# Pulsars and neutron stars/Searching for pulsars

## Introduction

Over two-thirds of the 558 pulsars published in the Taylor, Manchester & Lyne (1993) catalogue were discovered in one of ten large surveys using the Molonglo, Jodrell Bank, Parkes and Green Bank radio telescopes. The current (v1.53) ATNF pulsar catalogue lists 2453 radio pulsars. Over 800 of these pulsars was discovered in the Parkes multibeam pulsar survey. In this section we describe the methods used to search for pulsars.

### Introduction to survey methods

Most pulsar surveys can be divided into:

1. large-area pointed surveys, in which an extensive region of the sky is surveyed by making many individual, pointed observations.
2. drift-scan surveys, the telescope remains pointing in one direction and surveys any sky that passes through the beam.
3. targetted surveys, the telescope observes objects that are likely to contain pulsars such as supernova remnants, high-energy sources, globular clusters or the Magellanic clouds.

A typical search is processed as follows:

• After the observations are carried out the raw data files are recorded on tape or disk and transported to where they will be processed.
• The data are processed using a pipeline which searches for (and removes) radio-frequency-interference (RFI). The time series are dedispersed for a range of dispersion measures that, hopefully, covers all the pulsars. Each dedispersed time series is then searched either for individual pulses of emission or periodic pulse trains. The pipeline generally produces a large number of possible candidates.
• Candidates are confirmed to be pulsars usually by reobserving the same region of sky to see if the signal is redetected. If not, it is most-likely that the original candidate was caused by RFI, but it also may be an intermittent, strongly scintillating, or eclipsing pulsar. It is therefore worth reobserving candidates multiple times before rejecting them.
• Once confirmed, it is usual to "time" the pulsar over a period of ~1 year in order to obtain a high signal-to-noise profile, information about any possible orbital companion and a precise position.

## Survey sensitivity

The limiting flux density detectable for any radio telescope survey is given by:

${\displaystyle {\rm {S}}_{\rm {lim}}={\frac {\beta T_{\rm {sys}}}{G{\sqrt {n_{p}t_{\rm {obs}}\Delta f}}}}}$

where ${\displaystyle \beta }$ is a degradation factor, ${\displaystyle T_{\rm {sys}}}$ is the system temperature, ${\displaystyle G}$ is the telescope gain, ${\displaystyle n_{p}}$ is the number of polarisations added, ${\displaystyle \Delta f}$ is the system bandwidth and ${\displaystyle t_{\rm {obs}}}$ is the total observing time.

As a typical pulsar only radiates strongly for a small percentage of its period, the peak pulse signal is much greater than the mean signal strength. Therefore the minimum detectable pulsar flux density depends upon the pulsar's duty cycle and a detection signal-to-noise ratio threshold, ${\displaystyle \alpha }$, as:

${\displaystyle S_{\rm {min}}=S_{\rm {lim}}\alpha \left[{\frac {W_{e}}{(P-W_{e})}}\right]^{1/2}}$.

Dewey et al. (1984) showed that this effective pulse width, ${\displaystyle W_{e}}$, is calculated from the intrinsic pulse width (W), the amount of post-detection filtering applied and any pulse broadening caused by the propagation of the pulsar signal through the interstellar medium. This width is often written as:

${\displaystyle W_{e}=\left[W^{2}+\tau _{\rm {samp}}^{2}+\tau _{\rm {DM}}^{2}+\tau _{\rm {scatter}}^{2}\right]^{1/2}}$

where ${\displaystyle \tau _{\rm {samp}}}$ is the sampling time, ${\displaystyle \tau _{\rm {DM}}}$ the dispersion measure smearing and ${\displaystyle \tau _{\rm {scatter}}}$ the scattering time.

The dispersion smearing across one frequency channel is: ${\displaystyle \tau _{\rm {DM}}=8.3\mu s\times DM\times {\frac {\Delta f_{\rm {MHz}}}{f_{\rm {GHz}}^{3}}}}$

### Measuring the system temperature

#### Measuring the sky temperature

The sky temperature is usually modelled from an all-sky continuum radio survey. Pulsar astronomers have usually made use of the Haslam et al. map at 408 MHz and converted the measured temperatures to the survey observing frequency using:

${\displaystyle T_{\rm {sky}}=T_{\rm {sky}}^{\rm {Haslam}}\left({\frac {f{\rm {[MHz]}}}{408}}\right)^{-2.6}}$

### Drift-scan surveys

The majority of pulsar surveys have been "pointed" observations in which the telescope is pointed directly at a particular source or region of the sky for an observation. It is also possible to carry out drift-scan surveys in which the telescope remains pointing in a particular direction and the sky drifts overhead. This is usually carried out for a particular region of the sky, but it is also possible to carry out drift-scans in which a particular source drifts through the beam. For instance, very early science observations with the highly sensitive FAST telescope will require drift scans. Consideration is being given to letting sources such as globular clusters drift through the beam.

Clearly the sensitivity to a particular source is maximised when the source is directly in the centre of the beam. How the sensitivity degrades away from the centre depends upon the shape of the beam. in turn that depends on the receiver and particular observing frequency. The far-field beam pattern of an ideal, uniformly illuminated circular aperture is:

${\displaystyle P(U)=\left[{\frac {2J_{1}(U)}{U}}\right]^{2}}$

where ${\displaystyle U=\pi D\sin \theta /\lambda }$ and ${\displaystyle J_{1}}$ is the first-order Bessel function, ${\displaystyle \lambda }$ is the observing wavelength and ${\displaystyle D}$. The half-power beamwidth (often known as HPBW) is

${\displaystyle \theta _{\rm {HPBW}}=1.22{\frac {\lambda }{D}}}$

Note that real telescopes have tapered illumination which can lead to a larger beam.

## Searching for pulsars using continuum images

### Why has the Parkes radio telescope discovered so many pulsars?

The Parkes radio telescope is relatively small. However, it has been used to discover a very large number of the currently known pulsars. Reasons include:

• The site in the Southern hemisphere allows for long observations in the Galactic plane
• Relatively low levels of RFI
• A small telescope has a wider beam on the sky than a larger telescope and so it does not require as many pointings to cover the same sky area
• The installation of modern instrumentation - such as the multibeam receiver

### I have a pulsar search data set. How do I start looking for pulsars in it?

The answer depends on the size of the data set, your computing resources, what software you have installed, exactly what you want to search for and the RFI environment at the observatory. To get going try the following SIGPROC (and a bit of PRESTO) script which will process a single data file and produce postscript files of the candidates:

#!/bin/tcsh

filterbank $inFile -o$outFile.fil

set gulpSize = 1000000

# Consider removing RFI in the following line using the -k option
# $dm1 and$dm2 are the range of DMs to search

dedisperse_all $outFile.fil -d$dm1 $dm2 -g$gulpSize -l

foreach file (ls *.tim)
# Could consider setting the transform length here with the -t option
seek $file end # Create postscript files for the best candidates set nCand = wc -l allCands.lis | awk '{print$1}'
foreach candLine (seq 1 $nCand) set line = head -$candLine allCands.lis | tail -1
set period_sec = echo $line | awk '{print$1/1000.0}'
set dm = echo $line | awk '{print$3}'

set outputLabel = echo $label$dm $candLine | awk '{printf("%-0.4d_%s_%s",$3,$2,$1)}'
prepfold -topo -o {$outputLabel} -nsub 32 -noxwin -dm$dm -p $period_sec$outFile.fil
end