arXiv subjects

Yan-Fei Jiang

Publications and source records attributed to Yan-Fei Jiang.

At least 109 records · Page 6Linked to original sources

arXiv2019

One Solution to the Mass Budget Problem for Planet Formation: Optically Thick Disks with Dust Scattering

ALMA surveys have suggested that the dust in Class II disks may not be enough to explain the averaged solid mass in exoplanets, under the assumption that the mm disk continuum emission is optically thin. This optically thin assumption seems to be supported by recent DSHARP observations where the measured optical depths of spatially resolved disks are mostly less than one. However, we point out that dust scattering can considerably reduce the emission from an optically thick region. If that scattering is ignored, the optical depth will be considerably underestimated. An optically thick disk with scattering can be misidentified as an optically thin disk. Dust scattering in more inclined disks can reduce the intensity even further, making the disk look even fainter. The measured optical depth of $\sim$0.6 in several DSHARP disks can be naturally explained by optically thick dust with an albedo of $\sim$0.9 at 1.25 mm. Using the DSHARP opacity, this albedo corresponds to a dust population with the maximum grain size ($s_{max}$) of 0.1-1 mm. For optically thick scattering disks, the measured spectral index $α$ can be either larger or smaller than 2 depending on if the dust albedo increases or decreases with wavelength. Using the DSHARP opacity, $α<2$ corresponds to $s_{max}$ of 0.03-0.3 mm. We describe how this optically thick scattering scenario could explain the observed scaling between submm continuum sizes and luminosities, and might help ease the tension between the dust size constraints from polarization and dust continuum measurements. We suggest that a significant amount of disk mass can be hidden from ALMA observations at short millimeter wavelengths. For compact disks smaller than 30 au, we can easily underestimate the dust mass by more than a factor of 10. Longer wavelength observations (e.g. VLA or SKA) are desired to probe the dust mass in disks.

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arXiv2019

Global Radiation Magneto-hydrodynamic Simulations of Sub-Eddington Accretion Disks around Supermassive Black Holes

We use global three dimensional radiation magneto-hydrodynamic simulations to study the properties of inner regions of accretion disks around a 5\times 10^8 solar mass black hole with mass accretion rates reaching 7% and 20% of the Eddington value. This region of the disk is supported by magnetic pressure with surface density significantly smaller than the values predicted by the standard thin disk model but with a much larger disk scale height. The disks do not show any sign of thermal instability over many thermal time scales. More than half of the accretion is driven by radiation viscosity in the optically thin corona region for the lower accretion rate case, while accretion in the optically thick part of the disk is driven by the Maxwell and Reynolds stresses from MRI turbulence. Coronae with gas temperatures > 10^8 K are generated only in the inner \approx 10 gravitational radii in both simulations, being more compact in the higher accretion rate case. In contrast to the thin disk model, surface density increases with increasing mass accretion rate, which causes less dissipation in the optically thin region and a relatively weaker corona. The simulation results may explain the formation of X-ray coronae in Active Galactic Nuclei (AGNs), the compact size of such coronae, and the observed trend of optical to X-ray luminosity with Eddington ratio for many AGNs.

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arXiv2018

Three Dimensional Radiation Hydrodynamic Simulations of Massive Star Envelopes

(Abridged) Stars more massive than $20-30M_{\odot}$ are so luminous that the radiation force on the cooler, more opaque outer layers can balance or exceed the force of gravity. These near or super-Eddington outer envelopes represent a long standing challenge for calculating the evolution of massive stars in one dimension, a situation that limits our understanding of the stellar progenitors of some of the most exciting and energetic explosions in the universe. In particular, the proximity to the Eddington limit has been the suspected cause for the variability, large mass loss rate and giant eruptions of an enigmatic class of massive stars: the luminous blue variables (LBVs). When in quiescence, LBVs are usually found on the hot ($T_{eff} \approx 2 - 4 \times 10^4$ K) S Dor instability strip. While in outburst, most LBVs stay on the cold S Dor instability strip with a $T_{eff} \approx 9000$ K. Here we show that physically realistic three dimensional global radiation hydrodynamic simulations of radiation dominated massive stars with the largest supercomputers in the world naturally reproduce many observed properties of LBVs, specifically their location in the Hertzsprung-Russell (HR) diagram and their episodic mass loss with rates of $10^{-7}-10^{-5} M_{\odot}/yr$. The helium opacity peak is found to play an important role to determine these properties, which is not realized in the traditional one dimensional models of massive stars. The simulations also predict that convection causes irregular envelope oscillations and 10-30% brightness variations on a typical timescale of a few days. The variability is more prominent in our models that are on the cool part of the S Dor instability. These calculations pave the way to a quantitative understanding of the structure, stability and the dominant mode of mass loss of massive stars.

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arXiv2018

Dusty Cloud Acceleration by Radiation Pressure in Rapidly Star-Forming Galaxies

We perform two-dimensional and three-dimensional radiation hydrodynamic simulations to study cold clouds accelerated by radiation pressure on dust in the environment of rapidly star-forming galaxies dominated by infrared flux. We utilize the reduced speed of light approximation to solve the frequency-averaged, time-dependent radiative transfer equation. We find that radiation pressure is capable of accelerating the clouds to hundreds of kilometers per second while remaining dense and cold, consistent with observations. We compare these results to simulations where acceleration is provided by entrainment in a hot wind, where the momentum injection of the hot flow is comparable to the momentum in the radiation field. We find that the survival time of the cloud accelerated by the radiation field is significantly longer than that of a cloud entrained in a hot outflow. We show that the dynamics of the irradiated cloud depends on the initial optical depth, temperature of the cloud, and the intensity of the flux. Additionally, gas pressure from the background may limit cloud acceleration if the density ratio between the cloud and background is $\lesssim 10^{2}$. In general, a 10 pc-scale optically thin cloud forms a pancake structure elongated perpendicular to the direction of motion, while optically thick clouds form a filamentary structure elongated parallel to the direction of motion. The details of accelerated cloud morphology and geometry can also be affected by other factors, such as the cloud lengthscale, the reduced speed of light approximation, spatial resolution, initial cloud structure, and the dimensionality of the run, but these have relatively little affect on the cloud velocity or survival time.

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arXiv2017

A New Numerical Scheme for Cosmic Ray Transport

Numerical solutions of the cosmic-ray (CR) magneto-hydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad-hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time-step scales linearly with resolution (even when computing CR diffusion), and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR modified shocks, CR driven blast waves, and CR transport in multi-phase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.

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arXiv2017

Super-Eddington Accretion Disks around Supermassive black Holes

We use global three dimensional radiation magneto-hydrodynamical simulations to study accretion disks onto a $5\times 10^8M_{\odot}$ black hole with accretion rates varying from $\sim 250L_{Edd}/c^2$ to $1500 L_{Edd}/c^2$. We form the disks with torus centered at $50-80$ gravitational radii with self-consistent turbulence initially generated by the magneto-rotational instability. We study cases with and without net vertical magnetic flux. The inner regions of all disks have radiation pressure $\sim 10^4-10^6$ times the gas pressure. Non-axisymmetric density waves that steepen into spiral shocks form as gas flows towards the black hole. In simulations without net vertical magnetic flux, Reynolds stress generated by the spiral shocks are the dominant mechanism to transfer angular momentum. Maxwell stress from MRI turbulence can be larger than the Reynolds stress only when net vertical magnetic flux is sufficiently large. Outflows are formed with speed $\sim 0.1-0.4c$. When the accretion rate is smaller than $\sim 500 L_{Edd}/c^2$, outflows start around $10$ gravitational radii and the radiative efficiency is $\sim 5\%-7\%$ with both magnetic field configurations. With accretion rate reaching $1500 L_{Edd}/c^2$, most of the funnel region close to the rotation axis becomes optically thick and the outflow only develops beyond $50$ gravitational radii. The radiative efficiency is reduced to $1\%$. We always find the kinetic energy luminosity associated with the outflow is only $\sim 15\%-30\%$ of the radiative luminosity. The mass flux lost in the outflow is $\sim 15\%-50\%$ of the net mass accretion rates. We discuss implications of our simulation results on the observational properties of these disks.

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arXiv2016

Towards Self-Consistent Modelling of the Sgr A* Accretion Flow: Linking Theory and Observation

The interplay between supermassive black holes (SMBHs) and their environments is believed to command an essential role in galaxy evolution. The majority of these SMBHs are in the radiative inefficient accretion phase where this interplay remains elusive, but suggestively important, due to few observational constraints. To remedy this, we directly fit 2-D hydrodynamic simulations to Chandra observations of Sgr A* with Markov Chain Monte Carlo sampling, self-consistently modelling the 2-D inflow-outflow solution for the first time. We find the temperature and density at flow onset are consistent with the origin of the gas in the stellar winds of massive stars in the vicinity of Sgr A*. We place the first observational constraints on the angular momentum of the gas and estimate the centrifugal radius, r$_c$ $\approx$ 0.056 r$_b$ $\approx8\times10^{-3}$ pc, where r$_b$ is the Bondi radius. Less than 1\% of the inflowing gas accretes onto the SMBH, the remainder being ejected in a polar outflow. For the first time, we decouple the quiescent point-like emission from the spatially extended flow. We find this point-like emission, accounting for $\sim4$\% of the quiescent flux, is spectrally too steep to be explained by unresolved flares, nor Bremsstrahlung, but is likely a combination of a relatively steep synchrotron powerlaw and the high energy tail of inverse-Compton emission. With this self-consistent model of the accretion flow structure, we make predictions for the flow dynamics and discuss how future X-ray spectroscopic observations can further our understanding of the Sgr A* accretion flow.

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arXiv2016

Detection of Time Lags Between Quasar Continuum Emission Bands based on Pan-STARRS Light-curves

We study the time lags between the continuum emission of quasars at different wavelengths, based on more than four years of multi-band ($g$, $r$, $i$, $z$) light-curves in the Pan-STARRS Medium Deep Fields. As photons from different bands emerge from different radial ranges in the accretion disk, the lags constrain the sizes of the accretion disks. We select 240 quasars with redshifts $z \approx 1$ or $z \approx 0.3$ that are relatively emission line free. The light curves are sampled from day to month timescales, which makes it possible to detect lags on the scale of the light crossing time of the accretion disks. With the code JAVELIN, we detect typical lags of several days in the rest frame between the $g$ band and the $riz$ bands. The detected lags are $\sim 2-3$ times larger than the light crossing time estimated from the standard thin disk model, consistent with the recently measured lag in NGC5548 and micro-lensing measurements of quasars. The lags in our sample are found to increase with increasing luminosity. Furthermore, the increase in lags going from $g-r$ to $g-i$ and then to $g-z$ is slower than predicted in the thin disk model, particularly for high luminosity quasars. The radial temperature profile in the disk must be different from what is assumed. We also find evidence that the lags decrease with increasing line ratios between ultraviolet FeII lines and MgII, which may point to changes in the accretion disk structure at higher metallicity.

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arXiv2016

The Effects of Magnetic Fields on the Dynamics of Radiation Pressure Dominated Massive Star Envelopes

We use three dimensional radiation magneto-hydrodynamic simulations to study the effects of magnetic fields on the energy transport and structure of radiation pressure dominated main sequence massive star envelopes at the region of the iron opacity peak. We focus on the regime where the local thermal timescale is shorter than the dynamical timescale, corresponding to inefficient convective energy transport. We begin with initially weak magnetic fields relative to the thermal pressure, from 100-1000G in differing geometries. The unstable density inversion amplifies the magnetic field, increasing the magnetic energy density to values close to equipartition with the turbulent kinetic energy density. By providing pressure support, the magnetic field's presence significantly increases the density fluctuations in the turbulent envelope, thereby enhancing the radiative energy transport by allowing photons to diffuse out through low density regions. Magnetic buoyancy brings small scale magnetic fields to the photosphere and increases the vertical energy transport with the energy advection velocity proportional to the Alfvén velocity, although in all cases we study photon diffusion still dominates the energy transport. The increased radiative and advective energy transport causes the stellar envelope to shrink by several scale heights. We also find larger turbulent velocity fluctuations compared to the purely hydrodynamic case, reaching $\approx$ 100 km/s at the stellar photosphere. The photosphere also shows vertical oscillations with similar averaged velocities and periods of a few hours. The increased turbulent velocity and oscillations will have strong impacts on the line broadening and periodic signals in massive stars.

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arXiv2016

Prompt Radiation and Mass Outflows from the Stream-Stream Collisions of Tidal Disruption Events

Stream-stream collisions play an important role for the circularization of highly eccentric streams resulting from tidal disruption events (TDEs). We perform three dimensional radiation hydrodynamic simulations to show that stream collisions can contribute significant optical and ultraviolet light to the flares produced by TDEs, and can sometimes explain the majority of the observed emission. Our simulations focus on the region near the radiation pressure dominated shock produced by a collision and track how the kinetic energy of the stream is dissipated by the associated shock. When the mass flow rate of the stream $\dot{M}$ is a significant fraction of the Eddington accretion rate, $\gtrsim2\%$ of the initial kinetic energy is converted to radiation directly as a result of the collision. In this regime, the collision redistributes the specific kinetic energy into the downstream gas and more than $16\%$ of the mass can become unbound. The fraction of unbound gas decreases rapidly as $\dot{M}$ drops significantly below the Eddington limit, with no unbound gas being produced when $\dot{M}$ drops to $1\%$ of Eddington; we find however that the radiative efficiency increases slightly to $\lesssim 8\%$ in these low $\dot{M}$ cases. The effective radiation temperature and size of the photosphere is determined by the stream velocity and $\dot{M}$, which we find to be a few times $10^4$~K and $10^{14}$~cm in our calculations, comparable to the inferred values of some TDE candidates. The photosphere size is directly proportional to $\dot{M}$, which can explain the rapidly changing photosphere sizes seen in TDE candidates such as PS1-10jh.

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arXiv2016

Iron Opacity Bump Changes the Stability and Structure of Accretion Disks in Active Galactic Nuclei

Accretion disks around supermassive black holes have regions where the Rosseland mean opacity can be much larger than the electron scattering opacity primarily due to the large number of bound-bound transitions in iron. We study the effects of this iron opacity "bump" on the thermal stability and vertical structure of radiation pressure dominated accretion disks, utilizing three dimensional radiation magneto-hydrodynamic simulations in the local shearing box approximation. The simulations self-consistently calculate the heating due to MHD turbulence caused by magneto-rotational instability and radiative cooling by using the radiative transfer module based on a variable Eddington tensor in Athena. For a $5\times 10^8$ solar mass black hole with $\sim 3\%$ of the Eddington luminosity, a model including the iron opacity bump maintains its structure for more than $10$ thermal times without showing significant signs of thermal runaway. In contrast, if only electron scattering and free-free opacity are included as in the standard thin disk model, the disk collapses on the thermal time scale. The difference is caused by a combination of 1) an anti-correlation between the total optical depth and the temperature, and 2) enhanced vertical advective energy transport. These results suggest that the iron opacity bump may have a strong impact on the stability and structure of AGN accretion disks, and may contribute to a dependence of AGN properties on metallicity. Since this opacity is relevant primarily in UV emitting regions of the flow, it may help to explain discrepancies between observation and theory that are unique to AGNs.

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arXiv2015

Local Radiation Hydrodynamic Simulations of Massive Star Envelopes at the Iron Opacity Peak

We perform three dimensional radiation hydrodynamic simulations of the structure and dynamics of radiation dominated envelopes of massive stars at the location of the iron opacity peak. One dimensional hydrostatic calculations predict an unstable density inversion at this location, whereas our simulations reveal a complex interplay of convective and radiative transport whose behavior depends on the ratio of the photon diffusion time to the dynamical time. The latter is set by the ratio of the optical depth per pressure scale height, $τ_0$, to $τ_c=c/c_g$, where $c_g \approx$ 50 km/s is the isothermal sound speed in the gas alone. When $τ_0 \gg τ_c$, convection reduces the radiation acceleration and removes the density inversion. The turbulent energy transport in the simulations agrees with mixing length theory and provides its first numerical calibration in the radiation dominated regime. When $τ_0 \ll τ_c$, convection becomes inefficient and the turbulent energy transport is negligible. The turbulent velocities exceed $c_g$, driving shocks and large density fluctuations that allow photons to preferentially diffuse out through low-density regions. However, the effective radiation acceleration is still larger than the gravitational acceleration so that the time average density profile contains a modest density inversion. In addition, the simulated envelope undergoes large-scale oscillations with periods of a few hours. The turbulent velocity field may affect the broadening of spectral lines and therefore stellar rotation measurements in massive stars, while the time variable outer atmosphere could lead to variations in their mass loss and stellar radius.

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arXiv2014

A Global Three Dimensional Radiation Magneto-hydrodynamic Simulation of Super-Eddington Accretion Disks

We study super-Eddington accretion flows onto black holes using a global three dimensional radiation magneto-hydrodynamical simulation. We solve the time dependent radiative transfer equation for the specific intensities to accurately calculate the angular distribution of the emitted radiation. Turbulence generated by the magneto-rotational instability provides self-consistent angular momentum transfer. The simulation reaches inflow equilibrium with an accretion rate ~220L_edd/c^2 and forms a radiation driven outflow along the rotation axis. The mechanical energy flux carried by the outflow is ~20% of the radiative energy flux. The total mass flux lost in the outflow is about 29% of the net accretion rate. The radiative luminosity of this flow is ~10L_edd. This yields a radiative efficiency ~4.5%, which is comparable to the value in a standard thin disk model. In our simulation, vertical advection of radiation caused by magnetic buoyancy transports energy faster than photon diffusion, allowing a significant fraction of the photons to escape from the surface of the disk before being advected into the black hole. We contrast our results with the lower radiative efficiencies inferred in most models, such as the slim disk model, which neglect vertical advection. Our inferred radiative efficiencies also exceed published results from previous global numerical simulations, which did not attribute a significant role to vertical advection. We briefly discuss the implications for the growth of supermassive black holes in the early universe and describe how these results provided a basis for explaining the spectrum and population statistics of ultraluminous X-ray sources.

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arXiv2014

An Algorithm for Radiation Magnetohydrodynamics Based on Solving the Time-dependent Transfer Equation

(Abridged) We describe a new algorithm for solving the coupled frequency-integrated transfer equation and the equations of magnetohydrodynamics when the light-crossing time is only marginally shorter than dynamical timescales. The transfer equation is solved in the mixed frame, including velocity dependent source terms accurate to O(v/c). An operator split approach is used to compute the specific intensity along discrete rays, with upwind monotonic interpolation used along each ray to update the transport terms, and implicit methods used to compute the scattering and absorption source terms. Conservative differencing is used for the transport terms, which ensures the specific intensity (as well as energy and momentum) are conserved along each ray to round-off error. The use of implicit methods for the source terms ensures the method is stable even if the source terms are very stiff. To couple the solution of the transfer equation to the MHD algorithms in the Athena code, we perform direct quadrature of the specific intensity over angles to compute the energy and momentum source terms. We present the results of a variety of tests of the method, such as calculating the structure of a non-LTE atmosphere, an advective diffusion test, linear wave convergence tests, and the well-known shadow test. We use new semi-analytic solutions for radiation modified shocks to demonstrate the ability of our algorithm to capture the effects of an anisotropic radiation field accurately. Since the method uses explicit differencing of the spatial operators, it shows excellent weak scaling on parallel computers. The method is ideally suited for problems in which characteristic velocities are non-relativistic, but still within a few percent or more of the speed of light. The method is an intermediate step towards algorithms for fully relativistic flows.

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arXiv2014

Radiation Feedback in ULIRGS: Are Photons Movers and Shakers?

We use our variable Eddington tensor (VET) radiation hydrodynamics code to perform two-dimensional simulations to study the impact of radiation forces on atmospheres composed of dust and gas. Our setup closely follows that of Krumholz & Thompson, assuming that dust and gas are well-coupled and that the radiation field is characterized by blackbodies with temperatures >~ 80 K, as might be found in ultraluminous infrared galaxies. In agreement with previous work, we find that Rayleigh-Taylor instabilities develop in radiation supported atmospheres, leading to inhomogeneities that limit momentum exchange between radiation and dusty gas, and eventually providing a near balance of the radiation and gravitational forces. However, the evolution of the velocity and spatial distributions of the gas differs significantly from previous work, which utilized a less accurate flux-limited diffusion (FLD) method. Our VET simulations show continuous net acceleration of the gas, with no steady-state reached by the end of the simulation. In contrast, FLD results show little net acceleration of the gas and settle in to a quasi-steady, turbulent state with low velocity dispersion. The discrepancies result primarily from the inability of FLD to properly model the variation of the radiation field around structures that are less than a few optical depths across. We conclude that radiation feedback remains a viable mechanism for driving high-Mach number turbulence. We discuss implications for observed systems and global numerical simulations of feedback, but more realistic setups are needed to make robust observational predictions and assess the prospect of launching outflows with radiation.

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arXiv2014

Radiation Magneto-hydrodynamic Simulations of the Formation of Hot Accretion Disk Coronae

A new mechanism to form a magnetic pressure supported, high temperature corona above the photosphere of an accretion disk is explored using three dimensional radiation magneto-hydrodynamic (MHD) simulations. The thermal properties of the disk are calculated self-consistently by balancing radiative cooling through the surfaces of the disk with heating due to dissipation of turbulence driven by magneto-rotational instability (MRI). As has been noted in previous work, we find the dissipation rate per unit mass increases dramatically with height above the mid-plane, in stark contrast to the alpha-disk model which assumes this quantity is a constant. Thus, we find that in simulations with a low surface density (and therefore a shallow photosphere), the fraction of energy dissipated above the photosphere is significant (about 3.4% in our lowest surface density model), and this fraction increases as surface density decreases. When a significant fraction of the accretion energy is dissipated in the optically thin photosphere, the gas temperature increases substantially and a high temperature, magnetic pressure supported corona is formed. The volume-averaged temperature in the disk corona is more than 10 times larger than at the disk mid-plane. Moreover, gas temperature in the corona is strongly anti-correlated with gas density, which implies the corona formed by MRI turbulence is patchy. This mechanism to form an accretion disk corona may help explain the observed relation between the spectral index and luminosity from AGNs, and the soft X-ray excess from some AGNs. It may also be relevant to spectral state changes in X-ray binaries.

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arXiv2013

The effects of irradiation on the cloud evolution in active galactic nuclei

We report on the first phase of our study of cloud irradiation. We study irradiation by means of numerical, two-dimensional time-dependent radiation-hydrodynamic simulations of a cloud irradiated by a strong radiation. We adopt a very simple treatment of the opacity, neglect photoionization and gravity, and instead focus on assessing the role of the type and magnitude of the opacity on the cloud evolution. Our main result is that even relatively dense clouds that are radiatively heated (i.e., with significant absorption opacity) do not move as a whole instead they undergo a very rapid and major evolution in its shape, size and physical properties. In particular, the cloud and its remnants become optical thin within less than one sound crossing time and before they can travel over a significant distance (a distance of a few radii of the initial cloud). We also found that a cloud can be accelerated as a whole under quite extreme conditions, e.g., the opacity must be dominated by scattering. However, the acceleration due to the radiation force is relatively small and unless the cloud is optically thin the cloud quickly changes its size and shape. We discuss implications for the modelling and interpetation broad line regions of active galactic nuclei.

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arXiv2013

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 dissipation of MHD turbulence driven by the 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 is at least one pressure scale height, fluctuations associated with MRI turbulence and dynamo action in the disk eventually trigger a thermal runaway which 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 alpha 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.

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