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  1. Abstract

    Recently, many different pulsar timing array (PTA) collaborations have reported strong evidence for a common stochastic process in their data sets. The reported amplitudes are in tension with previously computed upper limits. In this paper, we investigate how using a subset of a set of pulsars biases Bayesian upper limit recovery. We generate 500 simulated PTA data sets, based on the NANOGrav 11 yr data set with an injected stochastic gravitational-wave background (GWB). We then compute the upper limits by sampling the individual pulsar likelihoods, and combine them through a factorized version of the PTA likelihood to obtain upper limits on the GWB amplitude, using different numbers of pulsars. We find that it is possible to recover an upper limit (95% credible interval) below the injected value, and that it is significantly more likely for this to occur when using a subset of pulsars to compute the upper limit. When picking pulsars to induce the maximum possible bias, we find that the 95% Bayesian upper limit recovered is below the injected value in 10.6% of the realizations (53 of 500). Further, we find that if we choose a subset of pulsars in order to obtain a lower upper limitmore »than when using the full set of pulsars, the distribution of the upper limits obtained from these 500 realizations is shifted to lower-amplitude values.

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  2. Abstract

    With strong evidence of a common-spectrum stochastic process in the most recent data sets from the NANOGrav Collaboration, the European Pulsar Timing Array (PTA), Parkes PTA, and the International PTA, it is crucial to assess the effects of the several astrophysical and cosmological sources that could contribute to the stochastic gravitational wave background (GWB). Using the same data set creation and injection techniques as in Pol et al., we assess the separability of multiple GWBs by creating single and multiple GWB source data sets. We search for these injected sources using Bayesian PTA analysis techniques to assess recovery and separability of multiple astrophysical and cosmological backgrounds. For a GWB due to supermassive black hole binaries and an underlying weaker background due to primordial gravitational waves with a GW energy-density ratio of ΩPGWSMBHB= 0.5, the Bayes’ factor for a second process exceeds unity at 17 yr, and increases with additional data. At 20 yr of data, we are able to constrain the spectral index and amplitude of the weaker GWB at this density ratio to a fractional uncertainty of 64% and 110%, respectively, using current PTA methods and techniques. Using these methods and findings, we outline a basic protocol tomore »search for multiple backgrounds in future PTA data sets.

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  3. Abstract Pulsar timing array (PTA) experiments are becoming increasingly sensitive to gravitational waves (GWs) in the nanohertz frequency range, where the main astrophysical sources are supermassive black hole binaries (SMBHBs), which are expected to form following galaxy mergers. Some of these individual SMBHBs may power active galactic nuclei, and thus their binary parameters could be obtained electromagnetically, which makes it possible to apply electromagnetic (EM) information to aid the search for a GW signal in PTA data. In this work, we investigate the effects of such an EM-informed search on binary detection and parameter estimation by performing mock data analyses on simulated PTA data sets. We find that by applying EM priors, the Bayes factor of some injected signals with originally marginal or sub-threshold detectability (i.e., Bayes factor ∼1) can increase by a factor of a few to an order of magnitude, and thus an EM-informed targeted search is able to find hints of a signal when an uninformed search fails to find any. Additionally, by combining EM and GW data, one can achieve an overall improvement in parameter estimation, regardless of the source’s sky location or GW frequency. We discuss the implications for the multi-messenger studies of SMBHBs withmore »PTAs.« less
  4. Abstract We search NANOGrav’s 12.5 yr data set for evidence of a gravitational-wave background (GWB) with all the spatial correlations allowed by general metric theories of gravity. We find no substantial evidence in favor of the existence of such correlations in our data. We find that scalar-transverse (ST) correlations yield signal-to-noise ratios and Bayes factors that are higher than quadrupolar (tensor-transverse, TT) correlations. Specifically, we find ST correlations with a signal-to-noise ratio of 2.8 that are preferred over TT correlations (Hellings and Downs correlations) with Bayesian odds of about 20:1. However, the significance of ST correlations is reduced dramatically when we include modeling of the solar system ephemeris systematics and/or remove pulsar J0030+0451 entirely from consideration. Even taking the nominal signal-to-noise ratios at face value, analyses of simulated data sets show that such values are not extremely unlikely to be observed in cases where only the usual TT modes are present in the GWB. In the absence of a detection of any polarization mode of gravity, we place upper limits on their amplitudes for a spectral index of γ = 5 and a reference frequency of f yr = 1 yr −1 . Among the upper limits for eight generalmore »families of metric theories of gravity, we find the values of A TT 95 % = ( 9.7 ± 0.4 ) × 10 − 16 and A ST 95 % = ( 1.4 ± 0.03 ) × 10 − 15 for the family of metric spacetime theories that contain both TT and ST modes.« less