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The post-Newtonian formalism plays an integral role in the models used to extract information from gravitational wave data, but models that incorporate this formalism are inherently approximations. Disagreement between an approximate model and nature will produce mismodeling biases in the parameters inferred from data, introducing systematic error. We here carry out a proof-of- principle study of such systematic error by considering signals produced by quasi-circular, inspiraling black hole binaries through an injection and recovery campaign. In particular, we study how un- known, but calibrated, higher-order post-Newtonian corrections to the gravitational wave phase impact systematic error in recovered parameters. As a first study, we produce injected data of non-spinning binaries as detected by a current, second-generation network of ground-based observatories and recover them with models of varying PN order in the phase. We find that the truncation of higher order (>3.5) post-Newtonian corrections to the phase can produce significant systematic error even at signal-to-noise ratios of current detector networks. We propose a method to mitigate systematic error by marginalizing over our ignorance in the waveform through the inclusion of higher-order post-Newtonian coefficients as new model parameters. We show that this method can reduce systematic error greatly at the cost of increasing statistical error. 

Abstract Hundreds of millions of supermassive black hole binaries are expected to contribute to the gravitational-wave signal in the nanohertz frequency band. Their signal is often approximated either as an isotropic Gaussian stochastic background with a power-law spectrum or as an individual source corresponding to the brightest binary. In reality, the signal is best described as a combination of a stochastic background and a few of the brightest binaries modeled individually. We present a method that uses this approach to efficiently create realistic pulsar timing array data sets using synthetic catalogs of binaries based on the Illustris cosmological hydrodynamic simulation. We explore three different properties of such realistic backgrounds that could help distinguish them from those formed in the early universe: (i) their characteristic strain spectrum, (ii) their statistical isotropy, and (iii) the variance of their spatial correlations. We also investigate how the presence of confusion noise from a stochastic background affects detection prospects of individual binaries. We calculate signal-to-noise ratios of the brightest binaries in different realizations for a simulated pulsar timing array based on the NANOGrav 12.5 yr data set extended to a time span of 15 yr. We find that ∼6% of the realizations produce systems with signal-to-noise ratios larger than 5, suggesting that individual systems might soon be detected (the fraction increases to ∼41% at 20 yr). These can be taken as a pessimistic prediction for the upcoming NANOGrav 15 yr data set, since it does not include the effect of potentially improved timing solutions and newly added pulsars. 

Abstract The nanohertz frequency band explored by pulsar timing arrays provides a unique discovery space for gravitational wave (GW) signals. In addition to signals from anticipated sources, such as those from supermassive black hole binaries, some previously unimagined sources may emit transient GWs (a.k.a. bursts) with unknown morphology. Unmodeled transients are not currently searched for in this frequency band, and they require different techniques from those currently employed. Possible sources of such GW bursts in the nanohertz regime are parabolic encounters of supermassive black holes, cosmic string cusps and kinks, or other, as-yet-unknown phenomena. In this paper we present BayesHopperBurst , a Bayesian search algorithm capable of identifying generic GW bursts by modeling both coherent and incoherent transients as a sum of Morlet–Gabor wavelets. A trans-dimensional reversible jump Markov chain Monte Carlo sampler is used to select the number of wavelets best describing the data. We test BayesHopperBurst on various simulated datasets including different combinations of signals and noise transients. Its capability to run on real data is demonstrated by analyzing data of the pulsar B1855 + 09 from the NANOGrav 9 year dataset. Based on a simulated dataset resembling the NANOGrav 12.5 year data release, we predict that at our most sensitive time–frequency location we will be able to probe GW bursts with a root-sum-squared amplitude higher than ∼5 × 10 −11  Hz −1/2 , which corresponds to ∼40 M ⊙ c 2 emitted in GWs at a fiducial distance of 100 Mpc. 

Recently we found compelling evidence for a gravitational-wave background with Hellings and Downs (HD) correlations in our 15 yr data set. These correlations describe gravitational waves as predicted by general relativity, which has two transverse polarization modes. However, more general metric theories of gravity can have additional polarization modes, which produce different interpulsar correlations. In this work, we search the NANOGrav 15 yr data set for evidence of a gravitational-wave background with quadrupolar HD and scalar-transverse (ST) correlations. We find that HD correlations are the best fit to the data and no significant evidence in favor of ST correlations. While Bayes factors show strong evidence for a correlated signal, the data does not strongly prefer either correlation signature, with Bayes factors ∼2 when comparing HD to ST correlations, and ∼1 for HD plus ST correlations to HD correlations alone. However, when modeled alongside HD correlations, the amplitude and spectral index posteriors for ST correlations are uninformative, with the HD process accounting for the vast majority of the total signal. Using the optimal statistic, a frequentist technique that focuses on the pulsar-pair cross-correlations, we find median signal-to-noise ratios of 5.0 for HD and 4.6 for ST correlations when fit for separately, and median signal-to-noise ratios of 3.5 for HD and 3.0 for ST correlations when fit for simultaneously. While the signal-to-noise ratios for each of the correlations are comparable, the estimated amplitude and spectral index for HD are a significantly better fit to the total signal, in agreement with our Bayesian analysis.