Yan-Fei Jiang

On the Thermal Stability of Radiation-dominated Accretion Disks

We study the long-term thermal stability of radiation-dominated disks in which the vertical structure is determined self-consistently by the balance of heating due to the dissipation of MHD turbulence driven by magneto-rotational instability (MRI) and cooling due to radiation emitted at the photosphere. The calculations adopt the local shearing box approximation and utilize the recently developed radiation transfer module in the Athena MHD code based on a variable Eddington tensor rather than an assumed local closure. After saturation of the MRI, in many cases the disk maintains a steady vertical structure for many thermal times. However, in every case in which the box size in the horizontal directions are at least one pressure scale height, fluctuations associated with MRI turbulence and dynamo action in the disk eventually trigger a thermal runaway that causes the disk to either expand or contract until the calculation must be terminated. During runaway, the dependence of the heating and cooling rates on total pressure satisfy the simplest criterion for classical thermal instability. We identify several physical reasons why the thermal runaway observed in our simulations differ from the standard α disk model; for example, the advection of radiation contributes a non-negligible fraction to the vertical energy flux at the largest radiation pressure, most of the dissipation does not happen in the disk mid-plane, and the change of dissipation scale height with mid-plane pressure is slower than the change of density scale height. We discuss how and why our results differ from those published previously. Such thermal runaway behavior might have important implications for interpreting temporal variability in observed systems, but fully global simulations are required to study the saturated state before detailed predictions can be made.

THE HOST GALAXIES OF LOW-MASS BLACK HOLES*

Using Hubble Space Telescope observations of 147 host galaxies of low-mass black holes (BHs), we systematically study the structures and scaling relations of these active galaxies. Our sample is selected to have central BHs with virial masses of ~105-106 M ?. The host galaxies have total I-band magnitudes of ?23.2 < MI < ?18.8?mag and bulge magnitudes of ?22.9 < MI < ?16.1?mag. Detailed bulge-disk-bar decompositions with GALFIT show that 93% of the galaxies have extended disks, 39% have bars, and 5% have no bulges at all at the limits of our observations. Based on the S?rsic index and bulge-to-total ratio, we conclude that the majority of the galaxies with disks are likely to contain pseudobulges and very few of these low-mass BHs live in classical bulges. The fundamental plane of our sample is offset from classical bulges and ellipticals in a way that is consistent with the scaling relations of pseudobulges. The sample has smaller velocity dispersion at fixed luminosity in the Faber-Jackson plane compared with classical bulges and elliptical galaxies. The galaxies without disks are structurally more similar to spheroidals than to classical bulges according to their positions in the fundamental plane, especially the Faber-Jackson projection. Overall, we suggest that BHs with mass 106 M ? live in galaxies that have evolved secularly over the majority of their history. A classical bulge is not a prerequisite to host a BH.

The evolution of wide binary stars

We study the orbital evolution of wide binary stars in the solar neighbourhood due to gravitational perturbations from passing stars. We include the effects of the Galactic tidal field and continue to follow the stars after they become unbound. For a wide variety of initial semimajor axes and formation times, we find that the number density (stars per unit logarithmic interval in projected separation) exhibits a minimum at a few times the Jacobi radius r J , which equals 1.7 pc for a binary of solar-mass stars. The density peak interior to this minimum arises from the primordial distribution of bound binaries, and the exterior density, which peaks at a separation of ∼100-300 pc, arises from formerly bound binaries that are slowly drifting apart. The exterior peak gives rise to a significant long-range correlation in the positions and velocities of disc stars that should be detectable in large astrometric surveys such as Gaia that can measure accurate three-dimensional distances and velocities.

A Radiation Transfer Solver for Athena Using Short Characteristics

We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athenas MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.

A GODUNOV METHOD FOR MULTIDIMENSIONAL RADIATION MAGNETOHYDRODYNAMICS BASED ON A VARIABLE EDDINGTON TENSOR

We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods. This algorithm solves the radiation moment equations in the mixed frame, without invoking any diffusion-like approximations. The moment equations are closed using a variable Eddington tensor whose components are calculated from a formal solution of the transfer equation at a large number of angles using the method of short characteristics. We use a comprehensive test suite to verify the algorithm, including convergence tests of radiation-modified linear acoustic and magnetosonic waves, the structure of radiation-modified shocks, and two-dimensional tests of photon bubble instability and the ablation of dense clouds by an intense radiation field. These tests cover a very wide range of regimes, including both optically thick and thin flows, and ratios of the radiation to gas pressure of at least 10–4-104. Across most of the parameter space, we find that the method is accurate. However, the tests also reveal there are regimes where the method needs improvement, for example when both the radiation pressure and absorption opacity are very large. We suggest modifications to the algorithm that will improve the accuracy in this case. We discuss the advantages of this method over those based on flux-limited diffusion. In particular, we find that the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications.

BLACK HOLE MASS AND BULGE LUMINOSITY FOR LOW-MASS BLACK HOLES

We study the scaling between bulge magnitude and central black hole (BH) mass in galaxies with virial BH masses 10^7 solar mass. Specfically, bulges span a much wider range of bulge luminosity, and on average the luminosity is larger, at fixed black hole mass. The trend holds both for the active galaxies from Bentz et al. and the inactive sample of Gultekin et al. and cannot be explained by differences in stellar populations, as it persists when we use dynamical bulge masses. Put another way, the ratio between bulge and BH mass is much larger than

SATURATION OF THE MAGNETO-ROTATIONAL INSTABILITY IN STRONGLY RADIATION-DOMINATED ACCRETION DISKS

\sim 1000

NONLINEAR EVOLUTION OF RAYLEIGH-TAYLOR INSTABILITY IN A RADIATION-SUPPORTED ATMOSPHERE

for our sample. This is consistent with recent suggestions that black hole mass does not scale with the pseudobulge luminosity. The low-mass scaling relations appear to flatten, consistent with predictions from Volonteri & Natarajan for massive seed BHs.

STAR FORMATION IN A QUASAR DISK

The saturation level of the magneto-rotational instability (MRI) in a strongly radiation-dominated accretion disk is studied using a new Godunov radiation MHD code in the unstratified shearing box approximation. Since vertical gravity is neglected in this work, our focus is on how the MRI saturates in the optically thick mid-plane of the disk. We confirm that turbulence generated by the MRI is very compressible in the radiation-dominated regime, as found by previous calculations using the flux-limited diffusion approximation. We also find little difference in the saturation properties in calculations that use a larger horizontal domain (up to four times the vertical scale height in the radial direction). However, in strongly radiation pressure dominated disks (one in which the radiation energy density reaches ~1% of the rest mass energy density of the gas), we find that Maxwell stress from the MRI turbulence is larger than the value produced when radiation pressure is replaced with the same amount of gas pressure. At the same time, the ratio between Maxwell stress and Reynolds stress is increased by almost a factor of eight compared with the gas pressure dominated case. We suggest that this effect is caused by radiation drag, which acts like bulk viscosity and changes the effective magnetic Prandtl number of the fluid. Radiation viscosity significantly exceeds both the microscopic plasma viscosity and resistivity, ensuring that radiation-dominated systems occupy the high magnetic Prandtl number regime. Nevertheless, we find that radiative shear viscosity is negligible compared to the Maxwell stress and Reynolds stress in the flow. This may have important implications for the structure of radiation-dominated accretion disks.

A new way to conserve total energy for Eulerian hydrodynamic simulations with self-gravity

The nonlinear regime of Rayleigh-Taylor instability (RTI) in a radiation supported atmosphere, consisting of two uniform fluids with different densities, is studied numerically. We perform simulations using our recently developed numerical algorithm for multi-dimensional radiation hydrodynamics based on a variable Eddington tensor (VET) as implemented in Athena, focusing on the regime where scattering opacity greatly exceeds absorption opacity. We find that the radiation field can reduce the growth and mixing rate of RTI, but this reduction is only significant when radiation pressure significantly exceeds gas pressure. Small-scale structures are also suppressed in this case. In the nonlinear regime, dense fingers sink faster than rarefied bubbles can rise, leading to asymmetric structures about the interface. By comparing the calculations that use a VET versus the Eddington approximation, we demonstrate that anisotropy in the radiation field can affect the nonlinear development of RTI significantly. We also examine the disruption of a shell of cold gas being accelerated by strong radiation pressure, motivated by models of radiation driven outflows in ultraluminous infrared galaxies. We find that when the growth timescale of RTI is smaller than acceleration timescale, the amount of gas that would be pushed away by the radiation field is reduced due to RTI.