Here 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 properly and 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 ) < 7 × 10 −15 (95%). This result is dominated by the timing of the two best pulsars in the set, PSRs J1713+0747 and J1909−3744.

The highly stable spin of neutron stars can be exploited for a variety of (astro-)physical investigations. In particular arrays of pulsars with rotational periods of the order of milliseconds can be used to detect correlated signals such as those caused by gravitational waves. Three such "Pulsar Timing Arrays" (PTAs) have been set up around the world over the past decades and collectively form the "International" PTA (IPTA). In this paper, we describe the first joint analysis of the data from the three regional PTAs, i.e. of the first IPTA data set. We describe the available PTA data, the approach presently followed for its combination and suggest improvements for future PTA research. Particular attention is paid to subtle details (such as underestimation of measurement uncertainty and long-period noise) that have often been ignored but which become important in this unprecedentedly large and inhomogeneous data set. We identify and describe in detail several factors that complicate IPTA research and provide recommendations for future pulsar timing efforts. The first IPTA data release presented here (and available online) is used to demonstrate the IPTA's potential of improving upon gravitational-wave limits placed by individual PTAs by a factor of ∼ 2 and provides a 2 − σ limit on the dimensionless amplitude of a stochastic GWB of 1.7 × 10 −15 at a frequency of 1 yr −1 . This is 1.7 times less constraining than the limit placed by , due mostly to the more recent, high-quality data they used. c 2015 RAS c 2015 RAS, MNRAS 000, 1-25 First IPTA Data Release 3 σJitter ∝ fJW eff 1 + m 2 I Np ,with fJ the jitter parameter, which needs to be determined experimentally (Liu et al. 2012;Shannon et al. 2014); W eff the pulse width; mI = σE/µE the modulation index, defined by the mean (µE) and standard deviation (σE) of the pulseenergy distribution; and Np = tint/P the number of pulses in the observation, which equals the total observing time divided by the pulse period. Consequently, the highest-precision timing efforts ideally require rapidly rotating pulsars (P 0.03 s) with high relatively flux densities (S1.4 GHz 0.5 mJy) and narrow pulses (δ 20%) are observed at sensitive (A eff /Tsys) telescopes with wide-bandwidth receivers (∆f ) and for long integration times (tint 30 min).

We analyse the stochastic properties of the 49 pulsars that comprise the first International Pulsar Timing Array (IPTA) data release. We use Bayesian methodology, performing model selection to determine the optimal description of the stochastic signals present in each pulsar. In addition to spin-noise and dispersion-measure (DM) variations, these models can include timing noise unique to a single observing system, or frequency band. We show the improved radio-frequency coverage and presence of overlapping data from different observing systems in the IPTA data set enables us to separate both system and band-dependent effects with much greater efficacy than in the individual PTA data sets. For example, we show that PSR J1643−1224 has, in addition to DM variations, significant band-dependent noise that is coherent between PTAs which we interpret as coming from time-variable scattering or refraction in the ionised interstellar medium. Failing to model these different contributions appropriately can dramatically alter the astrophysical interpretation of the stochastic signals observed in the residuals. In some cases, the spectral exponent of the spin noise signal can vary from 1.6 to 4 depending upon the model, which has direct implications for the long-term sensitivity of the pulsar to a stochastic gravitational-wave (GW) background. By using a more appropriate model, however, we can greatly improve a pulsar's sensitivity to GWs. For example, including system and band-dependent signals in the PSR J0437−4715 data set improves the upper limit on a fiducial GW background by ∼ 60% compared to a model that includes DM variations and spin-noise only.

We analyze dispersion measure (DM) variations of 37 millisecond pulsars in the nine-year North American Nanohertz Observatory for Gravitational Waves (NANOGrav) data release and constrain the sources of these variations. DM variations can result from a changing distance between Earth and the pulsar, inhomogeneities in the interstellar medium, and solar effects. Variations are significant for nearly all pulsars, with characteristic timescales comparable to or even shorter than the average spacing between observations. Five pulsars have periodic annual variations, 14 pulsars have monotonically increasing or decreasing trends, and 14 pulsars show both effects. Of the four pulsars with linear trends that have line-of-sight velocity measurements, three are consistent with a changing distance and require an overdensity of free electrons local to the pulsar. Several pulsars show correlations between DM excesses and lines of sight that pass close to the Sun. Mapping of the DM variations as a function of the pulsar trajectory can identify localized interstellar medium features and, in one case, an upper limit to the size of the dispersing region of 4 au. Four pulsars show roughly Kolmogorov structure functions (SFs), and another four show SFs less steep than Kolmogorov. One pulsar has too large an uncertainty to allow comparisons. We discuss explanations for apparent departures from a Kolmogorov-like spectrum, and we show that the presence of other trends and localized features or gradients in the interstellar medium is the most likely cause.