Some different correlations between optical-UV variability and other quasar properties, such as luminosity, black hole mass and rest-frame wavelength, were discovered. The positive correlation between optical-UV variability amplitude and black hole mass was first found by Wold et al., and this was confirmed by Wilhite et al. We suggest that the accretion disk model can explain these correlations, provided the optical-UV variability is triggered by the change of accretion rate. The disk temperature of accretion discs decreases with increasing black hole mass, which leads to systematical spectral shape difference with black hole mass even if the black hole is accreting at the same rate m_dot (m_dot = M_dot / M_dotEdd). The observed positive correlation between optical-UV variability and black hole mass can be well reproduced by our model calculations, if the mean accretion rate m_dot0 ~ 0.1 with variation of m_delta ~ 0.4 - 0.5 m_dot0. We also found that the observed correlations of optical-UV variability amplitude with luminosity or rest-frame wavelength can be qualitatively explained by this accretion disc model.Comment: 4 pages, 4 figures, accepted for publication in MNRAS Letter

The absence of thermal instability in the high/soft state of black hole X-ray binaries, in disagreement with the standard thin disk theory, has been a long-standing riddle for theoretical astronomers. We have tried to resolve this question by studying the thermal stability of a thin disk with magnetically driven winds in theṀ-Σ plane. It is found that disk winds can greatly decrease the disk temperature and thus help the disk become more stable at a given accretion rate. The critical accretion rate,Ṁ crit , corresponding to the thermal instability threshold, is significantly increased in the presence of disk winds. For α = 0.01 and B φ = 10B p , the disk is quite stable even for a very weak initial poloidal magnetic field [β p,0 ∼ 2000, β p = (P gas + P rad )/(B 2 p /8π )]. However, when B φ = B p or B φ = 0.1B p , a somewhat stronger (but still weak) field (β p,0 ∼ 200 or β p,0 ∼ 20) is required to make the disk stable. Nevertheless, despite the great increase ofṀ crit , the luminosity threshold, corresponding to instability, remains almost constant or decreases slowly with increasingṀ crit due to decreased gas temperature. The advection and diffusion timescales of the large-scale magnetic field threading the disk are also investigated in this work. We find that the advection timescale can be smaller than the diffusion timescale in a disk with winds, because the disk winds take away most of the gravitational energy released in the disk, resulting in the decrease of the magnetic diffusivity η and the increase of the diffusion timescale.

We study the global dynamics of advection-dominated accretion flows (ADAFs) with magnetically driven outflows. A fraction of gases in the accretion flow is accelerated into the outflows, which leads to decreasing of the mass accretion rate in the accretion flow towards the black hole. We find that the r-dependent mass accretion rate is close to a power-law one, m ∝ r s , as assumed in the advection-dominated inflow-outflow solution, in the outer region of the ADAF, while it deviates significantly from the power-law r-dependent accretion rate in the inner region of the ADAF. It is found that the structure of the ADAF is significantly changed in the presence of the outflows. The temperatures of the ions and electrons in the ADAF decreases in the presence of outflows, as a fraction of gravitational power released in the ADAF is tapped to accelerate the outflows.

We present a numerical method for spatially 1.5-dimensional, time-dependent studies of accretion disks around black holes. The method originates from a combination of the standard pseudospectral and adaptive domain decomposition methods found in the literature, but with a number of improvements in both the numerical and physical senses. In particular, we introduce a new treatment for the connection at the interfaces of decomposed subdomains, construct an adaptive function for the mapping between the Chebyshev-Gauss-Lobatto collocation points and the physical collocation points in each subdomain, and modify the oversimplified one-dimensional basic equations of accretion flows to account for the effects of viscous stresses in both the azimuthal and radial directions. Our method is verified by reproducing the best results obtained previously by Szuszkiewicz & Miller on the limit-cycle behavior of thermally unstable accretion disks with moderate viscosity. A new finding is that, according to our computations, the Bernoulli function of the matter in such disks is always and everywhere negative, so that outflows are unlikely to originate from these disks. We are encouraged to study the more difficult case of thermally unstable accretion disks with strong viscosity in ongoing work.