Aristotle Socrates

The kozai mechanism and the evolution of binary supermassive black holes

We consider the dynamical evolution of bound, hierarchical triples of supermassive black holes that might be formed in the nuclei of galaxies undergoing sequential mergers. The tidal force of the outer black hole on the inner binary produces eccentricity oscillations through the Kozai mechanism, and this can substantially reduce the gravitational wave merger time of the inner binary. We numerically calculate the merger time for a wide range of initial conditions and black hole mass ratios, including the effects of octupole interactions in the triple as well as general relativistic periastron precession in the inner binary. The semimajor axes and the mutual inclination of the inner and outer binaries are the most important factors affecting the merger time. We find that for a random distribution of inclination angles and approximately equal mass black holes, it is possible to reduce the merger time of a near circular inner binary by more than a factor of 10 in over 50% of all cases. We estimate that a typical exterior quadrupole moment from surrounding matter in the galaxy may also be sufficient to excite eccentricity oscillations in supermassive black hole binaries and to accelerate black hole mergers.

The Eddington Limit in Cosmic Rays: An Explanation for the Observed Faintness of Starbursting Galaxies

We show that the luminosity of a star-forming galaxy is capped by the production and subsequent expulsion of cosmic rays from its interstellar medium. By defining an Eddington luminosity in cosmic rays, we show that the star formation rate of a given galaxy is limited by its mass content and the cosmic-ray mean free path. When the cosmic-ray luminosity and pressure reach a critical value as a result of vigorous star formation, hydrostatic balance is lost, a galactic-scale cosmic-ray-driven wind develops, and star formation is choked off. Cosmic-ray pressure driven winds are likely to produce wind velocities in proportion to and significantly in excess of the galactic escape velocity. It is possible that cosmic-ray feedback results in the Faber-Jackson relation for a plausible set of input parameters that describe cosmic-ray production and transport, which are calibrated by observations of the Milky Ways interstellar cosmic rays as well as other nearby galaxies.

Local radiative hydrodynamic and magnetohydrodynamic instabilities in optically thick media

We examine the local conditions for radiative damping and driving of short-wavelength, propagating hydrodynamic and magnetohydrodynamic (MHD) waves in static, optically thick, stratified equilibria. We show that so-called strange modes in stellar oscillation theory and magnetic photon bubbles are intimately related and are both fundamentally driven by the background radiation flux acting on compressible waves. We identify the necessary criteria for unstable driving of these waves and show that this driving can exist in both gas pressure- and radiation pressure-dominated media, as well as pure Thomson scattering media in the MHD case. The equilibrium flux acting on opacity fluctuations can drive both hydrodynamic acoustic waves and magnetosonic waves unstable. In addition, magnetosonic waves can be driven unstable by a combination of the equilibrium flux acting on density fluctuations and changes in the background radiation pressure along fluid displacements. We briefly describe the conditions under which these instabilities might be manifested in both main-sequence stellar envelopes and accretion disks.

Local dynamical instabilities in magnetized, radiation pressure supported accretion disks

We present a general linear dispersion relation that describes the coupled behavior of magnetorotational, photon bubble, and convective instabilities in weakly magnetized, differentially rotating accretion disks. We presume the accretion disks to be geometrically thin and supported vertically by radiation pressure. We fully incorporate the effects of a nonzero radiative diffusion length on the linear modes. In an equilibrium with a purely vertical magnetic field, the vertical magnetorotational modes are completely unaffected by compressibility, stratification, and radiative diffusion. However, in the presence of azimuthal fields, which are expected in differentially rotating flows, the growth rate of all magnetorotational modes can be reduced substantially below the orbital frequency. This occurs if diffusion destroys radiation sound waves on the length scale of the instability and the magnetic energy density of the azimuthal component exceeds the nonradiative thermal energy density. While sluggish in this case, the magnetorotational instability still persists and will still tap the free energy of the differential rotation. Photon bubble instabilities are generically present in radiation pressure-dominated flows where diffusion is present. We show that their growth rates are limited to a maximum value that is reached at short wavelengths where the modes may be viewed as unstable slow magnetosonic waves. We also find that vertical radiation pressure destabilizes upward-propagating fast waves, and that Alfven waves can be unstable. These instabilities typically have smaller growth rates than the photon bubble/slow modes. We discuss how all these modes behave in various regimes of interest and speculate how they may affect the dynamics of real accretion disk flows.

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.

The effects of photon bubble instability in radiation-dominated accretion disks

We examine the effects of photon bubble instability in radiation-dominated accretion disks such as those found around black holes in active galactic nuclei and X-ray binary star systems. Two- and three-dimensional numerical radiation MHD calculations of small patches of disk are used. Modes with wavelengths shorter than the gas pressure scale height grow faster than the orbital frequency in the disk surface layers. The fastest growth rate observed is 5 times the orbital frequency and occurs on nearly vertical magnetic fields. The spectrum of linear modes is in good agreement with a WKB analysis that indicates still faster growth at unresolved scales, with a maximum growth rate proportional to the gravitational acceleration and inversely proportional to the gas sound speed. Disturbances reaching nonlinear amplitudes steepen into trains of shocks similar to a one-dimensional periodic nonlinear analytic solution. Variations in propagation speed result in merging of adjacent fronts, and over time the shock spacing and amplitude increase. Growth is limited by the strength of the magnetic field. The shock train structure is disrupted when the ram pressure of the disturbances exceeds the magnetic pressure. The maximum horizontal density variations are comparable to the ratio of magnetic to gas pressure and in our calculations exceed 100. Under the conditions considered, radiation diffuses through the inhomogeneneous flow 5 times faster than through the initial hydrostatic equilibrium, and the net cooling rate is several times greater than in a similar calculation without magnetic fields that shows the effects of convection. These results indicate that photon bubbles may be important in cooling radiation-dominated accretion disks. The Shaviv type I global instability grows faster than the orbital frequency in calculations of the disk surface layers with lower boundaries of fixed temperature, but is weak or absent in calculations spanning the disk thickness.

Ultraluminous X-Ray Sources Powered by Radiatively Efficient Two-Phase Super-Eddington Accretion onto Stellar-Mass Black Holes

A hard power-law component dominates the radiation spectra of many of the brightest ultraluminous X-ray sources (ULXs). Therefore, a hot, optically thin corona likely powers the emission by Comptonizing seed photons emitted by a cooler, optically thick accretion disk. Before its dissipation and conversion into coronal radiation, the randomized gravitational binding energy responsible for powering ULXs must separate from the mass of its origin by a means quicker than electron-scattering-mediated radiative diffusion. Therefore, the accretion power released in ULXs is not necessarily subject to photon trapping, as long as it occurs in a corona. Motivated by these considerations, we present a model of ULXs powered by geometrically thin accretion onto stellar-mass black holes. In the innermost region of the disk, where the majority of the binding energy is released, an adjacent corona covering the entire disk surface Comptonizes the cool thermal radiation. The intense photoionizing flux and subsequent high ionization level produces an albedo near unity for X-ray photons. Therefore, the amount of reprocessed emission in this region is small relative to the non-thermal output. If dissipation takes place within an optically thin corona, Compton drag and the winds low optical depth hamper the driving of a wind. If the magnetic field geometry of the corona is primarily closed, then fields of modest strength can, in principle, prevent the launching of a wind. In the outer region, the albedo is lower, and the surface area is larger. Therefore, the disk emits lower temperature thermal radiation resulting from both viscous dissipation within the body of the disk and reprocessed coronal power. Thus, this model qualitatively reproduces the main features of most highly luminous ULX spectra.

Turbulent comptonization in black hole accretion disks

In the innermost regions of radiation pressure-supported accretion disks, the turbulent magnetic pressure may greatly exceed that of the gas. If this is the case, it is possible for bulk Alfvenic motions driven by the magnetorotational instability (MRI) to surpass the electron thermal velocity. Bulk, rather than thermal, Comptonization may then be the dominant radiative process that mediates gravitational energy release. For sufficiently large turbulent stresses, we show that turbulent Comptonization produces a significant contribution to the far-UV and X-ray emission of black hole accretion disks. The existence of this spectral component provides a means of obtaining direct observational constraints on the nature of the turbulence itself. We describe how this component may affect the spectral energy distributions and variability properties of X-ray binaries and active galactic nuclei (AGN).

SWIFT J1644+57: AN ULTRA-LUMINOUS X-RAY EVENT

The photon spectral energy distribution of the powerful transient Sw J1644+57 resembles those of the brightest ultra-luminous X-ray sources (ULXs). The transient nature of Sw J1644+57 is likely the result of a tidal disruption of a star by a supermassive black hole. The stellar disk generates accretion power at super-Eddington rates and the observational properties of Sw J1644+57 indicate—in analogy with ULXs—that the accretion flow maintains a high level of radiative efficiency with a corresponding super-Eddington luminosity. Due to its similarity to ULXs, this powerful transient may be thought of as an ultra-luminous X-ray event (ULX-E). Observational tests for this ULX-E model are proposed as well.

RELATIVISTIC ACCRETION MEDIATED BY TURBULENT COMPTONIZATION

Black hole and neutron star accretion flows display unusually high levels of hard coronal emission in comparison to all other optically thick, gravitationally bound, turbulent astrophysical systems. Since these flows sit in deep relativistic gravitational potentials, their random bulk motions approach the speed of light, therefore allowing turbulent Comptonization to be an important effect. We show that the inevitable production of hard X-ray photons results from turbulent Comptonization in the limit where the turbulence is trans-sonic and the accretion power approaches the Eddington limit. In this regime, the turbulent Compton y-parameter approaches unity and the turbulent Compton temperature is a significant fraction of the electron rest mass energy, in agreement with the observed phenomena.