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 < 3.0 × 10 −15 at a reference frequency of 1yr −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 Ω gw ( f )h 2 < 1.1 × 10 −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 ∼ 5×10 −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, Gµ/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 Gµ/c 2 < 1.3 × 10 −7 , identical to that set by the Planck Collaboration, when combining Planck and high-Cosmic Microwave Background data from other experiments. For a stochastic relic background we set a limit of Ω relic gw ( f )h 2 < 1.2 × 10 −9 , a factor of 9 improvement over the most stringent limits previously set by a pulsar timing array. c 0000 RAS arXiv:1504.03692v3 [astro-ph.CO] 9 Sep 2015

We search for an isotropic stochastic gravitational-wave background (GWB) in the newly released 11-year dataset from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). While we find no evidence for a GWB, we place constraints on a population of inspiraling supermassive black hole (SMBH) binaries, a network of decaying cosmic strings, and a primordial GWB. For the first time, we find that the GWB constraints are sensitive to the Solar System ephemeris (SSE) model used, and that SSE errors arXiv:1801.02617v2 [astro-ph.HE] 7 Jun 2018 2 THE NANOGRAV COLLABORATION can mimic a GWB signal. We developed an approach that bridges systematic SSE differences, producing the first PTA constraints that are robust against SSE errors. We thus place a 95% upper limit on the GW strain amplitude of A GWB < 1.45 × 10 −15 at a frequency of f = 1-yr −1 for a fiducial f −2/3 power-law spectrum, and with inter-pulsar correlations modeled. This is a factor of ∼ 2 improvement over the NANOGrav 9-year limit, calculated using the same procedure. Previous PTA upper limits on the GWB (as well as their astrophysical and cosmological interpretations) will need revision in light of SSE systematic errors. We use our constraints to characterize the combined influence on the GWB of the stellar mass-density in galactic cores, the eccentricity of SMBH binaries, and SMBH-galactic-bulge scaling relationships. We constrain cosmic-string tension using recent simulations, yielding an SSE-marginalized 95% upper limit of Gµ < 5.3 × 10 −11 -a factor of ∼ 2 better than the published NANOGrav 9-year constraints. Our SSE-marginalized 95% upper limit on the energy density of a primordial GWB (for a radiation-dominated post-inflation Universe) is Ω GWB ( f )h 2 < 3.4 × 10 −10 .

We report on the high-precision timing of 42 radio millisecond pulsars (MSPs) observed by the European Pulsar Timing Array (EPTA). This EPTA Data Release 1.0 extends up to mid-2014 and baselines range from 7-18 years. It forms the basis for the stochastic gravitationalwave background, anisotropic background, and continuous-wave limits recently presented by the EPTA elsewhere. The Bayesian timing analysis performed with TempoNest yields the detection of several new parameters: seven parallaxes, nine proper motions and, in the case of six binary pulsars, an apparent change of the semi-major axis. We find the NE2001 Galactic electron density model to be a better match to our parallax distances (after correction from the Lutz-Kelker bias) than the M2 and M3 models by Schnitzeler (2012). However, we measure an average uncertainty of 80% (fractional) for NE2001, three times larger than what is typically assumed in the literature. We revisit the transverse velocity distribution for a set of 19 isolated and 57 binary MSPs and find no statistical difference between these two populations. We detect Shapiro delay in the timing residuals of PSRs J1600−3053 and J1918−0642, implying pulsar and companion masses m p = 1.22 +0.5 −0.35 M ⊙ , m c = 0.21 +0.06 −0.04 M ⊙ and m p = 1.25 +0.6 −0.4 M ⊙ , m c = 0.23 +0.07 −0.05 M ⊙ , respectively. Finally, we use the measurement of the orbital period derivative to set a stringent constraint on the distance to PSRs J1012+5307 and J1909−3744, and set limits on the longitude of ascending node through the search of the annual-orbital parallax for PSRs J1600−3053 and J1909−3744.

The International Pulsar Timing Array project combines observations of pulsars from both Northern and Southern hemisphere observatories with the main aim of detecting ultra-low frequency (∼ 10 −9 − 10 −8 Hz) gravitational waves. Here we introduce the project, review the methods used to search for gravitational waves emitted from coalescing supermassive binary black-hole systems in the centres of merging galaxies and discuss the status of the project.

We present high-precision timing data over time spans of up to 11 years for 45 millisecond pulsars observed as part of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) project, aimed at detecting and characterizing low-frequency gravitational waves. The pulsars were observed with the Arecibo Observatory and/or the Green Bank Telescope at frequencies ranging from 327 MHz to 2.3 GHz. Most pulsars were observed with approximately monthly cadence, and six high-timing-precision pulsars were observed weekly. All were observed at widely separated frequencies at each observing epoch in order to fit for time-variable dispersion delays. We describe our methods for data processing, time-of-arrival (TOA) calculation, and the implementation of a new, automated method for removing outlier TOAs. We fit a timing model for each pulsar that includes spin, astrometric, and (for binary pulsars) orbital parameters; time-variable dispersion delays; and parameters that 1 quantify pulse-profile evolution with frequency. The timing solutions provide three new parallax measurements, two new Shapiro delay measurements, and two new measurements of significant orbital-period variations. We fit models that characterize sources of noise for each pulsar. We find that 11 pulsars show significant red noise, with generally smaller spectral indices than typically measured for non-recycled pulsars, possibly suggesting a different origin. A companion paper uses these data to constrain the strength of the gravitational-wave background.