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Register a new userContinuous gravitational wave searches with pulsar timing arrays: Maximization versus marginalization over pulsar phase parameters
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Resolvable Supermassive Black Hole Binaries are promising sources for Pulsar Timing Array based gravitational wave searches. Search algorithms for such targets must contend with the large number of so-called pulsar phase parameters in the joint log-likelihood function of the data. We compare the localization accuracy for two approaches: Maximization over the pulsar phase parameters (MaxPhase) against marginalization over them (AvPhase). Using simulated data from a pulsar timing array with 17 pulsars, we find that for weak and moderately strong signals, AvPhase outperforms MaxPhase significantly, while they perform comparably for strong signals.
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By regularly monitoring the most stable millisecond pulsars over many years, pulsar timing arrays (PTAs) are positioned to detect and study correlations in the timing behaviour of those pulsars. Gravitational waves (GWs) from supermassive black hole binaries (SMBHBs) are an exciting potentially detectable source of such correlations. We describe a straight-forward technique by which a PTA can be phased-up to form time series of the two polarisation modes of GWs coming from a particular direction of the sky. Our technique requires no assumptions regarding the time-domain behaviour of a GW signal. This method has already been used to place stringent bounds on GWs from individual SMBHBs in circular orbits. Here, we describe the methodology and demonstrate the versatility of the technique in searches for a wide variety of GW signals including bursts with unmodeled waveforms. Using the first six years of data from the Parkes Pulsar Timing Array, we conduct an all-sky search for a detectable excess of GW power from any direction. For the lines of sight to several nearby massive galaxy clusters, we carry out a more detailed search for GW bursts with memory, which are distinct signatures of SMBHB mergers. In all cases, we find that the data are consistent with noise.
We have begun an exciting era for gravitational wave detection, as several world-leading experiments are breaching the threshold of anticipated signal strengths. Pulsar timing arrays (PTAs) are pan-Galactic gravitational wave detectors that are already cutting into the expected strength of gravitational waves from cosmic strings and binary supermassive black holes in the nHz-$mu$Hz gravitational wave band. These limits are leading to constraints on the evolutionary state of the Universe. Here, we provide a broad review of this field, from how pulsars are used as tools for detection, to astrophysical sources of uncertainty in the signals PTAs aim to see, to the primary current challenge areas for PTA work. This review aims to provide an up-to-date reference point for new parties interested in the field of gravitational wave detection via pulsar timing.
We explore the potential of Pulsar Timing Arrays (PTAs) such as NANOGrav, EPTA, and PPTA to detect the Stochastic Gravitational Wave Background (SGWB) in theories of massive gravity. In General Relativity, the function describing the dependence of the correlation between the arrival times of signals from two pulsars on the angle between them is known as the Hellings-Downs curve. We compute the analogous overlap reduction function for massive gravity, including the additional polarization states and the correction due to the mass of the graviton, and compare the result with the Hellings-Downs curve. The primary result is a complete analytical form for the analog Hellings-Downs curve, providing a starting point for future numerical studies aimed at a detailed comparison between PTA data and the predictions of massive gravity. We study both the massless limit and the stationary limit as checks on our calculation, and discuss how our formalism also allows us to study the impact of massive spin-2 dark matter candidates on data from PTAs.
The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported strong statistical evidence for a common-spectrum red-noise process for all pulsars, as seen in their 12.5-yr analysis for an isotropic stochastic gravitational-wave background. However, there is currently very little evidence for quadrupolar spatial correlations across the pulsars in the array, which is needed to make a confident claim of detection of a stochastic background. Here we give a frequentist analysis of a very simple signal+noise model showing that the current lack of evidence for spatial correlations is consistent with the magnitude of the correlation coefficients for pairs of Earth-pulsar baselines in the array, and the fact that pulsar timing arraysbare most-likely operating in the intermediate-signal regime. We derive analytic expressions that allow one to compare the expected values of the signal-to-noise ratios for both the common-spectrum and cross-correlation estimators.
Pulsar timing arrays act to detect gravitational waves by observing the small, correlated effect the waves have on pulse arrival times at Earth. This effect has conventionally been evaluated assuming the gravitational wave phasefronts are planar across the array, an assumption that is valid only for sources at distances $Rgg2pi{}L^2/lambda$, where $L$ is physical extent of the array and $lambda$ the radiation wavelength. In the case of pulsar timing arrays (PTAs) the array size is of order the pulsar-Earth distance (kpc) and $lambda$ is of order pc. Correspondingly, for point gravitational wave sources closer than $sim100$~Mpc the PTA response is sensitive to the source parallax across the pulsar-Earth baseline. Here we evaluate the PTA response to gravitational wave point sources including the important wavefront curvature effects. Taking the wavefront curvature into account the relative amplitude and phase of the timing residuals associated with a collection of pulsars allows us to measure the distance to, and sky position of, the source.
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