Feng Yuan

Xiamen University, Amoy, Fujian, China

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Publications (109)463.9 Total impact

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    Xue-Ning Bai · Jiani Ye · Jeremy Goodman · Feng Yuan
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    ABSTRACT: Global evolution and dispersal of protoplanetary disks (PPDs) is governed by disk angular momentum transport and mass-loss processes. Recent numerical studies suggest that angular momentum transport in the inner region of PPDs is largely driven by magnetized disk wind, yet the wind mass-loss rate remains unconstrained. On the other hand, disk mass loss has conventionally been attributed to photoevaporation, where external heating on the disk surface drives a thermal wind. We unify the two scenarios by developing a 1D model of magnetized disk winds with a simple treatment of thermodynamics as a proxy for external heating. The wind properties largely depend on 1) the magnetic field strength at the wind base, characterized by the poloidal Alfv\'en speed $v_{Ap}$, 2) the sound speed $c_s$ near the wind base, and 3) how rapidly poloidal field lines diverge (achieve $R^{-2}$ scaling). When $v_{Ap}\gg c_s$, corotation is enforced near the wind base, resulting in centrifugal acceleration. Otherwise, the wind is accelerated mainly by the pressure of the toroidal magnetic field. In both cases, the dominant role played by magnetic forces likely yields wind outflow rates that well exceed purely hydrodynamical mechanisms. For typical PPD accretion-rate and wind-launching conditions, we expect $v_{Ap}$ to be comparable to $c_s$ at the wind base. The resulting wind is heavily loaded, with total wind mass loss rate likely reaching a considerable fraction of wind-driven accretion rate. Implications for modeling global disk evolution and planet formation are also discussed.
    Preview · Article · Nov 2015
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    Amin Mosallanezhad · De-Fu Bu · Feng Yuan
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    ABSTRACT: We solve the two-dimensional magnetohydrodynamic (MHD) equations of black hole accretion with the presence of magnetic field. The field includes a turbulent component, whose role is represented by the viscosity, and a large-scale ordered component. The latter is further assumed to be evenly symmetric with the equatorial plane. The equations are solved in the r − θ plane of a spherical coordinate by assuming time-steady and radially self-similar. An inflow-wind solution is found. Around the equatorial plane, the gas is inflowing; while above and below the equatorial plane at a certain critical θ angle, θ ∼ 47°, the inflow changes its direction of radial motion and becomes wind. The driving forces are analysed and found to be the centrifugal force and the gradient of gas and magnetic pressure. The properties of wind are also calculated. The specific angular momentum of wind is found to be significantly larger than that of inflow, thus wind can transfer angular momentum outward. These analytical results are compared to those obtained by the trajectory analysis based on MHD numerical simulation data and good agreements are found.
    Preview · Article · Nov 2015 · Monthly Notices of the Royal Astronomical Society
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    ABSTRACT: In previous works, it has been shown that strong winds exist in hot accretion flows around black holes. Those works focus only on the region close to the black hole thus it is unknown whether or where the wind production stops at large radii. In this paper, we investigate this problem based on hydrodynamical numerical simulations. For this aim, we have taken into account the gravity of both the central black hole and the nuclear star clusters. When calculating the latter, we assume that the velocity dispersion of stars is a constant and the gravitational potential of the nuclear star cluster $\propto \sigma^2 \ln (r)$, where $\sigma$ is the velocity dispersion of stars and $r$ is the distance from the center of the galaxy. Different from previous works, we focus on the region where the gravitational potential is dominated by the star cluster. We find that, same as the accretion flow at small radii, the mass inflow rate decreases inward and the flow is convectively unstable. However, trajectory analysis has shown that there is very few wind launched from the accretion flow. Our result, combined with the results of Yuan et al. (2015), indicates that the mass flux of wind launched from hot accretion flow is described by $\dot{M}_{\rm wind}=\dot{M}_{\rm BH}(r/20r_s)$, with $r\la R_A\equiv GM_{\rm BH}/\sigma^2$. Here $\dot{M}_{\rm BH}$ is the mass accretion rate at the black hole horizon. The value of $R_A$ is similar to the Bondi radius. We argue that the inward decrease of inflow rate is not because of the mass loss via strong wind, but because of the convective motion. The disappearance of wind outside of $R_A$ must be because of the change of the gravitational potential, but the exact reason remains to be probed.
    No preview · Article · Oct 2015
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    Full-text · Article · Sep 2015
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    Fu-Guo Xie · Feng Yuan
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    ABSTRACT: Two types of correlations between the radio and X-ray luminosities (LR and LX) have been found in black hole X-ray binaries. For some sources, they follow the ‘original’ type of correlation which is described by a single power law. Later it was found that some other sources follow a different correlation consisting of three power-law branches, with each branch having different power-law indexes. In this work, we explain these two types of correlation under the coupled accretion–jet model. We attribute the difference between these two types of sources to the different value of viscosity parameter α. One possible reason for different α is the different configuration of magnetic field in the accretion material coming from the companion stars. For the ‘single power-law’ sources, their α is high; so their accretion is always in the mode of advection-dominated accretion flow (ADAF) for the whole range of X-ray luminosity. For those ‘hybrid power-law’ sources, the value of α is small so their accretion mode changes from an ADAF to a luminous hot accretion flow, and eventually to two-phase accretion as the accretion rate increases. Because the dependence of radiative efficiency on the mass accretion rate is different for these three accretion modes, different power-law indexes in the LR–LX correlation are expected. Constraints on the ratio of the mass-loss rate into the jet and the mass accretion rate in the accretion flow are obtained, which can be tested in future by radiative magnetohydrodynamic numerical simulations of jet formation.
    Preview · Article · Sep 2015 · Monthly Notices of the Royal Astronomical Society
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    ABSTRACT: X-ray flares have routinely been observed from the supermassive black hole, Sgr A*, at our Galactic center. The nature of these flares remains largely unclear, despite of many theoretical models,. In this paper, we study the statistical properties of the Sgr A* X-ray flares, by fitting the count rate (CR) distribution and the structure function (SF) of the light curve with a Markov Chain Monte Carlo (MCMC) method. With the 3 million second \textit{Chandra} observations accumulated in the Sgr A* X-ray Visionary Project, we construct the theoretical light curves through Monte Carlo simulations. We find that the $2-8$ keV X-ray light curve can be decomposed into a quiescent component with a constant count rate of $ 6\times10^{-3} $count s$^{-1}$ and a flare component with a power-law fluence distribution $dN/dE\propto E^{-\alpha_{\rm E}}$ with $\alpha_{\rm E}=1.65\pm0.17$. The duration-fluence correlation can also be modelled as a power-law $T\propto E^{\alpha_{\rm ET}}$ with $\alpha_{\rm ET} < 0.55$ ($95\%$ confidence). These statistical properties are consistent with the theoretical prediction of the self-organized criticality (SOC) system with the spatial dimension $S = 3$. We suggest that the X-ray flares represent plasmoid ejections driven by magnetic reconnection (similar to solar flares) in the accretion flow onto the black hole.
    Full-text · Article · Jun 2015 · The Astrophysical Journal
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    Guobin Mou · Feng Yuan · Zhaoming Gan · Mouyuan Sun
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    ABSTRACT: In a previous work, we have shown that the formation of the Fermi bubbles can be due to the interaction between winds launched from the hot accretion flow in Sgr A* and the interstellar medium (ISM). In that work, we focus only on the morphology. In this paper we continue our study by calculating the gamma-ray radiation. Some cosmic ray protons (CRp) and electrons must be contained in the winds, which are likely formed by physical processes such as magnetic reconnection. We have performed MHD simulations to study the spatial distribution of CRp, considering the advection and diffusion of CRp in the presence of magnetic field. We find that a permeated zone is formed just outside of the contact discontinuity between winds and ISM, where the collisions between CRp and thermal nuclei mainly occur. The decay of neutral pions generated in the collisions, combined with the inverse Compton scattering of background soft photons by the secondary leptons generated in the collisions and primary CR electrons can well explain the observed gamma-ray spectral energy distribution. Other features such as the uniform surface brightness along the latitude and the boundary width of the bubbles are also explained. The advantage of this accretion wind model is that the adopted wind properties come from the detailed small scale MHD numerical simulation of accretion flows and the value of mass accretion rate has independent observational evidences. The success of the model suggests that we may seriously consider the possibility that cavities and bubbles observed in other contexts such as galaxy clusters may be formed by winds rather than jets.
    Preview · Article · May 2015 · The Astrophysical Journal
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    ABSTRACT: The Local Group compact elliptical galaxy M32 hosts one of the nearest super-massive black holes (SMBHs), which has manifested itself only in X-rays to date. Based on sensitive observations taken with the {\it Karl G. Jansky} Very Large Array (VLA), we detect for the first time a compact radio source coincident with the nucleus of M32, which exhibits a flux density of $\sim$$47.3 \pm 5.9$ $\mu$Jy at 6.6 GHz. We discuss several possibilities for the nature of this source, favoring an origin of the long-sought radio emission from the central SMBH, for which we also revisit the X-ray properties based on recently acquired {\sl Chandra} and {\sl XMM-Newton} data. Our VLA observations also discover radio emission from three previously know optical planetary nebulae in the inner region of M32.
    Full-text · Article · Feb 2015
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    ABSTRACT: Previous MHD simulations have shown that wind must exist in black hole hot accretion flows. In this paper, we continue our study by investigating the detailed properties of wind, such as mass flux and poloidal speed, and the mechanism of wind production. For this aim, we make use of a three dimensional GRMHD simulation of hot accretion flows around a Schwarzschild black hole. The simulation is designed so that the magnetic flux is not accumulated significantly around the black hole. To distinguish real wind from turbulent outflows, we track the trajectories of the virtual Largrangian particles from simulation data. We find two types of real outflows, i.e., a quasi-relativistic jet close to the axis and a sub-relativistic wind subtending a much larger solid angle. Most of the wind originates from the surface layer of the accretion flow. The poloidal wind speed almost remains constant once they are produced, but the flux-weighted wind speed roughly follows $v_{\rm p, wind}(r)\approx 0.25 v_k(r)$. The mass flux of jet is much lower but the speed is much higher, $v_{\rm p,jet}\sim (0.3-0.4) c$. Consequently, both the energy and momentum fluxes of the wind are much larger than those of the jet. We find that the wind is produced and accelerated primarily by the combination of centrifugal force and magnetic pressure gradient, while the jet is mainly accelerated by magnetic pressure gradient. Finally, we find that the wind production efficiency $\epsilon_{\rm wind}\equiv\dot{E}_{\rm wind}/\dot{M}_{\rm BH}c^2\sim 1/1000$, in good agreement with the value required from large-scale galaxy simulations with AGN feedback.
    Preview · Article · Jan 2015 · The Astrophysical Journal
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    ABSTRACT: We investigate the observed correlation between the 2–10 keV X-ray luminosity (in unit of the Eddington luminosity; lX ≡ LX/LEdd) and the photon index (Γ) of the X-ray spectrum for both black hole X-ray binaries (BHBs) and active galactic nuclei (AGNs). We construct a large sample, with 10− 9 ≲ lX ≲ 10− 1. We find that Γ is positively and negatively correlated with lX when lX ≳ 10− 3 and 10− 6.5 ≲ lX ≲ 10− 3, respectively, while Γ is nearly a constant when lX ≲ 10− 6.5. We explain the above correlation in the framework of a coupled hot accretion flow–jet model. The radio emission always comes from the jet while the X-ray emission comes from the accretion flow and jet when lX is above and below 10−6.5, respectively. More specifically, we assume that with the increase of mass accretion rate, the hot accretion flow develops into a clumpy and further a disc–corona two-phase structure because of thermal instability. We argue that such kind of two-phase accretion flow can explain the observed positive correlation.
    Full-text · Article · Dec 2014 · Monthly Notices of the Royal Astronomical Society
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    Ya-Ping Li · Feng Yuan · Q. Daniel Wang
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    ABSTRACT: Sgr A* is probably the supermassive black hole being investigated most extensively due to its proximity. Several theoretical models for its steady state emission have been proposed in the past two decades. Both the radiative-inefficient accretion flow and the jet model have been shown to well explain the observed spectral energy distribution. Faraday rotation measure (RM) has been unambiguously measured at submillimeter wavelength, but has only been tested against the accretion flow model. Here we first calculate the RM based on the jet model and find that the predicted value is two orders of magnitude lower than the measured value. We then include an additional contribution from the accretion flow in front of the jet and show that the measured RM may be reconciled with the model under some tight constraints. The main constraint is that the inclination angle should be greater than $\sim 73^{\circ}$. But this requirement is not consistent with an existing observational estimate of the inclination angle.
    Full-text · Article · Oct 2014 · The Astrophysical Journal
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    De-Fu Bu · Feng Yuan
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    ABSTRACT: If the specific angular momentum of accretion gas at large radius is small compared to the local Keplerian value, one usually believes that there exists a "circularization radius" beyond which the angular momentum of accretion flow is almost a constant while within which a disk is formed and the angular momentum roughly follows the Keplerian distribution. In this paper, we perform numerical simulations to study whether the picture above is correct in the context of hot accretion flow. We find that for a steady accretion flow, the "circularization radius" does not exist and the angular momentum profile will be smooth throughout the flow. However, for transient accretion systems, such as the tidal disruption of a star by a black hole, a "turning point" should exist in the radial profile of the angular momentum, which is conceptually similar to the "circularization radius". At this radius, the viscous timescale equals the life time of the accretion event. The specific angular momentum is close to Keplerian within this radius, while beyond this radius the angular momentum is roughly constant.
    Preview · Article · May 2014
  • De-Fu Bu · Feng Yuan
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    ABSTRACT: If the specific angular momentum of accretion gas at large radius is small compared to the local Keplerian value, one usually believes that there exists a ‘circularization radius’ beyond which the angular momentum of accretion flow is almost a constant while within which a disc is formed and the angular momentum roughly follows the Keplerian distribution. In this paper, we perform numerical simulations to study whether the picture above is correct in the context of hot accretion flow. We find that for a steady accretion flow, the ‘circularization radius’ does not exist and the angular momentum profile will be smooth throughout the flow. However, for transient accretion systems, such as the tidal disruption of a star by a black hole, a ‘turning point’ should exist in the radial profile of the angular momentum, which is conceptually similar to the ‘circularization radius’. At this radius, the viscous time-scale equals the lifetime of the accretion event. The specific angular momentum is close to Keplerian within this radius, while beyond this radius the angular momentum is roughly constant.
    No preview · Article · Apr 2014 · Monthly Notices of the Royal Astronomical Society
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    Guobin Mou · Feng Yuan · Defu Bu · Mouyuan Sun · Meng Su
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    ABSTRACT: A pair of giant gamma-ray bubbles which extend ~50 degrees above and below the Galactic plane with a width of ~40 degrees are revealed by the Fermi Gamma-ray Space Telescope. The formation mechanism of the bubbles is still under debate. Many observations have strongly indicated that the activity of the supermassive black hole located in the Galactic center, Sgr A*, is likely much stronger than the present time, and the Fermi bubbles may be the result of this activity. Specifically the previous independent quantitative studies to the past activity show that while Sgr A* was also in a hot accretion regime, the accretion rate should be 3-4 orders of magnitude higher than the present value and last for 10^7 yr. Recent MHD numerical simulations of hot accretion flows have shown the existence of winds from hot accretion flows and obtained their main properties such as mass flux and velocity. Based on these knowledge and constraints, in this paper we have performed three-dimensional hydrodynamical numerical simulations to study the formation of the Fermi bubbles. We find that the winds can well explain the main observational features of the Fermi bubbles. The active phases is required to last for about 10 million years and the later quiescent state should last for no more than 0.2 million years. Disc-like and massive Central Molecular Zone (CMZ) changes the outflow orientation, to be approximately towards Galactic poles. Viscosity suppresses the Rayleigh- Taylor (RT) instability and Kelvin-Helmholtz (KH) instability, which induces a smooth edge. The observed ROSAT X-ray features can be interpreted by the shocked interstellar medium (ISM) and the interaction region between outflow gas and CMZ gas. Moreover, the thermal pressure and the temperature are in very good consistency with the recent Suzaku observational results.
    Preview · Article · Mar 2014 · The Astrophysical Journal
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    ABSTRACT: Based on two-dimensional high resolution hydrodynamic numerical simulation, we study the mechanical and radiative feedback effects from the central AGN on the cosmological evolution of an isolated elliptical galaxy. Physical processes such as star formation and supernovae are considered. The inner boundary of the simulation domain is carefully chosen so that the fiducial Bondi radius is resolved and the accretion rate of the black hole is determined self-consistently. In analogy to previous works, we assume that the specific angular momentum of the galaxy is low. It is well-known that when the accretion rates are high and low, the central AGNs will be in cold and hot accretion modes, which correspond to the radiative and kinetic feedback modes, respectively. The emitted spectrum from the hot accretion flows is harder than that from the cold accretion flows, which results in a higher Compton temperature accompanied by a more efficient radiative heating. Such a difference of the Compton temperature between the two feedback modes, the focus of this study, has been neglected in previous works. Significant differences in the kinetic feedback mode are found as a result of the stronger Compton heating and accretion becomes more chaotic. More importantly, if we constrain models to correctly predict black hole growth and AGN duty cycle after cosmological evolution, we find that the favored model parameters are constrained: mechanical feedback efficiency diminishes with decreasing luminosity (the maximum efficiency being $\simeq 10^{-3.5}$) and X-ray Compton temperature increases with decreasing luminosity, although models with fixed mechanical efficiency and Compton temperature can be found that are satisfactory as well. We conclude that radiative feedback in the kinetic mode is much more important than previously thought.
    Full-text · Article · Mar 2014 · The Astrophysical Journal
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    Feng Yuan · Ramesh Narayan
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    ABSTRACT: Black hole accretion flows can be divided into two broad classes: cold and hot. Cold accretion flows, which consist of cool optically thick gas, are found at relatively high mass accretion rates. Prominent examples are the standard thin disk, which occurs at a fraction of the Eddington mass accretion rate, and the slim disk at super-Eddington rates. These accretion flows are responsible for luminous systems such as active galactic nuclei radiating at or close to the Eddington luminosity and black hole X-ray binaries in the soft state. Hot accretion flows, the topic of this review, are virially hot and optically thin. They occur at lower mass accretion rates, and are described by models such as the advection-dominated accretion flow and luminous hot accretion flow. Because of energy advection, the radiative efficiency of these flows is in general lower than that of a standard thin accretion disk. Moreover, the efficiency decreases with decreasing mass accretion rate. Observations show that hot accretion flows are associated with jets. In addition, theoretical arguments suggest that hot flows should produce strong winds. Hot accretion flows are believed to be present in low-luminosity active galactic nuclei and in black hole X-ray binaries in the hard and quiescent states. The prototype is Sgr A*, the ultra-low-luminosity supermassive black hole at our Galactic center. The jet, wind and radiation from a supermassive black hole with a hot accretion flow can interact with the external interstellar medium and modify the evolution of the host galaxy. Details of this "maintenance-mode feedback" could, in principle, be worked out through theoretical studies and numerical simulations of hot accretion flows.
    Preview · Article · Jan 2014 · Annual Review of Astronomy and Astrophysics
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    ABSTRACT: Most supermassive black holes (SMBHs) are accreting at very low levels and are difficult to distinguish from the galaxy centers where they reside. Our own Galaxy's SMBH provides a uniquely instructive exception, and we present a close-up view of its quiescent X-ray emission based on 3 mega-second of Chandra observations. Although the X-ray emission is elongated and aligns well with a surrounding disk of massive stars, we can rule out a concentration of low-mass coronally active stars as the origin of the emission based on the lack of predicted Fe Kalpha emission. The extremely weak H-like Fe Kalpha line further suggests the presence of an outflow from the accretion flow onto the SMBH. These results provide important constraints for models of the prevalent radiatively inefficient accretion state.
    Full-text · Article · Aug 2013 · Science
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    Xiao-Hong Yang · Feng Yuan · Ken Ohsuga · De-Fu Bu
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    ABSTRACT: We study the dynamics of super-Eddington accretion flows by performing two-dimensional radiation-hydrodynamic simulations. Compared with previous works, in this paper we include the T ? component of the viscous stress and consider various values of the viscous parameter ?. We find that when T ? is included, the rotational speed of the high-latitude flow decreases, while the density increases and decreases at the high and low latitudes, respectively. We calculate the radial profiles of inflow and outflow rates. We find that the inflow rate decreases inward, following a power law form of . The value of s depends on the magnitude of ? and is within the range of ~0.4-1.0. Correspondingly, the radial profile of density becomes flatter compared with the case of a constant . We find that the density profile can be described by ?(r)?r ?p and the value of p is almost same for a wide range of ? ranging from ? = 0.1 to 0.005. The inward decrease of inflow accretion rate is very similar to hot accretion flows, which is attributed to the mass loss in outflows. To study the origin of outflow, we analyze the convective stability of the slim disk. We find that depending on the value of ?, the flow is marginally stable (when ? is small) or unstable (when ? is large). This is different from the case of hydrodynamical hot accretion flow, where radiation is dynamically unimportant and the flow is always convectively unstable. We speculate that the reason for the difference is because radiation can stabilize convection. The origin of outflow is thus likely because of the joint function of convection and radiation, but further investigation is required.
    Preview · Article · Jun 2013 · The Astrophysical Journal
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    ABSTRACT: We perform time-dependent, 2DHD numerical simulations to study the dynamics of a slowly rotating accretion flow from sub-pc to pc scales under the irradiation from the central AGN. Compared to previous work, we improve the calculation of the radiative force due to X-rays. More importantly, in addition to radiative pressure and radiative heating/cooling directly from the central AGN, in the momentum equation we also include the force due to the scattered and reprocessed photons. We find that the accretion flow properties change significantly due to this "re-radiation" effect. The inflow rate at the inner boundary is reduced, while the outflow rate at the outer boundary is enhanced by about one order of magnitude. This effect is more significant when the density at the outer boundary is higher. The properties of outflows such as velocity, momentum and energy fluxes, and the ratio of outflow rate and the accretion rate, are calculated. We find that the efficiency of transferring the radiation power into the kinetic power of outflow is typically $10^{-3}$, far below the value of $\sim 0.05$ which is assumed in some cosmological simulations. The effect of the temperature of the gas at the outer boundary ($T_0$) is investigated. When $T_0$ is high, the emitted luminosity of the accretion flow oscillates. This is because in this case the gas around the Bondi radius can be more easily heated to be above the virial temperature due to its high internal energy. Another question we hope to address is the so-called "sub-Eddington" puzzle. Observationally, the luminosity of almost all AGNs are sub-Eddington, while theoretically the luminosity of an accretion flow can easily be super-Eddington. We find that even when the re-radiation effect is included and outflow does become much stronger, the luminosity, while reduced, can still be super-Eddington.
    Preview · Article · Apr 2013 · Monthly Notices of the Royal Astronomical Society
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    De-Fu Bu · Feng Yuan · Maochun Wu · Jorge Cuadra
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    ABSTRACT: We study the effects of initial and boundary conditions, taking two-dimensional hydrodynamical numerical simulations of hot accretion flow as an example. The initial conditions considered include a rotating torus, a solution expanded from the one-dimensional global solution of hot accretion flows, injected gas with various angular momentum distributions, and the gas from a large-scale numerical simulation. Special attention is paid to the radial profiles of the mass accretion rate and density. Both can be described by a power-law function, Ṁ∝ rs and ρ ∝ r−p. We find that if the angular momentum is not very low, the value of s is not sensitive to the initial condition and lies within a narrow range, 0.47 ≲ s ≲ 0.55. However, the value of p is more sensitive to the initial condition and lies in the range 0.48 ≲ p ≲ 0.8. The diversity of the density profile is because different initial conditions give different radial profiles of radial velocity due to the different angular momentum of the initial conditions. When the angular momentum of the accretion flow is very low, the inflow rate is constant with radius. Taking the torus model as an example, we have also investigated the effects of inner and outer boundary conditions by considering the widely adopted ‘outflow’ boundary condition and the ‘mass flux conservation’ condition. We find that the results are not sensitive to these two boundary conditions.
    Preview · Article · Mar 2013 · Monthly Notices of the Royal Astronomical Society

Publication Stats

2k Citations
463.90 Total Impact Points


  • 2012-2015
    • Xiamen University
      Amoy, Fujian, China
  • 2006-2015
    • Chinese Academy of Sciences
      • • Shanghai Astronomical Observatory
      • • Galaxies, Cosmology Research Department
      Peping, Beijing, China
  • 2009
    • University of Strasbourg
      Strasburg, Alsace, France
  • 1996-2009
    • University of Science and Technology of China
      Luchow, Anhui Sheng, China
  • 2004-2008
    • Purdue University
      • Department of Physics
      ウェストラファイエット, Indiana, United States
  • 2007
    • East China University of Science and Technology
      Shanghai, Shanghai Shi, China
  • 2005
    • University of California, Berkeley
      • Department of Astronomy
      Berkeley, California, United States
  • 2001-2004
    • Harvard-Smithsonian Center for Astrophysics
      • • Smithsonian Astrophysical Observatory
      • • Institute for Theory and Computation
      Cambridge, Massachusetts, United States
  • 1999-2001
    • Nanjing University
      • Department of Astronomy
      Nanjing, Jiangsu Sheng, China
  • 2000
    • Korea Institute for Advanced Study
      Sŏul, Seoul, South Korea