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We describe the procedure, nuances, issues, and choices involved in creating times-of-arrival (TOAs), 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.
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The extremely regular, periodic radio emission from millisecond pulsars makes them useful tools for studying neutron star astrophysics, general relativity, and low-frequency gravitational waves. These studies require that the observed pulse times of arrival be fit to complex timing models that describe numerous effects such as the astrometry of the source, the evolution of the pulsars spin, the presence of a binary companion, and the propagation of the pulses through the interstellar medium. In this paper, we discuss the benefits of using Bayesian inference to obtain pulsar timing solutions. These benefits include the validation of linearized least-squares model fits when they are correct, and the proper characterization of parameter uncertainties when they are not; the incorporation of prior parameter information and of models of correlated noise; and the Bayesian comparison of alternative timing models. We describe our computational setup, which combines the timing models of Tempo2 with the nested-sampling integrator MultiNest. We compare the timing solutions generated using Bayesian inference and linearized least-squares for three pulsars: B1953+29, J2317+1439, and J1640+2224, which demonstrate a variety of the benefits that we posit.
A new Bayesian software package for the analysis of pulsar timing data is presented in the form of TempoNest which allows for the robust determination of the non-linear pulsar timing solution simultaneously with a range of additional stochastic parameters. This includes both red spin noise and dispersion measure variations using either power law descriptions of the noise, or through a model-independent method that parameterises the power at individual frequencies in the signal. We use TempoNest to show that at noise levels representative of current datasets in the European Pulsar Timing Array (EPTA) and International Pulsar Timing Array (IPTA) the linear timing model can underestimate the uncertainties of the timing solution by up to an order of magnitude. We also show how to perform Bayesian model selection between different sets of timing model and stochastic parameters, for example, by demonstrating that in the pulsar B1937+21 both the dispersion measure variations and spin noise in the data are optimally modelled by simple power laws. Finally we show that not including the stochastic parameters simultaneously with the timing model can lead to unpredictable variation in the estimated uncertainties, compromising the robustness of the scientific results extracted from such analysis.
Pulsar timing is a technique that uses the highly stable spin periods of neutron stars to investigate a wide range of topics in physics and astrophysics. Pulsar timing arrays (PTAs) use sets of extremely well-timed pulsars as a Galaxy-scale detector with arms extending between Earth and each pulsar in the array. These challenging experiments look for correlated deviations in the pulsars timing that are caused by low-frequency gravitational waves (GWs) traversing our Galaxy. PTAs are particularly sensitive to GWs at nanohertz frequencies, which makes them complementary to other space- and ground-based detectors. In this chapter, we will describe the methodology behind pulsar timing; provide an overview of the potential uses of PTAs; and summarise where current PTA-based detection efforts stand. Most predictions expect PTAs to successfully detect a cosmological background of GWs emitted by supermassive black-hole binaries and also potentially detect continuous-wave emission from binary supermassive black holes, within the next several years.
We have begun an exciting era for gravitational wave detection, as several world-leading experiments are breaching the threshold of anticipated signal strengths. Pulsar timing arrays (PTAs) are pan-Galactic gravitational wave detectors that are already cutting into the expected strength of gravitational waves from cosmic strings and binary supermassive black holes in the nHz-$mu$Hz gravitational wave band. These limits are leading to constraints on the evolutionary state of the Universe. Here, we provide a broad review of this field, from how pulsars are used as tools for detection, to astrophysical sources of uncertainty in the signals PTAs aim to see, to the primary current challenge areas for PTA work. This review aims to provide an up-to-date reference point for new parties interested in the field of gravitational wave detection via pulsar timing.
A pulsar timing array (PTA), in which observations of a large sample of pulsars spread across the celestial sphere are combined, allows investigation of global phenomena such as a background of gravitational waves or instabilities in atomic timescales that produce correlated timing residuals in the pulsars of the array. The Parkes Pulsar Timing Array (PPTA) is an implementation of the PTA concept based on observations with the Parkes 64-m radio telescope. A sample of 20 millisecond pulsars is being observed at three radio-frequency bands, 50cm (~700 MHz), 20cm (~1400 MHz) and 10cm (~3100 MHz), with observations at intervals of 2 - 3 weeks. Regular observations commenced in early 2005. This paper describes the systems used for the PPTA observations and data processing, including calibration and timing analysis. The strategy behind the choice of pulsars, observing parameters and analysis methods is discussed. Results are presented for PPTA data in the three bands taken between 2005 March and 2011 March. For ten of the 20 pulsars, rms timing residuals are less than 1 microsec for the best band after fitting for pulse frequency and its first time derivative. Significant red timing noise is detected in about half of the sample. We discuss the implications of these results on future projects including the International Pulsar Timing Array (IPTA) and a PTA based on the Square Kilometre Array. We also present an extended PPTA data set that combines PPTA data with earlier Parkes timing data for these pulsars.
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