Long-term precise timing of Galactic millisecond pulsars holds great promise for measuring the long-period (months-to-years) astrophysical gravitational waves. Several gravitational-wave observational programs, called Pulsar Timing Arrays (PTA), are being pursued around the world. Here we develop a Bayesian algorithm for measuring the stochastic gravitational-wave background (GWB) from the PTA data. Our algorithm has several strengths: (1) It analyses the data without any loss of information, (2) It trivially removes systematic errors of known functional form, including quadratic pulsar spin-down, annual modulations and jumps due to a change of equipment, (3) It measures simultaneously both the amplitude and the slope of the GWB spectrum, (4) It can deal with unevenly sampled data and coloured pulsar noise spectra. We sample the likelihood function using Markov Chain Monte Carlo (MCMC) simulations. We extensively test our approach on mock PTA datasets, and find that the algorithm has significant benefits over currently proposed counterparts. We show the importance of characterising all red noise components in pulsar timing noise by demonstrating that the presence of a red component would significantly hinder a detection of the GWB. Lastly, we explore the dependence of the signal-to-noise ratio on the duration of the experiment, number of monitored pulsars, and the magnitude of the pulsar timing noise. These parameter studies will help formulate observing strategies for the PTA experiments.
A low frequency stochastic background of gravitational waves may be detected by pulsar timing experiments in the next five to ten years. Using methods developed to analyze interferometric gravitational wave data, in this paper we lay out the optimal techniques to detect a background of gravitational waves using a pulsar timing array. We show that for pulsar distances and gravitational wave frequencies typical of pulsar timing experiments, neglecting the effect of the metric perturbation at the pulsar does not result in a significant deviation from optimality. We discuss methods for setting upp…
The majority of fast millisecond pulsars are in binary systems, so that any periodic signal they emit is modulated by both Doppler and relativistic effects. Here we show how well-established binary models can be used to account for these effects in searches for gravitational waves from known pulsars within binary systems. A seperate issue affecting certain pulsar signals is that of timing noise and we show how this, with particular reference to the Crab pulsar, can be compensated for by using regularly updated timing ephemerides.
We open the discussion into how the Laser Interferometer Space Antenna (LISA) observations of supermassive black-hole (SMBH) mergers (in the mass range ~10^6-10^8 Msun) may be complementary to pulsar timing-based gravitational wave searches. We consider the toy model of determining pulsar distances by exploiting the fact that LISA SMBH inspiral observations can place tight parameter constraints on the signal present in pulsar timing observations. We also suggest, as a future path of research, the use of LISA ring-down observations from the most massive (>~ a few 10^7 Msun) black-hole mergers, …
This paper discusses spectral sensitivity of solitary and binary pulsars to a low-frequency (colored) noise. It is a third paper in a series of papers devoted to analysis of the low-frequency noise in pulsar timing observations and its impact on observable fitting parameters of timing model.
Variations in the solar wind density introduce variable delays into pulsar timing observations. Current pulsar timing analysis programs only implement simple models of the solar wind, which not only limit the timing accuracy, but can also affect measurements of pulsar rotational, astrometric and orbital parameters. We describe a new model of the solar wind electron density content which uses observations from the Wilcox Solar Observatory of the solar magnetic field. We have implemented this model into the tempo2 pulsar timing package. We show that this model is more accurate than previous mode…
Given sufficient sensitivity, pulsar timing observations can make a direct detection of gravitational waves passing over the Earth. Pulsar timing is most sensitive to gravitational waves with frequencies in the nanoHertz region, with the most likely astronomical sources being binary super-massive black holes in galaxy cores. The Parkes Pulsar Timing Array project uses the Parkes 64-m radio telescope to make precision timing observations of a sample of about 20 millisecond pulsars with a principal goal of making a direct detection of gravitational waves. Observations commenced about one year ag…
The motivation for radio pulsar timing and its basic principles are reviewed. Present and future radio timing techniques and hardware are summarised and compared. The array of present timing programmes and their scientific goals are collated and described. Recent results and future prospects are discussed, with emphasis on multi-wavelength techniques where appropriate. Timing of radio pulsars at other wavelengths is summarised along with the provision of contemporary ephemerides for timing and searches at other wavelengths.
The effect of a narrow-band isotropic stochastic GW background on pulsar timing and astrometric measurements is studied. Such a background appears in some theories of gravity. We show that the existing millisecond pulsar timing accuracy ($\sim 0.2 \rm{μs}$) strongly constrains possible observational consequences of theory of massive gravity with spontaneous Lorentz braking \cite{dtt:2005}, essentially ruling out significant contribution of massive gravitons to the local dark halo density. The present-day accuracy of astrometrical measurements ($\sim 100 \rm{μas}$) sets less stringent constrain…
Anomalous X-ray Pulsars (AXPs), thought to be magnetars, exhibit poorly understood deviations from a simple spin-down called "timing noise". AXP timing noise has strong low-frequency components which pose significant challenges for quantification. We describe a procedure for extracting two quantities of interest, the intensity and power spectral index of timing noise. We apply this procedure to timing data from three sources: a monitoring campaign of five AXPs, observations of five young pulsars, and the stable rotator PSR B1937+21.
We describe the techniques used in pulsar timing observations, and show how these observations may be applied to tests of strong-field general relativity for double-neutron-star binary systems. We describe the tests of GR resulting from the PSRs B1913+16 and B1534+12 systems. For the latter pulsar, 5 "Post-Keplerian" timing parameters are measurable, including the orbital period derivative and the two Shapiro delay parameters.
The direct detection of gravitational waves is a major goal of current astrophysics. We provide details of a new method for detecting a stochastic background of gravitational waves using pulsar timing data. Our results show that regular timing observations of 40 pulsars each with a timing accuracy of 100 nano-seconds will be able to make a direct detection of the predicted stochastic background from coalescing black holes within five years. With an improved pre-whitening algorithm, or if the background is at the upper end of the predicted range, a significant detection should be possible with …
Pulsar timing at the Mt Pleasant observatory has focused on Vela, which can be tracked for 18 hours of the day. These nearly continuous timing records extend over 24 years allowing a greater insight into details of timing noise, micro glitches and other more exotic effects. In particular we report the glitch parameters of the 2004 event, along with the reconfirmation that the spin up for the Vela pulsar occurs instantaneously to the accuracy of the data. This places a lower limit of about 30 seconds for the acceleration of the pulsar to the new rotational frequency. We also confirm of the low …
We have analysed the arrival times for 374 pulsars that have been observed for more than six years using the 76-m Lovell telescope at Jodrell Bank Observatory. Here we present a qualitative analysis of structures seen in the timing residuals.
The first direct detection of gravitational waves may be made through observations of pulsars. The principal aim of pulsar timing array projects being carried out worldwide is to detect ultra-low frequency gravitational waves (f ~ 10^-9 to 10^-8 Hz). Such waves are expected to be caused by coalescing supermassive binary black holes in the cores of merged galaxies. It is also possible that a detectable signal could have been produced in the inflationary era or by cosmic strings. In this paper we review the current status of the Parkes Pulsar Timing Array project (the only such project in the So…
We have detected relativistic and/or kinematic post-Keplerian parameters of no fewer than five pulsar-white dwarf binary systems in long-term timing observations at Arecibo. We discuss the resulting constraints on pulsar and companion masses. The general trend is that the pulsar mass measurements are compatible with the canonical value of 1.35 solar masses, but in most cases somewhat higher masses are preferred.
Measurement of accurate positions, pulse periods and period derivatives is an essential follow-up to any pulsar survey. The procedures being used to obtain timing parameters for the pulsars discovered in the Parkes multibeam pulsar survey are described. Completed solutions have been obtained so far for about 80 pulsars. They show that the survey is preferentially finding pulsars with higher than average surface dipole magnetic fields. Eight pulsars have been shown to be members of binary systems and some of the more interesting results relating to these are presented.
Tempo2 is a new software package for the analysis of pulsar pulse times of arrival. In this paper we describe in detail the timing model used by tempo2, and discuss limitations on the attainable precision. In addition to the intrinsic slow-down behaviour of the pulsar, tempo2 accounts for the effects of a binary orbital motion, the secular motion of the pulsar or binary system, interstellar, Solar system and ionospheric dispersion, observatory motion (including Earth rotation, precession, nutation, polar motion and orbital motion), tropospheric propagation delay, and gravitational time dilatio…
Contemporary pulsar timing experiments have reached a sensitivity level where systematic errors introduced by existing analysis procedures are limiting the achievable science. We have developed tempo2, a new pulsar timing package that contains propagation and other relevant effects implemented at the 1ns level of precision (a factor of ~100 more precise than previously obtainable). In contrast with earlier timing packages, tempo2 is compliant with the general relativistic framework of the IAU 1991 and 2000 resolutions and hence uses the International Celestial Reference System, Barycentric Coo…
We present an analysis of the variations seen in the dispersion measures (DMs) of 20 millisecond pulsars observed as part of the Parkes Pulsar Timing Array project. We carry out a statistically rigorous structure function analysis for each pulsar and show that the variations seen for most pulsars are consistent with those expected for an interstellar medium characterised by a Kolmogorov turbulence spectrum. The structure functions for PSRs J1045-4509 and J1909-3744 provide the first clear evidence for a large inner scale, possibly due to ion-neutral damping. We also show the effect of the sola…
The Parkes multibeam pulsar survey is a sensitive survey of a strip of the Galactic plane with $|b|<5\degr$ and $260\degr < l < 50\degr$ at 1374 MHz. Here we report the discovery of 120 new pulsars and subsequent timing observations, primarily using the 76-m Lovell radio telescope at Jodrell Bank. The main features of the sample of 370 published pulsars discovered during the multibeam survey are described. Furthermore, we highlight two pulsars: PSR J1734$-$3333, a young pulsar with the second highest surface magnetic field strength among the known radio pulsars, $B_s = 5.4\times10^{13}$ G, and…
We present a timing study of the young rotation-powered pulsar 0540-69 in the Large Magellanic Cloud, based on 130 kiloseconds of archival ROSAT data spanning a $\sim 3$-year period. We use ``$f- \dot f$'' techniques to measure the pulsar frequency as a function of frequency derivative at 17 independent epochs. From these measurements we derive a timing solution with a braking index $n = 2.5^{+0.6}_{-0.7}$, and we compare this solution to previous timing studies of 0540-69. Using this frequency-based solution, we create 27 pulse profiles and perform a time-of-arrival (TOA) analysis to investig…
Relativistic phenomena (orbital precession, Shapiro delay, and/or orbital decay) have been measured in Arecibo timing observations of four pulsar-white dwarf binaries, leading to constraints on the neutron star masses. We have detected the decay of the PSR J0751+1807 orbit due to gravitational radiation emission, the first such measurement in a binary with a low mass ratio (m_2/m_1<<1). Timing data constrains the mass of this pulsar to bet between 1.6 and 2.8 solar masses. Masses of the other pulsars are in marginal agreement with the canonical pulsar mass of 1.35 solar masses, but higher valu…
We have measured the positions of 74 pulsars from regular timing observations using the Nanshan radio telescope at Urumqi Observatory between 2000 January and 2004 August (MJD 51500 -- 53240). Proper motions were determined for these pulsars by comparing their current positions with positions given in pulsar catalogues. We compare our results to earlier measurements in the literature and show that, in general, the values agree. New or improved proper motions are obtained for 16 pulsars. The effect of period fluctuations and other timing noise on the determination of pulsar positions is investi…
We analyze the effect of weak field gravitational waves on the timing of pulsars, with particular attention to gauge invariance, that is, to the effects that are independent of the choice of coordinates. We find: (i) the Doppler shift cannot be separated into gauge invariant gravitational wave and kinetic contributions; (ii) a gauge invariant separation can be made for the time derivative of the Doppler shift in which the gravitational wave contribution is directly related to the Riemann tensor, and the kinetic contribution is that for special relativity; (iii) the gauge dependent effects in t…
We present new results of timing and single pulse measurements for 18 radio pulsars discovered in 1993 - 1997 by the Penn State/NRL declination-strip survey conducted with the 305-m Arecibo telescope at 430 MHz. Long-term timing measurements have led to significant improvements of the rotational and the astrometric parameters of these sources, including the millisecond pulsar, PSR J1709+2313, and the pulsar located within the supernova remnant S147, PSR J0538+2817. Single pulse studies of the brightest objects in the sample have revealed an unusual "bursting" pulsar, PSR J1752+2359, two new dr…
We examine the timing history of several anomalous X-ray pulsars (AXPs), and find that they exhibit spin down irregularities statistically similar to those of radio pulsars. We propose that these irregularities are simply glitches like those of radio pulsars and fit glitching spin down solutions to the data available for 1E~2259+586, 1E~1048.1-5937 and 4U~0142+61. The inferred magnitude of the glitches ($ΔΩ$) is comparable to that exhibited in radio pulsar glitching. With these results we argue that the three AXPs that we studied are isolated neutron stars spinning down by magnetic dipole radi…
Exploiting a five-year span of data, we present improved timing solutions for the five millisecond pulsars known in the globular cluster NGC 6752. They include proper motion determinations for the two outermost pulsars in the cluster, PSR J1910-5959A and PSR J1910-5959C. The values of the proper motions are in agreement with each other within current uncertainties, but do not match (at 4 sigma and 2 sigma level respectively) with the value of the proper motion of the entire globular cluster derived in the optical band. Implications of these results for the cluster membership of the two pulsars…
We present results of a timing analysis of various isolated pulsars using ESA's \emph{XMM-Newton} observatory. Isolated pulsars are useful for calibration purposes because of their stable emission. We have analyzed six pulsars with different pulse profiles in a range of periods between 15 and 200 ms. All observations were made using the \emph{EPIC-pn camera} in its faster modes (Small window, Timing and Burst modes). We investigate the relative timing accuracy of the camera by comparing the pulse periods determined from the \emph{EPIC-pn camera} observations with those from radio observations.…
We present XMM-Newton MOS imaging and PN timing data of the millisecond pulsar PSR J0218+4232. We confirm the previously detected pulsations of PSR J0218+4232 and we show that the folded lightcurve is dependent on energy. We present the broad band (0.2-10.0 keV) spectrum of this millisecond pulsar, as well as the spectra of: the pulsed emission, the individual pulses, the interpulse and the non-pulsed region and we compare our results with previous data from Rosat, BeppoSAX and Chandra. We discuss the results of the spectral fitting in the context of recent pulsar models.
The pulsar PSR B1259-63 is in a highly eccentric 3.4-yr orbit with the Be star SS 2883. Timing observations of this pulsar, made over a 7-yr period using the Parkes 64-m radio telescope, cover two periastron passages, in 1990 August and 1994 January. The timing data cannot be fitted by the normal pulsar and Keplerian binary parameters. A timing solution including a (non-precessing) Keplerian orbit and timing noise (represented as a polynomial of fifth order in time) provide a satisfactory fit to the data. However, because the Be star probably has a significant quadrupole moment, we prefer to i…
Terrestrial timescales show instabilities due to the physical limitations of the atomic clocks. Stricter environmental isolation and increased numbers of improved cesium clocks and cavity-tuned hydrogen masers have resulted in time scales more accurate by a factor of about five. The use of different clock ensembles results in measurable changes in some millisecond pulsar timing data. We investigate the possible application of millisecond pulsars to define a precise long-term time standard and positional reference system in a nearly inertial reference frame. Although possible quantitative contr…
A new method of matrix template matching is presented in the context of pulsar timing analysis. Pulse arrival times are typically measured using only the observed total intensity light curve. The new technique exploits the additional timing information available in the polarization of the pulsar signal by modeling the transformation between two polarized light curves in the Fourier domain. For a number of millisecond pulsars, arrival time estimates derived from polarimetric data are predicted to exhibit greater precision and accuracy than those derived from the total intensity alone. Furthermo…
Pulsars are the most accurate naturally occurring clocks, and data about them can be used to set bounds on neutron-sector Lorentz violations. If SO(3) rotation symmetry is completely broken for neutrons, then pulsars' rotation speeds will vary periodically. Pulsar timing data limits the relevant Lorentz-violating coefficients to be smaller than 1.7 x 10^(-8) at at least 90% confidence.
Millisecond and binary pulsars are the most stable natural frequency standards which admits to introduce modified versions of universal and ephemeris time scales based correspondingly on the intrinsic rotation of pulsar and on its orbital motion around barycenter of a binary system. Measured stability of these time scales depends on numerous physical phenomena which affect rotational and orbital motion of the pulsar and observer on the Earth, perturb propagation of electromagnetic pulses from pulsar to the observer and bring about random fluctuations in the rate of atomic clock used as a prima…
