A Review of Pulsar Glitch Mechanisms Gregory Brett McDonald May 2007 ABSTRACT In this thesis, a review of the most prominent pulsar glitch mechanisms is pre- sented. This includes a discussion of the internal structure of neutron stars and the way in which glitches may be used to describe that structure. Particular at- tention is paid to the two-component model. This thesis also includes numerous simulations of the two-component model, which are fitted to observational data in order to determine how suitable this mechanism is as a description of pulsar glitches. The results show that this mechanism is in fact still relevant, in spite of its age. Abstract 3 Acknowledgements I would like to take this opportunity to thank a few people, without whom this thesis would not have been possible. First, I would like to thank my family for all of their love and support throughout the course of this project. Mom, Ruth and Josh, I love you guys. To Chris Engelbrecht and Fabio Frescura, thanks for all the input you gave me over the past few years, and for sparking my interest in the wonderful world of astrophysics. Thanks for the many useful conversations and discussions, and for convincing me that it would all turn out alright in the end, no matter how bleak it appeared at the time! To Marten, my co-conspirator and trusty side-kick, I will always remember the long lunchtime walks to the Student Center and the many games of squash we played when our frustrations threatened to overcome us. I hope you find every happiness in your future career. To the South African Square Kilometer Array Project Office (SASPO), thank you for your unfailing support of my studies, for providing such a wonderfully generous bursary, and the opportunity to study such a fascinating subject. I am saddened not to be continuing my work with you, but I hope that we will get the opportunity to work together in the future. And finally, I want to thank my Father for enabling me the opportunity to meet such wonderful people and study such an interesting subject.“You placed the stars in the sky, and you know them by name.” Without you I am nothing. CONTENTS 1. Overview of Neutron Stars ......................... 9 1.1 A Brief Overview of Neutron Star History and Discovery . 9 1.2 Pulsar Discovery and Interpretation . 10 1.3 The Structure of Neutron Stars . 11 1.4 Superfluidity . 14 1.4.1 Basic Superfluid Theory . 15 1.4.2 Basic Vortex Theory . 17 1.4.3 Quantised Vortices . 17 1.5 Vortex Pinning and Vortex Creep in Neutron Stars . 19 1.5.1 Factors influencing vortex creep rate . 19 1.5.2 Determining the Activation Energy . 21 2. Glitches and Glitch Mechanisms ...................... 27 2.1 Glitches . 27 2.2 Brief Summary of Glitch Mechanisms . 27 2.3 Crust-driven Glitch Mechanisms . 31 2.3.1 Crust Fracture Model . 31 2.3.2 Thermally Driven Glitches . 36 2.4 Core-driven Glitches . 42 2.4.1 Flux-tube Model . 42 2.4.2 Centrifugal Buoyancy Mechanism . 46 3. Two-component Model: Theory and History ............... 49 4. Simulations ................................. 57 4.1 Overview of Simulations . 57 4.2 Fitting Simulations to Observational Data . 64 4.2.1 Glitch Occurring in the Crab Pulsar in 1996 . 64 4.2.2 Glitch Occurring in the Crab Pulsar in 1975 . 69 4.2.3 Simulation Summary . 71 5. Concluding Remarks ............................ 76 6. References .................................. 78 LIST OF FIGURES 1.1 Figure showing neutron star mass results for fourteen pulsar binary systems. The dotted lines contain the region which has values agreeing with all measurements, i.e. M = 1.35±0.4M . (Thorsett, Chakrabarty 1999) . 11 1.2 Neutron star gravitational mass in solar units vs. neutron star radius, as given by various equations of state. The Friedman- Pandharipande EOS is given by the dashed line in the middle. (Heiselberg, Pandharipande 2000) . 12 1.3 Diagram showing the various regions in a neutron star. 14 1.4 Diagram showing the dynamics which lead to the creation of the Magnus force FM ............................ 20 1.5 An exaggerated diagram showing a pinned vortex bending under the influence of the Magnus force. The solid circles show the pin- ning sites. 22 1.6 Configuration used for the calculation of the energy for a single-site breakaway (Link, Epstein, 1991) . 23 1.7 Energy of a vortex line as a function of separation for a vortex line in the single-site breakaway regime (Link, Epstein 1991). 24 1.8 Energy of a vortex line as a function of separation for a vortex line in the single-site breakaway regime (Link, Epstein 1991). 25 2.1 Figure published by Radhakrishnan and Manchester (1969) show- ing the first observed glitch, which occurred in the Vela pulsar . 28 2.2 Diagram used to illustrate crust-cracking parameters (Ruderman, 1991).................................. 33 2.3 Diagram showing the structure of the cylindrical regime considered in the Thermal Glitch Mechanism, as given by Link & Epstein (1996) 38 2.4 The results obtained by Link and Epstein (1996) for a compar- ison of the thermal glitch mechanism simulation of magnitude −8 35 ∆Ωc/Ωc ' 7 × 10 and an energy deposition of 2.1 × 10 J (line) to data (dots) for the Crab pulsar . 40 2.5 The results obtained by Link and Epstein (1996) for a compar- ison of the thermal glitch mechanism simulation of magnitude −6 35 ∆Ωc/Ωc ' 10 and an energy deposition of 1.51 × 10 J (line) to data (dots) for the Vela pulsar . 41 List of Figures 6 2.6 Properties of various crust layers, as given by Negele and Vautherin (1973) ................................. 45 3.1 Simple picture showing a possible configuration for the two-component model. 49 3.2 Response of pulsar to glitch, as predicted by the simple two-component model. 52 4.1 Results of a Crab-like pulsar simulation. The results are for the post-glitch reaction of the theoretical pulsar. The coupling con- stant for this set of results is 5 days. The superfluid percentages are given by the legend. 59 4.2 Results of a Crab-like pulsar simulation. The results are for the post-glitch reaction of the theoretical pulsar. The coupling con- stant for this set of results is 10 days. The superfluid percentages are given by the legend. 60 4.3 Results of a Crab-like pulsar simulation. The results are for the post-glitch reaction of the theoretical pulsar. The coupling con- stant for this set of results is 20 days. The superfluid percentages are given by the legend. 61 4.4 Results of a Crab-like pulsar simulation. The results are for the post-glitch reaction of the theoretical pulsar. The coupling con- stant for this set of results is 30 days. The superfluid percentages are given by the legend. 62 4.5 Results of a Crab-like pulsar simulation. The results are for the post-glitch reaction of the theoretical pulsar. The coupling con- stant for this set of results is 50 days. The superfluid percentages are given by the legend. 63 4.6 Fit of simulation containing one coupling constant (τ = 8.6 days) to the data for the glitch occurring in the Crab pulsar in 1996. The simulation is given by the line, while the data are given by the dots. 65 4.7 Fit of simulation containing two coupling constants (τ1 = 10.3 days and τ2 = 0.3 days) to the data for the glitch occurring in the Crab pulsar in 1996. The simulation is given by the line, while the data are given by the dots. 66 4.8 Table showing the values obtained by my simulation as well as those obtained by Wong et al. for the 1996 Crab glitch . 67 4.9 Fit of simulation containing two coupling constants (τ1 = 10.9 days and τ2 = 0.3 days) to the data for the glitch occurring in the Crab pulsar in 1996, with corrected start point. The simulation is given by the line, with data given by dots. 68 List of Figures 7 4.10 Fit of simulation containing one coupling constant (τ = 9.9 days) to the data for the glitch occurring in the Crab pulsar in 1975. The simulation is given by the line, while the data are given by the dots. 69 4.11 Table showing the values obtained by my simulation as well as those obtained by Alpar et al. for the 1975 Crab glitch . 70 4.12 Diagram showing the fit obtained by Alpar et al. for the 1975 Crab Pulsar Glitch . 70 4.13 Table showing the coupling constant values obtained from the sim- ulations, as well as published results . 72 4.14 Graph showing the distribution of coupling constants as a function of characteristic age . 73 4.15 Graph showing the distribution of coupling constants as a function of characteristic age magnified to centre on the low characteristic age region . 74 4.16 Graph showing the distribution of coupling constants as a function of glitch magnitude . 75 List of Figures 8 Introduction Neutron stars, through their observation as pulsars, provide fascinating labora- tories for studying physical processes in extreme environments. The occurrence of glitches, their observation and subsequent analysis, offer physicists an extraor- dinary look into this world of incredibly high densities and ultra strong magnetic fields. It is here that some of the most exotic physics yet encountered is found. Yet, after nearly forty years of pulsar glitch study, there is still no conclusive model which can describe the exact mechanism by which these processes occur.