Aperture synthesis for gravitational-wave data analysis: Deterministic Sources

Gravitational wave detectors now under construction are sensitive to the phase of the incident gravitational waves. Correspondingly, the signals from the different detectors can be combined, in the analysis, to simulate a single detector of greater amplitude and directional sensitivity: in short, aperture synthesis. Here we consider the problem of aperture synthesis in the special case of a search for a source whose waveform is known in detail: \textit{e.g.,} compact binary inspiral. We derive the likelihood function for joint output of several detectors as a function of the parameters that describe the signal and find the optimal matched filter for the detection of the known signal. Our results allow for the presence of noise that is correlated between the several detectors. While their derivation is specialized to the case of Gaussian noise we show that the results obtained are, in fact, appropriate in a well-defined, information-theoretic sense even when the noise is non-Gaussian in character. The analysis described here stands in distinction to ``coincidence analyses'', wherein the data from each of several detectors is studied in isolation to produce a list of candidate events, which are then compared to search for coincidences that might indicate common origin in a gravitational wave signal. We compare these two analyses --- optimal filtering and coincidence --- in a series of numerical examples, showing that the optimal filtering analysis always yields a greater detection efficiency for given false alarm rate, even when the detector noise is strongly non-Gaussian.Comment: 39 pages, 4 figures, submitted to Phys. Rev.

Second Order Phase Transitions : From Infinite to Finite Systems

We investigate the Equation of State (EOS) of classical systems having 300 and 512 particles confined in a box with periodic boundary conditions. We show that such a system, independently on the number of particles investigated, has a critical density of about 1/3 the ground state density and a critical temperature of about $2.5~ MeV$. The mass distribution at the critical point exhibits a power law with $\tau = 2.23$. Making use of the grand partition function of Fisher's droplet model, we obtain an analytical EOS around the critical point in good agreement with the one extracted from the numerical simulations.Comment: RevTex file, 17 pages + 9 figures available upon request from [email protected]

How Many Templates for GW Chirp Detection? The Minimal-Match Issue Revisited

In a recent paper dealing with maximum likelihood detection of gravitational wave chirps from coalescing binaries with unknown parameters we introduced an accurate representation of the no-signal cumulative distribution of the supremum of the whole correlator bank. This result can be used to derive a refined estimate of the number of templates yielding the best tradeoff between detector's performance (in terms of lost signals among those potentially detectable) and computational burden.Comment: submitted to Class. Quantum Grav. Typing error in eq. (4.8) fixed; figure replaced in version

Testing Alternative Theories of Gravity using LISA

We investigate the possible bounds which could be placed on alternative theories of gravity using gravitational wave detection from inspiralling compact binaries with the proposed LISA space interferometer. Specifically, we estimate lower bounds on the coupling parameter \omega of scalar-tensor theories of the Brans-Dicke type and on the Compton wavelength of the graviton \lambda_g in hypothetical massive graviton theories. In these theories, modifications of the gravitational radiation damping formulae or of the propagation of the waves translate into a change in the phase evolution of the observed gravitational waveform. We obtain the bounds through the technique of matched filtering, employing the LISA Sensitivity Curve Generator (SCG), available online. For a neutron star inspiralling into a 10^3 M_sun black hole in the Virgo Cluster, in a two-year integration, we find a lower bound \omega > 3 * 10^5. For lower-mass black holes, the bound could be as large as 2 * 10^6. The bound is independent of LISA arm length, but is inversely proportional to the LISA position noise error. Lower bounds on the graviton Compton wavelength ranging from 10^15 km to 5 * 10^16 km can be obtained from one-year observations of massive binary black hole inspirals at cosmological distances (3 Gpc), for masses ranging from 10^4 to 10^7 M_sun. For the highest-mass systems (10^7 M_sun), the bound is proportional to (LISA arm length)^{1/2} and to (LISA acceleration noise)^{-1/2}. For the others, the bound is independent of these parameters because of the dominance of white-dwarf confusion noise in the relevant part of the frequency spectrum. These bounds improve and extend earlier work which used analytic formulae for the noise curves.Comment: 16 pages, 9 figures, submitted to Classical & Quantum Gravit

Performance of Newtonian filters in detecting gravitational waves from coalescing binaries

Coalescing binary systems are one of the most promising sources of gravitational waves. The technique of matched filtering used in the detection of gravitational waves from coalescing binaries relies on the construction of accurate templates. Until recently filters modelled on the quadrupole or the Newtonian approximation were deemed sufficient. Recently it was shown that post-Newtonian effects contribute to a secular growth in the phase difference between the actual signal and its corresponding Newtonian template. In this paper we investigate the possibility of compensating for the phase difference caused by the post-Newtonian terms by allowing for a shift in the Newtonian filter parameters. We find that Newtonian filters perform adequately for the purpose of detecting the presence of the signal for both the initial and the advanced LIGO detectors.Comment: Revtex 9 pages + 6 figures ( Can be obtained by "anonymous" ftp from 144.16.31.1 in dir /pub/rbs. Submitted to Physical Review D. IUCAA 1

Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations

Assuming that general relativity is the correct theory of gravity in the strong field limit, can gravitational wave observations distinguish between black hole and other compact object sources? Alternatively, can gravitational wave observations provide a test of one of the fundamental predictions of general relativity? Here we describe a definitive test of the hypothesis that observations of damped, sinusoidal gravitational waves originated from a black hole or, alternatively, that nature respects the general relativistic no-hair theorem. For astrophysical black holes, which have a negligible charge-to-mass ratio, the black hole quasi-normal mode spectrum is characterized entirely by the black hole mass and angular momentum and is unique to black holes. In a different theory of gravity, or if the observed radiation arises from a different source (e.g., a neutron star, strange matter or boson star), the spectrum will be inconsistent with that predicted for general relativistic black holes. We give a statistical characterization of the consistency between the noisy observation and the theoretical predictions of general relativity, together with a numerical example.Comment: 19 pages, 7 figure

Finite-Range Gravity and Its Role in Gravitational Waves, Black Holes and Cosmology

Theoretical considerations of fundamental physics, as well as certain cosmological observations, persistently point out to permissibility, and maybe necessity, of macroscopic modifications of the Einstein general relativity. The field-theoretical formulation of general relativity helped us to identify the phenomenological seeds of such modifications. They take place in the form of very specific mass-terms, which appear in addition to the field-theoretical analog of the usual Hilbert-Einstein Lagrangian. We interpret the added terms as masses of the spin-2 and spin-0 gravitons. The arising finite-range gravity is a fully consistent theory, which smoothly approaches general relativity in the massless limit, that is, when both masses tend to zero and the range of gravity tends to infinity. We show that all local weak-field predictions of the theory are in perfect agreement with the available experimental data. However, some other conclusions of the non-linear massive theory are in a striking contrast with those of general relativity. We show in detail how the arbitrarily small mass-terms eliminate the black hole event horizon and replace a permanent power-law expansion of a homogeneous isotropic universe with an oscillatory behaviour. One variant of the theory allows the cosmological scale factor to exhibit an `accelerated expansion'instead of slowing down to a regular maximum of expansion. We show in detail why the traditional, Fierz-Pauli, massive gravity is in conflict not only with the static-field experiments but also with the available indirect gravitational-wave observations. At the same time, we demonstrate the incorrectness of the widely held belief that the non-Fierz-Pauli theories possess `negative energies' and `instabilities'.Comment: 56 pages including 11 figures; significant modifications; in particular, we demonstrate the incorrectness of the widely held belief that the non-Fierz-Pauli theories should suffer from negative energies and instabilities; to appear in Int. J. Mod. Phys.

Colliding black holes: how far can the close approximation go?

We study the head-on collision of two equal-mass momentarily stationary black holes, using black hole perturbation theory up to second order. Compared to first-order results, this significantly improves agreement with numerically computed waveforms and energy. Much more important, second-order results correctly indicate the range of validity of perturbation theory. This use of second-order, to provide ``error bars,'' makes perturbation theory a viable tool for providing benchmarks for numerical relativity in more generic collisions and, in some range of collision parameters, for supplying waveform templates for gravitational wave detection.Comment: 6 pages, RevTeX, 2 figures included with eps

Processing of gas in cosmological filaments around Virgo cluster

Galaxies have different morphology, gas content, and star formation rate (SFR) in dense environments like galaxy clusters. The impact of environmental density extends to several virial radii, and galaxies are pre-processed in filaments and groups, before falling into the cluster. Our goal is to quantify this pre-processing, in terms of gas content and SFR, as a function of density in cosmic filaments. We have observed the two first CO transitions in 163 galaxies with the IRAM-30m telescope, and added 82 measurements from the literature, for a sample of 245 galaxies in the filaments around Virgo. We gathered HI-21cm measurements from the literature, and observed 69 galaxies with the Nan\c{c}ay telescope, to complete our sample. We compare our filament galaxies with comparable samples from the Virgo cluster and with the isolated galaxies of the AMIGA sample. We find a clear progression from field, to filament, and cluster galaxies for decreasing SFR, increasing fraction of galaxies in the quenching phase, increasing proportion of early-type galaxies and decreasing gas content. Galaxies in the quenching phase, defined as having SFR below 1/3 of the main sequence rate, are between 0-20\% in the isolated sample, while they are 20-60\% in the filaments and 30-80\% in the Virgo cluster. Processes that lead to star formation quenching are already at play in filaments. They depend mostly on the local galaxy density, while the distance to filament spine is a secondary parameter. While the HI to stellar mass ratio decreases with local density by ~1 dex in the filaments, and ~2 dex in the Virgo cluster with respect to the field, the decrease is much less for the H$_2$ to stellar mass ratio. As the environmental density increases, the gas depletion time decreases, since the gas content decreases faster than the SFR. This suggests that gas depletion significantly precedes star formation quenching.Comment: 24 pages, plus 98 pages of supplementary material, submitted to A&