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Register a new userExtending the frequency reach of pulsar timing array based gravitational wave search without high cadence observations
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Gravitational wave (GW) searches using pulsar timing arrays (PTAs) are assumed to be limited by the typical average observational cadence of $1/(2~{rm weeks})$ for a single pulsar to GW frequencies $lesssim 4times 10^{-7}$ Hz. We show that this assumption is incorrect and that a PTA can detect signals with much higher frequencies, which are preserved in the data due to aliasing, by exploiting asynchronous observations from multiple pulsars. This allows an observation strategy that is scalable to future large-scale PTAs containing $O(10^3)$ pulsars, enabled by the Five-hundred meter Aperture Spherical Telescope and the Square Kilometer Array, without requiring a higher per-pulsar observation cadence. We show that higher frequency GW observations, reaching up to $4times 10^{-4}$ Hz with an SKA-era PTA, have significant astrophysical implications, such as (i) a three orders of magnitude better constraint than current high-cadence observations on GW strain in the $[10,400]$ $mu{rm Hz}$ band, and (ii) sensitive tests of the no-hair theorem in the mass range of supermassive black hole binaries using their inspiral, merger, and ringdown signals.
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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.
The maximum frequency of gravitational waves (GWs) detectable with traditional pulsar timing methods is set by the Nyquist frequency ($f_{rm{Ny}}$) of the observation. Beyond this frequency, GWs leave no temporal-correlated signals; instead, they appear as white noise in the timing residuals. The variance of the GW-induced white noise is a function of the position of the pulsars relative to the GW source. By observing this unique functional form in the timing data, we propose that we can detect GWs of frequency $>$ $f_{rm{Ny}}$ (super-Nyquist frequency GWs; SNFGWs). We demonstrate the feasibility of the proposed method with simulated timing data. Using a selected dataset from the Parkes Pulsar Timing Array data release 1 and the North American Nanohertz Observatory for Gravitational Waves publicly available datasets, we try to detect the signals from single SNFGW sources. The result is consistent with no GW detection with 65.5% probability. An all-sky map of the sensitivity of the selected pulsar timing array to single SNFGW sources is generated, and the position of the GW source where the selected pulsar timing array is most sensitive to is $lambda_{rm{s}}=-0.82$, $beta_{rm{s}}=-1.03$ (rad); the corresponding minimum GW strain is $h=6.31times10^{-11}$ at $f=1times10^{-5}$ Hz.
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.
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.
A nanohertz-frequency stochastic gravitational-wave background can potentially be detected through the precise timing of an array of millisecond pulsars. This background produces low-frequency noise in the pulse arrival times that would have a characteristic spectrum common to all pulsars and a well-defined spatial correlation. Recently the North American Nanohertz Observatory for Gravitational Waves collaboration (NANOGrav) found evidence for the common-spectrum component in their 12.5-year data set. Here we report on a search for the background using the second data release of the Parkes Pulsar Timing Array. If we are forced to choose between the two NANOGrav models $unicode{x2014}$ one with a common-spectrum process and one without $unicode{x2014}$ we find strong support for the common-spectrum process. However, in this paper, we consider the possibility that the analysis suffers from model misspecification. In particular, we present simulated data sets that contain noise with distinctive spectra but show strong evidence for a common-spectrum process under the standard assumptions. The Parkes data show no significant evidence for, or against, the spatially correlated Hellings-Downs signature of the gravitational-wave background. Assuming we did observe the process underlying the spatially uncorrelated component of the background, we infer its amplitude to be $A = 2.2^{+0.4}_{-0.3} times 10^{-15}$ in units of gravitational-wave strain at a frequency of $1, text{yr}^{-1}$. Extensions and combinations of existing and new data sets will improve the prospects of identifying spatial correlations that are necessary to claim a detection of the gravitational-wave background.
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