W. A. Coles

The International Pulsar Timing Array project: using pulsars as a gravitational wave detector

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 (similar to 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.

Gravitational-Wave Limits from Pulsar Timing Constrain Supermassive Black Hole Evolution

Testing Black Holes Gravitational waves, predicted by General Relativity, are expected to be produced when very massive bodies, such as black holes, merge together. Shannon et al. (p. 334) used data from the Parkes Pulsar Timing Array project to estimate the gravitational wave background produced by pairs of supermassive black holes (those with masses between 106 and 1011 that of the Sun) in merging galaxies. The results can be used to test models of the supermassive black hole population. Analysis of pulsar timing data sets constraints on the gravitational-wave background produced by pairs of massive black holes. The formation and growth processes of supermassive black holes (SMBHs) are not well constrained. SMBH population models, however, provide specific predictions for the properties of the gravitational-wave background (GWB) from binary SMBHs in merging galaxies throughout the universe. Using observations from the Parkes Pulsar Timing Array, we constrain the fractional GWB energy density (ΩGW) with 95% confidence to be ΩGW(H0/73 kilometers per second per megaparsec)2 < 1.3 × 10−9 (where H0 is the Hubble constant) at a frequency of 2.8 nanohertz, which is approximately a factor of 6 more stringent than previous limits. We compare our limit to models of the SMBH population and find inconsistencies at confidence levels between 46 and 91%. For example, the standard galaxy formation model implemented in the Millennium Simulation Project is inconsistent with our limit with 50% probability.

Measurement and correction of variations in interstellar dispersion in high-precision pulsar timing

Signals from radio pulsars show a wavelength-dependent delay due to dispersion in the interstellar plasma. At a typical observing wavelength, this delay can vary by tens of microseconds on 5-yr time-scales, far in excess of signals of interest to pulsar timing arrays, such as that induced by a gravitational wave background. Measurement of these delay variations is not only crucial for the detection of such signals, but also provides an unparalleled measurement of the turbulent interstellar plasma at astronomical unit (au) scales. In this paper we demonstrate that without consideration of wavelength-independent red noise, ‘simple’ algorithms to correct for interstellar dispersion can attenuate signals of interest to pulsar timing arrays. We present a robust method for this correction, which we validate through simulations, and apply it to observations from the Parkes Pulsar Timing Array. Correction for dispersion variations comes at a cost of increased band-limited white noise. We discuss scheduling to minimize this additional noise, and factors, such as scintillation, that can exacerbate the problem. Comparison with scintillation measurements confirms previous results that the spectral exponent of electron density variations in the interstellar medium often appears steeper than expected. We also find a discrete change in dispersion measure of PSR J1603−7202 of ∼2 × 10^(−3) cm^(−3) pc for about 250 d. We speculate that this has a similar origin to the ‘extreme scattering events’ seen in other sources. In addition, we find that four pulsars show a wavelength-dependent annual variation, indicating a persistent gradient of electron density on an au spatial scale, which has not been reported previously.

Pulsar timing analysis in the presence of correlated noise

Pulsar timing observations are usually analysed with least-squares fitting procedures under the assumption that the timing residuals are uncorrelated (statistically ‘white’). Pulsar observers are well aware that this assumption often breaks down and causes severe errors in estimating the parameters of the timing model and their uncertainties. Ad hoc methods for minimizing these errors have been developed, but we show that they are far from optimal. Compensation for temporal correlation can be done optimally if the covariance matrix of the residuals is known using a linear transformation that whitens both the residuals and the timing model. We adopt a transformation based on the Cholesky decomposition of the covariance matrix, but the transformation is not unique. We show how to estimate the covariance matrix with sufficient accuracy to optimize the pulsar timing analysis. We also show how to apply this procedure to estimate the spectrum of any time series with a steep red power-law spectrum, including those with irregular sampling and variable error bars, which are otherwise very difficult to analyse.

Development of a pulsar-based time-scale

Using observations of pulsars from the Parkes Pulsar Timing Array (PPTA) project we develop the first pulsar-based time-scale that has a precision comparable to the uncertainties in International Atomic Time-scales (TAI). Our ensemble of pulsars provides an Ensemble Pulsar Scale (EPS) analogous to the free atomic time-scale Echelle Atomique Libre. The EPS can be used to detect fluctuations in atomic time-scales and therefore can lead to a new realization of Terrestrial Time, TT(PPTA11). We successfully follow features known to affect the frequency of the TAI, and we find marginally significant differences between TT(PPTA11) and TT(BIPM11). We discuss the various phenomena that lead to a correlated signal in the pulsar timing residuals and therefore limit the stability of the pulsar time-scale.

The Sensitivity of the Parkes Pulsar Timing Array to Individual Sources of Gravitational Waves

ABSTRACT We present the sensitivity of the Parkes Pulsar Timing Array to gravitational wavesemitted by individual super-massive black-hole binary systems in the early phases ofcoalescing at the cores of merged galaxies. Our analysis includes a detailed study of theeffects of fitting a pulsar timing model to non-white timing residuals. Pulsar timingis sensitive at nanoHertz frequencies and hence complementary to LIGO and LISA.We place a sky-averaged constraint on the merger rate of nearby (z<0.6) black-holebinaries in the early phases of coalescence with a chirp mass of 10 10 M ⊙ of less thanone merger every seven years. The prospects for future gravitational-wave astronomyof this type with the proposed Square Kilometre Array telescope are discussed.Key words: gravitational waves – pulsars: general. 1 INTRODUCTIONIn the era of ground- and space-based gravitational-wave(GW) detectors, GW astronomy is becoming increasinglyimportant for the wider astronomy and physics communi-ties. The ability of the current GW community to provide ei-ther limits on, or detections of, GW emission is of enormousimportance in characterising astrophysical sources of inter-est for further investigation. It is possible that GW detectionwill provide the only means to probe some of these sources.The sensitivity of existing and future observatories to indi-vidual GW sources, such as neutron-star binary systems andcoalescing black-hole binary systems, has been calculatedin the ∼kHz and ∼mHz frequency ranges. The sensitiv-ity curves of the Laser Interferometer Gravitational-WaveObservatory (Abbott et al. 2009)

MEASURING THE MASS OF SOLAR SYSTEM PLANETS USING PULSAR TIMING

High-precision pulsar timing relies on a solar system ephemeris in order to convert times of arrival (TOAs) of pulses measured at an observatory to the solar system barycenter. Any error in the conversion to the barycentric TOAs leads to a systematic variation in the observed timing residuals; specifically, an incorrect planetary mass leads to a predominantly sinusoidal variation having a period and phase associated with the planets orbital motion about the Sun. By using an array of pulsars (PSRs J0437–4715, J1744–1134, J1857+0943, J1909–3744), the masses of the planetary systems from Mercury to Saturn have been determined. These masses are consistent with the best-known masses determined by spacecraft observations, with the mass of the Jovian system, 9.547921(2) ×10–4 M ☉, being significantly more accurate than the mass determined from the Pioneer and Voyager spacecraft, and consistent with but less accurate than the value from the Galileo spacecraft. While spacecraft are likely to produce the most accurate measurements for individual solar system bodies, the pulsar technique is sensitive to planetary system masses and has the potential to provide the most accurate values of these masses for some planets.

Polarization observations of 20 millisecond pulsars

Polarization profiles are presented for 20 millisecond pulsars that are being observed as part of the Parkes Pulsar Timing Array project. The observations used the Parkes multibeam receiver with a central frequency of 1369 MHz and the Parkes digital filter bank pulsar signal-processing system PDFB2. Because of the large total observing time, the summed polarization profiles have very high signal-to-noise ratios and show many previously undetected profile features. 13 of the 20 pulsars show emission over more than half of the pulse period. Polarization variations across the profiles are complex, and the observed position angle variations are generally not in accord with the rotating vector model for pulsar polarization. Nevertheless, the polarization properties are broadly similar to those of normal (non-millisecond) pulsars, suggesting that the basic radio emission mechanism is the same in both classes of pulsar. The results support the idea that radio emission from millisecond pulsars originates high in the pulsar magnetosphere, probably close to the emission regions for high-energy X-ray and gamma-ray emission. Rotation measures were obtained for all 20 pulsars, eight of which had no previously published measurements.

Limitations in timing precision due to single-pulse shape variability in millisecond pulsars

High-sensitivity radio-frequency observations of millisecond pulsars usually show stochastic, broad-band, pulse-shape variations intrinsic to the pulsar emission process. These variations induce jitter noise in pulsar timing observations; understanding the properties of this noise is of particular importance for the effort to detect gravitational waves with pulsar timing arrays. We assess the short-term profile and timing stability of 22 millisecond pulsars that are part of the Parkes Pulsar Timing Array sample by examining intraobservation arrival time variability and single-pulse phenomenology. In 7 of the 22 pulsars, in the band centred at approximately 1400 MHz, we find that the brightest observations are limited by intrinsic jitter. We find consistent results, either detections or upper limits, for jitter noise in other frequency bands. PSR J1909−3744 shows the lowest levels of jitter noise, which we estimate to contribute ∼10 ns root mean square error to the arrival times for hour-duration observations. Larger levels of jitter noise are found in pulsars with wider pulses and distributions of pulse intensities. The jitter noise in PSR J0437−4715 decorrelates over a bandwidth of ∼2 GHz. We show that the uncertainties associated with timing pulsar models can be improved by including physically motivated jitter uncertainties. Pulse-shape variations will limit the timing precision at future, more sensitive, telescopes; it is imperative to account for this noise when designing instrumentation and timing campaigns for these facilities.

An all-sky search for continuous gravitational waves in the Parkes Pulsar Timing Array data set

We present results of an all-sky search in the Parkes Pulsar Timing Array (PPTA) Data Release 1 data set for continuous gravitational waves (GWs) in the frequency range from 5 x 10(-9) to 2 x 10(-7) Hz. Such signals could be produced by individual supermassive binary black hole systems in the early stage of coalescence. We phase up the pulsar timing array data set to form, for each position on the sky, two data streams that correspond to the two GW polarizations and then carry out an optimal search for GW signals on these data streams. Since no statistically significant GWs were detected, we place upper limits on the intrinsic GW strain amplitude h(0) for a range of GW frequencies. For example, at 10(-8) Hz our analysis has excluded with 95 per cent confidence the presence of signals with h(0) >= 1.7 x 10(-14). Our new limits are about a factor of 4 more stringent than those of Yardley et al. based on an earlier PPTA data set and a factor of 2 better than those reported in the recent Arzoumanian et al. paper. We also present PPTA directional sensitivity curves and find that for the most sensitive region on the sky, the current data set is sensitive to GWs from circular supermassive binary black holes with chirp masses of 10(9) M-circle dot out to a luminosity distance of about 100 Mpc. Finally, we set an upper limit of 4 x 10(-3) Mpc(-3) Gyr(-1) at 95 per cent confidence on the coalescence rate of nearby (z less than or similar to 0.1) supermassive binary black holes in circular orbits with chirp masses of 10(10) M-circle dot.