Supercritical Accretion Flows Research Articles

Phase-dependent Spectral Shape Changes in the Ultraluminous X-Ray Pulsar NGC 5907 ULX1

The discovery of coherent pulsations from several ultraluminous X-ray pulsars (ULXPs) has provided direct evidence of a supercritical accretion flow. However, the geometrical structure of such an accretion flow onto the central neutron star remains poorly understood. NGC 5907 ULX1 is one of the most luminous ULXPs, with a luminosity exceeding 1041 erg s−1. Here we present a broadband X-ray study of this ULXP using the data from simultaneous observations with XMM-Newton and NuSTAR conducted in 2014 July. The phase-resolved spectra are well reproduced by a model consisting of a multicolor disk blackbody emission with a temperature gradient of p = 0.5 (T ∝ r −p ) and a power law with an exponential cutoff. The disk component is phase-invariant and has an innermost temperature of ∼ 0.3 keV. Its normalization suggests a relatively low inclination angle of the disk, in contrast to the previous claims in other literature. The power-law component, attributed to the emission from the accretion flow inside the magnetosphere of the neutron star, indicates phase-dependent spectral shape changes; the spectrum is slightly harder in the pre-peak phase than in the post-peak phase. This implies that the magnetosphere has an asymmetric geometry around the magnetic axis and that hotter regions close to the magnetic pole become visible before the pulse peak.

Pulsed fraction of super-critical column accretion flows on to neutron stars: Modeling of ultraluminous X-ray pulsars

Abstract We calculate the pulsed fraction (PF) of the super-critical column accretion flows on to magnetized neutron stars (NSs), of which the magnetic axis is misaligned with the rotation axis, based on the simulation results by Kawashima et al. (2016, PASJ, 68, 83). Here, we solve the geodesic equation for light in the Schwarzschild spacetime in order to take into account the light-bending effect. The gravitational redshift and the relativistic Doppler effect from gas motions of the accretion columns are also incorporated. The pulsed emission appears since the observed luminosity, which exceeds the Eddington luminosity for the stellar-mass black holes, periodically changes via precession of the column caused by the rotation of the NS. The PF tends to increase as $\theta _{\rm obs}$ approaches to $\theta _{\rm B}$, where $\theta _{\rm obs}$ and $\theta _{\rm B}$ are the observer’s viewing angle and the polar angle of the magnetic axis measured from the rotation axis, respectively. The maximum PF is around 50%. Also, we find that the PF becomes less than 5% for $\theta _{\rm obs} \lesssim 5^\circ$ or for $\theta _{\rm B} \lesssim 5^\circ$. Our results are consistent with observations of ultraluminous X-ray pulsars (ULXPs) with few exceptions, since the ULXPs mostly exhibit the PF of $\lesssim 50$%. Our present study supports the hypothesis that the ULXPs are powered by the super-critical column accretion on to NSs.

Two-dimensional Inflow–Outflow Solution of Supercritical Accretion Flow

Abstract We present the two-dimensional inflow–outflow solutions of radiation hydrodynamic equations of supercritical accretion flows. Compared with prior studies, we include all components of the viscous stress tensor. We assume steady-state flow and use self-similar solutions in the radial direction to solve the equations in the r–θ domain of spherical coordinates. The set of differential equations have been integrated from the rotation axis to the equatorial plane. We find that the self-similarity assumption requires that the radial profile of density is described by ρ(r) ∝ r −0.5. Correspondingly, the radial profile of the mass inflow rate decreases with decreasing radius as . An inflow–outflow structure has been found in our solution. Inflow exists in the region θ > 65°, while above that the flow moves outward and outflow could launch. The driving forces of the outflow are analyzed and it is found that the radiation force is dominant and pushes the gas particles outward with poloidal velocity ∼0.25c. The properties of the outflow are also studied. The results show that the mass flux-weighted angular momentum of the inflow is lower than that of the outflow, thus the angular momentum of the flow can be transported by the outflow. We also analyze the convective stability of the supercritical disk and find that in the absence of a magnetic field, the flow is convectively unstable. Our analytical results are fully consistent with the previous numerical simulations of supercritical accretion flow.

Three-dimensional structure of clumpy outflow from supercritical accretion flow onto black holes

Abstract We perform global three-dimensional (3D) radiation-hydrodynamic (RHD) simulations of outflow from supercritical accretion flow around a 10 M⊙ black hole. We only solve the outflow part, starting from the axisymmetric 2D simulation data in a nearly steady state but with small perturbations in a sinusoidal form being added in the azimuthal direction. The mass accretion rate onto the black hole is ∼102LE/c2 in the underlying 2D simulation data, and the outflow rate is ∼10 LE/c2 (with LE and c being the Eddington luminosity and speed of light, respectively). We first confirm the emergence of clumpy outflow, which was discovered by the 2D RHD simulations, above the photosphere located at a few hundreds of Schwarzschild radii (rS) from the central black hole. As prominent 3D features we find that the clumps have the shape of a torn sheet, rather than a cut string, and that they are rotating around the central black hole with a sub-Keplerian velocity at a distance of ∼103 rS from the center. The typical clump size is ∼30 rS or less in the radial direction, and is more elongated in the angular directions, ∼ hundreds of rS at most. The sheet separation ranges from 50 to 150 rS. We expect stochastic time variations when clumps pass across the line of the sight of a distant observer. Variation timescales are estimated to be several seconds for a black hole with mass of ten to several tens of M⊙, in rough agreement with the observations of some ultra-luminous X-ray sources.

General Relativistic Radiation MHD Simulations of Supercritical Accretion onto a Magnetized Neutron Star: Modeling of Ultraluminous X-Ray Pulsars

Abstract By performing 2.5-dimensional general relativistic radiation magnetohydrodynamic simulations, we demonstrate supercritical accretion onto a non-rotating, magnetized neutron star, where the magnetic field strength of dipole fields is 1010 G on the star surface. We found the supercritical accretion flow consists of two parts: the accretion columns and the truncated accretion disk. The supercritical accretion disk, which appears far from the neutron star, is truncated at around ≃3 R * (R * = 106 cm is the neutron star radius), where the magnetic pressure via the dipole magnetic fields balances with the radiation pressure of the disks. The angular momentum of the disk around the truncation radius is effectively transported inward through magnetic torque by dipole fields, inducing the spin up of a neutron star. The evaluated spin-up rate, ∼−10−11 s s−1, is consistent with the recent observations of the ultraluminous X-ray pulsars. Within the truncation radius, the gas falls onto a neutron star along the dipole fields, which results in a formation of accretion columns onto the northern and southern hemispheres. The net accretion rate and the luminosity of the column are ≃66 L Edd/c 2 and ≲10 L Edd, where L Edd is the Eddington luminosity and c is the light speed. Our simulations support a hypothesis whereby the ultraluminous X-ray pulsars are powered by the supercritical accretion onto the magnetized neutron stars.

The influence of large-scale magnetic field in the structure of supercritical accretion flow with outflow

We present the effects of ordered large-scale magnetic field on the structure of supercritical accretion flow in the presence of an outflow. In the cylindrical coordinates (r, φ, z), we write the 1.5-dimensional, steady-state (⁠|$\frac{\partial }{\partial t}= 0$|⁠) and axisymmetric (⁠|$\frac{\partial }{\partial \varphi }= 0$|⁠) inflow–outflow equations by using self-similar solutions. Also, a model for radiation pressure supported accretion flow threaded by both toroidal and vertical components of magnetic field has been formulated. For studying the outflows, we adopt a radius-dependent mass accretion rate as |$\dot{M}=\dot{M}_{{\rm out}}{(\frac{r}{r_{{\rm out}}})^{s+\frac{1}{2}}}$| with |$s = \frac{1}{2}$|⁠. Also, by following the previous works, we have considered the interchange of mass, radial and angular momentum and the energy between inflow and outflow. We have found numerically that two components of magnetic field have the opposite effects on the thickness of the disc and similar effects on the radial and angular velocities of the flow. We have found that the existence of the toroidal component of magnetic field will lead to an increase in the radial and azimuthal velocities as well as the relative thickness of the disc. Moreover, in a magnetized flow, the thickness of the disc decreases with increase in the vertical component of magnetic field. The solutions indicated that the mass inflow rate and the specific energy of outflow strongly affect the advection parameter. We have shown that by increasing the two components of magnetic field, the temperature of the accretion flow decreases significantly. On the other hand, we have shown that the bolometric luminosity of the slim discs for high values of |$\dot{m} (\dot{m}>>1)$||$\dot{m}\,(\dot{m}\gg 1)$| is not sensitive to mass accretion rate and is kept constant (L ≈ 10LE).

A radiation-hydrodynamics model of accretion columns for ultra-luminous X-ray pulsars

Abstract Prompted by the recent discovery of pulsed emission from an ultra-luminous X-ray source, M 82 X-2 (“ULX-pulsar”), we perform a two-dimensional radiation-hydrodynamics simulation of a supercritical accretion flow onto a neutron star through a narrow accretion column. We set an accretion column with a cone shape filled with tenuous gas with the density of 10−4 g cm−3 above a neutron star and solve the two-dimensional gas motion and radiative transfer within the column. The side boundaries are set such that radiation can freely escape, but gas cannot. Since the initial gas layer is not in a hydrostatic balance, the column gas falls onto the neutron-star surface, and thereby a shock is generated. As a result, the accretion column is composed of two regions: an upper, nearly free-fall region and a lower settling region, as noted by Basko and Sunyaev (1976, MNRAS, 175, 395). The average accretion rate is very high; ${\skew{5}\dot{M}}\sim 10^{2{--}3} L_{\rm E}/c^{2}$ (with LE being the Eddington luminosity), and so radiation energy dominates over gas internal energy entirely within the column. Despite the high accretion rate, the radiation flux in the laboratory frame is kept barely below LE/(4πr2) at a distance r in the settling region so that matter can slowly accrete. This adjustment is made possible, since a large amount of photons produced via dissipation of kinetic energy of matter can escape through the side boundaries. The total luminosity can greatly exceed LE by several orders of magnitude, whereas the apparent luminosity observed from the top of the column is much less. Due to such highly anisotropic radiation fields, the observed flux should exhibit periodic variations with the rotation period, provided that the rotation and magnetic axes are misaligned.

THE INFLUENCE OF OUTFLOW IN SUPERCRITICAL ACCRETION FLOWS

ABSTRACT We solve the radiation-hydrodynamic equations of supercritical accretion flows in the presence of radiation force and outflow by using self-similar solutions. Similar to the pioneering works, in this paper we consider a power-law function for mass inflow rate as . We found that s = 1 when the radiative cooling term is included in the energy equation. Correspondingly, the effective temperature profile with respect to the radius was obtained as . In addition, we investigated the influence of the outflow on the dynamics of the accretion flow. We also calculated the continuum spectrum emitted from the disk surface as well as the bolometric luminosity of the accretion flow. Furthermore, our results show that the advection parameter, f, depends strongly on mass inflow rate.

Growing massive black holes through supercritical accretion of stellar-mass seeds

The rapid assembly of the massive black holes that power the luminous quasars observed at $z \sim 6-7$ remains a puzzle. Various direct collapse models have been proposed to head-start black hole growth from initial seeds with masses $\sim 10^5\,\rm M_\odot$, which can then reach a billion solar mass while accreting at the Eddington limit. Here we propose an alternative scenario based on radiatively inefficient super-critical accretion of stellar-mass holes embedded in the gaseous circum-nuclear discs (CNDs) expected to exist in the cores of high redshift galaxies. Our sub-pc resolution hydrodynamical simulations show that stellar-mass holes orbiting within the central 100 pc of the CND bind to very high density gas clumps that arise from the fragmentation of the surrounding gas. Owing to the large reservoir of dense cold gas available, a stellar-mass black hole allowed to grow at super-Eddington rates according to the "slim disc" solution can increase its mass by 3 orders of magnitudes within a few million years. These findings are supported by simulations run with two different hydro codes, RAMSES based on the Adaptive Mesh Refinement technique and GIZMO based on a new Lagrangian Godunov-type method, and with similar, but not identical, sub-grid recipes for star formation, supernova feedback, black hole accretion and feedback. The low radiative efficiency of super-critical accretion flows are instrumental to the rapid mass growth of our black holes, as they imply modest radiative heating of the surrounding nuclear environment.

COMPARISON BETWEEN RHD SIMULATION OF SUPERCRITICAL ACCRETION FLOWS AND A STEADY MODEL WITH OUTFLOWS

We apply our two-dimensional (2D), radially self-similar steady-state accretion flow model to the analysis of hydrodynamic simulation results of supercritical accretion flows. Self-similarity is checked and the input parameters for the model calculation, such as advective factor and heat capacity ratio, are obtained from time-averaged simulation data. Solutions of the model are then calculated and compared with the simulation results. We find that in the converged region of the simulation, excluding the part too close to the black hole, the radial distribution of azimuthal velocity $v_\phi$, density $\rho$ and pressure $p$ basically follows the self-similar assumptions, i.e. they are roughly proportional to $r^{-0.5}$, $r^{-n}$, and $r^{-(n+1)}$, respectively, where $n\sim0.85$ for the mass injection rate of $1000L_\mathrm{E}/c^2$, and $n\sim0.74$ for $3000L_\mathrm{E}/c^2$. The distribution of $v_r$ and $v_\theta$ agrees less with self-similarity, possibly due to convective motions in the $r\theta$ plane. The distribution of velocity, density and pressure in $\theta$ direction obtained by the steady model agrees well with the simulation results {within the calculation boundary of the steady model}. Outward mass flux in the simulations is overall directed toward polar angle of 0.8382 rad ($\sim 48.0^\circ$) for $1000L_\mathrm{E}/c^2$, and 0.7852 rad ($\sim 43.4^\circ$) for $3000L_\mathrm{E}/c^2$, and $\sim$94\% of the mass inflow are driven away as outflow, while outward momentum and energy fluxes are focused around the polar axis. Part of these fluxes lie in the region that are not calculated by the steady model, and special attention should be paid when the model is applied.

Radiation hydrodynamics simulations of wide-angle outflows from super-critical accretion disks around black holes

Abstract By performing two-dimensional radiation hydrodynamics simulations with a large computational domain of 5000 times the Schwarzschild radius, we revealed that wide-angle outflow is launched via the radiation force from the super-critical accretion flows around black holes. The angular size of the outflow, where the radial velocity (vr) exceeds the escape velocity (vesc), increases with an increase of the distance from the black hole. As a result, the mass is blown away with speed of vr > vesc in all directions except for in the vicinity of the equatorial plane, θ = 0°–85°, where θ is the polar angle. The mass ejected from the outer boundary per unit time by the outflow is larger than the mass accretion rate onto the black hole, ∼ 150 LEdd/c2, where LEdd and c are the Eddington luminosity and the speed of light. The kinetic power of such wide-angle high-velocity outflow is comparable to the photon luminosity and is a few times larger than the Eddington luminosity. This corresponds to ∼ 1039–1040 erg s−1 for the stellar mass black holes. Our model is consistent with the observations of shock excited bubbles observed in some ultra-luminous X-ray sources (ULXs), supporting a hypothesis that ULXs are powered by the super-critical accretion onto stellar mass black holes.

Radiation hydrodynamic instability in a plane-parallel, super-Eddington atmosphere: A mechanism for clump formation

Abstract In order to understand the physical processes underlying clump formation in outflow from supercritical accretion flow, we perform two-dimensional radiation hydrodynamic (RHD) simulations. We focus our discussion on the nature of RHD instability in a marginally optically thick, plane–parallel, super-Eddington atmosphere. Initially we set a two-layered atmosphere with a density contrast of 100 exposed to strong, upward continuum-radiation force; the lower layer is denser than the upper one, the condition for RHD instability. We assume non-zero but negligible gravitational force, compared with the radiation force. We find that short-wavelength perturbations grow first, followed by the growth of longer-wavelength patterns, which lead to the formation of clumpy structure. The typical size of clumps (clouds) corresponds to about one optical depth. An anti-correlation between the radiation pressure and the gas pressure is confirmed: this anti-correlation provides a damping mechanism for perturbations of longer wavelength than the typical clump size. Matter and radiation energy densities are correlated. These features are exactly what we found in the radiation-magnetohydrodynamic (radiation-MHD) simulations of supercritical outflow.

Numerical simulations of super-critical black hole accretion flows in general relativity

A new general relativistic radiation magnetohydrodynamical code KORAL, is described, which employs the M1 scheme to close the radiation moment equations. The code has been successfully verified against a number of tests. Axisymmetric simulations of super-critical magnetized accretion on a non-rotating black hole (a=0.0) and a spinning black hole (a=0.9) are presented. The accretion rates in the two models are \dot M = 100-200 \dot M_Edd. These first general relativistic simulations of super-critical black hole accretion are potentially relevant to tidal disruption events and hyper-accreting supermassive black holes in the early universe. Both simulated models are optically and geometrically thick, and have funnels through which energy escapes in the form of relativistic gas, Poynting flux and radiative flux. The jet is significantly more powerful in the a=0.9 run. The net energy outflow rate in the two runs correspond to efficiencies of 5% (a=0) and 33% (a=0.9), as measured with respect to the mass accretion rate at the black hole. These efficiencies agree well with those measured in previous simulations of non-radiative geometrically thick disks. Furthermore, in the a=0.9 run, the outflow power appears to originate in the spinning black hole, suggesting that the associated physics is again similar in non-radiative and super-critical accretion flows. While the two simulations are efficient in terms of total energy outflow, both runs are radiatively inefficient. Their luminosities are only \sim 1-10 L_Edd, which corresponds to a radiative efficiency \sim 0.1%. Interestingly, most of the radiative luminosity emerges through the funnels, which subtend a very small solid angle. Therefore, measured in terms of a local radiative flux, the emitted radiation is highly super-Eddington.

Outflow Launching Mechanisms

Outflow from accretion flow seems to be quite general features of accretion processes. A number of launching mechanisms are known for accretion flow onto black holes: thermal wind, (continuum and line) radiation-pressure driven wind, and magnetically driven wind. To investigate the physics of outflow it is essential first to build good models for underlying accretion flow. Historically, various accretion disk models have been constructed under radially one-zone approximations, but they are not appropriate for exploring the outflow mechanisms, since the multi-dimensional motion of gas in accretion flow, including outflows, is totally neglected. Another limitation comes from that the disk viscosity, the most important ingredient, is described by the phenomenological α-viscosity model. We, here, elucidate the theory of accretion flow and associated outflow based on global, two-dimensional radiation-magnetohydrodynamic (radiation MHD) simulations, not relying on the α-viscosity prescription. We have succeeded in producing three distinct states of accretion flow by controlling only one parameter, a density normalization, and confirmed the occurrence of ubiquitous outflow from all the three states of accretion flow: supercritical, standard, and low-luminosity states. Especially strong outflow is confirmed from the supercritical and low-luminosity accretion flow. Several noteworthy features of the supercritical (or super-Eddington) accretion flows are found; that is, relativistic, collimated outflows (jets), and low-velocity, uncollimated outflows with clumpy structure.

Clumpy Outflows from Supercritical Accretion Flow

Abstract A significant amount of matter in supercritical (or super-Eddington) accretion flow is blown away by radiation force, thus forming outflows; however, the properties of such radiation-driven outflows have been poorly understood. We have performed global two-dimensional radiaion-magnetohydrodynamic simulations of supercritical accretion flow onto a black hole with 10 or 10$^{8} M_{\odot}$ in a large simulation box of 514 $r_{\rm S} \times 514 r_{\rm S}$ (with $r_{\rm S}$ being the Schwarzschild radius). We confirm that uncollimated outflows with velocities of 10 percent of the speed of light emerge from the innermost part of the accretion flow at a wide angle of 10$^{\circ}$ –50$^{\circ}$ from the disk rotation axis. Importantly, the outflows exhibit clumpy structures above heights of $\sim 250 r_{\rm S}$. The typical size of the clumps is $\sim 10 r_{\rm S}$, which corresponds to one optical depth, and their shapes are slightly elongated along the outflow direction. Since clumps start to form in the layer above which the (upward) radiation is superior in force to the (downward) gravity, the Rayleigh–Taylor instability seems to be a primary cause. In addition, a radiation-hydrodynamic instability, which arises when radiation funnels through a radiation-pressure-supported atmosphere, may also help to form clumps of one optical depth. A magnetic photon bubble instability does not seem to be essential, since a similar clumpy outflow structure is obtained in nonmagnetic radiation-hydrodynamic simulations. Since the spatial covering factor of the clumps is estimated to be $\sim$ 0.3, and since they are marginally optically thick, they will explain at least some of the rapid light variations of active galactic nuclei. We further discuss a possibility of producing broad-line region clouds by the clumpy outflow.

COMPTONIZED PHOTON SPECTRA OF SUPERCRITICAL BLACK HOLE ACCRETION FLOWS WITH APPLICATION TO ULTRALUMINOUS X-RAY SOURCES

Radiation spectra of supercritical black hole accretion flows are computed using a Monte Carlo method by post-processing the results of axisymmetric radiation hydrodynamic simulations. We take into account thermal/bulk Comptonization, free-free absorption, and photon trapping. We found that a shock-heated region (~108 K) appears at the funnel wall near the black hole where the supersonic inflow is reflected by the centrifugal barrier of the potential. Both thermal and bulk Comptonization significantly harden photon spectra although most of the photons upscattered above 40 keV are swallowed by the black hole due to the photon trapping. When the accretion rate onto the black hole is 200L E/c 2, where L E is the Eddington luminosity, the spectrum has a power-law component which extends up to ~10 keV by upscattering of photons in the shock-heated region. In higher mass accretion rates, the spectra roll over around 5 keV due to downscattering of the photons by cool electrons in the dense outflow surrounding the jet. Our results are consistent with the spectral features of ultraluminous X-ray sources, which typically show either a hard power-law component extending up to 10 keV or a rollover around 5 keV. We found that the spectrum of NGC 1313 X-2 is quite similar to the spectrum numerically obtained for high accretion rate () source observed with low viewing angle (i = 10°-20°). Our numerical results also demonstrate that the face-on luminosity of supercritically accreting stellar mass black holes (10 M ☉) can significantly exceed 1040 erg s–1.

Disk modelling by radiation-magnetohydrodynamic simulations

Historically, various accretion models have been discussed under radially one-zone approximations. In such one-zone models, however, dynamical aspects of the accretion flow, such as internal circulation and outflows, have been totally neglected. Further, the disk viscosity is usually described by the phenomenological α-viscosity model. We, here, elucidate the theory of accretion flows and outflows based on our global, two-dimensional radiation-magnetohydrodynamic simulations, not relying on the α model. We have succeeded in producing three distinct states of accretion flow by controling only one parameter, a density normalization. Of particular importance is the presence of outflows in all three states. Several noteworthy features of the supercritical (or super-Eddington) accretion flows are found; that is, relativistic, collimated outflows (jets), and low-velocity, uncollimated outflows with clumpy structure. Observational implications are briefly discussed.

Spinning up black holes with super-critical accretion flows

We study the process of spinning up black holes by accretion from slim disks in a wide range of accretion rates. We show that for super-Eddington accretion rates and low values of the viscosity parameter alpha (\lesssim 0.01) the limiting value of the dimensionless spin parameter a_* can reach values higher than a_*=0.9978 inferred by Thorne (1974) in his seminal study. For \mdot=10\mdot_{Edd} and alpha=0.01 spin equilibrium is reached at a_*=0.9994. We show that the equilibrium spin value depends strongly on the assumed value of alpha. We also prove that for high accretion rates the impact of captured radiation on spin evolution is negligible.

Supercritical accretion and ULXs

AbstractSupercritical (or super‐Eddington) accretion seems to occur in various black hole objects, including microquasars and ultra‐luminous X‐ray sources. We, here, elucidate the theory of supercritical accretion flow based on our two‐dimensional (2‐D) global radiation‐hydrodynamic (RHD) and radiation‐magnetohydrodynamic (RMHD) simulations. We first confirm that there is practically no limit to the accretion rate onto black holes. We then discuss several noteworthy observable features of the supercritical flow; that is, mild beaming, relativistic, collimated outflow, and inverse‐Compton scattering spectra by optically thick outflow. For face‐on observers the maximum apparent (isotropic) luminosities of ∼22LE (with L E being the Eddington luminosity) can be achieved for the mass supply rate of ∼50LE/c2. Even larger isotropic luminosities are possible for higher mass supply rates. For edge‐on observers, conversely, the apparent luminosity will be much less. It will be even lower, if the the innermost bright part of the disk is obscured by the outer part. High velocity (>0.5c) jet accelerated by radiation‐pressure force and collimated by Lorentz force is also expected. We expect large kinetic luminosity, ∼0.1LE, and high mass outflow rate, ∼10LE/c2. This may account for large ionizing nebulae around ULXs (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modified Slim-Disk Model Based on Radiation-Hydrodynamic Simulation Data: The Conflict between Outflow and Photon Trapping

Abstract Photon trapping and outflow are two key physics issues associated with supercritical accretion flow. We investigated the conflict between these two processes based on two-dimensional radiation-hydrodynamic (RHD) simulation data, and constructed a simplified (radially) one-dimensional model. Mass loss due to outflow, which is not considered in the slim-disk model, reduces the surface density of the flow, and if very significantly, it can totally suppress the photon-trapping effects. If photon trapping is very significant, conversely, outflow can be suppressed because the radiation-pressure force is reduced. To see what actually occurs, we examined the RHD simulation data and evaluated the accretion and outflow rates as functions of the radius. We have found that the accretion rate monotonically decreases, while the outflow rate increases, as the radius decreases. However, the accretion remains constant at small radii, inside several Schwarzschild radii, since the outflow is suppressed by photon trapping effects. To understand the conflict between the photon trapping and outflow in a simpler way, we modeled the radial distribution of the accretion rate from our simulation data, and built up a new (radially) one-dimensional model, which is similar to the slim-disk model, but incorporates mass loss effects due to the outflow. We find that the surface density (and, hence, the optical depth) is greatly reduced even inside the trapping radius, compared to the case without outflow, whereas the effective temperature distribution hardly changes. That is, the emergent spectra do not sensitively depend on the amount of mass outflow. We conclude that the slim-disk approach is valid for interpreting observations, even if the outflow is taken into account. The observational implications of our findings are briefly discussed in relation to ultra-luminous X-ray sources.