Magnetodynamics Inside and Outside Magnetars

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Magnetodynamics Inside and Outside Magnetars Magnetodynamics Inside and Outside Magnetars Xinyu Li Submitted in partial fulfillment ofthe requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2019 ©2019 Xinyu Li All Rights Reserved Abstract Magnetodynamics Inside and Outside Magnetars Xinyu Li The ultra-strong magnetic fields of magnetars have profound implications for their radiative phenomena. We study the dynamics of strong magnetic fields inside and outside magnetars. Inside the magnetar, the strong magnetic stress can break the crust and trigger plastic failures. The interaction between magnetic fields and plastic failures is studied in two scenarios: 1. Internal Hall waves launched from the core-crust interface can initiate plastic failures and lead to X-ray outbursts. 2. External Alfven waves produced by giant flares can also initiate crustal plastic failures which dissipate the waves and give rise to delayed thermal afterglow. The crustal dissipation of Alfven waves competes with the magnetospheric dissipation outside the magnetar. Using a high order simulation of Force-Free Electrodynamics (FFE), we found that the magnetospheric dissipation of Alfven waves is generally slow and most wave energy will dissipate inside the magnetar. Contents List of Figures v Chapter 1 Introduction 1 1.1 Neutrons Stars . 2 1.1.1 Theoretical and observational discovery . .2 1.1.2 Structure of neutron stars . 5 1.2 Magnetars . 10 1.2.1 Discovery . 10 1.2.2 Magnetar Activities . 12 1.2.3 Theoretical Models . 16 1.3 This Dissertation . 24 Chapter 2 Magnetohydrodynamics (MHD) 26 2.1 Ideal MHD . 26 2.1.1 Nonrelativistic ideal MHD . 26 2.1.2 Waves in nonrelativistic ideal MHD . 28 2.1.3 Relativistic MHD (RMHD) . 29 2.2 Force-Free Electrodynamics (FFE) . 29 2.2.1 Wave solutions . 30 2.2.2 Wave-wave interactions . 33 i 2.3 Non-ideal corrections . 35 Chapter 3 Magnetar Outbursts from Avalanche of Hall Waves 38 3.1 Hall waves . 39 3.1.1 Generation of Hall waves . 41 3.2 Plastic failures . 44 3.2.1 Stress balance . 44 3.2.2 Mechanical failure . 45 3.2.3 Heat transfer and thermoplastic waves . 46 3.3 Hall-mediated avalanche . 48 3.4 Twisted external field . 52 3.5 Global Simulation . 54 3.5.1 Setup . 54 3.5.2 Results . 58 3.6 Discussion . 65 Chapter 4 Plastic Damping of Alfvén Waves in Magnetar Crusts 69 4.1 Wave transmission into the crust . 70 4.1.1 Transmission coefficient . 70 4.1.2 Numerical model . 74 4.2 Plastic Heating . 77 4.2.1 Pre-flare temperature profile . 77 4.2.2 Plastic flow . 79 4.2.3 Wave damping and post-flare crustal temperature . 81 4.3 Cooling . 84 4.4 Discussion . 88 4.4.1 Plastic damping and cooling . 88 ii 4.4.2 Other mechanisms of Alfvén wave damping . 91 4.4.3 Observed afterglow . 92 Chapter 5 Dissipation of Alfvén Waves in Magnetar Magnetospheres 95 5.1 Numerical setup . 98 5.1.1 Computational setting . 98 5.1.2 Solution scheme . 98 5.1.3 Constraint preservation . 100 5.1.4 Maintaining magnetic dominance . 101 5.1.5 Dissipation channels in FFE simulations . 101 5.1.6 Numerical diagnostics . 103 5.2 Spectral evolution of wave turbulence . 104 5.2.1 3D simulations . 104 5.2.2 2D simulations . 109 5.3 Local dissipation and escape of waves . 112 5.3.1 Turbulent dissipation rate without wave escape . 113 5.3.2 Turbulent cascade with escaping fast modes . 114 5.4 Enhanced immediate dissipation and FFE failure . 116 5.4.1 Immediate dissipation observed in FFE simulations . 116 5.4.2 MHD simulations and the spurious character of immediate dissipation in FFE . 120 5.5 Discussion . 124 5.5.1 Summary of results . 124 5.5.2 Fate of wave energy in magnetar flares . 127 Chapter 6 Conclusions 129 Bibliography 132 iii Appendix A Wave Turbulence 143 A.1 Weak nonlinearity expansion . 145 A.2 Generating function . 147 A.3 Kinetic equation . 151 Appendix B Resonant Three Wave Interactions in FFE 153 iv List of Figures Figure 1.1 A record of pulsating radio source . 4 Figure 1.2 A cartoon illustrates the structure of a neutron star . 6 Figure 1.3 Equation of state and mass-radius relation for neutron stars . 7 Figure 1.4 Neutrino cooling rate in the core of neutron stars . 8 Figure 1.5 P − PÛ diagram for pulsars and magnetars . 12 Figure 1.6 Light curve for the 2004 giant flare SGR 1806-20 . 14 Figure 1.7 Light curves of eight magnetar outbursts . 15 Figure 1.8 Relation between shear stress and strain of materials in the neutron star crust 17 Figure 1.9 Structure of the thermoplastic wave front . 18 Figure 1.10 Formation of the equatorial current sheet in an over-twisted magnetar magnetosphere. 20 Figure 1.11 The evolution of hotspots observed on transient magnetars following their outbursts . 22 Figure 1.12 Sketch of a twist magnetic loop. 23 Figure 3.1 Components of magnetic field in the self-similar solution of Hall waves .42 Figure 3.2 Generation of Hall waves in the magnetar crust . 43 Figure 3.3 Profile of the horizontal magnetic field . 49 Figure 3.4 Numerical simulation demonstrating the Hall-mediated failure of the crust 50 Figure 3.5 Illustration for the magnetic field lines in the crust and in the magnetosphere 54 v Figure 3.6 Snapshots of the magnetic field evolution . 58 Figure 3.7 Spacetime diagram for failure generation and propagation in the crust . 59 Figure 3.8 Radiation flux from the outburst simulation . 60 Figure 3.9 Spacetime diagram for a giant thermoplastic wave . 61 Figure 3.10 Radiation flux from the outburst simulation for a giant thermoplastic wave62 Figure 3.11 Evolution of surface displacement . 63 Figure 3.12 Evolution of the radiation flux . 64 Figure 3.13 Evolution of the free energy . 64 Figure 4.1 Density ρ¹zº and shear modulus µ¹zº of the neutron star crust . 71 Figure 4.2 Comparison between wavelength and characteristic scale in the crust . 73 Figure 4.3 Transmission coefficient T as a function of vertical magnetic field Bz . 74 Figure 4.4 A snapshot of the wave after four reflection/transmission events . 76 Figure 4.5 Shear wave propagation in the magnetar crust viewed on the spacetime diagram . 82 Figure 4.6 Energy evolution during the reflection of Alfvén waves off the crust .83 Figure 4.7 Temperature profile after the magnetospheric Alfvén waves have been absorbed by the crust . 84 Figure 4.8 Evolution of the crustal temperature profiles . 86 Figure 4.9 Fraction of the post-flare crustal heat lost through surface emission and various channels of neutrino emission . 87 Figure 4.10 Surface thermal flux caused by the plastic heating in the giant flare .87 Figure 5.1 Magnetic field lines passing through one of the Alfvén wave packets .105 Figure 5.2 Free energy evolution for different resolutions in 3D simulations . .106 Figure 5.3 Development of turbulent spectrum in 3D simulations . 107 Figure 5.4 Turbulence spectrum in k? in four 3D simulations . 108 Figure 5.5 Free energy evolution for different resolutions in the 2D model . .109 vi Figure 5.6 Spectrum evolution for the 2D simulation . 110 Figure 5.7 The evolution of U0/U ¹tº in 2D simulations . 112 Figure 5.8 Dissipation of Alfvén wave packet energy U0 in 3D simulations . 113 Figure 5.9 Comparison between free energy evolution U ¹tº in the simulations with and without damping of fast modes . 116 Figure 5.10 Dissipated energy fraction.
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