Pulsars and neutron stars/History of data processing

Processing pulsar data

Observations are carried out in order to study known pulsars or to search for new pulsars.

Pulsar searching

Most (but not all) pulsars have been discovered using a radio telescope. The first pulsar was found serendipitously, but more recent discoveries have required large amounts of observing time, peta-bytes of data storage and major high-performance computing systems. In order to detect fast spinning pulsars it is necessary to record the signal from the telescope with the fastest sampling possible. Modern surveys typically record data with a sampling time of ~50μs. It is also necessary to record a large number of frequency channels. Then, it is necessary to try and identify a pulsar signal within the data. Pulsar searching is usually based around searching for the periodic pulse signal and/or searching for individual bright pulses. An early search method was presented by Hamilton et al. (1973), but many updates to the algorithms have been suggested (e.g., Schwarzenberg-Czerny 1996, Ransom, Eikenberry & Middleditch 2002, Allen, Papa & Shutz 2002). Cordes & McLaughlin (2003) discussed methods for detecting fast radio transient events in pulsar data.

Pulsar search algorithms produce pulsar candidates. Some of these candidates will be produced by statistical fluctuations, other candidates will be from RFI (a method for dealing with RFI, in pulsar searching, was presented by Eatough, Keane & Lyne 2009). It is, therefore, often difficult to select true pulsars from the candidates. Rosen et al. (2010) described an outreach project in which high-school students search for pulsars and learn about analyzing astronomical data. The first pulsar discovery using global volunteer computing was reported by Knispel et al. (2010). Eatough et al. (2010) described how pulsar candidates can be ranked using artificial neutral networks.

Pulse profiles

Once a pulsar has been found, it is studied in detail. One of the fundamental properties of a pulsar is its pulse shape, but obtaining the correct pulse profile requires calibrating the data. Johnston (2002) demonstrated how pulsar observations with a single dish telescope can be calibrated, which was followed up by van Straten (2006). Karastergiou & Johnston (2006) demonstrated how to obtain absolute polarization position angles. A recent study of millisecond pulsar profiles with advanced methods was presented by Dai et al. (2015).

A measurement of the flux density of a pulsar in the particular observing band can be determined from the pulse profile. The observed pulse flux density varies in time and frequency because of intrinsic variability, but also because of scintillation in the interstellar medium. The first dynamic spectra (in which the pulse flux density is plotted as a function of frequency and time) of pulsars were obtained by Huguenin & Taylor (1969). Stinebring et al. (2001) demonstrated how a dynamic spectra can be processed in order to identify very small features in the interstellar medium.

Pulsar timing

The "pulsar timing" method is used to study the long-term rotational behavior of pulsars. Model predictions are made for when pulses are expected to be arriving at a telescope. Those predictions are compared with the actual measurements of pulse arrival times (see Pennucci, Demorest & Ransom 2014 for a description of a modern method for measuring these arrival times). Radio pulsar observations are carried out with telescopes on the Earth's surface. The measured pulse arrival times are therefore affected by the Earth's rotation and motion around the Sun. The measured arrival times are therefore referred to the solar system barycentre and subsequently analysed.

The first major update to the pulsar timing method came after the "Discovery of a pulsar in a binary system" by Hulse & Taylor (1975). The measured pulse arrival times from binary pulsars are affected by the orbital motion of the pulsar and this must be accounted for when predicting the arrival times. Blandford & Teukolsky (1976) described the mathematical formalism for analysing the arrival time of pulses from a relativistic binary pulsar. This model is still used and known as the BT binary model in modern pulsar timing software packages. Backer & Hellings (1986) described techniques for accounting for relativistic effects in the analysis of pulsar signals. The pulsar timing method is not only applied to radio pulsars. Deeter, Boynton & Pavdo (1981) presented results from a pulse-timing analysis of Hercules X-1.

Perhaps the greatest changes to the pulsar timing method came after the discovery of the first millisecond pulsar. To time pulsars at microsecond (or below) precision and accuracy required new time standards, the inclusion of new physical affects into the timing model and better solar system ephemerides. Blandford, Romani & Narayan (1984) described the arrival-time analysis for such millisecond pulsars. Fairhead (1990) used observations of PSR B1937+21 to demonstrate the effect of different solar system ephemerides and TT-TB time transformations and noted that great care must be taken when using results from different timing programs for astrometric purposes. The fundamental precision that can be reached by pulsar timing was discussed by Foster (1996).

Developments to the timing software were required as pulsars were found in globular clusters (Blandford, Romani & Appelgate 1987, orbiting main-sequence stars (Wex 1998) or had planetary systems (Konacki, Maciejewski & Wolszczan 2000). Freire et al. (2009) demonstrated a new method for analyzing and studying the radio emission in the double pulsar system.

The advent of the pulsar timing array projects led to the requirement that pulsar timing programs account for all physical affects at the sub-100ns level and also to be able to process and analyse multiple pulsars simultaneously. This led to the development of the TEMPO2 software package (Hobbs, Edwards & Manchester 2006 and Edwards, Hobbs & Manchester 2006) which was based upon the original TEMPO software. Bayesian analysis methods are now taking their place in pulsar timing methods. These came initially from Bayesian attempts to search for gravitational waves, but are fast becoming main-stream for standard pulsar timing projects. The first Bayesian attempt to place an upper limit on the gravitational wave background using pulsar timing was presented by McHugh et al. (1996). van Haasteren et al. (2009) developed a Bayesian algorithm for searching for a gravitational-wave background signal with pulsar data. Such work has culminated in temponest - a Bayesian addition to tempo2 Lentati et al. (2014).

As pulsar data timing data sets increase in length it becomes apparent that unexplained timing noise is present. Studying the timing noise requires more and more advanced time series analysis methods. Deshpande, Alessandro & McCulloch (1996) used a CLEAN method for the power spectral analysis of pulsar data. More recently Coles et al. (2011) used a globalized least-squares-fitting method to account for unmodelled red noise when determining pulsar parameters or measuring power spectra.