Vassiliki Kalogera

A Comprehensive Study of Binary Compact Objects as Gravitational Wave Sources: Evolutionary Channels, Rates, and Physical Properties

A new generation of ground-based interferometric detectors for gravitational waves is currently under construction or has entered the commissioning phase (Laser Interferometer Gravitational-wave Observatory [LIGO], VIRGO, GEO600, TAMA300). The purpose of these detectors is to observe gravitational waves from astrophysical sources and help improve our understanding of the source origin and physical properties. In this paper we study the most promising candidate sources for these detectors: inspiraling double compact objects. We use population synthesis methods to calculate the properties and coalescence rates of compact object binaries: double neutron stars, black hole-neutron star systems, and double black holes. We also examine the formation channels available to double compact object binaries. We explicitly account for the evolution of low-mass helium stars and investigate the possibility of common-envelope evolution involving helium stars as well as two evolved stars. As a result we identify a significant number of new formation channels for double neutron stars, in particular, leading to populations with very distinct properties. We discuss the theoretical and observational implications of such populations, but we also note the need for hydrodynamical calculations to settle the question of whether such common-envelope evolution is possible. We also present and discuss the physical properties of compact object binaries and identify a number of robust, qualitative features as well as their origin. Using the calculated coalescence rates we compare our results to earlier studies and derive expected detection rates for LIGO. We find that our most optimistic estimate for the first LIGO detectors reach a couple of events per year and our most pessimistic estimate for advanced LIGO detectors exceed 10 events per year.

Theoretical Black Hole Mass Distributions

We derive the theoretical distribution function of black hole masses by studying the formation processes of black holes. We use the results of recent two-dimensional simulations of stellar core collapse to obtain the relation between remnant and progenitor masses and fold it with an initial mass function for the progenitors. Thus, we are able to derive the binary black hole mass distribution. We examine how the calculated black hole mass distributions are modified by (1) strong-wind mass loss at different evolutionary stages of the progenitors and (2) the presence of close binary companions to the black hole progenitors. The compact-remnant distribution is dominated by neutron stars in the mass range 1.2-1.6 M☉ and falls off exponentially at higher remnant masses. Our results are most sensitive to mass loss from stellar winds (particularly from Wolf-Rayet stars), and the effects of winds are even more important in close binaries. Wind mass loss leads to flatter black hole mass distributions and limits the maximum possible black hole mass (10-15 M☉). We also study the effects of the uncertainties in the explosion and unbinding energies for different progenitors. The distributions are continuous and extend over a broad range. We find no evidence for a gap at low values (3-5 M☉) or for a peak at higher values (~7 M☉) of black hole masses, but we argue that our black hole mass distribution for binaries is consistent with the current sample of measured black hole masses in X-ray transients. We discuss possible biases against the detection or formation of X-ray transients with low-mass black holes. We also comment on the possibility of black hole kicks and their effect on binaries.

The Maximum Mass of a Neutron Star

Observational identification of black holes as members of binary systems requires the knowledge of the upper limit on the gravitational mass of a neutron star. We use modern equations of state for neutron star matter, fitted to experimental nucleon-nucleon scattering data and the properties of light nuclei, to calculate, within the framework of Rhoades & Ruffini (1974), the minimum upper limit on a neutron star mass. Regarding the equation of state as valid up to twice nuclear matter saturation density, ρnm, we obtain a secure upper bound on the neutron star mass equal to 2.9 M☉. We also find that in order to reach the lowest possible upper bound of 2.2 M☉, we need to understand the physical properties of neutron matter up to a density of ~4ρnm.

The Coalescence Rate of Double Neutron Star Systems

We estimate the coalescence rate of close binaries with two neutron stars (NS) and discuss the prospects for the detection of NS-NS inspiral events by ground-based gravitational-wave observatories, such as LIGO. We derive the Galactic coalescence rate using the observed sample of close NS-NS binaries (PSR B1913+16 and PSR B1534+12) and examine in detail each of the sources of uncertainty associated with the estimate. Specifically, we investigate (1) the dynamical evolution of NS-NS binaries in the Galactic potential and the vertical scale height of the population, (2) the pulsar lifetimes, (3) the effects of the faint end of the radio pulsar luminosity function and their dependence on the small number of observed objects, (4) the beaming fraction, and (5) the extrapolation of the Galactic rate to extragalactic distances expected to be reachable by LIGO. We find that the dominant source of uncertainty is the correction factor (up to 200) for faint (undetectable) pulsars. All other sources are much less important, each with uncertainty factors smaller than 2. Despite the relatively large uncertainty, the derived coalescence rate is consistent with previously derived upper limits, and is more accurate than rates obtained from population studies. We obtain a most conservative lower limit that the detection rate by LIGO II of about 2 events per year. Our upper limit on the rate is between 300 and 1000 events per year.

Orbital Characteristics of Binary Systems after Asymmetric Supernova Explosions

We present an analytical method for studying the changes of the orbital characteristics of binary systems with circular orbits due to a kick velocity imparted to the newborn neutron star during a supernova (SN) explosion. Assuming a Maxwellian distribution of kick velocities we derive analytical expressions for the distribution functions of orbital separations and eccentricities immediately after the explosion, of orbital separations after circularization of the post-SN orbits, and of systemic velocities of binaries that remain bound after the explosion. These distributions of binary characteristics can be used to perform analytical population synthesis calculations of various types of binaries, the formation of which involves a supernova explosion. We study in detail the dependence of the derived distributions on the kick velocity and the pre-SN characteristics, we identify all the limits imposed on the post-SN orbital characteristics, and we discuss their implications for the population of X-ray binaries and double neutron star systems. We show that large kick velocities do not necessarily result in large systemic velocities; for typical X-ray binary progenitors the maximum post-SN systemic velocity is comparable to the relative orbital velocity prior to the explosion. We also find that, unless accretion-induced collapse is a viable formation channel, X-ray binaries in globular clusters have most probably been formed by stellar dynamical interactions only and not directly from primordial binaries.

Double Neutron Star Systems and Natal Neutron Star Kicks

We study the four double neutron star systems found in the Galactic disk in terms of the orbital characteristics of their immediate progenitors and the natal kicks imparted to neutron stars. Analysis of the effect of the second supernova explosion on the orbital dynamics, combined with recent results from simulations of rapid accretion onto neutron stars, lead us to conclude that the observed systems could not have been formed had the explosion been symmetric. Their formation becomes possible if kicks are imparted to the radio-pulsar companions at birth. We identify the constraints imposed on the immediate progenitors of the observed double neutron stars and calculate the ranges within which their binary characteristics (orbital separations and masses of the exploding stars) are restricted. We also study the dependence of these limits on the magnitude of the kick velocity and the time elapsed since the second explosion. For each of the double neutron stars, we derive a minimum kick magnitude required for their formation, and for the two systems in close orbits (10 R☉), we find it to exceed 200 km s-1. Lower limits are also set to the center-of-mass velocities of double neutron stars, and we find them to be consistent with the current proper motion observations.

Formation- of low-mass X-ray binaries. II. Common envelope evolution of primordial binaries with extreme mass ratios

We study the formation of low-mass X-ray binaries (LMXBs) through helium star supernovae in binary systems that have each emerged from a common envelope phase. LMXB progenitors must satisfy a large number of evolutionary and structural constraints, including survival through common envelope evolution, through the post-common envelope phase, where the precursor of the neutron star becomes a Wolf-Rayet star, and survival through the supernova event. Furthermore, the binaries that survive the explosion must reach interaction within a Hubble time and must satisfy stability criteria for mass transfer. These constraints, imposed under the assumption of a symmetric supernova explosion, prohibit the formation of short-period LMXBs transferring mass at sub-Eddington rates through any channel in which the intermediate progenitor of the neutron star is not completely degenerate. Barring accretion-induced collapse, the existence of such systems therefore requires that natal kicks be imparted to neutron stars. We use an analytical method to synthesize the distribution of nascent LMXBs over donor masses and orbital periods and evaluate their birthrate and systemic velocity dispersion. Within the limitations imposed by observational incompleteness and selection effects, and our neglect of secular evolution in the LMXB state, we compare our results with observations. However, our principal objective is to evaluate how basic model parameters (common envelope ejection efficiency, rms kick velocity, primordial mass ratio distribution) influence these results. We conclude that the characteristics of newborn LMXBs are primarily determined by age and stability constraints and the efficiency of magnetic braking and are largely independent of the primordial binary population and the evolutionary history of LMXB progenitors (except for extreme values of the average kick magnitude or of the common envelope ejection efficiency). Theoretical estimates of total LMXB birthrates are not credible, since they strongly depend on the observationally indeterminate frequency of primordial binaries with extreme mass ratios in long-period orbits.

Constraints on supernova kicks from the double neutron star system PSR B1913+16

We use recent information on geodetic precession of the binary pulsar B1913+16 along with measurements of its orbital parameters and proper motion to derive new constraints on the immediate progenitor of this double neutron star system. As part of our analysis, we model the motion of the binary in the Galaxy after the second supernova explosion, and we derive constraints on the unknown radial velocity. We also obtain limits on the magnitude and direction of the kick velocity imparted to the pulsar companion during the second supernova explosion. We consider the complete set of possible cases, depending on the kinematic age of the system and the 180° ambiguity in the pulsar spin orientation. Most interestingly, we find that the natal kick must have been directed almost perpendicular to the spin axis of the neutron star progenitor, independent of the specific presupernova configuration. Such a tight constraint on the kick direction has important implications for the physical mechanism responsible for the kick.

Formation of low-mass X-ray binaries. I. Constraints on hydrogen-rich donors at the onset of the X-ray phase

We identify and quantify the set of constraints that neutron star-normal star binaries must satisfy in order to become observable LMXBs. These constraints are related to (i) the thermal and hydrostatic equilibrium of the donors, (ii) the degree to which the mass transfer process is conservative, and (iii) the age of the systems. They divide the parameter space of potential LMXBs in several distinct parts, of which those that actually become LMXBs at the onset of mass transfer occupy only a small part. Of the remainder, many become unstable to dynamical time scale mass transfer either at the onset or later in the course of mass transfer, and enter common envelope evolution. Others experience super-Eddington mass transfer but may eventually survive to become LMXBs. These survivors arguably include binary millisecond pulsars with orbital periods in excess of

Spin-Orbit Misalignment in Close Binaries with Two Compact Objects

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