Limits on luminosity and mass accretion rate of a radiation pressure dominated accretion disc

There is a maximum for the gravity of a black hole in the vertical direction in the accretion disc. Outflows may probably be driven from the disc if the radiation flux of the disc is greater than a critical value corresponding to the maximal vertical gravity. We find that outflows are driven by the radiation force from the disc if the accretion rate is greater than the Eddington rate. The radiation of the disc is therefore limited by such outflows. The disc luminosity, L=L_Edd\propto ln mdot, at large-mdot cases. The Eddington ratio of the disc is ~3 for mdot~100, which is significantly lower than that of a conventional slim disc without outflows. This implies that the emission from some ultra-luminous X-ray sources with highly super Eddington luminosity should be Doppler beamed, or intermediate mass black holes are in these sources instead of stellar mass black holes. The spectra of the discs with outflows are saturated in the high frequency end provided mdot>2. We suggest that the saturated emission can be observed to estimate the masses of the black holes accreting at high rates, such as the narrow-line Seyfert galaxies, with the model calculations. The rate of the mass accreted by the black hole is always around the Eddington rate even if the mass accretion rate at the outer radius is very high, because most of the gas is removed into the outflows. This implies that the luminous quasars at high redshifts z>6 should have grown up through persistent accretion at a rate close to the Eddington rate.Comment: 8 pages, accepted by MNRA

Stability of braneworlds with non-minimally coupled multi-scalar fields

Linear stability of braneworld models constructed with multi-scalar fields is very different from that of single-scalar field models. It is well known that both the tensor and scalar perturbation equations of the later can always be written as a supersymmetric Schr\"{o}dinger equation, so it can be shown that the perturbations are stable at linear level. However, in general it is not true for multi-scalar field models and especially there is no effective method to deal with the stability problem of the scalar perturbations for braneworld models constructed with non-minimally coupled multi-scalar fields. In this paper we present a method to investigate the stability of such braneworld models. It is easy to find that the tensor perturbations are stable. For the stability problem of the scalar perturbations, we present a systematic covariant approach. The covariant quadratic order action and the corresponding first-order perturbed equations are derived. By introducing the orthonormal bases in field space and making the Kaluza-Klein decomposition, we show that the Kaluza-Klein modes of the scalar perturbations satisfy a set of coupled Schr\"{o}dinger-like equations, with which the stability of the scalar perturbations and localization of the scalar zero modes can be analyzed according to nodal theorem. The result depends on the explicit models. For superpotential derived barane models, the scalar perturbations are stable, but there exist normalizable scalar zero modes, which will result in unaccepted fifth force on the brane. We also use this method to analyze the $f(R)$ braneworld model with an explicit solution and find that the scalar perturbations are stable and the scalar zero modes can not be localized on the brane, which ensure that there is no extra long-range force and the Newtonian potential on the brane can be recovered.Comment: 13 pages, 3 figure