Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

Synchrotron Emission from Hot Accretion Flows and the Cosmic Microwave Background Anisotropy

Current estimates of number counts of radio sources in the frequency range where the most sensitive Cosmic Microwave Background (CMB) experiments are carried out significantly under-represent sources with strongly inverted spectra. Hot accretion flows around supermassive black holes in the nuclei of nearby galaxies are expected to produce inverted radio spectra by thermal synchrotron emission. We calculate the temperature fluctuations and power spectra of these sources in the Planck Surveyor 30 GHz energy channel, where their emission is expected to peak. We find that their potential contribution is generally comparable to the instrumental noise, and approaches the CMB anisotropy level at small angular scales. Forthcoming CMB missions, which will provide a large statistical sample of inverted-spectra sources, will be crucial for determining the distribution of hot accretion flows in nearby quiescent galactic nuclei. Detection of these sources in different frequency channels will help constrain their spectral characteristics, hence their physical properties.Comment: 10 pages, 4 figures, accepted for publication in Ap

Warped discs and the directional stability of jets in Active Galactic Nuclei

Warped accretion discs in Active Galactic Nuclei (AGN) exert a torque on the black hole that tends to align the rotation axis with the angular momentum of the outer disc. We compute the magnitude of this torque by solving numerically for the steady state shape of the warped disc, and verify that the analytic solution of Scheuer and Feiler (1996) provides an excellent approximation. We generalise these results for discs with strong warps and arbitrary surface density profiles, and calculate the timescale on which the black hole becomes aligned with the angular momentum in the outer disc. For massive holes and accretion rates of the order of the Eddington limit the alignment timescale is always short (less than a Myr), so that jets accelerated from the inner disc region provide a prompt tracer of the angular momentum of gas at large radii in the disc. Longer timescales are predicted for low luminosity systems, depending on the degree of anisotropy in the disc's hydrodynamic response to shear and warp, and for the final decay of modest warps at large radii in the disc that are potentially observable via VLBI. We discuss the implications of this for the inferred accretion history of those Active Galactic Nuclei whose jet directions appear to be stable over long timescales. The large energy deposition rate at modest disc radii during rapid realignment episodes should make such objects transiently bright at optical and infrared wavelengths.Comment: MNRAS, in press. Revised to match accepted version, with one new figure showing alignment timescale as a function of black hole mas

Heating the bubbly gas of galaxy clusters with weak shocks and sound waves

Using hydrodynamic simulations and a technique to extract the rotational component of the velocity field, we show how bubbles of relativistic gas inflated by AGN jets in galaxy clusters act as a catalyst, transforming the energy carried by sound and shock waves to heat. The energy is stored in a vortex field around the bubbles which can subsequently be dissipated. The efficiency of this process is set mainly by the fraction of the cluster volume filled by (sub-)kpc scale filaments and bubbles of relativistic plasma.Comment: Accepted for publication in ApJ Letters after minor wording changes, 4 figures, 4 page

Lense-Thirring precession of accretion disks around compact objects

Misaligned accretion disks surrounding rotating compact objects experience a torque due to the Lense-Thirring effect, which leads to precession of the inner disk. It has been suggested that this effect could be responsible for some low frequency Quasi-Periodic Oscillations observed in the X-ray lightcurves of neutron star and galactic black hole systems. We investigate this possibility via time-dependent calculations of the response of the inner disk to impulsive perturbations for both Newtonian point mass and Paczynski-Wiita potentials, and compare the results to the predictions of the linearized twisted accretion disk equations. For most of a wide range of disk models that we have considered, the combination of differential precession and viscosity causes the warps to decay extremely rapidly. Moreover, at least for relatively slowly rotating objects, linear calculations in a Newtonian point mass potential provide a good measure of the damping rate, provided only that the timescale for precession is much shorter than the viscous time in the inner disk. The typically rapid decay rates suggest that coherent precession of a fluid disk would not be observable, though it remains possible that the damping rate of warp in the disk could be low enough to permit weakly coherent signals from Lense-Thirring precession.Comment: ApJ, in press. Minor revisions to match accepted version. Animations showing warp evolution are available at http://www.cita.utoronto.ca/~armitage/lense_thirring.htm

Polarimetry of Compact Symmetric Objects

We present multi-frequency VLBA observations of two polarized Compact Symmetric Objects (CSOs), J0000+4054 and J1826+1831, and a polarized CSO candidate, J1915+6548. Using the wavelength-squared dependence of Faraday rotation, we obtained rotation measures (RMs) of -180 \pm 10 rad m^-2 and 1540 \pm 7 rad m^-2 for the latter two sources. These are lower than what is expected of CSOs (several 1000 rad m^-2) and, depending on the path length of the Faraday screens, require magnetic fields from 0.03 to 6 \mu G. These CSOs may be more heavily affected by Doppler boosting than their unpolarized counterparts, suggesting that a jet-axis orientation more inclined towards the line of sight is necessary to detect any polarization. This allows for low RMs if the polarized components are oriented away from the depolarizing circumnuclear torus. These observations also add a fourth epoch to the proper motion studies of J0000+4054 and J1826+1831, constraining their kinematic age estimates to >610 yrs and 2600 \pm 490 yrs, respectively. The morphology, spectrum, and component motions of J1915+6548 are discussed in light of its new classification as a CSO candidate, and its angle to the line of sight (~50\deg) is determined from relativistic beaming arguments.Comment: 29 pages, including 9 figures; Accepted by Astrophysical Journal, 16 Feb 0

The distribution and cosmic evolution of massive black hole spins

We study the expected distribution of massive black hole (MBH) spins and its evolution with cosmic time in the context of hierarchical galaxy formation theories. Our model uses Monte Carlo realizations of the merger hierarchy in a LCDM cosmology, coupled to semi-analytical recipes, to follow the merger history of dark matter halos, the dynamics of the MBHs they host, and their growth via gas accretion and binary coalescences. The coalescence of comparable mass holes increases the spin of MBHs, while the capture of smaller companions in randomly-oriented orbits acts to spin holes down. We find that, given the distribution of MBH binary mass ratios in hierarchical models, binary coalescences alone do not lead to a systematic spin-up or spin-down of MBHs with time: the spin distribution retains memory of its initial conditions. By contrast, because of the Bardeen-Petterson effect, gas accretion via a thin disk tends to spin holes up even if the direction of the spin axis changes randomly in time. In our models, accretion dominates over black hole captures and efficiently spins holes up. The spin distribution is heavily skewed towards fast-rotating Kerr holes, is already in place at early epochs, and does not change much below redshift 5. If accretion is via a thin disk, about 70% of all MBHs are maximally rotating and have radiative efficiencies approaching 30% (assuming a "standard'' spin-efficiency conversion). Even in the conservative case where accretion is via a geometrically thick disk, about 80% of all MBHs have spin parameters a/m > 0.8 and accretion efficiencies > 12%. Rapidly spinning holes with high radiative efficiencies may satisfy constraints based on comparing the local MBH mass density with the mass density inferred from luminous quasars (Soltan's argument).Comment: 15 pages, 9 figures, accepted for publication in the Astrophysical Journa

Kinematic Age Estimates for 4 Compact Symmetric Objects from the Pearson-Readhead Survey

Based on multi-epoch observations at 15 and 43 GHz with the Very Long Baseline Array (VLBA) we detect significant angular expansions between the two hot spots of 4 Compact Symmetric Objects (CSOs). From these relative motions we derive kinematic ages of between 300 and 1200 years for the radio emission. These ages lend support to the idea that CSOs are produced in a recent phase of activity. These observations also allow us to study the evolution of the hot spots dynamically in individual sources. In all 4 sources the hot spots are separating along the source axis, but in 1031+567 the tip of one hot spot appears to be moving almost orthogonally to the source axis. Jet components, seen in 3 of the 4 sources observed, are found to be moving relativistically outward from the central engines towards the more slowly moving hot spots.Comment: in press at ApJ for v. 541 Oct. 1, 2000, 23 page LaTeX document includes 6 postscript figure

J1420--0545: The radio galaxy larger than 3C236

We report the discovery of the largest giant radio galaxy, J1420-0545: a FR type II radio source with an angular size of 17.4' identified with an optical galaxy at z=0.3067. Thus, the projected linear size of the radio structure is 4.69 Mpc (if we assume that H_{0}=71 km\s\Mpc, Omega_{m}=0.27, and Omega_{\Lambda}=0.73). This makes it larger than 3C236, which is the largest double radio source known to date. New radio observations with the 100 m Effelsberg telescope and the Giant Metrewave Radio Telescope, as well as optical identification with a host galaxy and its optical spectroscopy with the William Herschel Telescope are reported. The spectrum of J1420-0545 is typical of elliptical galaxies in which continuum emission with the characteristic 4000A discontinuity and the H and K absorption lines are dominated by evolved stars. The dynamical age of the source, its jets' power, the energy density, and the equipartition magnetic field are calculated and compared with the corresponding parameters of other giant and normal-sized radio galaxies from a comparison sample. The source is characterized by the exceptionally low density of the surrounding IGM and an unexpectedly high expansion speed of the source along the jet axis. All of these may suggest a large inhomogeneity of the IGM.Comment: 20 pages, 5 figures, 3 table

Obscuration of the Parsec Scale Jets in the Compact Symmetric Object 1946+708

We present results of VLA and VLBA observations of the 1.420 GHz neutral hydrogen absorption associated with the Compact Symmetric Object 1946+708 (z=0.101). We find significant structure in the gas on parsec scales. The peak column density in the HI (N_HI~2.2x10^23 cm^-2 (T_s/8000K)) occurs toward the center of activity of the source, as does the highest velocity dispersion (FWHM~350 \kms). In addition, we find that the continuum spectra of the various radio components associated with these jets strongly indicate free-free absorption. This effect is particularly pronounced toward the core and inner components of the receding jet, suggesting the presence of a screen local to the source, perhaps part of an obscuring torus.Comment: revised version, some text added, 1 figure changed; accepted to Astrophysical Journal, 22 page LaTeX document includes 8 postscript figure