arXiv subjects

Tong Liu

Publications and source records attributed to Tong Liu.

At least 415 records · Page 23Linked to original sources

arXiv2012

The vertical composition of neutrino-dominated accretion disks in gamma-ray bursts

We investigate the vertical structure and elements distribution of neutrino-dominated accretion flows around black holes in spherical coordinates with the reasonable nuclear statistical equilibrium. According our calculations, heavy nuclei tend to be produced in a thin region near the disk surface, whose mass fractions are primarily determined by the accretion rate and the vertical distribution of temperature and density. In this thin region, we find that $^{56}\rm Ni$ is dominant for the flow with low accretion rate (e.g., $0.05 $$M_{\odot}$ $\rm s^{-1}$) but $^{56}\rm Fe$ is dominant for the high counterpart (e.g., $1 M_{\odot}$ $\rm s^{-1}$). The dominant $^{56}\rm Ni$ in the special region may provide a clue to understand the bumps in the optical light curve of core-collapse supernovae.

astro-ph.HE↗

arXiv2012

Understanding Simulations of Thin Accretion Disks by Energy Equation

We study the fluctuations of standard thin accretion disks by linear analysis of the time-dependent energy equation together with the vertical hydrostatic equilibrium and the equation of state. We show that some of the simulation results in Hirose et al. (2009b), such as the time delay, the relationship of power spectra, and the correlation between magnetic energy and radiation energy, can be well understood by our analytic results.

astro-ph.HE↗

arXiv2012

Is There a Relation between Duration and E_iso in Gamma-Ray Bursts?

The system of accretion disk and black hole is usually considered as the central engine of Gamma-ray Bursts (GRBs). It is usually thought that the disk in the central engine of GRBs is the advection-dominated accretion disk, which is developed from a massive (mass M_disk) torus at radius r_disk. We find a positive correlation between the isotropic gamma-ray energy E_iso and duration (so-called T_90) for GRBs. We interpret this correlation within the advection-dominated accretion disk model, associating E_iso and T_90 with M_ disk and viscous timescale respectively.

astro-ph.HE↗

arXiv2012

Radial Angular Momentum Transfer and Magnetic Barrier for Short-Type Gamma-Ray Burst Central Engine Activity

Soft extended emission (EE) following initial hard spikes up to 100 seconds was observed with {\em Swift}/BAT for about half of short-type gamma-ray bursts (SGRBs). This challenges the conversional central engine models of SGRBs, i.e., compact star merger models. In the framework of the black hole-neutron star merger models, we study the roles of the radial angular momentum transfer in the disk and the magnetic barrier around the black hole for the activity of SGRB central engines. We show that the radial angular momentum transfer may significantly prolong the lifetime of the accretion process and multiple episodes may be switched by the magnetic barrier. Our numerical calculations based on the models of the neutrino-dominated accretion flows suggest that the disk mass is critical for producing the observed EE. In case of the mass being $\sim 0.8M_{\odot}$, our model can reproduce the observed timescale and luminosity of both the main and EE episodes in a reasonable parameter set. The predicted luminosity of the EE component is lower than the observed EE with about one order of magnitude and the timescale is shorter than 20 seconds if the disk mass being $\sim 0.2M_{\odot}$. {\em Swift}/BAT-like instruments may be not sensitive enough to detect the EE component in this case. We argue that the EE component would be a probe for merger process and disk formation for compact star mergers.

astro-ph.HE↗

arXiv2012

An intermediate distribution between Gaussian and Cauchy distributions

In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce weighted moments. Specifically, we consider weighted moments under two types of weighted functions: the cut-off function and the exponential function. Through these two types of weighted functions, we can obtain weighted moments for almost all distributions. We consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory. Moreover, we utilize the intermediate distribution to the problem of the stock market return in quantitative finance.

physics.data-an↗

arXiv2012

Gravitational Waves of Jet Precession in Gamma-ray Bursts

The physical nature of gamma-ray bursts (GRBs) are believed to involve an ultra-relativistic jet. The observed complex structure of light curves motivate 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.

astro-ph.HE↗

arXiv2011

The influence of outflows on the 1/f-like luminosity fluctuations

In accretion systems, outflows may have significant influence on the luminosity fluctuations. In this paper, following the Lyubarskii's general scheme, we revisit the power spectral density of luminosity fluctuations by taking into account the role of outflows. Our analysis is based on the assumption that the coupling between the local outflow and inflow is weak on the accretion rate fluctuations. We find that, for the inflow mass accretion rate $\dot M \propto r^{s}$, the power spectrum of flicker noise component will present a power-law distribution $p(f) \propto f^{-(1+4s/3)}$ for advection-dominated flows. We also obtain descriptions of $p(f)$ for both standard thin discs and neutrino-cooled discs, which show that the power-law index of a neutrino-cooled disc is generally larger than that of a photon-cooled disc. Furthermore, the obtained relationship between $p(f)$ and $s$ indicates the possibility of evaluating the strength of outflows by the power spectrum in X-ray binaries and gamma-ray bursts. In addition, we discuss the possible influence of the outflow-inflow coupling on our results.

astro-ph.HE↗

arXiv2011

Revisiting vertical structure of neutrino-dominated accretion disks: Bernoulli parameter, neutrino trapping and other distributions

We revisit the vertical structure of neutrino dominated accretion flows (NDAFs) in spherical coordinates with a new boundary condition based on the mechanical equilibrium. The solutions show that NDAF is significantly thick. The Bernoulli parameter and neutrino trapping are determined by the mass accretion rate and the viscosity parameter. According to the distribution of the Bernoulli parameter, the possible outflow may appear in the outer region of the disk. The neutrino trapping can essentially affect the neutrino radiation luminosity. The vertical structure of NDAF is like a "sandwich", and the multilayer accretion may account for the flares in gamma-ray bursts.

astro-ph.HE↗

arXiv2011

Galois Representations with Quaternion Multiplications Associated to Noncongruence Modular Forms

In this paper we study the compatible family of degree-4 Scholl representations $ρ_{\ell}$ associated with a space $S$ of weight $κ> 2$ noncongruence cusp forms satisfying Quaternion Multiplications over a biquadratic field $K$. It is shown that when either $K$ is totally real or $κ$ is odd, $ρ_\ell$ is automorphic, that is, its associated L-function has the same Euler factors as the L-function of an automorphic form for $GL_4(\mathbb Q)$. Further, it yields a relation between the Fourier coefficients of noncongruence cusp forms in $S$ and those of certain automorphic forms via the three-term Atkin and Swinnerton-Dyer congruences.

math.NT↗

arXiv2011

Crystalline extensions and the weight part of Serre's conjecture

Let p>2 be prime. We complete the proof of the weight part of Serre's conjecture for rank two unitary groups for mod p representations in the totally ramified case, by proving that any weight which occurs is a predicted weight. Our methods are a mixture of local and global techniques, and in the course of the proof we establish some purely local results on crystalline extension classes.

math.NT↗

arXiv2010

Jet Precession Driven by Neutrino-Cooled Disc for Gamma-Ray Bursts

A model of jet precession driven by a neutrino-cooled disc around a spinning black hole is present in order to explain the temporal structure and spectral evolution of gamma-ray bursts (GRBs). The differential rotation of the outer part of a neutrino dominated accretion disc may result in precession of the inner part of the disc and the central black hole, hence drives a precessed jet via neutrino annihilation around the inner part of the disc. Both analytic and numeric results for our model are present. Our calculations show that a black hole-accretion disk system with black hole mass $M \simeq 3.66 M_\odot$, accretion rate $\dot{M} \simeq 0.54 M_\odot \rm s^{-1}$, spin parameter $a=0.9$ and viscosity parameter $α=0.01$ 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 $M \simeq 5.59 M_\odot$, $\dot{M} \simeq 0.74 M_\odot \rm s^{-1}$, $a=0.1$, and $α=0.01$, possibly being responsible for the short GRBs. Both the temporal and spectral evolution in GRB pulse may explained with our model. GRB central engines likely power a precessed jet driven by a neutrino-cooled disc. 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 be due to an viewing effect due to the jet precession.

astro-ph.HE↗

arXiv2009

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 one or two orders of magnitude. The empty funnel along the rotation axis can naturally explain the neutrino annihilable ejection.

astro-ph.HE↗

arXiv2009

Advection-Dominated Accretion Disks: Geometrically Slim or Thick?

We revisit the vertical structure of black hole accretion disks in spherical coordinates. By comparing the advective cooling with the viscous heating, we show that advection-dominated disks are geometrically thick, i.e., with the half-opening angle > 2π/5, rather than slim as supposed previously in the literature.

astro-ph.HE↗

arXiv2008

Some Bounds for ramification of $p^n$-torsion semi-stable representations

Let p be an odd prime, K a finite extension of Q_p, G=Gal(\bar K/K) the Galois group and e=e(K/Q_p) the ramification index. Suppose T is a p^n torsion representation such that T is isomorphic to a quotient of two G-stable Z_p-lattices in a semi-stable representation with Hodge-Tate weights in {0,...,r}. We prove that there exists a constant μexplicitly depending on n, e and r such that the upper numbering ramification group G^{(μ)} acts on T trivially.

math.NT↗

arXiv2007

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 their each radius. This may be suggestive of an interpretation for the origin of X-ray flares observed in gamma-ray bursts.

astro-ph↗

arXiv2007

A note on lattices in semi-stable representations

Let p>2 be a prime, K a finite extension over Q_p and G :=Gal(\bar K/K). We extend Kisin's theory on ϕ-modules of finite E(u)-height to give a new classification of G-stable Z_p-lattices in semi-stable representations

math.NT↗

arXiv2007

Quasi-semi-stable representations

Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of p-adic torsion representations of G_\infty, named quasi-semi-stable. We prove that these representations are "explicitly" described by a certain category of linear algebra objects. The results of this note should be consider as a first step in the understanding of the structure of quotients of two lattices in a crystalline (resp. semi-stable) Galois representation.

math.NT↗

arXiv2007

Structure and Luminosity of Neutrino-cooled Accretion Disks

Neutrino-cooled hyperaccretion disks around stellar mass black holes are plausible candidates for the central engine 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, with 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 enlarges the absorption optical depth for neutrinos, and it along with the neutronization processes favored by high temperature cause the electron fraction to drop to be below 0.1 in the inner region of the disk. The resulting neutrino annihilation luminosity is considerably reduced comparing with that obtained in previous works where 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 and has an anisotropic distribution.

astro-ph↗