Bernard F. Schutz

Physics, astrophysics and cosmology with gravitational waves.

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.

Secular instability of rotating Newtonian stars

The effect of gravitational radiation and of viscosity on the stability of rotating self-gravitating fluids is considered. Previous cirteria governing secular stability to radiation are shown to fail as a result of the trival displacements introduced in a previous paper (1). The required modification is obtained by describing perturbations in terms of canonical displacements (displacements orthogonal to the trivials). There nevertheless remain physical perturbations having angular dependence e/sup i/mphi which, for sufficiently large m, make the stability functional (the canonical energy E/sub c/) negative, and it follows that all rotating stars are unstable or marginally unstable to gravitational radiation. In the case of stability against viscosity, the corresponding stability criterion is shown to involve the the canonical energy in a rotating frame, E/sub c/,R, a functional invariant under gauge transformations associated with the trival displacements. By using the functional E/sub c/,R to analyze local stability, it is found that a star is locally stable against viscosity if and only if the special entropy increases outward (in the sense of decreasing pressure). Finally, the behavior of normal modes is discussed and used to elucidate the generic radiation-induced instability; and certain orthogonality properties are derived.

Low-frequency gravitational-wave science with eLISA/NGO

We review the expected science performance of the New Gravitational-Wave Observatory (NGO, a.k.a. eLISA), a mission under study by the European Space Agency for launch in the early 2020s. eLISA will survey the low-frequency gravitational-wave sky (from 0.1 mHz to 1 Hz), detecting and characterizing a broad variety of systems and events throughout the Universe, including the coalescences of massive black holes brought together by galaxy mergers; the inspirals of stellar-mass black holes and compact stars into central galactic black holes; several millions of ultra-compact binaries, both detached and mass transferring, in the Galaxy; and possibly unforeseen sources such as the relic gravitational-wave radiation from the early Universe. eLISAs high signal-to-noise measurements will provide new insight into the structure and history of the Universe, and they will test general relativity in its strong-field dynamical regime.

Gravitational waves from hot young rapidly rotating neutron stars

Gravitational radiation drives an instability in the r-modes of young rapidly rotating neutron stars. This instability is expected to carry away most of the angular momentum of the star by gravitational radiation emission, leaving a star rotating at about 100 Hz. In this paper we model in a simple way the development of the instability and evolution of the neutron star during the year-long spindown phase. This allows us to predict the general features of the resulting gravitational waveform. We show that a neutron star formed in the Virgo cluster could be detected by the LIGO and VIRGO gravitational wave detectors when they reach their “enhanced” level of sensitivity, with an amplitude signal-to-noise ratio that could be as large as about 8 if near-optimal data analysis techniques are developed. We also analyze the stochastic background of gravitational waves produced by the r-mode radiation from neutron-star formation throughout the universe. Assuming a substantial fraction of neutron stars are born with spin frequencies near their maximum values, this stochastic background is shown to have an energy density of about 10^(−9) of the cosmological closure density, in the range 20 Hz to 1 kHz. This radiation should be detectable by “advanced” LIGO as well.

Data analysis of gravitational-wave signals from spinning neutron stars. I. The signal and its detection

We present a theoretical background for the data analysis of the gravitational-wave signals from spinning neutron stars for Earth-based laser interferometric detectors. We introduce a detailed model of the signal including both the frequency and the amplitude modulations. We include the effects of the intrinsic frequency changes and the modulation of the frequency at the detector due to Earths motion. We estimate the effects of the stars proper motion and of relativistic corrections. Moreover we consider a signal consisting of two components corresponding to a frequency

Black Hole Normal Modes: A Semianalytic Approach

f

The GEO 600 gravitational wave detector

and twice that frequency. From the maximum likelihood principle we derive the detection statistics for the signal and we calculate the probability density function of the statistics. We obtain the data analysis procedure to detect the signal and to estimate its parameters. We show that for optimal detection of the amplitude modulated signal we need four linear filters instead of one linear filter needed for a constant amplitude signal. Searching for the doubled frequency signal increases further the number of linear filters by a factor of 2. We indicate how the fast Fourier transform algorithm and resampling methods commonly proposed in the analysis of periodic signals can be used to calculate the detection statistics for our signal. We find that the probability density function of the detection statistics is determined by one parameter: the optimal signal-to-noise ratio. We study the signal-to-noise ratio by means of the Monte Carlo method for all long-arm interferometers that are currently under construction. We show how our analysis can be extended to perform a joint search for periodic signals by a network of detectors and we perform a Monte Carlo study of the signal-to-noise ratio for a network of detectors.

Constraining the equation of state with moment of inertia measurements

A new semianalytic technique for determining the complex normal mode frequencies of black holes is presented. The method is based on the WKB approximation. It yields a simple analytic formula that gives the real and imaginary parts of the frequency in terms of the parameters of the black hole and of the field whose perturbation is under study, and in terms of the quantity (n + 1/2), where n = 0, 1, 2,... and labels the fundamental mode, first overtone mode, and so on. In the case of the fundamental gravitational normal modes of the Schwarzschild black hole, the WKB estimates agree with numerical results to better than 7 percent in the real part of the frequency and 0.7 percent in the imaginary part, with the relative agreement improving with increasing angular harmonic. Carried to higher order the method may provide an accurate and systematic means to study black hole normal modes.

Gravitational wave astronomy

The GEO 600 laser interferometer with 600 m armlength is part of a worldwide network of gravitational wave detectors. Due to the use of advanced technologies like multiple pendulum suspensions with a monolithic last stage and signal recycling, the anticipated sensitivity of GEO 600 is close to the initial sensitivity of detectors with several kilometres armlength. This paper describes the subsystems of GEO 600, the status of the detector by September 2001 and the plans towards the first science run.

Searching for periodic sources with LIGO

We estimate that the moment of inertia of star A in the recently discovered double pulsar system PSR J0737-3039 may be determined after a few years of observation to ~10% accuracy. This would enable accurate estimates of the radius of the star and the pressure of matter in the vicinity of 1-2 times the nuclear saturation density, which would in turn provide strong constraints on the equation of state of neutron stars and the physics of their interiors.