On tests of general relativity with binary radio pulsars

The timing of radio pulsars in binary systems provides a superb testing ground of general relativity. Here we propose a Bayesian approach to carry out these tests, and a relevant efficient numerical implementation, that has several conceptual and practical advantages with respect to traditional methods based on least-square-fits that have been used so far: (i) it accounts for the actual structure of the likelihood function - and it is not predicated on the Laplace approximation which is implicitly built in least-square fits that can potentially bias the inference - (ii) it provides the ratio of the evidences of any two models under consideration as the statistical quantity to compare different theories, and (iii) it allows us to put joint constraints from the monitoring of multiple systems, that can be expressed in terms of ratio of evidences or probability intervals of global (thus not system-dependent) parameters of the theory, if any exists. Our proposed approach optimally exploits the progress in timing of radio pulsars and the increase in the number of observed systems. We demonstrate the power of this framework using simulated data sets that are representative of current observations.Comment: Accepted for publication on MNRAS Letter

How serious can the stealth bias be in gravitational wave parameter estimation?

The upcoming direct detection of gravitational waves will open a window to probing the strong-field regime of general relativity (GR). As a consequence, waveforms that include the presence of deviations from GR have been developed (e.g. in the parametrized post-Einsteinian approach). TIGER, a data analysis pipeline which builds Bayesian evidence to support or question the validity of GR, has been written and tested. In particular, it was shown recently that data from the LIGO and Virgo detectors will allow to detect deviations from GR smaller than can be probed with Solar System tests and pulsar timing measurements or not accessible with conventional tests of GR. However, evidence from several detections is required before a deviation from GR can be confidently claimed. An interesting consequence is that, should GR not be the correct theory of gravity in its strong field regime, using standard GR templates for the matched filter analysis of interferometer data will introduce biases in the gravitational wave measured parameters with potentially disastrous consequences on the astrophysical inferences, such as the coalescence rate or the mass distribution. We consider three heuristic possible deviations from GR and show that the biases introduced by assuming GR's validity manifest in various ways. The mass parameters are usually the most affected, with biases that can be as large as $30$ standard deviations for the symmetric mass ratio, and nearly one percent for the chirp mass, which is usually estimated with sub-percent accuracy. We conclude that statements about the nature of the observed sources, e.g. if both objects are neutron stars, depend critically on the explicit assumption that GR it the right theory of gravity in the strong field regime.Comment: 10 pages, 9 figures, 5 table

Observational Black Hole Spectroscopy: A time-domain multimode analysis of GW150914

The detection of the least damped quasi-normal mode from the remnant of the gravitational wave event GW150914 realised the long sought possibility to observationally study the properties of quasi-stationary black hole spacetimes through gravitational waves. Past literature has extensively explored this possibility and the emerging field has been named "black hole spectroscopy". In this study, we present results regarding the ringdown spectrum of GW150914, obtained by application of Bayesian inference to identify and characterise the ringdown modes. We employ a pure time-domain analysis method which infers from the data the time of transition between the non-linear and quasi-linear regime of the post-merger emission in concert with all other parameters characterising the source. We find that the data provides no evidence for the presence of more than one quasi-normal mode. However, from the central frequency and damping time posteriors alone, no unambiguous identification of a single mode is possible. More in-depth analysis adopting a ringdown model based on results in perturbation theory over the Kerr metric, confirms that the data do not provide enough evidence to discriminate among an $l=2$ and the $l=3$ subset of modes. Our work provides the first comprehensive agnostic framework to observationally investigate astrophysical black holes' ringdown spectra.Comment: 9 pages, 8 figure

Efficient computation of the gravitational wave spectrum emitted by eccentric massive black hole binaries in stellar environments

We present a fast and versatile method to calculate the characteristic spectrum $h_c$ of the gravitational wave background (GWB) emitted by a population of eccentric massive black hole binaries (MBHBs). We fit the spectrum of a reference MBHB with a simple analytic function and show that the spectrum of any other MBHB can be derived from this reference spectrum via simple scalings of mass, redshift and frequency. We then apply our calculation to a realistic population of MBHBs evolving via 3-body scattering of stars in galactic nuclei. We demonstrate that our analytic prescription satisfactorily describes the signal in the frequency band relevant to pulsar timing array (PTA) observations. Finally we model the high frequency steepening of the GWB to provide a complete description of the features characterizing the spectrum. For typical stellar distributions observed in massive galaxies, our calculation shows that 3-body scattering alone is unlikely to affect the GWB in the PTA band and a low frequency turnover in the spectrum is caused primarily by high eccentricities.Comment: 12 pages, 9 figures, published in MNRA

Estimating parameters of binary black holes from gravitational-wave observations of their inspiral, merger and ringdown

We characterize the expected statistical errors with which the parameters of black-hole binaries can be measured from gravitational-wave (GW) observations of their inspiral, merger and ringdown by a network of second-generation ground-based GW observatories. We simulate a population of black-hole binaries with uniform distribution of component masses in the interval $(3,80)~M_\odot$, distributed uniformly in comoving volume, with isotropic orientations. From signals producing signal-to-noise ratio $\geq 5$ in at least two detectors, we estimate the posterior distributions of the binary parameters using the Bayesian parameter estimation code LALInference. The GW signals will be redshifted due to the cosmological expansion and we measure only the "redshifted" masses. By assuming a cosmology, it is possible to estimate the gravitational masses by inferring the redshift from the measured posterior of the luminosity distance. We find that the measurement of the gravitational masses will be in general dominated by the error in measuring the luminosity distance. In spite of this, the component masses of more than $50\%$ of the population can be measured with accuracy better than $\sim 25\%$ using the Advanced LIGO-Virgo network. Additionally, the mass of the final black hole can be measured with median accuracy $\sim 18\%$. Spin of the final black hole can be measured with median accuracy $\sim 5\% ~(17\%)$ for binaries with non-spinning (aligned-spin) black holes. Additional detectors in Japan and India significantly improve the accuracy of sky localization, and moderately improve the estimation of luminosity distance, and hence, that of all mass parameters. We discuss the implication of these results on the observational evidence of intermediate-mass black holes and the estimation of cosmological parameters using GW observations.Comment: 9 pages, 5 figure

Stellar binary black holes in the LISA band: a new class of standard sirens

The recent Advanced LIGO detections of coalescing black hole binaries (BHBs) imply a large population of such systems emitting at milli-Hz frequencies, accessible to the Laser Interferometer Space Antenna (LISA). We show that these systems provide a new class of cosmological standard sirens. Direct LISA luminosity distance -$D_l$- measurements, combined with the inhomogeneous redshift -$z$- distribution of possible host galaxies provide an effective way to populate the $D_l-z$ diagram at $z<0.1$, thus allowing a precise local measurement of the Hubble expansion rate. To be effective, the method requires a sufficiently precise LISA distance determination and sky localization of a sizeable number of BHBs, which is best achieved for a 6-link detector configuration. We find that, for a BHB population consistent with current fiducial LIGO rates, the Hubble constant $H_0$ can be determined at the $\sim$5% and $\sim$2% level (68% confidence) assuming two and five million Km arm-length respectively.Comment: 9 pages 4 figures, to be submitted to MNRA

Testing general relativity with compact coalescing binaries: comparing exact and predictive methods to compute the Bayes factor

The second generation of gravitational-wave detectors is scheduled to start operations in 2015. Gravitational-wave signatures of compact binary coalescences could be used to accurately test the strong-field dynamical predictions of general relativity. Computationally expensive data analysis pipelines, including TIGER, have been developed to carry out such tests. As a means to cheaply assess whether a particular deviation from general relativity can be detected, Cornish et al. and Vallisneri recently proposed an approximate scheme to compute the Bayes factor between a general-relativity gravitational-wave model and a model representing a class of alternative theories of gravity parametrised by one additional parameter. This approximate scheme is based on only two easy-to-compute quantities: the signal-to-noise ratio of the signal and the fitting factor between the signal and the manifold of possible waveforms within general relativity. In this work, we compare the prediction from the approximate formula against an exact numerical calculation of the Bayes factor using the lalinference library. We find that, using frequency-domain waveforms, the approximate scheme predicts exact results with good accuracy, providing the correct scaling with the signal-to-noise ratio at a fitting factor value of 0.992 and the correct scaling with the fitting factor at a signal-to-noise ratio of 20, down to a fitting factor of $\sim$ 0.9. We extend the framework for the approximate calculation of the Bayes factor which significantly increases its range of validity, at least to fitting factors of $\sim$ 0.7 or higher.Comment: 13 pages, 4 figures, accepted for publication in Classical and Quantum Gravit

No tension between assembly models of supermassive black hole binaries and pulsar observations

Pulsar timing arrays (PTAs) are presently the only means to search for the gravitational wave stochastic background from supermassive black hole binary populations, considered to be within the grasp of current or near future observations. However, the stringent upperlimit set by the Parkes PTA (Shannon et al. 2013, 2015) has been interpreted as excluding at $> 90\%$ confidence the current paradigm of binary assembly through galaxy mergers and hardening via stellar interactions, suggesting evolution is accelerated (by stars and/or gas) or stalled. Using Bayesian hierarchical modelling, we consider implications of this upperlimit for a comprehensive range of astrophysical scenarios, without invoking stalling nor more exotic physical processes. We find they are fully consistent with the upperlimit, but (weak) bounds on population parameters can be inferred. Bayes factors between models vary between $\approx 1.03$ -- $5.81$ and Kullback-Leibler divergences between characteristic amplitude prior and posterior lie between $0.37$ -- $0.85$. Considering prior astrophysical information on galaxy merger rates, recent upwards revisions of the black hole-galaxy bulge mass relation (Kormendy & Ho 2013) are disfavoured at $1.6\sigma$ against lighter models (e.g. Shankar et al. 2016). We also show, if no detection is achieved once sensitivity improves by an order of magnitude, the most optimistic scenario is disfavoured at $3.9\sigma$.Comment: 20 pages, 7 figure

Studio della Luminosità Bolometrica pr le Novae Classiche nella Grande Nube di Magellano

In questa tesi verranno trattati alcuni aspetti legati al'ipotesi di luminosità bolometrica costante con lo scopo di chiarire il ruolo della Maximum Magnitude Rate of Decline come indicatore di distanza. Nella prima parte verranno trattati gli aspetti fisici principali riguardanti i sistemi binari compatti formati da una nana bianca e da una stella di tipo tardo, essendo questi i sistemi che possono evolvere in novae. Saranno considerati principalmente gli impatti sui parametri fisici del sistema binario dovuti allo scambio di materiale gassoso tra le due componenti e al successivo outburst della nova che rilasciando quantità di gas dell'ordine di 10⁻⁴-10⁻⁵ M_{⊙} modifica sostanzialmente momento angolare e quindi periodo e semiasse maggiore del sistema binario. Verrà inoltre brevemente discussa la fisica del trasferimento di gas guidata dal processo di trabocco del lobo di Roche e la formazione del disco di accrescimento attorno alla nana bianca. Vengono poi discusse le caratteristiche principali delle nane bianche come strutture di gas sorrette dalla pressione di degenerazione elettronica e le conseguenze che queste hanno sul materiale accresciuto in caduta dal disco circumstellare. Verranno sintetizzati gli aspetti principali trattabili fenemenologicamente del processo di ThermoNuclear Runaway che inizia il fenomeno nova, come l'accensione del ciclo CNO in ambiente degenere e l'esplosione dello strato esterno della nova insieme a vari aspetti riguardanti la nucleosintesi esplosiva. La fisica dell'espansione libera susseguente viene discussa in virtù di fare luce sul processo di formazione degli spettri, unita all'influenza che può avere sulla MMRD la presenza di condensazioni iniziali nell'eietto dovute ad instabilità idrodinamiche. Quindi ogni fase della nova viene discussa tenendo sempre in conto quanto è stato osservato fino ad oggi dai telescopi e tentando di spiegare nel modo più semplice quando possibile l'evoluzione temporale degli spettri tramite una discussione portata avanti grazie ad un parallelo tra visibile e ultravioletto, incentrata principalmente su quest'ultimo, al fine di chiarirne l'evoluzione fotometrica in rapporto a quella spettroscopica. Le tecniche utilizzate saranno le medesime usate per studiare le novae galattiche. In particolare verrà messo in relazione il tempo del turn-off delle reazioni nucleari e la CBL per verificare quando la MMRD proposta da Della Valle & Livio nel 1995 smette di essere valida. A tal fine verrà costruito un modello di ricombinazione in condizioni di espansione libere per l'elio ionizzato e per l'azoto ionizzato 2,3 e 4 volte così da stimare il tempo del turn-off nucleare e quindi porre un limite alla durata della fase di CBL. La seconda parte della tesi invece consta principalmente di analisi dei dati nell'archivio delle osservazioni di IUE. Dopo una breve discussione delle caratteristiche principali dell'Internation Ultraviolet Explorer verrà presentato il campione delle novae analizzate. Tutte appartengono alla Grande Nube di Magellano in quanto per tale galassia sono meglio noti l'assorbimento dovuto al gas e alle polveri interstellari e la distanza, quindi rappresenta un campione migliore su cui basare una eventuale calibrazione rispetto alle novae galattiche per cui tali quantità fondamentali sono molto più incerte. Per ogni nova verranno discusse le caratteristiche spettrali principali in funzione del tempo e verrà testata l'ipotesi di CBL. Inoltre sarà ricavata una stima per il tempo del turn-off per ciascuna nova i cui dati lo permettano in modo da costruire una prescrizione per l'applicabilità della MMRD come indicatore secondario di distanza

Probing Extreme-Density Matter with Gravitational Wave Observations of Binary Neutron Star Merger Remnants

We present a proof-of-concept study, based on numerical-relativity simulations, of how gravitational waves (GWs) from neutron star merger remnants can probe the nature of matter at extreme densities. Phase transitions and extra degrees of freedom can emerge at densities beyond those reached during the inspiral, and typically result in a softening of the equation of state (EOS). We show that such physical effects change the qualitative dynamics of the remnant evolution, but they are not identifiable as a signature in the GW frequency, with the exception of possible black-hole formation effects. The EOS softening is, instead, encoded in the GW luminosity and phase and is in principle detectable up to distances of the order of several Mpcs with advanced detectors and up to hundreds of Mpcs with third generation detectors. Probing extreme-density matter will require going beyond the current paradigm and developing a more holistic strategy for modeling and analyzing postmerger GW signals.Comment: 5 pages, 3 figures. Matches version accepted on ApJ