Wei-Min Gu

Structure and luminosity of neutrino-cooled accretion disks

Neutrino-cooled hyperaccretion disks around stellar-mass black holes are plausible candidates for the central engines of gamma-ray bursts. We calculate the one-dimensional structure and the annihilation luminosity of such disks. The neutrino optical depth is of crucial importance in determining the neutrino cooling rate and is in turn dependent on the electron fraction, the free nucleon fraction, and the electron degeneracy, for a given density and temperature of the disk matter. We construct a bridging formula for the electron fraction that works for various neutrino optical depths and give exact definitions for the free proton fraction and free neutron fraction. We show that the electron degeneracy has important effects, in the sense that it increases the absorption optical depth for neutrinos and, along with the neutronization processes favored by high temperature, causes the electron fraction to drop below 0.1 in the inner region of the disk. The resulting neutrino annihilation luminosity is considerably reduced in comparison with that obtained in previous works in which the electron degeneracy was not considered and the electron fraction was simply taken to be 0.5, but it is still likely to be adequate for gamma-ray bursts, and it is ejected mainly from the inner region of the disk with an anisotropic distribution.

Neutrino-Dominated Accretion Models for Gamma-Ray Bursts: Effects of General Relativity and Neutrino Opacity

We first refine the fixed concept in the literature that the usage of the Newtonian potential in studies of black hole accretion is invalid and the general relativistic effect must be considered. As our main results, we then show that the energy released by neutrino annihilation in neutrino-dominated accretion flows is sufficient for gamma-ray bursts when the contribution from the optically thick region of the flow is included, and that in the optically thick region advection does not necessarily dominate over neutrino cooling because the advection factor is relevant to the geometrical depth rather than the optical depth of the flow.

Constraints on the Mass Accretion Rate of Neutrino-cooled Disks in Gamma-Ray Bursts

We present a unified description of all the three known classes of optically thick accretion disks around black holes, namely Shakura-Sunyaev disks, slim disks, and neutrino-dominated accretion flows (NDAFs). It is found that NDAFs have both a maximal and a minimal possible mass accretion rate at each radius. This may suggest an interpretation for the origin of X-ray flares observed in gamma-ray bursts.

Global dynamics of advection-dominated accretion revisited

We numerically solve the set of dynamical equations describing advection-dominated accretion flows (ADAFs) around black holes, using a method similar to that of Chakrabarti. We choose the sonic radius of the flow Rs and the integration constant in angular momentum equation j as free parameters and integrate the equations from the sonic point inward to see if the solution can extend supersonically to the black hole horizon and outward to see if and where an acceptable outer boundary of the flow can be found. We recover the ADAF-thin disk solution constructed by Narayan, Kato, & Honma in a paper representative of previous works on global ADAF solutions, although in that paper an apparently very different procedure was adopted. The use of our method has the following advantages. First, we obtain all the solutions belonging to the ADAF-thin disk class, not only some examples, as in the paper by Narayan and colleagues. Second, we find other classes of solutions that were not noticed by these authors, namely, an ADAF-thick disk solution, in which an ADAF connects outward to a thick disk, and an α-type solution, which can extend either only to the black hole horizon or only to the outer boundary. The ADAF-thick disk solution may have astrophysical implications in view of the fact that in some cases models based on the ADAF-thin disk solution encounter some difficulties. The α-type solution is also worth studying, in the sense that such a solution could be a part of a shock-included global solution. Apart from all these classes of solutions, there are definite ranges of incorrect values of Rs and j for which no solutions exist at all. Taking all these results together, we obtain a complete picture in the form of Rs-j parameter space, which sums up the situation of ADAF solution at a glance. For comparison we also present the distribution of global solutions for inviscid flows in the Rs-j space, which supports the view that there should be some similarities between the dynamical behavior of ADAFs and that of adiabatic flows, and that there should be a continuous change from the properties of viscous flows to those of inviscid ones.

Mechanism of Outflows in Accretion System: Advective Cooling Cannot Balance Viscous Heating?

Based on no-outflow assumption, we investigate steady state, axisymmetric, optically thin accretion flows in spherical coordinates. By comparing the vertically integrated advective cooling rate with the viscous heating rate, we find that the former is generally less than 30% of the latter, which indicates that the advective cooling itself cannot balance the viscous heating. As a consequence, for radiatively inefficient flows with low accretion rates such as

Jet precession driven by neutrino-cooled disk for gamma-ray bursts

\dot M \la 10^{-3} \dot M_{Edd}

VERTICAL STRUCTURE OF NEUTRINO-DOMINATED ACCRETION DISK AND APPLICATIONS TO GAMMA-RAY BURSTS

, where

A note on the slim accretion disk model

\dot M_{Edd}

RADIAL ANGULAR MOMENTUM TRANSFER AND MAGNETIC BARRIER FOR SHORT-TYPE GAMMA-RAY-BURST CENTRAL ENGINE ACTIVITY

is the Eddington accretion rate, the viscous heating rate will be larger than the sum of the advective cooling rate and the radiative cooling one. Thus, no thermal equilibrium can be established under the no-outflow assumption. We therefore argue that in such case outflows ought to occur and take away more than 70% of the thermal energy generated by viscous dissipation. Similarly, for optically thick flows with extremely large accretion rates such as

RELATIVISTIC GLOBAL SOLUTIONS OF NEUTRINO-DOMINATED ACCRETION FLOWS

\dot M \ga 10 \dot M_{Edd}