A Note on the Slim Accretion Disk Model

We show that when the gravitational force is correctly calculated in dealing with the vertical hydrostatic equilibrium of black hole accretion disks, the relationship that is valid for geometrically thin disks, i.e., $c_s/\Omega_K H =$ constant, where $c_s$ is the sound speed, $\Omega_K$ is the Keplerian angular velocity, and $H$ is the half-thickness of the disk, does not hold for slim disks. More importantly, by adopting the correct vertical gravitational force in studies of thermal equilibrium solutions, we find that there exists a maximally possible accretion rate for each radius in the outer region of optically thick accretion flows, so that only the inner region of these flows can possibly take the form of slim disks, and strong outflows from the outer region are required to reduce the accretion rate in order for slim disks to be realized.Comment: 14 pages, 5 figures, accepted by Ap

Why Is Supercritical Disk Accretion Feasible?

Although the occurrence of steady supercritical disk accretion onto a black hole has been speculated about since the 1970s, it has not been accurately verified so far. For the first time, we previously demonstrated it through two-dimensional, long-term radiation-hydrodynamic simulations. To clarify why this accretion is possible, we quantitatively investigate the dynamics of a simulated supercritical accretion flow with a mass accretion rate of ~10^2 L_E/c^2 (with L_E and c being, respectively, the Eddington luminosity and the speed of light). We confirm two important mechanisms underlying supercritical disk accretion flow, as previously claimed, one of which is the radiation anisotropy arising from the anisotropic density distribution of very optically thick material. We qualitatively show that despite a very large radiation energy density, E_0>10^2L_E/(4 pi r^2 c) (with r being the distance from the black hole), the radiative flux F_0 cE_0/tau could be small due to a large optical depth, typically tau 10^3, in the disk. Another mechanism is photon trapping, quantified by vE_0, where v is the flow velocity. With a large |v| and E_0, this term significantly reduces the radiative flux and even makes it negative (inward) at r<70r_S, where r_S is the Schwarzschild radius. Due to the combination of these effects, the radiative force in the direction along the disk plane is largely attenuated so that the gravitational force barely exceeds the sum of the radiative force and the centrifugal force. As a result, matter can slowly fall onto the central black hole mainly along the disk plane with velocity much less than the free-fall velocity, even though the disk luminosity exceeds the Eddington luminosity. Along the disk rotation axis, in contrast, the strong radiative force drives strong gas outflows.Comment: 8 pages, 7 figures, accepted for publication in Ap

The hard X-ray spectral evolution in X-ray binaries and its application to constrain the black hole mass of ultraluminous X-ray sources

We investigate the relationship between the hard X-ray photon index $\Gamma$ and the Eddington ratio ($\xi=L_{X}(0.5-25 \rm keV)/L_{Edd}$) in six X-ray binaries (XRBs) with well constrained black hole masses and distances. We find that different XRBs follow different anti-correlations between $\Gamma$ and $\xi$ when $\xi$ is less than a critical value, while $\Gamma$ and $\xi$ generally follow the same positive correlation when $\xi$ is larger than the critical value. The anti-correlation and the positive correlation may suggest that they are in different accretion modes (e.g., radiatively inefficient accretion flow (RIAF) and standard disk). We fit both correlations with the linear least-square method for individual sources, from which the crosspoint of two fitted lines is obtained. Although the anti-correlation varies from source to source, the crosspoints of all sources roughly converge to the same point with small scatter($\log \xi=-2.1\pm0.2, \Gamma=1.5\pm 0.1$), which may correspond to the transition point between RIAF and standard accretion disk. Motivated by the observational evidence for the similarity of the X-ray spectral evolution of ultraluminous X-ray sources (ULXs) to that of XRBs, we then constrain the black hole masses for seven ULXs assuming that their X-ray spectral evolution is similar to that of XRBs. We find that the BH masses of these seven luminous ULXs are around 10^{4}\msun, which are typical intermediate-mass BHs (IMBHs). Our results are generally consistent with the BH masses constrained from the timing properties (e.g., break frequency) or the model fitting with a multi-color disk.Comment: accepted for publication in ApJ, 18 pages, 2 figures, Comments is welcomed

Thermal Equilibria of Magnetically Supported, Black Hole Accretion Disks

We present new thermal equilibrium solutions for optically thin and thick disks incorporating magnetic fields. The purpose of this paper is to explain the bright hard state and the bright/slow transition observed in the rising phases of outbursts in BHCs. On the basis of the results of 3D MHD simulations, we assume that magnetic fields inside the disk are turbulent and dominated by the azimuthal component and that the azimuthally averaged Maxwell stress is proportional to the total pressure. We prescribe the magnetic flux advection rate to determine the azimuthal magnetic flux at a given radius. We find magnetically supported, thermally stable solutions for both optically thin and thick disks, in which the heating enhanced by the strong magnetic field balances the radiative cooling. The temperature in a low-$\beta$ disk is lower than that in an ADAF/RIAF but higher than that in a standard disk. We also study the radial dependence of the thermal equilibrium solutions. The optically thin, low-$\beta$ branch extends to $\dot M \gtrsim 0.1 {\dot M}_{\rm Edd}$, in which the temperature anti-correlates with the mass accretion rate. Thus optically thin low-$\beta$ disks can explain the bright hard state. Optically thick, low-$\beta$ disks have the radial dependence of the effective temperature $T_{\rm eff} \propto \varpi^{-3/4}$. Such disks will be observed as staying in a high/soft state. Furthermore, limit cycle oscillations between an optically thick low-$\beta$ disk and a slim disk will occur because the optically thick low-$\beta$ branch intersects with the radiation pressure dominated standard disk branch. These limit cycle oscillations will show a smaller luminosity variation than that between a standard disk and a slim disk.Comment: 23 pages, 9 figures, accepted for publication in Ap

Spectral Evolution of NGC 1313 X-2: Evidence Against The Cool Disk Model

The presence of a cool multicolor disk component with an inner disk temperature kT=0.1~0.3 keV at a luminosity L>10^40 erg/s has been interpreted as evidence that the ultraluminous X-ray source NGC 1313 X-2 harbors an intermediate-mass black hole (IMBH). The temperature of a disk component should vary with luminosity as $L\propto T^4$. However, upon investigating the spectral evolution with multiple XMM-Newton observations, we found that the cool disk component failed to follow this relation with a confidence level of 0.999964. Indeed, the luminosity decreases as the temperature increases, and the luminosities at high temperatures are more than an order of magnitude less than expected from the $L\propto T^4$ extrapolation of luminosities at low temperatures. This places a strong constraint against the validity of modeling the X-ray spectra of NGC 1313 X-2 as emission from the accretion disk of an IMBH. The decrease in luminosity with increasing temperature of the soft component follows the trend suggested by a model in which the soft emission arises from an outflow from a stellar-mass black hole with super-Eddington accretion viewed along the symmetry axis. Alternatively, the spectra can be adequately fitted by a p-free disk model with kT=~2 keV and p=~0.5. The spectral evolution is consistent with the $L\propto T^4$ relation and appears to be a high luminosity extension of the L-kT relation of Galactic black holes. This, again, would suggest that the emission is from a super-Eddington accreting stellar mass black hole.Comment: 5 pages, 4 figures, ApJ Letter in press; minor changes in v2 to match the published versio

An analytic relation for the thickness of accretion flows

We take the vertical distribution of the radial and azimuthal velocity into account in spherical coordinates, and find that the analytic relation c_{s0}/(v_K \Theta) = [(\gamma -1)/(2\gamma)]^{1/2} is valid for both geometrically thin and thick accretion flows, where c_{s0} is the sound speed on the equatorial plane, v_K is the Keplerian velocity, \Theta is the half-opening angle of the flow, and \gamma is the adiabatic index.Comment: 4 pages, 2 figures, accepted by Science in China Series

Nustar and Chandra insight into the nature of the 3-40 kev nuclear emission in NGC 253

We present results from three nearly simultaneous Nuclear Spectroscopic Telescope Array (NuSTAR) and Chandra monitoring observations between 2012 September 2 and 2012 November 16 of the local star-forming galaxy NGC 253. The 3-40 keV intensity of the inner ~20 arcsec (~400 pc) nuclear region, as measured by NuSTAR, varied by a factor of ~2 across the three monitoring observations. The Chandra data reveal that the nuclear region contains three bright X-ray sources, including a luminous (L_(2-10) keV ~ few × 10^39 erg s^–1) point source located ~1 arcsec from the dynamical center of the galaxy (within the 3σ positional uncertainty of the dynamical center); this source drives the overall variability of the nuclear region at energies ≳3 keV. We make use of the variability to measure the spectra of this single hard X-ray source when it was in bright states. The spectra are well described by an absorbed (N_H ≈ 1.6 × 10^23 cm^–2) broken power-law model with spectral slopes and break energies that are typical of ultraluminous X-ray sources (ULXs), but not active galactic nuclei (AGNs). A previous Chandra observation in 2003 showed a hard X-ray point source of similar luminosity to the 2012 source that was also near the dynamical center (θ ≈ 0.4 arcsec); however, this source was offset from the 2012 source position by ≈1 arcsec. We show that the probability of the 2003 and 2012 hard X-ray sources being unrelated is ≫99.99% based on the Chandra spatial localizations. Interestingly, the Chandra spectrum of the 2003 source (3-8 keV) is shallower in slope than that of the 2012 hard X-ray source. Its proximity to the dynamical center and harder Chandra spectrum indicate that the 2003 source is a better AGN candidate than any of the sources detected in our 2012 campaign; however, we were unable to rule out a ULX nature for this source. Future NuSTAR and Chandra monitoring would be well equipped to break the degeneracy between the AGN and ULX nature of the 2003 source, if again caught in a high state

X-ray spectral variability in the ultraluminous X-ray source Holmberg IX X-1

We use XMM–Newton and Swift data to study a spectral variability in the ultraluminous X-ray source (ULX), Holmberg IX X−1. The source luminosity varies by a factor of 3–4, giving rise to corresponding spectral changes which are significant, but subtle, and not well tracked by a simple hardness ratio. Instead, we co-add the Swift data in intensity bins and do full spectral fitting with disc plus thermal Comptonization models. All the data are well fitted by a low temperature, optically thick Comptonizing corona, and the variability can be roughly characterized by decreasing temperature and increasing optical depth as the source becomes brighter, as expected if the corona is becoming progressively mass loaded by material blown off the super-Eddington inner disc. This variability behaviour is seen in other ULX which has similar spectra, but is opposite to the trend seen in the ULX with much softer spectra. This supports the idea that there are two distinct physical regimes in ULXs, where the spectra go from being dominated by a disc-corona to being dominated by a wind