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We describe the procedure, nuances, issues, and choices involved in creating times-of-arrival, residuals and error bars from a set of radio pulsar timing data. We discuss the issue of mis-matched templates, the problem that wide-bandwidth backends introduce, possible solutions to that problem, and correcting for offsets introduced by various observing systems.

Sources of noise in pulsar timing measurements are discussed along with spin stability of neutron stars. Estimates and scaling laws are given for spin noise, timing errors from fluctuations in pulsar magnetospheres, dispersion and scattering in the interstellar plasma, and in the matched filtering technique used to estimate arrival times. The composite noise spectrum is presented and an assessment of the detectability of gravitational waves (GWs) is given in terms of the sources of error and their mitigation. The scaling laws indicate that substantial improvement in sensitivity to GWs can be expected from implementation of new, wideband spectrometers at radio observatories, by using new algorithms to further reduce the levels of plasma propagation effects, and by increasing the number of millisecond pulsars used in pulsar timing arrays.

Searches for millisecond pulsars (which we here loosely define as those with periods < 20 ms) in the galactic field have undergone a renaissance in the past five years. New or recently refurbished radio telescopes utilizing cooled receivers and state-of-the art digital data acquisition systems are carrying out surveys of the entire sky at a variety of radio frequencies. Targeted searches for millisecond pulsars in point sources identified by the Fermi Gamma-ray Space Telescope have proved phenomenally successful, with over 50 discoveries in the past five years. The current sample of millisecond pulsars now numbers almost 200 and, for the first time in 25 years, now outnumbers their counterparts in galactic globular clusters. While many of these searches are motivated to find pulsars which form part of pulsar timing arrays, a wide variety of interesting systems are now being found. Following a brief overview of the millisecond pulsar phenomenon, we describe these searches and present some of the highlights of the new discoveries in the past decade. We conclude with predictions and prospects for ongoing and future surveys.

The direct detection of gravitational waves (GWs) by pulsar timing arrays (PTAs) is very likely within the next decade. While the stochastic GW background is a promising candidate for detection it is also possible that single resolvable sources may be detectable as well. In this work we will focus on the detection and characterization of single GW sources from supermassive black hole binaries. We introduce a fully Bayesian data analysis pipeline that is meant to carry out a search, characterization, and evaluation phase. This will allow us to rapidly locate the global maxima in parameter space, map out the posterior, and finally weigh the evidence of a GW detection through a Bayes factor. Here we will make use of an adaptive metropolis algorithm and parallel tempering. We test this algorithm on realistic simulated data that are representative of modern PTAs.

An astrophysical population of supermassive black hole binaries is thought to be the strongest source of gravitational waves in the frequency range covered by pulsar timing arrays (PTAs). A potential cause for concern is that the standard cross-correlation method used in PTA data analysis assumes that the signals are isotropically distributed and Gaussian random, while the signals from a black hole population are likely to be anisotropic and deterministic. Here we show that while the conventional analysis is not optimal for detecting signals from black hole binaries, the technique still works as the standard Hellings–Downs correlation curve turns out to hold for point sources. Moreover, the small effective number of signal samples blurs the distinction between Gaussian and deterministic signals. Possible improvements to the standard cross-correlation analysis that account for the anisotropy of the signal are discussed.

Time variable delays due to radio wave propagation in the ionized interstellar medium are a substantial source of error in pulsar timing array efforts. We describe the physical origin of these effects, discussing dispersive and scattering effects separately. Where possible, we give estimates of the magnitude of timing errors produced by these effects and their scaling with radio frequency. Although there is general understanding of the interstellar medium propagation errors to be expected with pulsar timing array observations, detailed comparison between theory and practice is still in its infancy, particularly with regard to scattering effects.

The aims of the Parkes Pulsar Timing Array project are to (1) make a direct detection of gravitational waves, (2) improve the solar system planetary ephemeris and (3) develop a pulsar-based timescale. In this paper we describe the project, explain how the data are collected and processed and describe current research. Our current data sets are able to place an upper bound on the gravitational wave background that is the most stringent to date.

The North American Nanohertz Observatory for Gravitational Waves is a collaboration of researchers who are actively engaged in using North American radio telescopes to detect and study gravitational waves (GWs) via pulsar timing. To achieve this goal, we regularly observe millisecond pulsars with the Arecibo and Green Bank telescopes and develop and implement new instrumentation and algorithms for searching for and observing pulsars, calculating arrival times, understanding and correcting for propagation delays and sources of noise in our data and detecting and characterizing a variety of GW sources. We collaborate on these activities with colleagues in the International Pulsar Timing Array. We also educate students of all levels and the public about the detection and study of GWs via pulsar timing.

The European Pulsar Timing Array (EPTA) and the Large European Array for Pulsars (LEAP) play crucial roles in the global effort to detect gravitational waves (GWs) with a Pulsar Timing Array (PTA) experiment. While the EPTA uses five of the world's largest cm-radio telescopes, LEAP harvests their combined power to synthesize a 194 m equivalent dish to provide high-precision PTA data for most of the sky. The EPTA has already produced a large variety of results, including astrophysical studies of individual pulsars, tests of theories of gravity, stringent limits on a GW background produced by super-massive binary black holes or the vibration of cosmic strings. It has also undertaken the development of new analysis methods and techniques, and studies of the astrophysics and population of expected GW background sources. This review gives an overview of the EPTA and LEAP set-ups and corresponding activities.

The International Pulsar Timing Array (IPTA) is an organization whose raison d'être is to facilitate collaboration between the three main existing PTAs (the EPTA in Europe, NANOGrav in North America and the PPTA in Australia) in order to realize the benefits of combined PTA data sets in reaching the goals of PTA projects. Currently, shared data sets for 50 pulsars are available for IPTA-based projects. Operation of the IPTA is administered by a Steering Committee consisting of six members, two from each PTA, plus the immediate past Chair in a non-voting capacity. A Constitution and several Agreements define the framework for the collaboration. Web pages provide information both to members of participating PTAs and to the general public. With support from an NSF PIRE grant, the IPTA facilitates the organization of annual Student Workshops and Science Meetings. These are very valuable both in training new students and in communicating current results from IPTA-based research.

The Square Kilometre Array (SKA) is envisioned as the meter- and centimeter-wavelength telescope of the 21st century, and gravitational wave studies via a pulsar timing array (PTA) form a key aspect of its science program. In its ultimate implementation, the SKA (phase 2) should enable the construction of a PTA consisting of as many as 100 spin-stable millisecond pulsars. The sensitivity of the SKA–PTA could approach gravitational wave strain amplitudes of 6 × 10⁻¹⁶ or better at fiducial gravitational wave frequencies of order 1 yr⁻¹, at least an order of magnitude improvement in the gravitational wave strain amplitude that can be measured. Any nearby individual supermassive black hole binaries could be detected, and the existence of non-tensor modes can be tested. Beyond its PTA capabilities, the SKA will also enable a range of other tests of fundamental physics, such as tests of gravity in ultra-relativistic binaries and constraints on the nuclear equation of state.

Pulsar timing arrays (PTAs) may eventually be able to detect not only the stochastic gravitational-wave (GW) background of SMBH binaries, but also individual, particularly massive binaries whose signals stick out above the background. In this contribution, we discuss the possibility of identifying and studying such 'resolved' binaries through their electromagnetic emission. The host galaxies of such binaries are themselves expected to be also very massive and rare, so that out to redshifts z ≈ 0.2 a unique massive galaxy may be identified as the host. At higher redshifts, the PTA error boxes are larger and may contain as many as several hundred massive-galaxy interlopers. In this case, the true counterpart may be identified, if it is accreting gas efficiently, as an active galactic nucleus (AGN) with a peculiar spectrum and variable emission features. Specifically, the binary's tidal torques expel the gas from the inner part of the accretion disc, making it unusually dim in x-ray and UV bands and in broad optical emission lines. The tails of the broad wings of any FeKα emission line may also be 'clipped' and missing. The binary's orbital motion, as well as the gas motions it induces, may trigger quasiperiodic variations. These include coherent flux variability, such as luminous, multi-wavelength flares, as well as Doppler shifts of broad emission lines and 'see-saw' oscillations in the FeKα line. Additional features, such as evidence for a recent major merger or dual collimated jets, could also corroborate the counterpart. These properties would make resolved PTA sources stand out among AGN with similar overall luminosities and allow their identification.

Pulsar timing arrays are sensitive to gravitational waves from supermassive black hole (SMBH) binaries at orbital separations of ≪1 pc. There is currently an observational paucity of such systems, although they are central figures in studies of galaxy evolution, merger dynamics, and active nucleus formation. We review the prospects of detecting SMBH binaries through electromagnetic radiative processes thought to be associated with galaxy mergers and late-stage binary evolution. We then discuss the scientific goals of joint pulsar timing and electromagnetic studies of these systems, including the facilitation of binary parameter estimation, identifying galactic hosts of gravitational wave emitters, and relevant studies of merger dynamics and cosmology. The use of upcoming high-precision timing arrays with the International pulsar timing array and the square kilometre array, combined with ongoing electromagnetic observing campaigns to identify active SMBH binaries, provide generous possibilities for multi-messenger astrophysics in the near future.

Pulsar timing arrays (PTAs) are designed to detect the predicted gravitational wave (GW) background produced by a cosmological population of supermassive black hole (SMBH) binaries. In this contribution, I review the physics of such GW background, highlighting its dependence on the overall binary population, the relation between SMBHs and their hosts, and their coupling with the stellar and gaseous environment. The latter is particularly relevant when it drives the binaries to extreme eccentricities (e > 0.9), which might be the case for stellar-driven systems. This causes a substantial suppression of the low-frequency signal, potentially posing a serious threat to the effectiveness of PTA observations. A future PTA detection will allow us to directly observe for the first time subparsec SMBH binaries on their way to the GW-driven coalescence, providing important answers of the outstanding questions related to the physics underlying the formation and evolution of these spectacular sources.

We derive scaling laws for the signal-to-noise ratio of the optimal cross-correlation statistic, and show that the large power-law increase of the signal-to-noise ratio as a function of the observation time T that is usually assumed holds only at early times. After enough time has elapsed, pulsar timing arrays enter a new regime where the signal to noise only scales as $\sqrt{T}$. In addition, in this regime the quality of the pulsar timing data and the cadence become relatively unimportant. This occurs because the lowest frequencies of the pulsar timing residuals become gravitational-wave dominated. Pulsar timing arrays enter this regime more quickly than one might naively suspect. For T = 10 yr observations and typical stochastic background amplitudes, pulsars with residual root-mean-squares of less than about 1 μs are already in that regime. The best strategy to increase the detectability of the background in this regime is to increase the number of pulsars in the array. We also perform realistic simulations of the NANOGrav pulsar timing array, which through an aggressive pulsar survey campaign adds new millisecond pulsars regularly to its array, and show that a detection is possible within a decade, and could occur as early as 2016.

In this paper, we focus on testing gravity theories in the radiative regime using pulsar timing array observations. After reviewing current techniques to measure the dispersion and alternative polarization of gravitational waves, we extend the framework to the most general situations, where the combinations of a massive graviton and alternative polarization modes are considered. The atlas of the Hellings–Downs functions is completed by the new calculations for these dispersive alternative polarization modes. We find that each mode and corresponding graviton mass introduce characteristic features in the Hellings–Downs function. Thus, in principal, we can not only detect each polarization mode, measure the corresponding graviton mass, but also discriminate the different scenarios. In this way, we can test gravity theories in the radiative regime in a generalized fashion, and such method is a direct experiment, where one can address the gauge symmetry of the gravity theories in their linearized limits. Although current pulsar timing still lacks enough stable pulsars and sensitivity for such practices, we expect that future telescopes with larger collecting areas could make such experiments feasible.