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We present new limits on an isotropic stochastic gravitational-wave background (GWB) using a six pulsar dataset spanning 18 yr of observations from the 2015 European Pulsar Timing Array data release. Performing a Bayesian analysis, we fit simultaneously for the intrinsic noise parameters for each pulsar, along with common correlated signals including clock, and Solar System ephemeris errors, obtaining a robust 95$%$ upper limit on the dimensionless strain amplitude $A$ of the background of $A<3.0times 10^{-15}$ at a reference frequency of $1mathrm{yr^{-1}}$ and a spectral index of $13/3$, corresponding to a background from inspiralling super-massive black hole binaries, constraining the GW energy density to $Omega_mathrm{gw}(f)h^2 < 1.1times10^{-9}$ at 2.8 nHz. We also present limits on the correlated power spectrum at a series of discrete frequencies, and show that our sensitivity to a fiducial isotropic GWB is highest at a frequency of $sim 5times10^{-9}$~Hz. Finally we discuss the implications of our analysis for the astrophysics of supermassive black hole binaries, and present 95$%$ upper limits on the string tension, $Gmu/c^2$, characterising a background produced by a cosmic string network for a set of possible scenarios, and for a stochastic relic GWB. For a Nambu-Goto field theory cosmic string network, we set a limit $Gmu/c^2<1.3times10^{-7}$, identical to that set by the {it Planck} Collaboration, when combining {it Planck} and high-$ell$ Cosmic Microwave Background data from other experiments. For a stochastic relic background we set a limit of $Omega^mathrm{relic}_mathrm{gw}(f)h^2<1.2 times10^{-9}$, a factor of 9 improvement over the most stringent limits previously set by a pulsar timing array.
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We search for isotropic stochastic gravitational-wave background (SGWB) in the International Pulsar Timing Array second data release. By modeling the SGWB as a power-law, we find very strong Bayesian evidence for a common-spectrum process, and further this process has scalar transverse (ST) correlations allowed in general metric theory of gravity as the Bayes factor in favor of the ST-correlated process versus the spatially uncorrelated common-spectrum process is $30pm 2$. The median and the $90%$ equal-tail amplitudes of ST mode are $mathcal{A}_{mathrm{ST}}= 1.29^{+0.51}_{-0.44} times 10^{-15}$, or equivalently the energy density parameter per logarithm frequency is $Omega_{mathrm{GW}}^{mathrm{ST}} = 2.31^{+2.19}_{-1.30} times 10^{-9}$, at frequency of 1/year. However, we do not find any statistically significant evidence for the tensor transverse (TT) mode and then place the $95%$ upper limits as $mathcal{A}_{mathrm{TT}}< 3.95 times 10^{-15}$, or equivalently $Omega_{mathrm{GW}}^{mathrm{TT}}< 2.16 times 10^{-9}$, at frequency of 1/year.
We have searched for continuous gravitational wave (CGW) signals produced by individually resolvable, circular supermassive black hole binaries (SMBHBs) in the latest EPTA dataset, which consists of ultra-precise timing data on 41 millisecond pulsars. We develop frequentist and Bayesian detection algorithms to search both for monochromatic and frequency-evolving systems. None of the adopted algorithms show evidence for the presence of such a CGW signal, indicating that the data are best described by pulsar and radiometer noise only. Depending on the adopted detection algorithm, the 95% upper limit on the sky-averaged strain amplitude lies in the range $6times 10^{-15}<A<1.5times10^{-14}$ at $5{rm nHz}<f<7{rm nHz}$. This limit varies by a factor of five, depending on the assumed source position, and the most constraining limit is achieved towards the positions of the most sensitive pulsars in the timing array. The most robust upper limit -- obtained via a full Bayesian analysis searching simultaneously over the signal and pulsar noise on the subset of ours six best pulsars -- is $Aapprox10^{-14}$. These limits, the most stringent to date at $f<10{rm nHz}$, exclude the presence of sub-centiparsec binaries with chirp mass $cal{M}_c>10^9$M$_odot$ out to a distance of about 25Mpc, and with $cal{M}_c>10^{10}$M$_odot$ out to a distance of about 1Gpc ($zapprox0.2$). We show that state-of-the-art SMBHB population models predict $<1%$ probability of detecting a CGW with the current EPTA dataset, consistent with the reported non-detection. We stress, however, that PTA limits on individual CGW have improved by almost an order of magnitude in the last five years. The continuing advances in pulsar timing data acquisition and analysis techniques will allow for strong astrophysical constraints on the population of nearby SMBHBs in the coming years.
We present an analysis of high-precision pulsar timing data taken as part of the North American Nanohertz Observatory for Gravitational waves (NANOGrav) project. We have observed 17 pulsars for a span of roughly five years using the Green Bank and Arecibo radio telescopes. We analyze these data using standard pulsar timing models, with the addition of time-variable dispersion measure and frequency-variable pulse shape terms. Sub-microsecond timing residuals are obtained in nearly all cases, and the best root-mean-square timing residuals in this set are ~30-50 ns. We present methods for analyzing post-fit timing residuals for the presence of a gravitational wave signal with a specified spectral shape. These optimally take into account the timing fluctuation power removed by the model fit, and can be applied to either data from a single pulsar, or to a set of pulsars to detect a correlated signal. We apply these methods to our dataset to set an upper limit on the strength of the nHz-frequency stochastic supermassive black hole gravitational wave background of h_c (1 yr^-1) < 7x10^-15 (95%). This result is dominated by the timing of the two best pulsars in the set, PSRs J1713+0747 and J1909-3744.
We compute upper limits on the nanohertz-frequency isotropic stochastic gravitational wave background (GWB) using the 9-year data release from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration. We set upper limits for a GWB from supermassive black hole binaries under power law, broken power law, and free spectral coefficient GW spectrum models. We place a 95% upper limit on the strain amplitude (at a frequency of yr$^{-1}$) in the power law model of $A_{rm gw} < 1.5times 10^{-15}$. For a broken power law model, we place priors on the strain amplitude derived from simulations of Sesana (2013) and McWilliams et al. (2014). We find that the data favor a broken power law to a pure power law with odds ratios of 22 and 2.2 to one for the McWilliams and Sesana prior models, respectively. The McWilliams model is essentially ruled out by the data, and the Sesana model is in tension with the data under the assumption of a pure power law. Using the broken power-law analysis we construct posterior distributions on environmental factors that drive the binary to the GW-driven regime including the stellar mass density for stellar-scattering, mass accretion rate for circumbinary disk interaction, and orbital eccentricity for eccentric binaries, marking the first time that the shape of the GWB spectrum has been used to make astrophysical inferences. We then place the most stringent limits so far on the energy density of relic GWs, $Omega_mathrm{gw}(f),h^2 < 4.2 times 10^{-10}$, yielding a limit on the Hubble parameter during inflation of $H_*=1.6times10^{-2}~m_{Pl}$, where $m_{Pl}$ is the Planck mass. Our limit on the cosmic string GWB, $Omega_mathrm{gw}(f), h^2 < 2.2 times 10^{-10}$, translates to a conservative limit of $Gmu<3.3times 10^{-8}$ - a factor of 4 better than the joint Planck and high-$l$ CMB data from other experiments.
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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