tempo2: a new pulsar timing package – III. Gravitational wave simulation

Analysis of pulsar timing data sets may provide the first direct detection of gravitational waves. This paper, the third in a series describing the mathematical framework implemented into the tempo2 pulsar timing package, reports on using tempo2 to simulate the timing residuals induced by gravitational waves. The tempo2 simulations can be used to provide upper bounds on the amplitude of an isotropic, stochastic, gravitational wave background in our Galaxy and to determine the sensitivity of a given pulsar timing experiment to individual, supermassive, binary black hole systems.     

tempo2, a new pulsar-timing package – I. An overview

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 1-ns 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 Coordinate Time and up-to-date precession, nutation and polar motion models. tempo2 provides a generic and extensible set of tools to aid in the analysis and visualization of pulsar-timing data. We provide an overview of the timing model, its accuracy and differences relative to earlier work. We also present a new scheme for predictive use of the timing model that removes existing processing artefacts by properly modelling the frequency dependence of pulse phase.     

Dispersion measure variations and their effect on precision pulsar timing

We present an analysis of the variations seen in the dispersion measures (DMs) of 20-ms 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 characterized 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 solar wind on the DMs and show that the simple models presently implemented into pulsar timing packages cannot reliably correct for this effect. For the first time we clearly show how DM variations affect pulsar timing residuals and how they can be corrected in order to obtain the highest possible timing precision. Even with our presently limited data span, the residuals (and all parameters derived from the timing) for six of our pulsars have been significantly improved by correcting for the DM variations.     

The Deutsch field gamma-ray pulsar – II. Application of the model

A new model for gamma-ray pulsars presented by Higgins & Henriksen is applied to the cases of the seven known gamma-ray pulsars. Those pulsars that are not presently observed in gamma-rays, but are candidates for observation by the next generation of gamma-ray telescopes, are discussed. The case of millisecond pulsars is discussed, and it is shown that these objects should radiate at detectable levels, in opposition to the predictions of other gamma-ray pulsar models.     

Data analysis of continuous gravitational wave: Fourier transform – II

In this paper we obtain the Fourier Transform of a continuous gravitational wave. We have analysed the data set for (i) a 1-yr observation time and (ii) an arbitrary observation time, for an arbitrary location of detector and source, taking into account the effects arising due to the rotational as well as orbital motion of the Earth. As an application of the transform we considered spin-down and N -component signal analysis.     

The Parkes Multibeam Pulsar Survey – VI. Discovery and timing of 142 pulsars and a Galactic population analysis

We present the discovery and follow-up observations of 142 pulsars found in the Parkes 20-cm multibeam pulsar survey of the Galactic plane. These new discoveries bring the total number of pulsars found by the survey to 742. In addition to tabulating spin and astrometric parameters, along with pulse width and flux density information, we present orbital characteristics for 13 binary pulsars which form part of the new sample. Combining these results from another recent Parkes multibeam survey at high Galactic latitudes, we have a sample of 1008 normal pulsars which we use to carry out a determination of their Galactic distribution and birth rate. We infer a total Galactic population of  30 000 ± 1100  potentially detectable pulsars (i.e. those beaming towards us) having 1.4-GHz luminosities above 0.1 mJy kpc². Adopting the Tauris & Manchester beaming model, this translates to a total of  155 000 ± 6000  active radio pulsars in the Galaxy above this luminosity limit. Using a pulsar current analysis, we derive the birth rate of this population to be  1.4 ± 0.2  pulsars per century. An important conclusion from our work is that the inferred radial density function of pulsars depends strongly on the assumed distribution of free electrons in the Galaxy. As a result, any analyses using the most recent electron model of Cordes & Lazio predict a dearth of pulsars in the inner Galaxy. We show that this model can also bias the inferred pulsar scaleheight with respect to the Galactic plane. Combining our results with other Parkes multibeam surveys we find that the population is best described by an exponential distribution with a scaleheight of 330 pc. Surveys underway at Parkes and Arecibo are expected to improve the knowledge of the radial distribution outside the solar circle, and to discover several hundred new pulsars in the inner Galaxy.     

A stochastic Monte Carlo approach to model real star cluster evolution – II. Self-consistent models and primordial binaries

The new approach outlined in Paper I to follow the individual formation and evolution of binaries in an evolving, equal point-mass star cluster is extended for the self-consistent treatment of relaxation and close three- and four-body encounters for many binaries (typically a few per cent of the initial number of stars in the cluster mass). The distribution of single stars is treated as a conducting gas sphere with a standard anisotropic gaseous model. A Monte Carlo technique is used to model the motion of binaries, their formation and subsequent hardening by close encounters, and their relaxation (dynamical friction) with single stars and other binaries. The results are a further approach towards a realistic model of globular clusters with primordial binaries without using special hardware. We present, as our main result, the self-consistent evolution of a cluster consisting of 300 000 equal point-mass stars, plus 30 000 equal-mass binaries over several hundred half-mass relaxation times, well into the phase where most of the binaries have been dissolved and evacuated from the core. The cluster evolution is about three times slower than found by Gao et al. Other features are rather comparable. At every moment we are able to show the individual distribution of binaries in the cluster.     

The Effect of Lunisolar Precession on Pulsar Observations

In the measurements of pulsars’ periods and their rates of change there exists the effect of lunisolar precession. Via the analysis of this effect, we find that it can affect the accurate measurements of the periods of certain pulsars. An investigation of the periods of 1771 pulsars reveals that the measured periods of 81 pulsars suffer the influence of lunisolar precession in the range of the accuracy of measurements. With the improvement of the precision of measurements of pulsars’ periods and their change rates, this effect should get the corresponding corrections.     

An interference removal technique for radio pulsar searches

Searches for radio pulsars are becoming increasingly difficult because of a rise in impulsive man-made terrestrial radio-frequency interference. Here, we present a new technique, zero dispersion measure filtering, which can significantly reduce the effects of such signals in pulsar search data. The technique has already been applied to a small portion of the data from the Parkes multi-beam pulsar survey, resulting in the discovery of four new pulsars, so illustrating its efficacy.     

Stellar forensics — II. Millisecond pulsar binaries

We use the grid of models described in Paper I to analyse those millisecond pulsar binaries whose secondaries have been studied optically. In particular, we find cooling ages for these binary systems that range from < 1 to ∼ 15 Gyr. Comparison of cooling ages and characteristic spin-down ages allows us to constrain the initial spin periods and spin-up histories for individual systems, showing that at least some millisecond pulsars had sub-Eddington accretion rates and long magnetic field decay times.     

Data analysis of continuous gravitational wave: Fourier transform – I

We present the Fourier Transform of a continuous gravitational wave. We have analysed the data set for a 1-d observation time and our analysis is applicable for an arbitrary location of detector and source. We have taken into account the effects arising due to the rotational as well as orbital motions of the Earth.     

Periodic nulls in the pulsar B1133+16

Numerous studies of the brightest Cambridge pulsar, B1133+16, have revealed little order in its individual pulses, apart from a weak 30-odd-rotation-period fluctuation feature and that some 15 per cent of the star's pulsars are 'nulls'. New Arecibo observations confirm this fluctuation feature and that it modulates all the emission, not simply the 'saddle' region. By replacing each pulse with a scaled version of the average profile, we were able to quench all subpulse modulation and thereby demonstrate that the star's 'null' pulses exhibit a similar periodicity. A subbeam carousel model with a sparse and irregular 'beamlet' population appears to be compatible with these characteristics.