Ju-Fu Lu

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.

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

Aims. A model of jet precession driven by a neutrino-cooled disk around a spinning black hole is presented to explain the temporal structure and spectral evolution of gamma-ray bursts (GRBs). Methods. The differential rotation of the outer part of a neutrino-dominated accretion disk may result in precession of the inner part of the disk and the central black hole, hence driving a precessed jet via neutrino annihilation around the inner part of the disk. Results. Both analytic and numeric results for our model are presented. Our calculations show that a black-hole, accretion-disk system with the black hole mass M similar or equal to 3.66 M(circle dot), accretion rate. M similar or equal to 0.54 M(circle dot) s(-1), spin parameter a = 0.9, and viscosity parameter alpha = 0.01 may drive a precessed jet with period P = 1 s and luminosity L = 10(51) erg s(-1), corresponding to the scenario for long GRBs. A precessed jet with P = 0.1 s and L = 10(50) erg s(-1) may be powered by a system with M similar or equal to 5.59 M(circle dot), M similar or equal to 0.74 M similar or equal to s(-1), a = 0.1, and alpha = 0.01, and is possibly responsible for the short GRBs. Both the temporal and spectral evolution in GRB pulse may be explained with our model. Conclusions. GRB central engines most likely power a precessed jet driven by a neutrino-cooled disk. The global GRB lightcurves thus could be modulated by the jet precession during the accretion timescale of the GRB central engine. Both the temporal and spectral evolution in GRB pulse may stem from a viewing effect of the jet precession.

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

We revisit the vertical structure of neutrino-dominated accretion flows in spherical coordinates. We stress that the flow should be geometrically thick when advection becomes dominant. In our calculation, the luminosity of neutrino annihilation is enhanced by 1 or 2 orders of magnitude. The empty funnel along the rotation axis can naturally explain the neutrino annihilable ejection.

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., cs/ΩKH = constant, where cs is the sound speed, ΩK 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 maximal possible accretion rate for each radius in the outer region of optically thick accretion flows, such that only the inner regions 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.

RELATIVISTIC GLOBAL SOLUTIONS OF NEUTRINO-DOMINATED ACCRETION FLOWS

National Basic Research Program (973 Program) of China [2009CB824800]; National Natural Science Foundation of China [11003016, 11073015, 11103015, 11222328, 11233006]; Natural Science Foundation of Fujian Province of China [2010J01017]

Studies of Thermally Unstable Accretion Disks around Black Holes with Adaptive Pseudospectral Domain Decomposition. I. Limit-Cycle Behavior in the Case of Moderate Viscosity

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.

GRAVITATIONAL WAVES OF JET PRECESSION IN GAMMA-RAY BURSTS

The physical nature of gamma-ray bursts (GRBs) is believed to involve an ultra-relativistic jet. The observed complex structure of light curves motivates the idea of jet precession. In this work, we study the gravitational waves of jet precession based on neutrino-dominated accretion disks around black holes, which may account for the central engine of GRBs. In our model, the jet and the inner part of the disk may precess along with the black hole, which is driven by the outer part of the disk. Gravitational waves are therefore expected to be significant from this black-hole-inner-disk precession system. By comparing our numerical results with the sensitivity of some detectors, we find that it is possible for DECIGO and BBO to detect such gravitational waves, particularly for GRBs in the Local Group.