Machine learning analysis of pulsar timing data

Abstract

In 1967, radio pulsations from a celestial body were discovered by a graduate student Jocelyn Bell and her advisor Antony Hewish. This was the first sample of about three thousand similar sources, called pulsars, to be discovered in our galaxy to date. It has been understood that pulsars are rapidly spinning, strongly magnetized neutron stars. Neutron stars are very dense objects formed by the collapse of the cores of massive stars at the end of their life. Each pulsar has its characteristic pulse shape and rotational frequency. The rotational frequency of pulsars can be measured very precisely. The rotation frequencies of pulsars are observed to decrease in time. Pulsars tap their radiative energy from their rotational kinetic energy. The mechanisms by which pulsars achieve this energy conversion is not well-understood. According to a prominent model, the pulsars convert their kinetic energy into radiation by emission of magnetic dipole radiation (MDR). However, studies with young pulsar data show that the MDR model does not fully explain the observations and there should be other mechanisms assisting the spin-down. The ejection of high-energy particles, the growth of the dipole magnetic field over time, interaction with a supernova debris disc, increasing inclination angle between the rotation and magnetic axis, and gravitational wave emission are some of the processes proposed to affect spin-evolution. Occasionally, some pulsars suffer sudden increases in their spin, also known as "glitches" which decay in the following weeks or months. When they were first discovered, it was thought that glitches result from the breaking of the crust and hence they were called "stellar quakes". Today, it is conceived that this model can only account for the smallest glitches or that it could be a triggering mechanism for the main cause of the glitches. According to the more favoured view, the glitches are caused by the dynamics of the crustal superfluid. Sometimes a new glitch occurs before the previous glitch decayed. The presence of glitches in the pulsar data complicates the understanding of the spin evolution. The aim of the thesis is to contribute to the understanding of the spin evolution of pulsars by machine learning methods. To this end, long-term time-dependent spin frequency data of Crab and Vela pulsars are used. These are the two best-known pulsars that have been studied the most. Since the frequency changes by a small fraction throughout the time-span of the observations, we have eliminated the basic trend by fitting the data with a polynomial function. By subtracting this basic trend from the data, we obtained the residuals that clearly show the complicated features of spin evolution such as glitches. We tested the performance of two machine learning methods in reproducing the evolution of the residuals. The first method is called the sparse identification of nonlinear dynamics (SINDY). Given a time-series data, SINDY can identify the governing system of ordinary differential equations. We thus used this method to find the governing equations for the evolution of the residuals. The SINDy method gave information about the order of the equations and their coefficients. In addition, we used a recurrent neural network (RNN) architecture called long short-term memory (LSTM) method on the same data sets. We found that LSTM can predict the dates of glitches in the test data. The results show that SINDy and LSTM applications can contribute to the studies on the spin evolution of pulsars and may take place more in studies related to pulsars in the future.