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We show that r-mode oscillations distort the magnetic fields of neutron stars and that their occurrence is likely to be limited by this interaction. If the field is gtrsim 10^{16} (Omega/Omega_B) G, where Omega and Omega_B are the angular velocities of the star and at which mass shedding occurs, r-mode oscillations cannot occur. Much weaker fields will prevent gravitational radiation from exciting r-mode oscillations or damp them on a relatively short timescale by extracting energy from the modes faster than gravitational wave emission can pump energy into them. For example, a 10^{10} G poloidal magnetic field that threads the star's superconducting core is likely to prevent the ell=2 mode from being excited unless Omega exceeds 0.35 Omega_B. If Omega is larger than 0.35 Omega_B initially, the ell=2 mode may be excited but is likely to decay rapidly once Omega falls below 0.35 Omega_B, which happens in lesssim 15^d if the saturation amplitude is gtrsim 0.1. The r-mode oscillations may play an important role in determining the structure of neutron star magnetic fields., Comment: 4 pages, 1 postscript figure, uses emulateapj; submitted to ApJ Letters 1999 Nov 8; accepted 2000 Jan 25; this version is essentially identical to the original version except that Figure 2 was deleted in order to fit within the ApJ Letters page limit

We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such ``hypermassive'' models in full general relativity and show that there do exist configurations which are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst., Comment: 4 pages, 2 figures, uses emulateapj.sty; to appear in ApJ Letters

Recent numerical simulations address a conjecture by Shapiro that when two neutron stars collide head-on from rest at infinity, sufficient thermal pressure may be generated to support the hot remnant in quasi-static equilibrium against collapse prior to neutrino cooling. The conjecture is meant to apply even when the total remnant mass exceeds the maximum mass of a cold neutron star. One set of simulations seems to corroborate the conjecture, while another, involving higher mass progenitors each very close to the maximum mass, does not. In both cases the total mass of the remnant exceeds the maximum mass. We point out numerical subtleties in performing such simulations when the progenitors are near the maximum mass; they can explain why the simulations might have difficulty assessing the conjecture in such high-mass cases., Comment: 3 pages

We determine the effect of rotation on the luminosity of supermassive stars. We apply the Roche model to calculate analytically the emitted radiation from a uniformly rotating, radiation-dominated supermassive configuration. We find that the luminosity at maximum rotation, when mass at the equator orbits at the Kepler period, is reduced by ~36% below the usual Eddington luminosity from the corresponding nonrotating star. A supermassive star is believed to evolve in a quasistationary manner along such a maximally rotating ``mass-shedding'' sequence before reaching the point of dynamical instability; hence this reduced luminosity determines the evolutionary timescale. Our result therefore implies that the lifetime of a supermassive star prior to dynamical collapse is ~56% longer than the value typically estimated by employing the usual Eddington luminosity., Comment: 5 pages, 2 figures, uses emulateapj.sty; to appear in ApJ

We launch a fully relativistic study of the formation of supermassive black holes via the collapse of supermassive stars. Here we initiate our investigation by analyzing the secular evolution of supermassive stars up to the onset of dynamical instability and collapse. We focus on the effects of rotation, assumed uniform, and general relativity. We identify the critical configuration at which radial instability sets in and determine its structure in detail. We show that the key nondimensional ratios R/M, T/|W| and J/M^2 (T is the rotational kinetic energy and W is the gravitational potential energy) for this critical configuration are universal numbers, independent of the mass, spin, radius or history of the star. We compare results from an approximate, analytic treatment with a fully relativistic, numerical calculation and find good agreement. We solve analytically for the time evolution of these parameters up to the onset of instability. Cooling by photon radiation drives the evolution, which is accompanied by mass, angular momentum and entropy loss. The critical configuration serves as initial data for a future relativistic, hydrodynamical, 3D simulation of the collapse of an unstable supermassive star. Since this implosion starts from a universal critical configuration, the collapse is also uniquely determined and should produce a universal gravitational waveform. In this paper we briefly speculate on the possible outcome of this collapse and asses to what extent it offers a promising route to forming a supermassive black hole., Comment: 13 pages, 6 figures, uses emulateapj.sty; to appear in ApJ

We improve and extend Shapiro's model of a relativistic, compact object which is stable in isolation but is driven dynamically unstable by the tidal field of a binary companion. Our compact object consists of a dense swarm of test particles moving in randomly-oriented, initially circular, relativistic orbits about a nonrotating black hole. The binary companion is a distant, slowly inspiraling point mass. The tidal field of the companion is treated as a small perturbation on the background Schwarzschild geometry near the hole; the resulting metric is determined by solving the perturbation equations of Regge and Wheeler and Zerilli in the quasi-static limit. The perturbed spacetime supports Bekenstein's conjecture that the horizon area of a near-equilibrium black hole is an adiabatic invariant. We follow the evolution of the system and confirm that gravitational collapse can be induced in a compact collisionless cluster by the tidal field of a binary companion., Comment: 9 Latex pages, 14 postscript figures

We include matter sources in Einstein's field equations and show that our recently proposed 3+1 evolution scheme can stably evolve strong-field solutions. We insert in our code known matter solutions, namely the Oppenheimer-Volkoff solution for a static star and the Oppenheimer-Snyder solution for homogeneous dust sphere collapse to a black hole, and evolve the gravitational field equations. We find that we can evolve stably static, strong-field stars for arbitrarily long times and can follow dust sphere collapse accurately well past black hole formation. These tests are useful diagnostics for fully self-consistent, stable hydrodynamical simulations in 3+1 general relativity. Moreover, they suggest a successive approximation scheme for determining gravitational waveforms from strong-field sources dominated by longitudinal fields, like binary neutron stars: approximate quasi-equilibrium models can serve as sources for the transverse field equations, which can be evolved without having to re-solve the hydrodynamical equations (``hydro without hydro'')., Comment: 4 postscript figures. Submitted to Phys. Rev. D15 as a Brief Report

Coalescing compact binaries with neutron star or black hole components provide the most promising sources of gravitational radiation for detection by the LIGO/VIRGO/GEO/TAMA laser interferometers now under construction. This fact has motivated several different theoretical studies of the inspiral and hydrodynamic merging of compact binaries. Analytic analyses of the inspiral waveforms have been performed in the Post-Newtonian approximation. Analytic and numerical treatments of the coalescence waveforms from binary neutron stars have been performed using Newtonian hydrodynamics and the quadrupole radiation approximation. Numerical simulations of coalescing black hole and neutron star binaries are also underway in full general relativity. Recent results from each of these approaches will be described and their virtues and limitations summarized., Comment: Invited Topical Review paper to appear in Classical and Quantum Gravity, 35 pages, including 5 figures

Many numerical codes now under development to solve Einstein's equations of general relativity in 3+1 dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial metric and extrinsic curvature tensors. Following Shibata and Nakamura, we modify these equations by factoring out the conformal factor and introducing three ``connection functions''. The evolution equations can then be reduced to wave equations for the conformal metric components, which are coupled to evolution equations for the connection functions. We evolve small amplitude gravitational waves and make a direct comparison of the numerical performance of the modified equations with the standard ADM equations. We find that the modified form exhibits much improved stability., Comment: 7 pages, 3 figures, RevTeX, to appear in Phys. Rev. D

The head-on collision of identical neutron stars from rest at infinity requires a numerical simulation in full general relativity for a complete solution. Undaunted, we provide a relativistic, analytic argument to suggest that during the collision, sufficient thermal pressure is always generated to support the hot remnant in quasi-static stable equilibrium against collapse prior to slow cooling via neutrino emission. Our conclusion is independent of the total mass of the progenitors and holds even if the remnant greatly exceeds the maximum mass of a cold neutron star., Comment: to appear in Physical Review D (revtex, 3 figs, 5 pgs)

We have performed a series of systematic tests to evaluate the effects of spurious transport in three-dimensional smoothed particle hydrodynamics (SPH) calculations. Our tests investigate (i) particle diffusion, (ii) shock heating, (iii) numerical viscosity, and (iv) angular momentum transport. The results are useful for quantifying the accuracy of the SPH scheme, especially for problems where shear flows or shocks are present, as well as for problems where true hydrodynamic mixing is relevant. We examine the different forms of artificial viscosity (AV) which have been proposed by Monaghan, by Hernquist & Katz, and by Balsara. For each form, our tests suggest a single set of values for the AV parameters $\alpha$ and $\beta$ (coefficients of the linear and quadratic terms) which are appropriate in a large number of situations. We also discuss how these parameters should be adjusted depending on the goals of the particular application. We find that both the Hernquist & Katz and Balsara forms introduce relatively small amounts of numerical viscosity. Furthermore, both Monaghan's and Balsara's AV do well at treating shocks and at limiting the amount of spurious mixing. For these reasons, we endorse the Balsara AV for use in a broad range of applications., Comment: 49 pages, 26 figures as 30 postscript files, submitted to The Journal of Computational Physics

We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution., Comment: 20 pages, RevTeX

We have recently constructed a numerical code that evolves a spherically symmetric spacetime using a hyperbolic formulation of Einstein's equations. For the case of a Schwarzschild black hole, this code works well at early times, but quickly becomes inaccurate on a time scale of 10-100 M, where M is the mass of the hole. We present an analytic method that facilitates the detection of instabilities. Using this method, we identify a term in the evolution equations that leads to a rapidly-growing mode in the solution. After eliminating this term from the evolution equations by means of algebraic constraints, we can achieve free evolution for times exceeding 10000M. We discuss the implications for three-dimensional simulations., Comment: 13 pages, 9 figures. To appear in Phys. Rev. D

Observations combined with theoretical modeling of the light curve of the recently discovered supernova 1997D in NGC 1536 suggest that it might host a black hole formed in the aftermath of the explosion. We consider some observable consequences of a black hole in SN 1997D and estimate the late--time accretion luminosity of the material which falls back onto the hole. We find that this luminosity, decaying with a characteristic power--law dependence on time, may emerge above the emission of the envelope in just a few years. Its detection would thus provide unmistakable evidence for the presence of a black hole., Comment: 8 pages, LaTeX, aaspp4.sty style file (AASTEX package), 2 postscript figures (included). To appear in The Astrophysical Journal Letters (scheduled for August 1, 1998 issue, Vol. 502)

We present the first fully relativistic investigation of matter fallback in a supernova. We investigate spherically symmetric supernova fallback using a relativistic radiation hydrodynamics Lagrangian code that handles radiation transport in all regimes. Our goal is to answer the fundamental question: did SN1987A produce a black hole and, if so, when will the hole become detectable ? We compute the light curve, assuming that a black hole has been formed during the explosion, and compare it with the observations. Our preliminary calculations lack radioactive energy input and adopt a very simple chemical composition (pure hydrogen). As a result, our computed models cannot fit the observed data of SN1987A in detail. Nevertheless, we can show that, during the first hours, the accretion flow is self--regulated and the accretion luminosity stays very close to the Eddington limit. The light curve is completely dominated, during the first few weeks, by the emission of the stellar envelope thermal energy, and resembles that obtained in ``standard'' supernova theory. Only long after hydrogen recombination takes place is there even a chance to actually detect radiation from the accreting black hole above the emission of the expanding envelope. The presence of a black hole is thus not inconsistent with observations to date. Because of the exponential decay of the $^{44}$Ti radioactive heating rate, the date of the emergence of the black hole is not very sensitive to the actual parameters of the models and turns out to be about 1000 years. The bulk of the emission then is expected to be in the visible band, but will be unobservable with present instrumentation. We discuss the implications of our results in connection with the possible emergence of a black hole in other supernovae., Comment: 29 pages, LaTeX, aaspp4.sty style file (AASTEX package), 2 tables (postscript), 22 figures (postscript). To appear in ApJ (scheduled for the September 1, 1998 issue, Vol. 504)

We study neutrino emission from the remnant of an inspiraling binary neutron star following coalescence. The mass of the merged remnant is likely to exceed the stability limit of a cold, rotating neutron star. However, the angular momentum of the remnant may also approach or even exceed the Kerr limit, J/M^2 = 1, so that total collapse may not be possible unless some angular momentum is dissipated. We find that neutrino emission is very inefficient in decreasing the angular momentum of these merged objects and may even lead to a small increase in J/M^2. We illustrate these findings with a post-Newtonian, ellipsoidal model calculation. Simple arguments suggest that the remnant may form a bar mode instability on a timescale similar to or shorter than the neutrino emission timescale, in which case the evolution of the remnant will be dominated by the emission of gravitational waves., Comment: 12 pages AASTeX, 2 figures, to appear in ApJ

We present results from a fully relativistic investigation of matter fallback in a supernova, assuming that the central compact star is a black hole (BH). Our goal is to answer the following questions: can we infer from the light curve whether a stellar black hole (BH) has formed in the aftermath of a supernova explosion ? Did SN1897A produce a BH and, if so, when will the hole become detectable ? We show that it should not be possible to infer the presence of a BH in the remnant for another several hundred to a thousand years. In the case of SN1987A, we estimate the BH luminosity to be $L\simeq 5\times 10^{34}$ erg s$^{-1}$, which is well below the present day bolometric luminosity of the remnant ($\sim 10^{36}erg/s$; Suntzeff 1997)., Comment: 5 pages, LaTeX, AIP style file (aipproc.sty), 2 postscript figures. To appear in the Proceedings of the 8th Annual Astrophysics Conference in Maryland, "Accretion Processes in Astrophysical Systems", S. S. Holt & T. Kallman eds

We present a method for constructing equilibrium disks with net angular momentum in general relativity. The method solves the relativistic Vlasov equation coupled to Einstein's equations for the gravitational field. We apply the method to construct disks that are relativistic versions of Newtonian Kalnajs disks. In Newtonian gravity these disks are analytic, and are stable against ring formation for certain ranges of their velocity dispersion. We investigate the existence of fully general relativistic equilibrium sequences for differing values of the velocity dispersion. These models are the first rotating, relativistic disk solutions of the collisionless Boltzman equation.

We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case., Comment: 23 pages RevTeX plus 7 PostScript figures. Submitted to Phys. Rev. D

Using an energy variational method, we calculate quasi-equilibrium configurations of binary neutron stars modeled as compressible triaxial ellipsoids obeying a polytropic equation of state. Our energy functional includes terms both for the internal hydrodynamics of the stars and for the external orbital motion. We add the leading post-Newtonian (PN) corrections to the internal and gravitational energies of the stars, and adopt hybrid orbital terms which are fully relativistic in the test-mass limit and always accurate to PN order. The total energy functional is varied to find quasi-equilibrium sequences for both corotating and irrotational binaries in circular orbits. We examine how the orbital frequency at the innermost stable circular orbit depends on the polytropic index n and the compactness parameter GM/Rc^2. We find that, for a given GM/Rc^2, the innermost stable circular orbit along an irrotational sequence is about 17% larger than the innermost secularly stable circular orbit along the corotating sequence when n=0.5, and 20% larger when n=1. We also examine the dependence of the maximum neutron star mass on the orbital frequency and find that, if PN tidal effects can be neglected, the maximum equilibrium mass increases as the orbital separation decreases., Comment: 53 pages, LaTex, 9 figures as 10 postscript files, accepted by Phys. Rev. D, replaced version contains updated references

We explore the evolution of collisionally merged stars in the blue straggler region of the HR diagram. The starting models for our stellar evolution calculations are the results of the smoothed particle hydrodynamics (SPH) simulations of parabolic collisions between main sequence stars performed by Lombardi, Rasio and Shapiro (1996). Since SPH and stellar evolution codes employ different and often contradictory approximations, it is necessary to treat the evolution of these products carefully. The mixture and disparity of the relevant timescales (hydrodynamic, thermal relaxation and nuclear burning) and of the important physical assumptions between the codes makes the combined analysis of the problem challenging, especially during the initial thermal relaxation of the star. In particular, the treatment of convection is important, and semiconvection must be modeled in some detail. The products of seven head-on collisions are evolved through their initial thermal relaxation, and then through the main sequence phase to the base of the giant branch. Their evolutionary tracks are presented. In contrast to the assumptions in previous work, these collision products do not develop substantial convective regions during their thermal relaxation, and therefore are not mixed significantly after the collision., Comment: 45 pages, 8 figures (encapsulated postscript), uses AASTeX, to be published in Astrophysical Journal volume 487

We present a numerical scheme that solves the initial value problem in full general relativity for a binary neutron star in quasi-equilibrium. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to lose energy and slowly spiral inwards. However, since inspiral occurs on a time scale much longer than the orbital period, we can adopt a quasi-equilibrium approximation. In this approximation, we integrate a subset of the Einstein equations coupled to the equations of relativistic hydrodynamics to solve the initial value problem for binaries of arbitrary separation, down to the innermost stable orbit., Comment: 3 pages LaTeX using sprocl.sty, 2 figures, to appear in: Proceedings of the 18th Texas Symposium on Relativistic Astrophysics (eds Olinto, Frieman and Schramm, World Scientific)

Locating apparent horizons is not only important for a complete understanding of numerically generated spacetimes, but it may also be a crucial component of the technique for evolving black-hole spacetimes accurately. A scheme proposed by Libson et al., based on expanding the location of the apparent horizon in terms of symmetric trace-free tensors, seems very promising for use with three-dimensional numerical data sets. In this paper, we generalize this scheme and perform a number of code tests to fully calibrate its behavior in black-hole spacetimes similar to those we expect to encounter in solving the binary black-hole coalescence problem. An important aspect of the generalization is that we can compute the symmetric trace-free tensor expansion to any order. This enables us to determine how far we must carry the expansion to achieve results of a desired accuracy. To accomplish this generalization, we describe a new and very convenient set of recurrence relations which apply to symmetric trace-free tensors., Comment: 14 pages (RevTeX 3.0 with 3 figures)

Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on isolated, rapidly rotating, relativistic stars. Since these objects are in equilibrium, it is crucial that the approximation work well if we are to believe its predictions for more complicated systems like binaries. Our results are very encouraging., Comment: 9 pages (RevTeX 3.0 with 6 uuencoded figures), CRSR-1079

We report the results of new SPH calculations of parabolic collisions between main-sequence (MS) stars. The stars are assumed to be close to the MS turn-off point in a globular cluster and are therefore modeled as $n=3$, $\Gamma=5/3$ polytropes. We find that the high degree of central mass concentration in these stars has a profound effect on the hydrodynamics. In particular, very little hydrodynamic mixing occurs between the dense, helium-rich inner cores and the outer envelopes. As a result, and in contrast to what has been assumed in previous studies, blue stragglers formed by direct stellar collisions are not necessarily expected to have anomalously high helium abundances in their envelopes or to have their cores replenished with fresh hydrogen fuel., Comment: uuencoded compressed postscript with figures, 10 pages (Figure 1 available upon request from best@sns.ias.edu)

We present a new numerical code that evolves a spherically symmetric configuration of collisionless matter in the Brans-Dicke theory of gravitation. In this theory the spacetime is dynamical even in spherical symmetry, where it can contain gravitational radiation. Our code is capable of accurately tracking collapse to a black hole in a dynamical spacetime arbitrarily far into the future, without encountering either coordinate pathologies or spacetime singularities. This is accomplished by truncating the spacetime at a spherical surface inside the apparent horizon, and subsequently solving the evolution and constraint equations only in the exterior region. We use our code to address a number of long-standing theoretical questions about collapse to black holes in Brans-Dicke theory., Comment: 46 pages including figures, uuencoded gz-compressed postscript, Submitted to Phys Rev D

We discuss a number of long-standing theoretical questions about collapse to black holes in the Brans-Dicke theory of gravitation. Using a new numerical code, we show that Oppenheimer-Snyder collapse in this theory produces black holes that are identical to those of general relativity in final equilibrium, but are quite different from those of general relativity during dynamical evolution. We find that there are epochs during which the apparent horizon of such a black hole passes {\it outside\/} the event horizon, and that the surface area of the event horizon {\it decreases\/} with time. This behavior is possible because theorems which prove otherwise assume $R_{ab}l^al^b \ge 0$ for all null vectors $l^a$. We show that dynamical spacetimes in Brans-Dicke theory can violate this inequality, even in vacuum, for any value of $\omega$., Comment: 24 pages including figures, uuencoded gz-compressed postscript, Submitted to Phys Rev D

Many simulations of gravitational collapse to black holes become inaccurate before the total emitted gravitational radiation can be determined. The main difficulty is that a significant component of the radiation is still in the near-zone, strong field region at the time the simulation breaks down. We show how to calculate the emitted waveform by matching the numerical simulation to a perturbation solution when the final state of the system approaches a Schwarzschild black hole. We apply the technique to two scenarios: the head-on collision of two black holes, and the collapse of a disk to a black hole. This is the first reasonably accurate calculation of the radiation generated from colliding black holes that form from matter collapse., Comment: 8 pages (RevTex 3.0 with 7 uuencoded figures)

The radial collapse of a homogeneous disk of collisionless particles can be solved analytically in Newtonian gravitation. To solve the problem in general relativity, however, requires the full machinery of numerical relativity. The collapse of a disk is the simplest problem that exhibits the two most significant and challenging features of strong-field gravitation: black hole formation and gravitational wave generation. We carry out dynamical calculations of several different relativistic disk systems. We explore the growth of ring instabilities in equilibrium disks, and how they are suppressed by sufficient velocity dispersion. We calculate wave forms from oscillating disks, and from disks that undergo gravitational collapse to black holes. Studies of disk collapse to black holes should also be useful for developing new techniques for numerical relativity, such as apparent horizon boundary conditions for black hole spacetimes., Comment: CRSR 1072, 10 pages (RevTex 3.0 with 9 uuencoded figures)

We develop a new formalism to study the dynamics of fluid polytropes in three dimensions. The stars are modeled as compressible ellipsoids and the hydrodynamic equations are reduced to a set of ordinary differential equations for the evolution of the principal axes and other global quantities. Both viscous dissipation and the gravitational radiation reaction are incorporated. We establish the validity of our approximations and demonstrate the simplicity and power of the method by rederiving a number of known results concerning the stability and dynamical oscillations of rapidly rotating polytropes. In particular, we present a generalization to compressible fluids of Chandrasekhar's classical results for the secular and dynamical instabilities of incompressible Maclaurin spheroids. We also present several applications of our method to astrophysical problems of great current interest such as the tidal disruption of a star by a massive black hole, the coalescence of compact binaries driven by the emission of gravitational waves, and the development of instabilities in close binary systems., Comment: 43 pages, plain TeX file, figures available upon request from Best@sns.ias.edu. IAS number AST 94/12