, (θ_0 = 229±18 km/s), are compatible with measurements made using other methods. The increased black hole mass found in this study, compared to that determined using projected mass estimators, implies a longer period for the innermost stable orbit, longer resonant relaxation timescales for stars in the vicinity of the black hole and a better agreement with the M_(bh)-σ relation.

Formation of Galactic Nuclei

We investigate a model in which galactic nuclei form via the coalescence of preexisting stellar systems containing supermassive black holes. Merger simulations are carried out using N-body algorithms that can follow the formation and decay of a black hole binary and its effect on the surrounding stars down to subparsec scales. Our initial stellar systems have steep central density cusps similar to those in low-luminosity elliptical galaxies. Immediately following the merger, the density profile of the remnant is homologous with the initial density profile and the steep nuclear cusp is preserved. However, the formation of a black hole binary transfers energy to the stars and lowers the central density; continued decay of the binary creates a ρ ~ r-1 density cusp similar to those observed in bright elliptical galaxies, with a break radius that extends well beyond the sphere of gravitational influence of the black holes. Our simulations are the first to successfully produce shallow power-law cusps from mergers of galaxies with steep cusps, and our results support a picture in which the observed dependence of nuclear cusp slope on galaxy luminosity is a consequence of galaxy interactions. We follow the decay of the black hole binary over a factor of ~20 in separation after formation of a hard binary, considerably farther than in previous simulations. We see almost no dependence of the binarys decay rate on number of particles in the simulation, contrary to earlier studies in which a lower initial density of stars led to a more rapid depletion of the binarys loss cone. We nevertheless argue that the decay of a black hole binary in a real galaxy would be expected to stall at separations of 0.01-1 pc unless some additional mechanism is able to extract energy from the binary. We discuss the implications of our results for the survivability of dark matter cusps.

The ACS Virgo Cluster Survey. VI. Isophotal Analysis and the Structure of Early-Type Galaxies*

We present a detailed analysis of the morphology, isophotal parameters, and surface brightness profiles for 100 early-type members of the Virgo Cluster, from dwarfs (MB = -15.1 mag) to giants (MB = -21.8 mag), imaged in the g and z passbands using the Advanced Camera for Surveys on board the Hubble Space Telescope. Dust and complex morphological structures are common. Dust is detected in 42% of galaxies brighter than BT = 12.15 mag, while kiloparsec-scale stellar disk, bars, and nuclear stellar disks are seen in 60% of galaxies with intermediate luminosity. Isophotal parameters are derived typically within 8 kpc from the center for the brightest galaxies, and 1.5 kpc for the faintest systems, with a resolution of 7 pc. For most galaxies, the surface brightness profiles are well described by a Sersic model with index n that increases steadily with the galaxy luminosity; only for 8 of the 10 brightest galaxies are the inner profiles (typically within 100 pc of the center) lower than expected based on an extrapolation of the outer Sersic model, and are better described by a single power-law function. Contrary to previous claims, we find no evidence in support of a strong bimodal behavior of the logarithmic slope of the inner surface brightness profile, γ; in particular the γ distribution for galaxies that do not show evidence of multiple morphological components is unimodal across the entire magnitude range spanned by the ACSVCS galaxies. Although the brightest galaxies have shallow inner profiles, the shallowest profiles are found in faint dwarf systems. The widely adopted separation of early-type galaxies between core and power-law types is questioned based on the present study.

The acs virgo cluster survey. IX. The color distributions of globular cluster systems in early-type galaxies

We present the color distributions of globular cluster (GC) systems for 100 early-type galaxies observed in the ACS Virgo Cluster Survey, the deepest and most homogeneous survey of this kind to date. On average, galaxies at all luminosities in our study (-22 < MB < -15) appear to have bimodal or asymmetric GC color distributions. Almost all galaxies possess a component of metal-poor GCs, with the average fraction of metal-rich GCs ranging from 15% to 60% and increasing with luminosity. The colors of both subpopulations correlate with host galaxy luminosity and color, with the red GCs having a steeper slope. To convert color to metallicity, we introduce a preliminary (g - z)-[Fe/H] relation calibrated to Galactic, M49, and M87 GCs. This relation is nonlinear, with a steeper slope for [Fe/H] -0.8. As a result, the metallicities of the metal-poor and metal-rich GCs vary similarly with respect to galaxy luminosity and stellar mass, with relations of [Fe/H]MP ∝ L0.16±0.04 ∝ M and [Fe/H]MR ∝ L0.26±0.03 ∝ M, respectively. Although these relations are shallower than the mass-metallicity relation predicted by wind models and observed for dwarf galaxies, they are very similar to the relation observed for star-forming galaxies in the same mass range. The offset between the two GC populations is approximately 1 dex across 3 orders of magnitude in mass, suggesting a nearly universal amount of enrichment between the formation of the two populations of GCs. We also find that although the metal-rich GCs show a larger dispersion in color, it is the metal-poor GCs that have an equal or larger dispersion in metallicity. The similarity in the M-[Fe/H] relations for the two populations implies that the conditions of GC formation for metal-poor and metal-rich GCs could not have been too different. Like the color-magnitude relation, these relations derived from globular clusters present stringent constraints on the formation and evolution of early-type galaxies.

The ACS Virgo Cluster Survey. X. Half-Light Radii of Globular Clusters in Early-Type Galaxies: Environmental Dependencies and a Standard Ruler for Distance Estimation

We have measured half-light radii, rh, for thousands of globular clusters (GCs) belonging to the 100 early-type galaxies observed in the ACS Virgo Cluster Survey and the elliptical galaxy NGC 4697. An analysis of the dependencies of the measured half-light radii on both the properties of the GCs themselves and their host galaxies reveals that, in analogy with GCs in the Galaxy but in a milder fashion, the average half-light radius increases with increasing galactocentric distance or, alternatively, with decreasing galaxy surface brightness. For the first time, we find that the average half-light radius decreases with the host galaxy color. We also show that there is no evidence for a variation of rh with the luminosity of the GCs. Finally, we find in agreement with previous observations that the average rh depends on the color of GCs, with red GCs being ~17% smaller than their blue counterparts. We show that this difference is probably a consequence of an intrinsic mechanism, rather than projection effects, and that it is in good agreement with the mechanism proposed by Jordan. We discuss these findings in light of two simple pictures for the origin of the rh of GCs and show that both lead to a behavior in rough agreement with the observations. After accounting for the dependencies on galaxy color, galactocentric radius, and underlying surface brightness, we show that the average GC half-light radii rh can be successfully used as a standard ruler for distance estimation. We outline the methodology, provide a calibration for its use, and discuss the prospects for this distance estimator with future observing facilities. We find rh = 2.7 ± 0.35 pc for GCs with (g - z) = 1.2 mag in a galaxy with color (g - z)gal = 1.5 mag and at an underlying surface z-band brightness of μz = 21 mag arcsec-2. Using this technique, we place an upper limit of 3.4 Mpc on the 1 σ line-of-sight depth of the Virgo Cluster. Finally, we examine the form of the rh distribution for our sample galaxies and provide an analytic expression that successfully describes this distribution.

Long-Term Evolution of Massive Black Hole Binaries

The long-term evolution of massive black hole binaries at the centers of galaxies is studied in a variety of physical regimes, with the aim of resolving the final parsec problem, i.e., how black hole binaries manage to shrink to separations at which emission of gravity waves becomes efficient. A binary ejects stars by the gravitational slingshot and carves out a loss cone in the host galaxy. Continued decay of the binary requires a refilling of the loss cone. We show that the standard treatment of loss cone refilling, derived for collisionally relaxed systems like globular clusters, can substantially underestimate the refilling rates in galactic nuclei. We derive expressions for nonequilibrium loss cone dynamics and calculate timescales for the decay of massive black hole binaries following galaxy mergers, obtaining significantly higher decay rates than heretofore. Even in the absence of two-body relaxation, decay of binaries can persist as a result of repeated ejection of stars returning to the nucleus on eccentric orbits. We show that this recycling of stars leads to a gradual, approximately logarithmic dependence of the binary binding energy on time. We derive an expression for the loss cone refilling induced by the Brownian motion of a black hole binary. We also show that numerical N-body experiments are not well suited to probe these mechanisms over long times as a result of spurious relaxation.

An eccentric circumbinary accretion disk and the detection of binary massive black holes

We present a two-dimensional grid-based hydrodynamic simulation of a thin, viscous, locally isothermal corotating disk orbiting an equal-mass Newtonian binary point mass on a fixed circular orbit. We study the structure of the disk after multiple viscous times. The binary maintains a central hole in the viscously relaxed disk with radius equal to about twice the binary semimajor axis. Disk surface density within the hole is reduced by orders of magnitude relative to the density in the disk bulk. The inner truncation of the disk resembles the clearing of a gap in a protoplanetary disk. An initially circular disk becomes elliptical and then eccentric. Disturbances in the disk contain a component that is stationary in the rotating frame in which the binary is at rest; this component is a two-armed spiral density wave. We measure the distribution of the binary torque in the disk and find that the strongest positive torque is exerted inside the central low-density hole. We make connection with the linear theory of disk forcing at outer Lindblad resonances (OLRs) and find that the measured torque density distribution is consistent with forcing at the 3:2 (m = 2) OLR, well within the central hole. We also measure the time dependence of the rate at which gas accretes across the hole and find quasi-periodic structure. We discuss implications for variability and detection of active galactic nuclei containing a binary massive black hole.

Massive Black Hole Binary Evolution

Coalescence of binary supermassive black holes (SBHs) would constitute the strongest sources of gravitational waves to be observed by LISA. While the formation of binary SBHs during galaxy mergers is almost inevitable, coalescence requires that the separation between binary components first drop by a few orders of magnitude, due presumably to interaction of the binary with stars and gas in a galactic nucleus. This article reviews the observational evidence for binary SBHs and discusses how they would evolve. No completely convincing case of a bound, binary SBH has yet been found, although a handful of systems (e.g. interacting galaxies; remnants of galaxy mergers) are now believed to contain two SBHs at projected separations of <~ 1kpc. N-body studies of binary evolution in gas-free galaxies have reached large enough particle numbers to reproduce the slow, “diffusive” refilling of the binary’s loss cone that is believed to characterize binary evolution in real galactic nuclei. While some of the results of these simulations - e.g. the binary hardening rate and eccentricity evolution - are strongly N-dependent, others - e.g. the “damage” inflicted by the binary on the nucleus - are not. Luminous early-type galaxies often exhibit depleted cores with masses of ~ 1-2 times the mass of their nuclear SBHs, consistent with the predictions of the binary model. Studies of the interaction of massive binaries with gas are still in their infancy, although much progress is expected in the near future. Binary coalescence has a large influence on the spins of SBHs, even for mass ratios as extreme as 10:1, and evidence of spin-flips may have been observed.

Galaxy cores as relics of black hole mergers

ABSTRA C T We investigate the hypothesis that the cores of elliptical galaxies and bulges are created from the binding energy liberated by the coalescence of supermassive binary black holes during galaxy mergers. Assuming that the central density profiles of galaxies were initially steep power laws, r , r 22 , we define the ‘mass deficit’ as the mass in stars that had to be removed from the nucleus in order to produce the observed core. We use non-parametric deprojection to compute the mass deficit in a sample of 35 early-type galaxies with high-resolution imaging data. We find that the mass deficit correlates well with the mass of the nuclear black hole, consistent with the predictions of merger models. We argue that cores in haloes of noninteracting dark matter particles should be comparable in size to those observed in the stars.

The ACS Virgo Cluster Survey. III. Chandra and Hubble Space Telescope Observations of Low-Mass X-Ray Binaries and Globular Clusters in M87

The ACIS instrument on board the Chandra X-Ray Observatory has been used to carry out the first systematic study of low-mass X-ray binaries (LMXBs) in M87, the giant elliptical galaxy near the dynamical center of the Virgo Cluster. These images—with a total exposure time of 154 ks—are the deepest X-ray observations yet obtained of M87. We identify 174 X-ray point sources, of which ~150 are likely LMXBs. This LMXB catalog is combined with deep F475W and F850LP images taken with ACS on the Hubble Space Telescope (HST) (as part of the ACS Virgo Cluster Survey) to examine the connection between LMXBs and globular clusters in M87. Of the 1688 globular clusters in our catalog, fX = 3.6% ± 0.5% contain an LMXB. Dividing the globular cluster sample by metallicity, we find that the metal-rich clusters are 3 ± 1 times more likely to harbor an LMXB than their metal-poor counterparts. In agreement with previous findings for other galaxies based on smaller LMXB samples, we find the efficiency of LMXB formation to scale with both cluster metallicity Z and luminosity, in the sense that brighter, more metal-rich clusters are more likely to contain an LMXB. For the first time, however, we are able to demonstrate that the probability pX that a given cluster will contain an LMXB depends sensitively on the dynamical properties of the host cluster. Specifically, we use the HST images to measure the half-light radius, concentration index, and central density ρ0 for each globular and define a parameter Γ, which is related to the tidal capture and binary-neutron star exchange rate. Our preferred form for pX is then pX ∝ Γρ(Z/Z☉)0.33±0.1. We argue that if the form of pX is determined by dynamical processes, then the observed metallicity dependence is a consequence of an increased number of neutron stars per unit mass in metal-rich globular clusters. Finally, we present a critical examination of the LMXB luminosity function in M87 and reexamine the published LMXB luminosity functions for M49 and NGC 4697. We find no compelling evidence for a break in the luminosity distribution of resolved X-ray point sources in any of these galaxies. Instead, the LMXB luminosity function in all three galaxies is well described by a power law with an upper cutoff at LX ~ 1039 ergs s-1.