Generalized thermal instability criterion of black hole accretion disks

The conventional thermal instability criterion can not be applied to the advection-dominated accretion disks around black holes where the radiative cooling is insufficient to balance the viscous heating. The surface density change associated with the temperature perturbations, which was usually neglected in deriving the conventional criterion, was recently shown to be much significant in the advection-dominated disks. Considering both advection and surface density change, I suggested a generalized thermal instability criterion. By applying it to the optically thin and optically thick advection-dominated disks, I found that the former one is thermally stable and the latter one is thermally unstable against short wavelength perturbations, which agrees well to those found recently by both analytic and quantitative stability analyses.Comment: 5 pages, LaTex file, accepted for publication in Chinese Physics Letter

Small eigenvalues of closed Riemann surfaces for large genus

In this article we study the asymptotic behavior of small eigenvalues of Riemann surfaces for large genus. We show that for any positive integer $k$, as the genus $g$ goes to infinity, the smallest $k$-th eigenvalue of Riemann surfaces in any thick part of moduli space of Riemann surfaces of genus $g$ is uniformly comparable to $\frac{1}{g^2}$ in $g$. In the proof of the upper bound, for any constant $\epsilon>0$, we will construct a closed Riemann surface of genus $g$ in any $\epsilon$-thick part of moduli space such that it admits a pants decomposition whose boundary curves all have length equal to $\epsilon$, and the number of separating systole curves in this surface is uniformly comparable to $g$.Comment: 22 pages, 8 figures, comments are welcom

Magnetic Energy Injection in GRB 080913

GRB 080913, with a spectroscopically determined redshift of z=6.7, was the record holder of the remotest stellar object before the discovery of the recent gamma-ray burst GRB 090423, whose redshift is about 8.2. The gradually accumulated high redshift GRB sample has shed light on the origin and physics of GRBs during the cosmic re-ionization epoch. We here present a detailed numerical fit to the multi-wavelength data of the optical afterglow of GRB 080913 and then constrain its circum-burst environment and the other model parameters. We conclude that the late optical/X-ray plateau at about one day since the burst is due to the Poynting-flux dominated injection from the central engine which is very likely a massive spinning black hole with super strong magnetic fields.Comment: 3 pages, pdf only. accepted for publication in Science in China Series

Robust Limits on Photon Mass from Statistical Samples of Extragalactic Radio Pulsars

The photon zero-mass hypothesis has been investigated for a long time using the frequency-dependent time delays of radio emissions from astrophysical sources. However, the search for a rest mass of the photon has been hindered by the similarity between the frequency-dependent dispersions due to the plasma and nonzero photon mass effects. Considering the contributions to the observed dispersion measure from both the plasma and nonzero photon mass effects, and assuming the dispersion induced by the plasma effect is an unknown constant, we obtain a robust limit on the photon mass by directly fitting a combination of the dispersion measures of radio sources. Using the observed dispersion measures from two statistical samples of extragalactic pulsars, here we show that at the 68\% confidence level, the constraints on the photon mass can be as low as $m_{\gamma}\leq1.51\times10^{-48}~\rm kg\simeq8.47\times10^{-13}~{\rm eV}/c^{2}$ for the sample of 22 radio pulsars in the Large Magellanic Cloud and $m_{\gamma}\leq1.58\times10^{-48}~\rm kg\simeq8.86\times10^{-13} {\rm eV}/c^{2}$ for the other sample of 5 radio pulsars in the Small Magellanic Cloud, which are comparable with that obtained by a single extragalactic pulsar. Furthermore, the statistical approach presented here can also be used when more fast radio bursts with known redshifts are detected in the future.Comment: 11 pages, 4 figures, 1 table. Accepted for publication in JCA

The Local Stability of Accretion Disks with Advection

The local stability of accretion disks with advection is studied together with the considerations of radial viscous force and thermal diffusion. For a geometrically thin, radiative cooling dominated disk, the thermal diffusion has nearly no effects on the thermal and viscous modes. The including of thermal diffusion, however, tends to stabilize the acoustic modes which, if without advection, are unstable if the disk is optically thick, radiation pressure dominated or optically thin, and are stable if the disk is optically thick, gas pressure dominated. The including of very little advection has significant effects on two acoustic modes. Independent on the optical depth, the instability of the outward propagating mode (O-mode) is enhanced and that of the inward propagating mode (I-mode) is damped if the disk is gas pressure dominated, while the instability of O-mode is damped and that of I-mode is enhanced if the disk is radiation pressure dominated. For a geometrically slim, advection-dominated disk, both the thermal and viscous modes, as well as I-mode, are always stable if the disk is optically thin. The including of thermal diffusion tends to make these modes more stable. However, the O-mode can become unstable when $q/m$ is very large ($q$ is the ratio of advective to viscous dissipated energy and $m$ the Mach number), even if the thermal diffusion is considered. On the other hand, if the advection-dominated disk is optically thick, we found there is no self-consistent acoustic modes in our local analyses. The thermal diffusion has no effect on the stable viscous mode but has a significant contribution to enhance the thermal instability.Comment: 19 pages, LaTeX file. 12 figures are available upon a request to [email protected]. Submitted to Ap

A Further Test of Lorentz Violation from the Rest-Frame Spectral Lags of Gamma-Ray Bursts

Lorentz invariance violation (LIV) can manifest itself by an energy-dependent vacuum dispersion of light, which leads to arrival-time differences of photons with different energies originating from the same astronomical source. The spectral lags of gamma-ray bursts (GRBs) have been widely used to investigate the possible LIV effect. However, all current investigations used lags extracted in the observer frame only. In this work, we present, for the first time, an analysis of the LIV effect and its redshift dependence in the cosmological rest frame. Using a sample of 56 GRBs with known redshifts, we obtain a robust limit on LIV by fitting their rest-frame spectral lag data both using a maximization of the likelihood function and a minimum $\chi^{2}$ statistic. Our analysis indicates that there is no evidence of LIV. Additionally, we test the LIV in different redshift ranges by dividing the full sample into four redshift bins. We also find no evidence for the redshift variation of the LIV effect.Comment: 7 pages, 3 figures, 1 table. Accepted for publication in Ap

Expectations for SZ cluster counts: mass function versus X-ray luminosity function

We present a comparison of the SZ cluster counts predicted by the Press-Schechter (PS) mass function (MF) and the X-ray luminosity function (XLF) of clusters. The employment of the cluster XLF, together with the observationally determined X-ray luminosity(Lx)-temperature(T) relation, may allow us to estimate the SZ cluster counts in a more realistic manner, although such an empirical approach depends sensitively on our current knowledge of the dynamical properties of intracluster gas and its cosmic evolution. Using both the non-evolving and evolving XLFs of clusters suggested by X-ray observations, we calculate the expectations for SZ surveys of clusters with X-ray luminosity Lx>3X10^{44} erg/s and Lx>1X10^{43} erg/s in the 0.5 - 2.0 band, respectively. The non-evolving XLF results in a significant excess of SZ cluster counts at high redshifts as compared with the evolving XLF, while a slightly steeper Lx-T relation than the observed one is needed to reproduce the distributions of SZ clusters predicted by the standard PS formalism. It is pointed out that uncertainties in the cosmological application of future SZ cluster surveys via the standard PS formalism should be carefully studied.Comment: 6 pages, 2 figures, accepted for publication in Ap

Precision Test of the Weak Equivalence Principle from Gamma-Ray Burst Polarization

If the weak equivalence principle (WEP) is broken, the measured values of the parametrized post-Newtonian parameter $\gamma$ from photons with left- and right-handed circular polarizations should differ slightly, leading to the arrival-time difference of these two circular components. Thus, the polarization vector of a linearly polarized light may rotate during the propagation. The rotation angle of the polarization vector depends on both the photon energy and the distance of the source. It is believed that if the rotation angle differs by more than $\pi/2$ over an energy range, then the net polarization of the signal would be significantly suppressed and could not be as high as the observed level. Thus, the detection of highly polarized photons implies that the relative rotation angle ($\Delta\Theta$) should not be too large. In this paper, we give a detailed calculation on the evolution of gamma-ray burst (GRB) polarization arising from a possible violation of the WEP, and we find that more than $60\%$ of the initial polarization degree can be conserved even if $\Delta\Theta$ is larger than $\pi/2$. In addition, to tightly constrain the WEP violation, GRBs with harder spectra and polarization observations in a wider energy range seem to be favored. Applying our formulas to the measurements of linear polarization from GRB 110721A and GRB 061122, we obtain strict limits on the differences of the $\gamma$ values as low as $\Delta\gamma<1.3\times10^{-33}$ and $\Delta\gamma<0.8\times10^{-33}$. These provide the most stringent limits to date on a deviation from the WEP, improving at least 6 orders of magnitude over previous bounds.Comment: 6 pages, 3 figures. Published in PR

The Effect of radiative cooling on the scale-dependence of global stellar and gas contents of groups and clusters of galaxies

It is widely believed that the global baryon content and mass-to-light ratio of groups and clusters of galaxies are a fair representative of the matter mix of the universe and therefore, can be used to reliably determine the cosmic mass density parameter Omega_M. However, this fundamental assumption is challenged by growing evidence from optical and X-ray observations that the average gas mass fraction and mass-to-light ratio increase mildly with scale from poor groups to rich clusters. Although a number of time-consuming hydrodynamical simulations combined with semi-analytic approaches have been carried out, which permit a sophisticated treatment of some complicated processes in the formation and evolution of cosmic structures, the essential physics behind the phenomenon still remains a subject of intense debate. In this Letter, using a simple analytic model, we show that radiative cooling of the hot intragroup/intracluster gas may allow one to reproduce the observed scale-dependence of the global stellar and gas mass fractions and mass-to-light ratio of groups and clusters, provided that about half of the cooled gas is converted into stars. Together with the recent success in the recovery of the entropy excess and the steepening of the X-ray luminosity-temperature relations detected in groups and clusters, radiative cooling provides a simple, unified scheme for the evolution of hot gas and the formation of stars in the largest virialized systems of the universe.Comment: 7 pages, 4 figures, accepted for publication in the June 10 2002 Issue of ApJ Let

Optimal small data Scattering for the generalized derivative nonlinear Schr\"odinger equations

In this work, we consider the following generalized derivative nonlinear Schr\"odinger equation \begin{align*} i\partial_t u+\partial_{xx} u +i |u|^{2\sigma}\partial_x u=0, \quad (t,x)\in \mathbb R\times \mathbb R. \end{align*} We prove that when $\sigma\ge 2$, the solution is global and scattering when the initial data is small in $H^s(\mathbb R)$, $\frac 12\leq s\leq1$. Moreover, we show that when $0<\sigma<2$, there exist a class of solitary wave solutions $\{\phi_c\}$ satisfying $$\|\phi_c\|_{H^1(\mathbb R)}\to 0,$$ when $c$ tends to some endpoint, which is against the small data scattering statement. Therefore, in this model, the exponent $\sigma\ge2$ is optimal for small data scattering. We remark that this exponent is larger than the short range exponent and the Strauss exponent.Comment: 26 page