On August 17, 2017 at 12∶41:04 UTC the Advanced LIGO and Advanced Virgo gravitational-wave detectors made their first observation of a binary neutron star inspiral. The signal, GW170817, was detected with a combined signal-to-noise ratio of 32.4 and a false-alarm-rate estimate of less than one per 8.0×10^{4}  years. We infer the component masses of the binary to be between 0.86 and 2.26  M_{⊙}, in agreement with masses of known neutron stars. Restricting the component spins to the range inferred in binary neutron stars, we find the component masses to be in the range 1.17-1.60  M_{⊙}, with the total mass of the system 2.74_{-0.01}^{+0.04}M_{⊙}. The source was localized within a sky region of 28  deg^{2} (90% probability) and had a luminosity distance of 40_{-14}^{+8}  Mpc, the closest and most precisely localized gravitational-wave signal yet. The association with the γ-ray burst GRB 170817A, detected by Fermi-GBM 1.7 s after the coalescence, corroborates the hypothesis of a neutron star merger and provides the first direct evidence of a link between these mergers and short γ-ray bursts. Subsequent identification of transient counterparts across the electromagnetic spectrum in the same location further supports the interpretation of this event as a neutron star merger. This unprecedented joint gravitational and electromagnetic observation provides insight into astrophysics, dense matter, gravitation, and cosmology.

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GW170817: observation of gravitational waves from a binary neutron star inspiral

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

We report the observation of a gravitational-wave signal produced by the coalescence of two stellar-mass black holes. The signal, GW151226, was observed by the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC. The signal was initially identified within 70 s by an online matched-filter search targeting binary coalescences. Subsequent off-line analyses recovered GW151226 with a network signal-to-noise ratio of 13 and a significance greater than 5 σ. The signal persisted in the LIGO frequency band for approximately 1 s, increasing in frequency and amplitude over about 55 cycles from 35 to 450 Hz, and reached a peak gravitational strain of 3.4+0.7−0.9×10−22. The inferred source-frame initial black hole masses are 14.2+8.3−3.7M⊙ and 7.5+2.3−2.3M⊙ and the final black hole mass is 20.8+6.1−1.7M⊙. We find that at least one of the component black holes has spin greater than 0.2. This source is located at a luminosity distance of 440+180−190 Mpc corresponding to a redshift 0.09+0.03−0.04. All uncertainties define a 90 % credible interval. This second gravitational-wave observation provides improved constraints on stellar populations and on deviations from general relativity.

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GW151226: observation of gravitational waves from a 22-solar-mass binary black hole coalescence

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

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The Confrontation Between General Relativity and Experiment

Advanced Virgo is the project to upgrade the Virgo interferometric detector of gravitational waves, with the aim of increasing the number of observable galaxies (and thus the detection rate) by three orders of magnitude. The project is now in an advanced construction phase and the assembly and integration will be completed by the end of 2015. Advanced Virgo will be part of a network, alongside the two Advanced LIGO detectors in the US and GEO HF in Germany, with the goal of contributing to the early detection of gravitational waves and to opening a new window of observation on the universe. In this paper we describe the main features of the Advanced Virgo detector and outline the status of the construction.

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Advanced Virgo: a second-generation interferometric gravitational wave detector

We infer the velocity distribution of radio pulsars based on large-scale 0.4 GHz pulsar surveys. We do so by modelling evolution of the locations, velocities, spins, and radio luminosities of pulsars; calculating pulsed flux according to a beaming model and random orientation angles of spin and beam; applying selection effects of pulsar surveys; and comparing model distributions of measurable pulsar properties with survey data using a likelihood function. The surveys analyzed have well-defined characteristics and cover approx. 95% of the sky. We maximize the likelihood in a 6-dimensional space of observables P, dot-P, DM, absolute value of b, mu, F (period, period derivative, dispersion measure, Galactic latitude, proper motion, and flux density). The models we test are described by 12 parameters that characterize a population's birth rate, luminosity, shutoff of radio emission, birth locations, and birth velocities. We infer that the radio beam luminosity (i) is comparable to the energy flux of relativistic particles in models for spin-driven magnetospheres, signifying that radio emission losses reach nearly 100% for the oldest pulsars; and (ii) scales approximately as E(exp 1/2) which, in magnetosphere models, is proportional to the voltage drop available for acceleration of particles. We find that a two-component velocity distribution with characteristic velocities of 90 km/ s and 500 km/ s is greatly preferred to any one-component distribution; this preference is largely immune to variations in other population parameters, such as the luminosity or distance scale, or the assumed spin-down law. We explore some consequences of the preferred birth velocity distribution: (1) roughly 50% of pulsars in the solar neighborhood will escape the Galaxy, while approx. 15% have velocities greater than 1000 km/ s (2) observational bias against high velocity pulsars is relatively unimportant for surveys that reach high Galactic absolute value of z distances, but is severe for spatially bounded surveys; (3) an important low-velocity population exists that increases the fraction of neutron stars retained by globular clusters and is consistent with the number of old objects that accrete from the interstellar medium; (4) under standard assumptions for supernova remnant expansion and pulsar spin-down, approx. 10% of pulsars younger than 20 kyr will appear to lie outside of their host remnants. Finally, we comment on the ramifications of our birth velocity distribution for binary survival and the population of inspiraling binary neutron stars relevant to some GRB models and potential sources for LIGO.

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The Velocity distribution of isolated radio pulsars

Close binary systems of compact objects with less than ten minutes remaining before coalescence are readily identifiable sources of gravitational radiation for the United States Laser Interferometer Gravitational-Wave Observatory (LIGO) and the French-Italian VIRGO gravitational-wave observatory. As a start toward assessing the full capabilities of the LIGO-VIRGO detector network, we investigate the sensitivity of individual LIGO-VIRGO-like interferometers and the precision with which they can determine the characteristics of an inspiralling binary system. Since the two interferometers of the LIGO detector share nearly the same orientation, their joint sensitivity is similar to that of a single, more sensitive interferometer. We express our results for a single interferometer of both initial and advanced LIGO design, and also for the LIGO detector in the limit that its two interferometers share exactly the same orientation. We approximate the secular evolution of a binary system as driven exclusively by its leading-order quadrupole gravitational radiation. Observations of a binary in a single interferometer are described by four characteristic quantities: an amplitude $\mathcal{A}$, a chirp mass $\mathcal{M}$, a time $T$, and a phase $\ensuremath{\psi}$. We find the amplitude signal-to-noise ratio (SNR) $\ensuremath{\rho}$ of an observed binary system as a function of $\mathcal{A}$ and $\mathcal{M}$ for a particular orientation of the binary with respect to the interferometer, and also the distribution of SNR's for randomly oriented binaries at a constant distance. To assess the interferometer sensitivity, we calculate the rate at which sources are expected to be observed and the range to which they are observable. Assuming a conservative rate density for coalescing neutron-star binary systems of 8\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ ${\mathrm{yr}}^{\ensuremath{-}1}$ ${\mathrm{Mpc}}^{\ensuremath{-}3}$, we find that the advanced LIGO detector will observe approximately 69 ${\mathrm{yr}}^{\ensuremath{-}1}$ with an amplitude SNR greater than 8. Of these, approximately 7 ${\mathrm{yr}}^{\ensuremath{-}1}$ will be from binaries at distances greater than 950 Mpc. We give analytic and numerical results for the precision with which each of the characteristic quantities can be determined by interferometer observations. For neutron-star binaries, the fractional $1\ensuremath{\sigma}$ statistical error in the determination of $\mathcal{A}$ is equal to $\frac{1}{\ensuremath{\rho}}$. For $\ensuremath{\rho}g8$, the fractional 1\ensuremath{\sigma} error in the measurement of $\mathcal{M}$ in the advanced LIGO detectors is less than 2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$, a phenomenal precision. The characteristic time is related to the moment when coalescence occurs, and can be measured in the advanced detectors with a $1\ensuremath{\sigma}$ uncertainty of less than 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ s (assuming $\ensuremath{\rho}g8$). We also explore the sensitivity of these results to a tunable parameter in the interferometer design (the recycling frequency). The optimum choice of the parameter is dependent on the goal of the observations, e.g., maximizing the rate of detections or maximizing the precision of measurement. We determine the optimum parameter values for these two cases. The calculations leading to the SNR and the precision of measurement assume that the interferometer observations extend over only the last several minutes of binary inspiral, during which time the orbital frequency increases from approximately 5 Hz to 500 Hz. We examine the sensitivity of our results to the elapsed time of the observation and show that observations of longer duration lead to very little improvement in the SNR or the precision of measurement.

Observing binary inspiral in gravitational radiation: One interferometer

Globular cluster evolution is studied, modeling relaxation and energy exchange between the stars. A comprehensive survey is presented of Galactic globular cluster evolution until core collapse. Mass loss during the first five billion years is sufficiently strong to disrupt weakly bound clusters with a Salpeter initial mass function (IMF). The slope of the IMF is the critical parameter governing cluster survival during the mass-loss phase. Cluster which survive this initial phase then begin to collapse. Those with smaller mass and/or smaller Galactocentric orbital radii complete their core collapse by the present time. Two evolutionary endpoints are studied in detail: (1) the disruption of weakly bound clusters by mass loss due to stellar evolution, and (2) core collapse of multimass clusters. The state in which the multimass clusters exist today, if they have neither disrupted nor collapsed, is discussed. A number of observables based on stellar evolution calculations are presented. 83 refs.

Evolution of globular clusters in the Galaxy

We use astrometric, distance, and spindown data on pulsars to (1) estimate three-dimensional velocity components, birth distances from the Galactic plane, and ages of individual objects; (2) determine the distribution of space velocities and the scale height of pulsar progenitors; (3) test spindown laws for pulsars; (4) test for correlations between space velocities and other pulsar parameters; and (5) place empirical requirements on mechanisms than can produce high-velocity neutron stars. Our approach incorporates measurement errors, uncertainties in distances, deceleration in the Galactic potential, and differential Galactic rotation. We focus on a sample of proper motion measurements of young ( ?24+19 km s-1 and 700 -->?132+300 km s-1, representing ~86% and ~14% of the population, respectively. The sample velocities are inconsistent with a single-component Gaussian model and are well described by a two-component Gaussian model but do not require models of additional complexity. From the best-fit distribution, we estimate that about 20% of the known pulsars will escape the Galaxy, assuming an escape speed of 500 km s-1. The best-fit, dual-component model, if augmented by an additional, low-velocity ( 1000 km s-1) may be underrepresented (in the observed sample) by a factor ~2.3 owing to selection effects in pulsar surveys. The estimates of scale height and velocity parameters are insensitive to the explicit relation of chronological and spindown ages. A further analysis starting from our inferred velocity distribution allows us to test spindown laws and age estimates. There exist comparably good descriptions of the data involving different combinations of braking index and torque decay timescale. We find that a braking index of 2.5 is favored if torque decay occurs on a timescale of ~3 Myr, while braking indices ~4.5 ? 0.5 are preferred if there is no torque decay. For the sample as a whole, the most probable chronological ages are typically smaller than conventional spindown ages by factors as large as 2. We have also searched for correlations between three-dimensional speeds of individual pulsars and combinations of spin period and period derivative. None appears to be significant. We argue that correlations identified previously between velocity and (apparent) magnetic moment reflect the different evolutionary paths taken by young, isolated (nonbinary), high-field pulsars and older, low-field pulsars that have undergone accretion-driven spinup. We conclude that any such correlation measures differences in spin and velocity selection in the evolution of the two populations and is not a measure of processes taking place in the core collapse that produces neutron stars in the first place. We assess mechanisms for producing high-velocity neutron stars, including disruption of binary systems by symmetric supernovae and neutrino, baryonic, or electromagnetic rocket effects during or shortly after the supernova. The largest velocities seen (~1600 km s-1), along with the paucity of low-velocity pulsars, suggest that disruption of binaries by symmetric explosions is insufficient. Rocket effects appear to be a necessary and general phenomenon. The required kick amplitudes and the absence of a magnetic field-velocity correlation do not yet rule out any of the rocket models. However, the required amplitudes suggest that the core collapse process in a supernova is highly dynamic and aspherical and that the impulse delivered to the neutron star is larger than existing simulations of core collapse have achieved.

http://cds.cern.ch/record/330884/files/9707308.pdf

Neutron Star Population Dynamics. II. Three-dimensional Space Velocities of Young Pulsars

We use astrometric, distance and spindown data on pulsars to: (1) estimate three-dimensional velocity components, birth distances from the galactic plane, and ages of individual objects; (2) determine the distribution of space velocities and the scale height of pulsar progenitors; (3) test spindown laws for pulsars; (4) test for correlations between space velocities and other pulsar parameters; and (5) place empirical requirements on mechanisms than can produce high velocity neutron stars. Our approach incorporates measurement errors, uncertainties in distances, deceleration in the Galactic potential, and differential galactic rotation. 
We find that the scale height of the progenitors is approximately 0.13 kpc, that the 3D velocities are distributed in two components with characteristic speeds of 175(+20,-30) km/s and 700(+200,-150) km/s representing 83% and 17% of the population respectively. These results are insensitive to the explicit relation of chronological and spindown ages. We infer that the most probable chronological ages are typically smaller than conventional spindown ages by factors as large as two. We assess mechanisms for producing high-velocity neutron stars in view of the derived velocity distribution function.

https://arxiv.org/pdf/astro-ph/9707308.pdf

David F. Chernoff

Papers

The Velocity distribution of isolated radio pulsars

Observing binary inspiral in gravitational radiation: One interferometer

Evolution of globular clusters in the Galaxy

Neutron Star Population Dynamics. II. Three-dimensional Space Velocities of Young Pulsars

Neutron Star Population Dynamics.II: 3D Space Velocities of Young Pulsars