Single pulse and profile variability study of PSR J1022+1001

Millisecond pulsars (MSPs) are known as highly stable celestial clocks. Nevertheless, recent studies have revealed the unstable nature of their integrated pulse profiles, which may limit the achievable pulsar timing precision. In this paper, we present a case study on the pulse profile variability of PSR J1022+1001. We have detected approximately 14,000 sub-pulses (components of single pulses) in 35-hr long observations, mostly located at the trailing component of the integrated profile. Their flux densities and fractional polarisation suggest that they represent the bright end of the energy distribution in ordinary emission mode and are not giant pulses. The occurrence of sub-pulses from the leading and trailing components of the integrated profile is shown to be correlated. For sub-pulses from the latter, a preferred pulse width of approximately 0.25 ms has been found. Using simultaneous observations from the Effelsberg 100-m telescope and the Westerbork Synthesis Radio Telescope, we have found that the integrated profile varies on a timescale of a few tens of minutes. We show that improper polarisation calibration and diffractive scintillation cannot be the sole reason for the observed instability. In addition, we demonstrate that timing residuals generated from averages of the detected sub-pulses are dominated by phase jitter, and place an upper limit of ~700 ns for jitter noise based on continuous 1-min integrations.

PEACE: Pulsar Evaluation Algorithm for Candidate Extraction -- A software package for post-analysis processing of pulsar survey candidates

Modern radio pulsar surveys produce a large volume of prospective candidates, the majority of which are polluted by human-created radio frequency interference or other forms of noise. Typically, large numbers of candidates need to be visually inspected in order to determine if they are real pulsars. This process can be labor intensive. In this paper, we introduce an algorithm called PEACE (Pulsar Evaluation Algorithm for Candidate Extraction) which improves the efficiency of identifying pulsar signals. The algorithm ranks the candidates based on a score function. Unlike popular machine-learning based algorithms, no prior training data sets are required. This algorithm has been applied to data from several large-scale radio pulsar surveys. Using the human-based ranking results generated by students in the Arecibo Remote Command enter programme, the statistical performance of PEACE was evaluated. It was found that PEACE ranked 68% of the student-identified pulsars within the top 0.17% of sorted candidates, 95% within the top 0.34%, and 100% within the top 3.7%. This clearly demonstrates that PEACE significantly increases the pulsar identification rate by a factor of about 50 to 1000. To date, PEACE has been directly responsible for the discovery of 47 new pulsars, 5 of which are millisecond pulsars that may be useful for pulsar timing based gravitational-wave detection projects.

Application of the Gaussian mixture model in pulsar astronomy -- pulsar classification and candidates ranking for {it Fermi} 2FGL catalog

Machine learning, algorithms to extract empirical knowledge from data, can be used to classify data, which is one of the most common tasks in observational astronomy. In this paper, we focus on Bayesian data classification algorithms using the Gaussian mixture model and show two applications in pulsar astronomy. After reviewing the Gaussian mixture model and the related Expectation-Maximization algorithm, we present a data classification method using the Neyman-Pearson test. To demonstrate the method, we apply the algorithm to two classification problems. Firstly, it is applied to the well known period-period derivative diagram, where we find that the pulsar distribution can be modeled with six Gaussian clusters, with two clusters for millisecond pulsars (recycled pulsars) and the rest for normal pulsars. From this distribution, we derive an empirical definition for millisecond pulsars as $frac{dot{P}}{10^{-17}} leq3.23(frac{P}{100 textrm{ms}})^{-2.34}$. The two millisecond pulsar clusters may have different evolutionary origins, since the companion stars to these pulsars in the two clusters show different chemical composition. Four clusters are found for normal pulsars. Possible implications for these clusters are also discussed. Our second example is to calculate the likelihood of unidentified textit{Fermi} point sources being pulsars and rank them accordingly. In the ranked point source list, the top 5% sources contain 50% known pulsars, the top 50% contain 99% known pulsars, and no known active galaxy (the other major population) appears in the top 6%. Such a ranked list can be used to help the future follow-up observations for finding pulsars in unidentified textit{Fermi} point sources.

The optimal schedule for pulsar timing array observations

In order to maximize the sensitivity of pulsar timing arrays to a stochastic gravitational wave background, we present computational techniques to optimize observing schedules. The techniques are applicable to both single and multi-telescope experiments. The observing schedule is optimized for each telescope by adjusting the observing time allocated to each pulsar while keeping the total amount of observing time constant. The optimized schedule depends on the timing noise characteristics of each individual pulsar as well as the performance of instrumentation. Several examples are given to illustrate the effects of different types of noise. A method to select the most suitable pulsars to be included in a pulsar timing array project is also presented.

Gravitational wave astronomy of single sources with a pulsar timing array

Abbreviated: We investigate the potential of detecting the gravitational wave from individual binary black hole systems using pulsar timing arrays (PTAs) and calculate the accuracy for determining the GW properties. This is done in a consistent analysis, which at the same time accounts for the measurement of the pulsar distances via the timing parallax. We find that, at low redshift, a PTA is able to detect the nano-Hertz GW from super massive black hole binary systems with masses of $sim10^8 - 10^{10},M_{sun}$ less than $sim10^5$,years before the final merger, and those with less than $sim10^3 - 10^4$ years before merger may allow us to detect the evolution of binaries. We derive an analytical expression to describe the accuracy of a pulsar distance measurement via timing parallax. We consider five years of bi-weekly observations at a precision of 15,ns for close-by ($sim 0.5 - 1$,kpc) pulsars. Timing twenty pulsars would allow us to detect a GW source with an amplitude larger than $5times 10^{-17}$. We calculate the corresponding GW and binary orbital parameters and their measurement precision. The accuracy of measuring the binary orbital inclination angle, the sky position, and the GW frequency are calculated as functions of the GW amplitude. We note that the pulsar term, which is commonly regarded as noise, is essential for obtaining an accurate measurement for the GW source location. We also show that utilizing the information encoded in the GW signal passing the Earth also increases the accuracy of pulsar distance measurements. If the gravitational wave is strong enough, one can achieve sub-parsec distance measurements for nearby pulsars with distance less than $sim 0.5 - 1$,kpc.

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.