Flux enhancement in the inner region of a geometrically and optically thick accretion disk

The surface flux (and the corresponding observed flux) of a geometrically thick ``funnel'' shaped disk is computed taking into account the radiation impinging on the surface from other parts of the disk. It is found that the ratio of the maximum apparent luminosity to the real luminosity of the disk is only a factor $\approx 5$ even when the opening angle of the disk is small ($\approx 15^o$). Thus, geometrically beamed emission from ``funnel'' shaped sub-Eddington disks around stellar mass black holes, cannot explain the Ultra-Luminous X-ray sources detected in nearby galaxies.Comment: accepted for publication in Ap

Gravitational waves from nonspinning black hole-neutron star binaries: dependence on equations of state

We report results of a numerical-relativity simulation for the merger of a black hole-neutron star binary with a variety of equations of state (EOSs) modeled by piecewise polytropes. We focus in particular on the dependence of the gravitational waveform at the merger stage on the EOSs. The initial conditions are computed in the moving-puncture framework, assuming that the black hole is nonspinning and the neutron star has an irrotational velocity field. For a small mass ratio of the binaries (e.g., MBH/MNS = 2 where MBH and MNS are the masses of the black hole and neutron star, respectively), the neutron star is tidally disrupted before it is swallowed by the black hole irrespective of the EOS. Especially for less-compact neutron stars, the tidal disruption occurs at a more distant orbit. The tidal disruption is reflected in a cutoff frequency of the gravitational-wave spectrum, above which the spectrum amplitude exponentially decreases. A clear relation is found between the cutoff frequency of the gravitational-wave spectrum and the compactness of the neutron star. This relation also depends weakly on the stiffness of the EOS in the core region of the neutron star, suggesting that not only the compactness but also the EOS at high density is reflected in gravitational waveforms. The mass of the disk formed after the merger shows a similar correlation with the EOS, whereas the spin of the remnant black hole depends primarily on the mass ratio of the binary, and only weakly on the EOS. Properties of the remnant disks are also analyzed.Comment: 27pages, 21 figures; erratum is added on Aug 5. 201

Exploring binary-neutron-star-merger scenario of short-gamma-ray bursts by gravitational-wave observation

We elucidate the feature of gravitational waves (GWs) from binary neutron star merger collapsing to a black hole by general relativistic simulation. We show that GW spectrum imprints the coalescence dynamics, formation process of disk, equation of state for neutron stars, total masses, and mass ratio. A formation mechanism of the central engine of short $\gamma$-ray bursts, which are likely to be composed of a black hole and surrounding disk, therefore could be constrained by GW observation.Comment: Accepted to PR

Time-oscillating Lyapunov modes and auto-correlation functions for quasi-one-dimensional systems

The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed in two types of Lyapunov modes, one associated with the time translational invariance and another with the spatial translational invariance, and their phase relation is specified. It is shown that the longest period of the Lyapunov modes is twice as long as the period of the longitudinal momentum auto-correlation function. A simple explanation for this relation is proposed. This result gives the first quantitative connection between the Lyapunov modes and an experimentally accessible quantity.Comment: 4 pages, 3 figure

Tidal Interaction between a Fluid Star and a Kerr Black Hole in Circular Orbit

We present a semi-analytic study of the equilibrium models of close binary systems containing a fluid star (mass $m$ and radius $R_0$) and a Kerr black hole (mass $M$) in circular orbit. We consider the limit $M\gg m$ where spacetime is described by the Kerr metric. The tidally deformed star is approximated by an ellipsoid, and satisfies the polytropic equation of state. The models also include fluid motion in the stellar interior, allowing binary models with nonsynchronized stellar spin (as expected for coalescing neutron star-black hole binaries) to be constructed. Tidal disruption occurs at orbital radius $r_{\rm tide}\sim R_0(M/m)^{1/3}$, but the dimensionless ratio $\hat r_{\rm tide}=r_{\rm tide}/[R_0(M/m)^{1/3}]$ depends on the spin parameter of the black hole as well as on the equation of state and the internal rotation of the star. We find that the general relativistic tidal field disrupts the star at a larger $\hat r_{\rm tide}$ than the Newtonian tide; the difference is particularly prominent if the disruption occurs in the vicinity of the black hole's horizon. In general, $\hat r_{\rm tide}$ is smaller for a (prograde rotating) Kerr black hole than for a Schwarzschild black hole. We apply our results to coalescing black hole-neutron star and black hole-white dwarf binaries. The tidal disruption limit is important for characterizing the expected gravitational wave signals and is relevant for determining the energetics of gamma ray bursts which may result from such disruption.Comment: 29 pages including 8 figures. Minor changes and update. To appear in ApJ, March 20, 2000 (Vol.532, #1

Observations of Dense Molecular Gas in a Quasar Host Galaxy at z=6.42: Further Evidence for a Non-Linear Dense Gas - Star Formation Relation at Early Cosmic Times

We report a sensitive search for the HCN(J=2-1) emission line towards SDSS J1148+5251 at z=6.42 with the VLA. HCN emission is a star formation indicator, tracing dense molecular hydrogen gas (n(H2) >= 10^4 cm^-3) within star-forming molecular clouds. No emission was detected in the deep interferometer maps of J1148+5251. We derive a limit for the HCN line luminosity of L'(HCN) < 3.3 x 10^9 K km/s pc^2, corresponding to a HCN/CO luminosity ratio of L'(HCN)/L'(CO) < 0.13. This limit is consistent with a fraction of dense molecular gas in J1148+5251 within the range of nearby ultraluminous infrared galaxies (ULIRGs; median value: L'(HCN)/L'(CO) = 0.17 {+0.05/-0.08}) and HCN-detected z>2 galaxies (0.17 {+0.09/-0.08}). The relationship between L'(HCN) and L(FIR) is considered to be a measure for the efficiency at which stars form out of dense gas. In the nearby universe, these quantities show a linear correlation, and thus, a practically constant average ratio. In J1148+5251, we find L(FIR)/L'(HCN) > 6600. This is significantly higher than the average ratios for normal nearby spiral galaxies (L(FIR)/L'(HCN) = 580 {+510/-270}) and ULIRGs (740 {+505/-50}), but consistent with a rising trend as indicated by other z>2 galaxies (predominantly quasars; 1525 {+1300/-475}). It is unlikely that this rising trend can be accounted for by a contribution of AGN heating to L(FIR) alone, and may hint at a higher median gas density and/or elevated star-formation efficiency toward the more luminous high-redshift systems. There is marginal evidence that the L(FIR)/L'(HCN) ratio in J1148+5251 may even exceed the rising trend set by other z>2 galaxies; however, only future facilities with very large collecting areas such as the SKA will offer the sensitivity required to further investigate this question.Comment: 5 pages, 2 figures, 2 tables, to appear in ApJL (accepted October 24, 2007