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Register a new userGravitational-Wave Detection and Astrophysics with Pulsar Timing Arrays
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Sarah Burke-Spolaor
Publication date
2015
fields
Physics
and research's language is
English
Authors
Sarah Burke-Spolaor
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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.
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The NANOGrav Collaboration reported strong Bayesian evidence for a common-spectrum stochastic process in its 12.5-yr pulsar timing array dataset, with median characteristic strain amplitude at periods of a year of $A_{rm yr} = 1.92^{+0.75}_{-0.55} times 10^{-15}$. However, evidence for the quadrupolar Hellings & Downs interpulsar correlations, which are characteristic of gravitational wave signals, was not yet significant. We emulate and extend the NANOGrav dataset, injecting a wide range of stochastic gravitational wave background (GWB) signals that encompass a variety of amplitudes and spectral shapes, and quantify three key milestones: (I) Given the amplitude measured in the 12.5 yr analysis and assuming this signal is a GWB, we expect to accumulate robust evidence of an interpulsar-correlated GWB signal with 15--17 yrs of data, i.e., an additional 2--5 yrs from the 12.5 yr dataset; (II) At the initial detection, we expect a fractional uncertainty of $40%$ on the power-law strain spectrum slope, which is sufficient to distinguish a GWB of supermassive black-hole binary origin from some models predicting more exotic origins;(III) Similarly, the measured GWB amplitude will have an uncertainty of $44%$ upon initial detection, allowing us to arbitrate between some population models of supermassive black-hole binaries. In addition, power-law models are distinguishable from those having low-frequency spectral turnovers once 20~yrs of data are reached. Even though our study is based on the NANOGrav data, we also derive relations that allow for a generalization to other pulsar-timing array datasets. Most notably, by combining the data of individual arrays into the International Pulsar Timing Array, all of these milestones can be reached significantly earlier.
Within the next several years, pulsar-timing array programs will likely usher in the next era of gravitational-wave astronomy through the detection of a stochastic background of nanohertz-frequency gravitational waves, originating from a cosmological population of inspiraling supermassive binary black holes. While the source positions will likely be isotropic to a good approximation, the gravitational-wave angular power distribution will be anisotropic, with the most massive and/or nearby binaries producing signals that may resound above the background. We study such a realistic angular power distribution, developing fast and accurate sky-mapping strategies to localize pixels and extended regions of excess power while simultaneously modeling the background signal from the less massive and more distant ensemble. We find that power anisotropy will be challenging to discriminate from isotropy for realistic gravitational-wave skies, requiring SNR $>10$ in order to favor anisotropy with $10:1$ posterior odds in our case study. Amongst our techniques, modeling the population signal with multiple point sources in addition to an isotropic background provides the most physically-motivated and easily interpreted maps, while spherical-harmonic modeling of the square-root power distribution, $P(hatOmega)^{1/2}$, performs best in discriminating from overall isotropy. Our techniques are modular and easily incorporated into existing pulsar-timing array analysis pipelines.
We discuss the theory of pulsar-timing and astrometry probes of a stochastic gravitational-wave background with a recently developed total-angular-momentum (TAM) formalism for cosmological perturbations. We review the formalism, emphasizing in particular the features relevant for this work and describe the observables we consider (i.e. the pulsar redshift and stellar angular displacement). Using the TAM approach, we calculate the angular power spectra for the observables and from them derive angular auto- and cross-correlation functions. We provide the full set of power spectra and correlation functions not only for the standard transverse-traceless propagating degrees of freedom in general relativity, but also for the four additional non-Einsteinian polarizations that may arise in alternative-gravity theories. We discuss how pulsar-timing and astrometry surveys can complement and serve as cross checks to one another and comment on the importance of testing the chirality of the gravitational-wave background as a tool to understand the nature of its sources. A simple rederivation of the power spectra from the plane-wave formalism is provided in an Appendix.
Detecting continuous nanohertz gravitational waves (GWs) generated by individual close binaries of supermassive black holes (CB-SMBHs) is one of the primary objectives of pulsar timing arrays (PTAs). The detection sensitivity is slated to increase significantly as the number of well-timed millisecond pulsars will increase by more than an order of magnitude with the advent of next-generation radio telescopes. Currently, the Bayesian analysis pipeline using parallel tempering Markov chain Monte Carlo has been applied in multiple studies for CB-SMBH searches, but it may be challenged by the high dimensionality of the parameter space for future large-scale PTAs. One solution is to reduce the dimensionality by maximizing or marginalizing over uninformative parameters semi-analytically, but it is not clear whether this approach can be extended to more complex signal models without making overly simplified assumptions. Recently, the method of diffusive nested (DNest) sampling shown the capability of coping with high dimensionality and multimodality effectively in Bayesian analysis. In this paper, we apply DNest to search for continuous GWs in simulated pulsar timing residuals and find that it performs well in terms of accuracy, robustness, and efficiency for a PTA including $mathcal{O}(10^2)$ pulsars. DNest also allows a simultaneous search of multiple sources elegantly, which demonstrates its scalability and general applicability. Our results show that it is convenient and also high beneficial to include DNest in current toolboxes of PTA analysis.
The regularity of pulsar emissions becomes apparent once we reference the pulses times of arrivals to the inertial rest frame of the solar system. It follows that errors in the determination of Earths position with respect to the solar-system barycenter can appear as a time-correlated bias in pulsar-timing residual time series, affecting the searches for low-frequency gravitational waves performed with pulsar timing arrays. Indeed, recent array datasets yield different gravitational-wave background upper limits and detection statistics when analyzed with different solar-system ephemerides. Crucially, the ephemerides do not generally provide usable error representations. In this article we describe the motivation, construction, and application of a physical model of solar-system ephemeris uncertainties, which focuses on the degrees of freedom (Jupiters orbital elements) most relevant to gravitational-wave searches with pulsar timing arrays. This model, BayesEphem, was used to derive ephemeris-robust results in NANOGravs 11-yr stochastic-background search, and it provides a foundation for future searches by NANOGrav and other consortia. The analysis and simulations reported here suggest that ephemeris modeling reduces the gravitational-wave sensitivity of the 11-yr dataset; and that this degeneracy will vanish with improved ephemerides and with the longer pulsar timing datasets that will become available in the near future.
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