Collapse of Uniformly Rotating Stars to Black Holes and the Formation of Disks

Simulations in general relativity show that the outcome of collapse of a marginally unstable, uniformly rotating star spinning at the mass-shedding limit depends critically on the equation of state. For a very stiff equation of state, which is likely to characterize a neutron star, essentially all of the mass and angular momentum of the progenitor are swallowed by the Kerr black hole formed during the collapse, leaving nearly no residual gas to form a disk. For a soft equation of state with an adiabatic index \Gamma - 4/3 << 1, which characterizes a very massive or supermassive star supported predominantly by thermal radiation pressure, as much as 10% of the mass of the progenitor avoids capture and goes into a disk about the central hole. We present a semi-analytic calculation that corroborates these numerical findings and shows how the final outcome of such a collapse may be determined from simple physical considerations. In particular, we employ a simple energy variational principle with an approximate, post-Newtonian energy functional to determine the structure of a uniformly rotating, polytropic star at the onset of collapse as a function of polytropic index n, where \Gamma = 1+1/n. We then use this data to calculate the mass and spin of the final black hole and ambient disk. We show that the fraction of the total mass that remains in the disk falls off sharply as 3-n (equivalently, \Gamma - 4/3) increases.Comment: 11 pages, 2 figures, 2 tables, AASTeX; accepted to appear in The Astrophysical Journa

A Theoretical Model for the Mbh−σM_{\rm bh}-\sigma Relation for Supermassive Black Holes in Galaxies

We construct a model for the formation of black holes within galactic bulges. The initial state is a slowly rotating isothermal sphere, characterized by effective transport speed \aeff and rotation rate $\Omega$. The black hole mass is determined when the centrifugal radius of the collapse flow exceeds the capture radius of the central black hole. This model reproduces the observed correlation between black hole masses and galactic velocity dispersions, \mbh \approx 10^8 M_\odot (\sigma/200 \kms)^4, where \sigma = \sqrt{2} \aeff. This model also predicts the ratio \mrat of black hole mass to host mass: \mrat $\approx$ 0.004 (\sigma/200 \kms).Comment: 9 pages, 2 figures, submitted to Astrophysical Journal Letter

HE 0047-1756: A new gravitationally lensed double QSO

The quasar HE 0047-1756, at z=1.67, is found to be split into two images 1.44" apart by an intervening galaxy acting as a gravitational lens. The flux ratio for the two components is roughly 3.5:1, depending slightly upon wavelength. The lensing galaxy is seen on images obtained at 800 nm and 2.1 \mu; there is also a nearby faint object which may be responsible for some shear. The spectra of the two quasar images are nearly identical, but the emission line ratio between the two components scale differently from the continuum. Moreover, the fainter component has a bluer continuum slope than the brighter one. We argue that these small differences are probably due to microlensing. There are hints of an Einstein ring emanating from the brighter image toward the fainter one.Comment: 4 pages, submitted to A&A Letter

Central Mass Concentration and Bar Dissolution in Nearby Spiral Galaxies

We use data from the BIMA Survey of Nearby Galaxies (SONG) to investigate the relationship between ellipticity and central mass concentration in barred spirals. Existing simulations predict that bar ellipticity decreases as inflowing mass driven by the bar accumulates in the central regions, ultimately destroying the bar. Using the ratio of the bulge mass to the mass within the bar radius as an estimate of the central mass concentration, we obtain dynamical mass estimates from SONG CO 1-0 rotation curve data. We find an inverse correlation between bar ellipticity and central mass concentration, consistent with simulations of bar dissolution.Comment: 10 pages, 2 figures and 2 tables, accepted for publication in the Astrophysical Journa

Parameter estimation of coalescing supermassive black hole binaries with LISA

Laser Interferometer Space Antenna (LISA) will routinely observe coalescences of supermassive black hole (BH) binaries up to very high redshifts. LISA can measure mass parameters of such coalescences to a relative accuracy of $10^{-4}-10^{-6}$, for sources at a distance of 3 Gpc. The problem of parameter estimation of massive nonspinning binary black holes using post-Newtonian (PN) phasing formula is studied in the context of LISA. Specifically, the performance of the 3.5PN templates is contrasted against its 2PN counterpart using a waveform which is averaged over the LISA pattern functions. The improvement due to the higher order corrections to the phasing formula is examined by calculating the errors in the estimation of mass parameters at each order. The estimation of the mass parameters ${\cal M}$ and $\eta$ are significantly enhanced by using the 3.5PN waveform instead of the 2PN one. For an equal mass binary of $2\times10^6M_\odot$ at a luminosity distance of 3 Gpc, the improvement in chirp mass is $\sim 11$ and that of $\eta$ is $\sim 39$. Estimation of coalescence time $t_c$ worsens by 43%. The improvement is larger for the unequal mass binary mergers. These results are compared to the ones obtained using a non-pattern averaged waveform. The errors depend very much on the location and orientation of the source and general conclusions cannot be drawn without performing Monte Carlo simulations. Finally the effect of the choice of the lower frequency cut-off for LISA on the parameter estimation is studied.Comment: 12 pages, 5 figures (eps) significant revision, accepted for publication in Phys. Rev. D. Matches with the published versio

Supermassive Black Holes in Active Galactic Nuclei. I. The Consistency of Black Hole Masses in Quiescent and Active Galaxies

We report the first results of a program to measure accurate stellar velocity dispersions in the bulges of the host galaxies of active galactic nuclei (AGNs) for which accurate black hole (BH) masses have been determined via reverberation mapping. We find good agreement between BH masses obtained from reverberation mapping, and from the M(BH) - sigma relation as defined by quiescent galaxies, indicating a common relationship between active and quiescent black holes and their large-scale environments.Comment: Submitted to ApJ

Radio Observations of Infrared Luminous High Redshift QSOs

We present Very Large Array (VLA) observations at 1.4 GHz and 5 GHz of a sample of 12 Quasi-stellar Objects (QSOs) at z = 3.99 to 4.46. The sources were selected as the brightest sources at 250 GHz from the recent survey of Omont et al. (2001). We detect seven sources at 1.4 GHz with flux densities, S_{1.4} > 50 microJy. These centimeter (cm) wavelength observations imply that the millimeter (mm) emission is most likely thermal dust emission. The radio-through-optical spectral energy distributions for these sources are within the broad range defined by lower redshift, lower optical luminosity QSOs. For two sources the radio continuum luminosities and morphologies indicate steep spectrum, radio loud emission from a jet-driven radio source. For the remaining 10 sources the 1.4 GHz flux densities, or limits, are consistent with those expected for active star forming galaxies. If the radio emission is powered by star formation in these systems, then the implied star formation rates are of order 1e3 M_solar/year. We discuss the angular sizes and spatial distributions of the radio emitting regions, and we consider briefly these results in the context of co-eval black hole and stellar bulge formation in galaxies.Comment: to appear in the A

Values of H_0 from Models of the Gravitational Lens 0957+561

The lensed double QSO 0957+561 has a well-measured time delay and hence is useful for a global determination of H0. Uncertainty in the mass distribution of the lens is the largest source of uncertainty in the derived H0. We investigate the range of \hn produced by a set of lens models intended to mimic the full range of astrophysically plausible mass distributions, using as constraints the numerous multiply-imaged sources which have been detected. We obtain the first adequate fit to all the observations, but only if we include effects from the galaxy cluster beyond a constant local magnification and shear. Both the lens galaxy and the surrounding cluster must depart from circular symmetry as well. Lens models which are consistent with observations to 95% CL indicate H0=104^{+31}_{-23}(1-\kthirty) km/s/Mpc. Previous weak lensing measurements constrain the mean mass density within 30" of G1 to be kthirty=0.26+/-0.16 (95% CL), implying H0=77^{+29}_{-24}km/s/Mpc (95% CL). The best-fitting models span the range 65--80 km/s/Mpc. Further observations will shrink the confidence interval for both the mass model and \kthirty. The range of H0 allowed by the full gamut of our lens models is substantially larger than that implied by limiting consideration to simple power law density profiles. We therefore caution against use of simple isothermal or power-law mass models in the derivation of H0 from other time-delay systems. High-S/N imaging of multiple or extended lensed features will greatly reduce the H0 uncertainties when fitting complex models to time-delay lenses.Comment: AASTEX, 48 pages 4 figures, 2 tables. Also available at: http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

The Black Hole in the Compact, High-dispersion Galaxy NGC 1271

Located in the Perseus cluster, NGC 1271 is an early-type galaxy with a small effective radius of 2.2 kpc and a large stellar velocity dispersion of 276 km/s for its K-band luminosity of 8.9x10^{10} L_sun. We present a mass measurement for the black hole in this compact, high-dispersion galaxy using observations from the integral field spectrograph NIFS on the Gemini North telescope assisted by laser guide star adaptive optics, large-scale integral field unit observations with PPAK at the Calar Alto Observatory, and Hubble Space Telescope WFC3 imaging observations. We are able to map out the stellar kinematics on small spatial scales, within the black hole sphere of influence, and on large scales that extend out to four times the galaxy's effective radius. We find that the galaxy is rapidly rotating and exhibits a sharp rise in the velocity dispersion. Through the use of orbit-based stellar dynamical models, we determine that the black hole has a mass of (3.0^{+1.0}_{-1.1}) x 10^9 M_sun and the H-band stellar mass-to-light ratio is 1.40^{+0.13}_{-0.11} M_sun/L_sun (1-sigma uncertainties). NGC 1271 occupies the sparsely-populated upper end of the black hole mass distribution, but is very different from the Brightest Cluster Galaxies (BCGs) and giant elliptical galaxies that are expected to host the most massive black holes. Interestingly, the black hole mass is an order of magnitude larger than expectations based on the galaxy's bulge luminosity, but is consistent with the mass predicted using the galaxy's bulge stellar velocity dispersion. More compact, high-dispersion galaxies need to be studied using high spatial resolution observations to securely determine black hole masses, as there could be systematic differences in the black hole scaling relations between these types of galaxies and the BCGs/giant ellipticals, thereby implying different pathways for black hole and galaxy growth.Comment: accepted for publication in Ap