arXiv subjects

Frederic A. Rasio

Publications and source records attributed to Frederic A. Rasio.

At least 181 records · Page 10Linked to original sources

arXiv2001

Ruling Out Chaos in Compact Binary Systems

We investigate the orbits of compact binary systems during the final inspiral period before coalescence by integrating numerically the second-order post-Newtonian equations of motion. We include spin-orbit and spin-spin coupling terms, which, according to a recent study by Levin [J. Levin, Phys. Rev. Lett. 84, 3515 (2000)], may cause the orbits to become chaotic. To examine this claim, we study the divergence of initially nearby phase-space trajectories and attempt to measure the Lyapunov exponent gamma. Even for systems with maximally spinning objects and large spin-orbit misalignment angles, we find no chaotic behavior. For all the systems we consider, we can place a strict lower limit on the divergence time t_L=1/gamma that is many times greater than the typical inspiral time, suggesting that chaos should not adversely affect the detection of inspiral events by upcoming gravitational-wave detectors.

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arXiv2001

Binaries and Globular Cluster Dynamics

We summarize the results of recent theoretical work on the dynamical evolution of globular clusters containing primordial binaries. Even a very small initial binary fraction (e.g., 10%) can play a key role in supporting a cluster against gravothermal collapse for many relaxation times. Inelastic encounters between binaries and single stars or other binaries provide a very significant energy source for the cluster. These dynamical interactions also lead to the production of large numbers of exotic systems such as ultracompact X-ray binaries, recycled radio pulsars, double degenerate systems, and blue stragglers. Our work is based on a new parallel supercomputer code implementing Henon's Monte Carlo method for simulating the dynamical evolution of dense stellar systems in the Fokker-Planck approximation. This new code allows us to calculate very accurately the evolution of a cluster containing a realistic number of stars (N ~ 10^5 - 10^6) in typically a few hours to a few days of computing time. The discrete, star-by-star representation of the cluster in the simulation makes it possible to treat naturally a number of important processes, including single and binary star evolution, all dynamical interactions of single stars and binaries, and tidal interactions with the Galaxy.

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arXiv2001

Monte Carlo Simulations of Globular Cluster Evolution - II. Mass Spectra, Stellar Evolution and Lifetimes in the Galaxy

We study the dynamical evolution of globular clusters using our new 2-D Monte Carlo code, and we calculate the lifetimes of clusters in the Galactic environment. We include the effects of a mass spectrum, mass loss in the Galactic tidal field, and stellar evolution. We consider initial King models containing N = 10^5 - 3x10^5 stars, and follow the evolution up to core collapse, or disruption, whichever occurs first. We find that the lifetimes of our models are significantly longer than those obtained using 1-D Fokker-Planck (F-P) methods. We also find that our results are in very good agreement with recent 2-D F-P calculations, for a wide range of initial conditions. Our results show that the direct mass loss due to stellar evolution can significantly accelerate the mass loss through the tidal boundary, causing most clusters with a low initial central concentration (Wo <~ 3) to disrupt quickly in the Galactic tidal field. Only clusters born with high initial central concentrations (Wo >~ 7) or steep initial mass functions are likely to survive to the present and undergo core collapse. We also study the orbital characteristics of escaping stars, and find that the velocity distribution of escaping stars in collapsing clusters looks significantly different from the distribution in disrupting clusters. We calculate the lifetime of a cluster on an eccentric orbit in the Galaxy, such that it fills its Roche lobe only at perigalacticon. We find that such an orbit can extend the lifetime by at most a factor of a few compared to a circular orbit in which the cluster fills its Roche lobe at all times.

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arXiv2001

Hydrodynamics of Neutron Star Mergers

The final burst of gravitational radiation emitted by coalescing binary neutron stars carries direct information about the neutron star fluid, and, in particular, about the equation of state of nuclear matter at extreme densities. The final merger may also be accompanied by a detectable electromagnetic signal, such as a gamma-ray burst. In this paper, we summarize the results of theoretical work done over the past decade that has led to a detailed understanding of this hydrodynamic merger process for two neutron stars, and we discuss the prospects for the detection and physical interpretation of the gravity wave signals by ground-based interferometers such as LIGO. We also present results from our latest post-Newtonian SPH calculations of binary neutron star coalescence, using up to 10^6 SPH particles to compute with higher spatial resolution than ever before the merger of an initially irrotational system. We discuss the detectability of our calculated gravity wave signals based on power spectra.

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arXiv2001

Stellar Collisions and Blue Straggler Formation

We review recent 3D hydrodynamic calculations of stellar collisions using the Smoothed Particle Hydrodynamics (SPH) method, and we discuss the implications of the results for the formation and evolution of blue stragglers in globular clusters. We also discuss the construction of simple analytic models for merger remnants, approximating the mass loss, shock heating, mixing, and angular momentum transport during a collision with simple algorithms that can be calibrated using our 3D hydrodynamic results. The thermodynamic and chemical composition profiles predicted by these simple models are compared with those from our SPH simulations, demonstrating that our new models provide accurate representations of true collisional merger remnants.

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arXiv2000

Dynamical Instabilities in Extrasolar Planetary Systems Containing Two Giant Planets

Instabilities and strong dynamical interactions between several giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities would seem to provide a natural mechanism for producing the highly eccentric orbits seen in many systems. Here we present results from numerical integrations for the dynamical evolution of planetary systems containing two identical giant planets in nearly circular orbits very close to the dynamical stability limit. We determine the statistical properties of the three main types of systems resulting from the development of an instability: systems containing one planet, following either a collision between the two initial planets, or the ejection of one of them to infinity, and systems containing two planets in a new, quasi-stable configuration. We discuss the implications of our results for the formation and evolution of observed extrasolar planetary systems. We conclude that the distributions of eccentricities and semimajor axes for observed systems cannot be explained easily by invoking dynamical interactions between two planets initially on circular orbits. While highly eccentric orbits can be produced naturally by these interactions, collisions between the two planets, which occur frequently in the range of observed semimajor axes, would result in many more nearly circular orbits than in the observed sample.

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arXiv2000

Post-Newtonian SPH calculations of binary neutron star coalescence. II. Binary mass ratio, equation of state, and spin dependence

Using our new Post-Newtonian SPH (smoothed particle hydrodynamics) code, we study the final coalescence and merging of neutron star (NS) binaries. We vary the stiffness of the equation of state (EOS) as well as the initial binary mass ratio and stellar spins. Results are compared to those of Newtonian calculations, with and without the inclusion of the gravitational radiation reaction. We find a much steeper decrease in the gravity wave peak strain and luminosity with decreasing mass ratio than would be predicted by simple point-mass formulae. For NS with softer EOS (which we model as simple $Γ=2$ polytropes) we find a stronger gravity wave emission, with a different morphology than for stiffer EOS (modeled as $Γ=3$ polytropes as in our previous work). We also calculate the coalescence of NS binaries with an irrotational initial condition, and find that the gravity wave signal is relatively suppressed compared to the synchronized case, but shows a very significant second peak of emission. Mass shedding is also greatly reduced, and occurs via a different mechanism than in the synchronized case. We discuss the implications of our results for gravity wave astronomy with laser interferometers such as LIGO, and for theoretical models of gamma-ray bursts (GRBs) based on NS mergers.

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arXiv2000

Evolution of Stellar Collision Products in Globular Clusters - II. Off-axis Collision

We continue our exploration of collisionally merged stars in the blue straggler region of the color-magnitude diagram. We report the results of new SPH calculations of parabolic collisions between two main-sequence stars, with the initial structure and composition profiles of the parent stars having been determined from stellar evolution calculations. Parallelization of the SPH code has permitted much higher numerical resolution of the hydrodynamics. We also present evolutionary tracks for the resulting collision products, which emerge as rapidly rotating blue stragglers. The rotating collision products are brighter, bluer and remain on the main sequence longer than their non-rotating counterparts. In addition, they retain their rapid rotation rates throughout their main sequence lifetime. Rotationally-induced mixing strongly affects the evolution of the collision products, although it is not sufficient to mix the entire star. We discuss the implications of these results for studies of blue straggler populations in clusters. This work shows that off-axis collision products cannot become blue stragglers unless they lose a large fraction of their initial angular momentum. The mechanism for this loss is not apparent, although some possibilities are discussed.

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arXiv2000

Post-Newtonian SPH calculations of binary neutron star coalescence. I. Method and first results

We present the first results from our Post-Newtonian (PN) Smoothed Particle Hydrodynamics (SPH) code, which has been used to study the coalescence of binary neutron star (NS) systems. The Lagrangian particle-based code incorporates consistently all lowest-order (1PN) relativistic effects, as well as gravitational radiation reaction, the lowest-order dissipative term in general relativity. We test our code on sequences of single NS models of varying compactness, and we discuss ways to make PN simulations more relevant to realistic NS models. We also present a PN SPH relaxation procedure for constructing equilibrium models of synchronized binaries, and we use these equilibrium models as initial conditions for our dynamical calculations of binary coalescence. Though unphysical, since tidal synchronization is not expected in NS binaries, these initial conditions allow us to compare our PN work with previous Newtonian results. We compare calculations with and without 1PN effects, for NS with stiff equations of state, modeled as polytropes with $Γ=3$. We find that 1PN effects can play a major role in the coalescence, accelerating the final inspiral and causing a significant misalignment in the binary just prior to final merging. In addition, the character of the gravitational wave signal is altered dramatically, showing strong modulation of the exponentially decaying waveform near the end of the merger. We also discuss briefly the implications of our results for models of gamma-ray bursts at cosmological distances.

gr-qc↗

arXiv2000

Formation of Short-Period Binary Pulsars in Globular Clusters

We present a new dynamical scenario for the formation of short-period binary millisecond pulsars in globular clusters. Our work is motivated by the recent observations of 20 radio pulsars in 47 Tuc. In a dense cluster such as 47 Tuc, most neutron stars acquire binary companions through exchange interactions with primordial binaries. The resulting systems have semimajor axes in the range \~0.1-1 AU and neutron star companion masses ~1-3 Msun. For many of these systems we find that, when the companion evolves off the main sequence and fills its Roche lobe, the subsequent mass transfer is dynamically unstable. This leads to a common envelope phase and the formation of short-period neutron star - white dwarf binaries. For a significant fraction of these binaries, the decay of the orbit due to gravitational radiation will be followed by a period of stable mass transfer driven by a combination of gravitational radiation and tidal heating of the companion. The properties of the resulting short-period binaries match well those of observed binary pulsars in 47 Tuc.

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arXiv2000

Smoothed Particle Hydrodynamics Calculations of Stellar Interactions

Smoothed Particle Hydrodynamics is a multidimensional Lagrangian method of numerical hydrodynamics that has been used to tackle a wide variety of problems in astrophysics. Here we develop the basic equations of the SPH scheme, and we discuss some of its numerical properties and limitations. As an illustration of typical astrophysical applications, we discuss recent calculations of stellar interactions, including collisions between main sequence stars and the coalescence of compact binaries.

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arXiv2000

Secular Evolution of Hierarchical Triple Star Systems

We derive octupole-level secular perturbation equations for hierarchical triple systems, using classical Hamiltonian perturbation techniques. By extending previous work done to leading (quadrupole) order to octupole level (i.e., including terms of order alpha^3, where alpha = a_1/a_2 < 1 is the ratio of semimajor axes) we obtain expressions that are applicable to a much wider range of parameters. For triple systems containing a close inner binary, we also discuss the possible interaction between the classical Newtonian perturbations and the general relativistic precession of the inner orbit. In some cases we show that this interaction can lead to resonances and a significant increase in the maximum amplitude of eccentricity perturbations. We establish the validity of our analytic expressions by providing detailed comparisons with the results of direct numerical integrations of the three-body problem obtained for a large number of representative cases. We also discuss applications of the theory in the context of several observed triple systems of current interest, including the millisecond pulsar PSR B1620-26 in M4, the giant planet in 16 Cygni, and the protostellar binary TMR-1. [short version]

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arXiv1999

The Final Fate of Coalescing Binary Neutron Stars: Collapse to a Black Hole?

Coalescing compact binaries with neutron star (NS) or black hole (BH) components are important sources of gravitational waves for the laser-interferometer detectors currently under construction, and may also be sources of gamma-ray bursts at cosmological distances. This paper focuses on the final hydrodynamic coalescence and merger of NS--NS binaries, and addresses the question of whether black hole formation is the inevitable final fate of these systems.

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arXiv1999

Particle Methods in Astrophysical Fluid Dynamics

Particle methods play an important role in the study of a wide variety of astrophysical fluid dynamics problems. The different methods currently in use are all variants of the so-called Smoothed Particle Hydrodynamics (SPH) scheme introduced by Lucy and Gingold & Monaghan more than twenty years ago. This paper presents a complete introduction to SPH in its modern form, and discusses some of the main numerical properties of the scheme. In particular, the convergence properties of SPH are studied, as a function of the number of particles N and the number of interacting neighbors N_n, using a simple analysis based on sound waves. It is shown that consistency of SPH (i.e., convergence towards a physical solution) requires both N -> infinity and N_n -> infinity, with the smoothing length h -> 0, i.e., N_n/N -> 0.

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arXiv1999

Theoretical Implications of the 47 Tuc Pulsars

Twenty millisecond radio pulsars have now been observed in the globular cluster 47 Tuc. This is by far the largest sample of radio pulsars known in any globular cluster. These recent observations provide a unique opportunity to re-examine theoretically the formation and evolution of recycled pulsars in globular clusters.

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arXiv1999

Coalescing Binary Neutron Stars

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.

gr-qc↗

arXiv1998

Structure and Evolution of Nearby Stars with Planets. I. Short-Period Systems

Using the Yale stellar evolution code, we have calculated theoretical models for nearby stars with planetary-mass companions in short-period nearly circular orbits: 51 Pegasi, Tau Bootis, Upsilon Andromedae, Rho Cancri, and Rho Coronae Borealis. We present tables listing key stellar parameters such as mass, radius, age, and size of the convective envelope as a function of the observable parameters (luminosity, effective temperature, and metallicity), as well as the unknown helium fraction. For each star we construct best models based on recently published spectroscopic data and the present understanding of galactic chemical evolution. We discuss our results in the context of planet formation theory, and, in particular, tidal dissipation effects and stellar metallicity enhancements.

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arXiv1998

Tests of Spurious Transport in Smoothed Particle Hydrodynamics

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 $α$ and $β$ (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.

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