arXiv subjects

S. L. Shapiro

Publications and source records attributed to S. L. Shapiro.

23 records · Page 2Linked to original sources

arXiv1994

Hydrodynamic Evolution of Coalescing Compact Binaries

In addition to their possible relevance to gamma-ray bursts, coalescing binary neutron stars have long been recognized as important sources of gravitational radiation that should become detectable with the new generation of laser interferometers such as LIGO. Hydrodynamics plays an essential role near the end of the coalescence when the two stars finally merge together into a single object. The shape of the corresponding burst of gravitational waves provides a direct probe into the interior structure of a neutron star and the nuclear equation of state. The interpretation of the gravitational waveform data will require detailed theoretical models of the complicated three-dimensional hydrodynamic processes involved. Here we review the results of our recent work on this problem, using both approximate quasi-analytic methods and large-scale numerical hydrodynamics calculations on supercomputers. We also discuss briefly the coalescence of white-dwarf binaries, which are also associated with a variety of interesting astrophysical phenomena.

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arXiv1994

Hydrodynamics of Binary Coalescence. II. Polytropes with Gamma=5/3

We present a new numerical study of the equilibrium and stability properties of close binary systems using the smoothed-particle hydrodynamics (SPH) technique. We adopt a simple polytropic equation of state $p=Kρ^\gam$ with $\gam=5/3$ and $K=\,$constant within each star, applicable to low-mass degenerate dwarfs as well as low-mass main-sequence stars. Along a sequence of binary equilibrium configurations for two identical stars, we demonstrate the existence of both secular and dynamical instabilities, confirming directly the results of recent analytic work. We use the SPH method to calculate the nonlinear development of the dynamical instability and to determine the final fate of the system. We find that the two stars merge together into a single, rapidly rotating object in just a few orbital periods. Equilibrium sequences are also constructed for systems containing two nonidentical stars. These sequences terminate at a Roche limit, which we can determine very accurately using SPH. For two low-mass main-sequence stars with mass ratio $q\lo0.4$ we find that the (synchronized) Roche limit configuration is secularly unstable. Degenerate binary configurations remain hydrodynamically stable all the way to the Roche limit for all mass ratios $q\ne1$. Dynamically unstable mass transfer can also lead to the rapid coalescence of a binary system, but the details of the hydrodynamic evolution are quite different. We discuss the implications of our results for double white-dwarf and W Ursae Majoris systems.

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arXiv1994

Hydrodynamics of Binary Coalescence.I. Polytropes with Stiff Equations of State

We have performed a series of three-dimensional hydrodynamic calculations of binary coalescence using the smoothed particle hydrodynamics (SPH) method. The initial conditions are exact polytropic equilibrium configurations with $\gam > 5/3$, on the verge of dynamical instability. We calculate the emission of gravitational radiation in the quadrupole approximation. The fully nonlinear development of the instability is followed until a new equilibrium configuration is reached. We find that the properties of this final configuration depend sensitively on both the compressibility and mass ratio. An {\em axisymmetric} merged configuration is always produced when $\gam\lo2.3$. As a consequence, the emission of gravitational radiation shuts off abruptly right after the onset of dynamical instability. In contrast, {\em triaxial\/} merged configurations are obtained when $\gam\go2.3$, and the system continues to emit gravitational waves after the final coalescence. Systems with mass ratios $q\ne1$ typically become dynamically unstable before the onset of mass transfer. Stable mass transfer from one neutron star to another in a close binary is therefore probably ruled out. The maximum amplitude $h_{max}$ and peak luminosity $L_{max}$ of the gravitational waves emitted during the final coalescence are nearly independent of $\gam$, but depend very sensitively on the mass ratio $q$.

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arXiv1993

Equilibrium, Stability and Orbital Evolution of Close Binary Systems

We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We consider both synchronized and nonsynchronized systems, constructing the compressible generalizations of the classical Darwin and Darwin-Riemann configurations. Our method can be applied to a wide variety of binary models where the stellar masses, radii, spins, entropies, and polytropic indices are all allowed to vary over wide ranges and independently for each component. We find that both secular and dynamical instabilities can develop before a Roche limit or contact is reached along a sequence of models with decreasing binary separation. High incompressibility always makes a given binary system more susceptible to these instabilities, but the dependence on the mass ratio is more complicated. As simple applications, we construct models of double degenerate systems and of low-mass main-sequence-star binaries. We also discuss the orbital evolution of close binary systems under the combined influence of fluid viscosity and secular angular momentum losses from processes like gravitational radiation. We show that the existence of global fluid instabilities can have a profound effect on the terminal evolution of coalescing binaries. The validity of our analytic solutions is examined by means of detailed comparisons with the results of recent numerical fluid calculations in three dimensions.

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arXiv1993

Hydrodynamic Instability and Coalescence of Binary Neutron Stars

We study the importance of hydrodynamic effects on the evolution of coalescing binary neutron stars. Using an approximate energy functional constructed from equilibrium solutions for polytropic binary configurations, we incorporate hydrodynamic effects into the calculation of the orbital decay driven by gravitational wave emission. In particular, we follow the transition between the quasi-static, secular decay of the orbit at large separation and the rapid dynamical evolution of configurations approaching contact. We show that a purely Newtonian hydrodynamic instability can significantly accelerate the coalescence at small separation. Such an instability occurs in all close binary configurations containing sufficiently incompressible stars. Calculations are performed for various neutron star masses, radii, spins, and effective polytropic indices. Typically, we find that the radial infall velocity just prior to contact is about 10\% of the tangential orbital velocity. Post-Newtonian effects can move the stability limit to a larger binary separation, and may induce an even larger radial velocity. We also consider the possibility of mass transfer from one neutron star to the other. We show that stable mass transfer is impossible except when the mass of one of the components is very small (less than about 0.4 solar mass) and the viscosity is high enough to maintain corotation.

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