Scott Tremaine

THE M-σ AND M-L RELATIONS IN GALACTIC BULGES, AND DETERMINATIONS OF THEIR INTRINSIC SCATTER

We derive improved versions of the relations between supermassive black hole mass (M BH) and host-galaxy bulge velocity dispersion (σ) and luminosity (L; the M-σ and M-L relations), based on 49 M BH measurements and 19 upper limits. Particular attention is paid to recovery of the intrinsic scatter (e0) in both relations. We find log(M BH/M) = α + βlog(σ/200 km s-1) with (α, β, e0) = (8.12 0.08, 4.24 0.41, 0.44 0.06) for all galaxies and (α, β, e0) = (8.23 0.08, 3.96 0.42, 0.31 0.06) for ellipticals. The results for ellipticals are consistent with previous studies, but the intrinsic scatter recovered for spirals is significantly larger. The scatter inferred reinforces the need for its consideration when calculating local black hole mass function based on the M-σ relation, and further implies that there may be substantial selection bias in studies of the evolution of the M-σ relation. We estimate the M-L relationship as log(M BH/M) = α + βlog(LV /1011 L V) of (α, β, e0) = (8.95 0.11, 1.11 0.18, 0.38 0.09); using only early-type galaxies. These results appear to be insensitive to a wide range of assumptions about the measurement errors and the distribution of intrinsic scatter. We show that culling the sample according to the resolution of the black holes sphere of influence biases the relations to larger mean masses, larger slopes, and incorrect intrinsic residuals.

Co-evolution of galactic nuclei and globular cluster systems

We revisit the hypothesis that dense galactic nuclei are formed from inspiraling globular clusters. Recent advances in the understanding of the continuous formation of globular clusters over cosmic time and the concurrent evolution of the galaxy stellar distribution allow us to construct a simple model that matches the observed spatial and mass distributions of clusters in the Galaxy and the giant elliptical galaxy M87. In order to compare with observations, we model the effects of dynamical friction and dynamical evolution, including stellar mass loss, tidal stripping of stars, and tidal disruption of clusters by the growing galactic nucleus. We find that inspiraling globular clusters form a dense central structure, with mass and radius comparable to the typical values in observed nuclear star clusters (NSCs) in late-type and low-mass early-type galaxies. The density contrast associated with the NSC is less pronounced in giant elliptical galaxies. Our results indicate that the NSC mass as a fraction of mass of the galaxy stellar spheroid scales as . Thus disrupted globular clusters could contribute most of the mass of NSCs in galaxies with stellar mass below 1011 M ?. The inner part of the accumulated cluster may seed the growth of a central black hole via stellar dynamical core collapse, thereby relieving the problem of how to form luminous quasars at high redshift. The seed black hole may reach ~105 M ? within 1 Gyr of the beginning of globular cluster formation.

Resonant relaxation and the warp of the stellar disc in the Galactic Centre

Observations of the spatial distribution and kinematics of young stars in the Galactic centre can be interpreted as showing that the stars occupy one, or possibly two, discs of radii � 0:05–0.5 pc. The most prominent (‘clockwise’) disc exhibits a strong warp: the normals to the mean orbital planes in the inner and outer third of the disc differ by � 60 � . Using an analytical model based on Laplace-Lagrange theory, we show that such warps arise naturally and inevitably through vector resonant relaxation between the disc and the surrounding old stellar cluster.

SUPER-ECCENTRIC MIGRATING JUPITERS

An important class of formation theories for hot Jupiters involves the excitation of extreme orbital eccentricity (e = 0.99 or even larger) followed by tidal dissipation at periastron passage that eventually circularizes the planetary orbit at a period less than 10 days. In a steady state, this mechanism requires the existence of a significant population of super-eccentric (e > 0.9) migrating Jupiters with long orbital periods and periastron distances of only a few stellar radii. For these super-eccentric planets, the periastron is fixed due to conservation of orbital angular momentum and the energy dissipated per orbit is constant, implying that the rate of change in semi-major axis a is a-dot {proportional_to}a{sup 1/2} and consequently the number distribution satisfies dN/d log a{proportional_to}a{sup 1/2}. If this formation process produces most hot Jupiters, Kepler should detect several super-eccentric migrating progenitors of hot Jupiters, allowing for a test of high-eccentricity migration scenarios.

Dynamics of warped accretion discs

Accretion discs are present around both stellar-mass black holes in X-ray binaries and supermassive black holes in active galactic nuclei. A wide variety of circumstantial evidence implies that many of these discs are warped. The standard Bardeen--Petterson model attributes the shape of the warp to the competition between Lense--Thirring torque from the central black hole and viscous angular-momentum transport within the disc. We show that this description is incomplete, and that torques from the companion star (for X-ray binaries) or the self-gravity of the disc (for active galactic nuclei) can play a major role in determining the properties of the warped disc. Including these effects leads to a rich set of new phenomena. For example, (i) when a companion star is present and the warp arises from a misalignment between the companions orbital axis and the black holes spin axis, there is no steady-state solution of the Pringle--Ogilvie equations for a thin warped disc when the viscosity falls below a critical value; (ii) in AGN accretion discs, the warp can excite short-wavelength bending waves that propagate inward with growing amplitude until they are damped by the disc viscosity. We show that both phenomena can occur for plausible values of the black hole and disc parameters, and briefly discuss their observational implications.

OBSERVATIONAL SELECTION EFFECTS AND THE M-σ RELATION

We examine the possibility that the observed relation between black hole mass and host-galaxy stellar velocity dispersion (the M–σ relation) is biased by an observational selection effect, the difficulty of detecting a black hole whose sphere of influence is smaller than the telescope resolution. In particular, we critically investigate recent claims that the M–σ relation only represents the upper limit to a broad distribution of black hole masses in galaxies of a given velocity dispersion. We find that this hypothesis can be rejected at a high confidence level, at least for the early-type galaxies with relatively high velocity dispersions (median 268 km s −1 ) that comprise most of our sample. We also describe a general procedure for incorporating observational selection effects in estimates of the properties of the M–σ relation. Applying this procedure we find results that are consistent with earlier estimates that did not account for selection effects, although with larger error bars. In particular, (1) the width of the M–σ relation is not significantly increased, (2) the slope and normalization of the M–σ relation are not significantly changed, and (3) most or all luminous early-type galaxies contain central black holes at zero redshift. Our results may not apply to late-type or small galaxies, which are not well represented in our sample.

CONSTRAINING SUB-PARSEC BINARY SUPERMASSIVE BLACK HOLES IN QUASARS WITH MULTI-EPOCH SPECTROSCOPY. II. THE POPULATION WITH KINEMATICALLY OFFSET BROAD BALMER EMISSION LINES*

A small fraction of quasars have long been known to show bulk velocity offsets (of a few hundred to thousands of km s–1) in the broad Balmer lines with respect to the systemic redshift of the host galaxy. Models to explain these offsets usually invoke broad-line region gas kinematics/asymmetry around single black holes (BHs), orbital motion of massive (~sub-parsec (sub-pc)) binary black holes (BBHs), or recoil BHs, but single-epoch spectra are unable to distinguish between these scenarios. The line-of-sight (LOS) radial velocity (RV) shifts from long-term spectroscopic monitoring can be used to test the BBH hypothesis. We have selected a sample of 399 quasars with kinematically offset broad Hβ lines from the Sloan Digital Sky Survey (SDSS) Seventh Data Release quasar catalog, and have conducted second-epoch optical spectroscopy for 50 of them. Combined with the existing SDSS spectra, the new observations enable us to constrain the LOS RV shifts of broad Hβ lines with a rest-frame baseline of a few years to nearly a decade. While previous work focused on objects with extreme velocity offset (>103 km s–1), we explore the parameter space with smaller (a few hundred km s–1) yet significant offsets (99.7% confidence). Using cross-correlation analysis, we detect significant (99% confidence) radial accelerations in the broad Hβ lines in 24 of the 50 objects, of ~10-200 km s–1 yr–1 with a median measurement uncertainty of ~10 km s–1 yr–1, implying a high fraction of variability of the broad-line velocity on multi-year timescales. We suggest that 9 of the 24 detections are sub-pc BBH candidates, which show consistent velocity shifts independently measured from a second broad line (either Hα or Mg II) without significant changes in the broad-line profiles. Combining the results on the general quasar population studied in Paper I, we find a tentative anti-correlation between the velocity offset in the first-epoch spectrum and the average acceleration between two epochs, which could be explained by orbital phase modulation when the time separation between two epochs is a non-negligible fraction of the orbital period of the motion causing the line displacement. We discuss the implications of our results for the identification of sub-pc BBH candidates in offset-line quasars and for the constraints on their frequency and orbital parameters.

STABILITY OF THE DISTANT SATELLITES OF THE GIANT PLANETS IN THE SOLAR SYSTEM

We conduct a systematic survey of the regions in which distant satellites can orbit stably around the four giant planets in the solar system, using orbital integrations of up to 109 yr. In contrast to previous investigations, we use a grid of initial conditions on a surface of section to explore phase space uniformly inside and outside the planets Hill sphere (radius r H; satellites outside the Hill sphere sometimes are also known as quasi-satellites). Our confirmations and extensions of old results and new findings include the following: (1) many prograde and retrograde satellites can survive out to radii ~0.5r H and ~0.7r H, respectively, while some coplanar retrograde satellites of Jupiter and Neptune can survive out to ~r H; (2) stable orbits do not exist within the Hill sphere at high ecliptic inclinations when the semimajor axis is large enough that the solar tide is the dominant non-Keplerian perturbation; (3) there is a gap between ~r H and 2r H in which no stable orbits exist; (4) at distances 2r H stable satellite orbits exist around Jupiter, Uranus, and Neptune (but not Saturn). For Uranus and Neptune, in particular, stable orbits are found at distances as large as ~10r H; (5) the differences in the stable zones beyond the Hill sphere arise mainly from differences in the planet/Sun mass ratio and perturbations from other planets; in particular, the absence of stable satellites around Saturn is mainly due to perturbations from Jupiter. It is, therefore, likely that satellites at distances 2r H could survive for the lifetime of the solar system around Uranus, Neptune, and, perhaps, Jupiter.

Relativistic redshifts in quasar broad lines

The broad emission lines commonly seen in quasar spectra have velocity widths of a few percent of the speed of light, so special- and general-relativistic effects have a significant influence on the line profile. We have determined the redshift of the broad Hβ line in the quasar rest frame (determined from the core component of the [O III] line) for over 20,000 quasars from the Sloan Digital Sky Survey Data Release 7 quasar catalog. The mean redshift as a function of line width is approximately consistent with the relativistic redshift that is expected if the line originates in a randomly oriented Keplerian disk that is obscured when the inclination of the disk to the line of sight exceeds ~30°-45°, consistent with simple active galactic nucleus unification schemes. This result also implies that the net line-of-sight inflow/outflow velocities in the broad-line region are much less than the Keplerian velocity when averaged over a large sample of quasars with a given line width.

Comparison of simple mass estimators for slowly rotating elliptical galaxies

We compare the performance of mass estimators for elliptical galaxies that rely on the directly observable surface brightness and velocity dispersion profiles, without invoking computationally expensive detailed modeling. These methods recover the mass at a specific radius where the mass estimate is expected to be least sensitive to the anisotropy of stellar orbits. One method (Wolf et al. 2010) uses the total luminosity-weighted velocity dispersion and evaluates the mass at a 3D half-light radius