京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20912号 / 理博第4364号 / 新制||理||1626(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 井岡 邦仁, 教授 川合 光, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

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This dissertation deals with the following topics related to the magnetic activity of neutron stars and black holes: (I) Magnetic field evolution of neutron stars: We develop a numerical code which models the internal magnetic field evolution of neutron stars in axisymmetry. Our code includes the Hall drift and Ohmic effects in the crust, and the drift of superconducting flux tubes and superfluid vortices inside the liquid core. We enforce the correct hydromagnetic equilibrium in the core. We also model the elastic deformation of the crust and its feedback on the magnetic field evolution. We find that (i) The Hall attractor found by Gourgouliatos and Cumming in the crust also exists for B-fields which penetrate the core. (ii) If the flux tube drift is fast in the core, the pulsar magnetic fields are depleted on the Ohmic timescale (~150 Myr for hot neutron stars, or ~1.8 Gyr for cold neutron stars such as recycled pulsars, depending on impurity levels). (iii) The outward motion of superfluid vortices during the rapid spin-down of a young highly magnetized pulsar, can partially expel magnetic flux from the core when 𝐵 ≲ 10¹³ G. (II) Neutron star quakes and glitches: We develop a theoretical model to explain the remarkable null pulse coincident with the 2016 glitch in Vela rotation. We propose that a crustal quake associated with the glitch strongly disturbed the Vela magnetosphere and thus interrupted its radio emission. We develop the first numerical code which models the global dynamics of a neutron star quake. Our code resolves the elasto-dynamics of the entire crust and follows the evolution of Alfven waves excited in the magnetosphere. We find that Alfven waves launched by the quake become de-phased in the magnetosphere, and generate strong electric currents, capable of igniting electric discharge. Most likely, the discharge floods the magnetosphere with electron-positron plasma, quenching the pulsar radio emission. The observed ~0.2 s duration of the disturbance indicates that the crust is magnetically coupled to the superconducting core of the neutron star. (III) Pulsar magnetospheres and radio emission: We present an extreme high resolution kinetic plasma simulation of a pulsar magnetosphere using the Pigeon code. The simulation shows from first-principles how and where radio emission can be produced in pulsar magnetospheres. We observe the self-consistent formation of electric gaps which periodically ignite electron-positron discharge. The gaps form above the polar-cap, and in the bulk return-current. Discharge of the gaps excites electromagnetic modes which share several features with the radio emission of real pulsars. We also observe the excitation of plasma waves and charge bunches by streaming instabilities in the outer magnetosphere. (IV) Black hole magnetospheres and no-hair theorem: We explore the evolution of highly magnetized magnetospheres on Kerr black holes by performing general relativistic kinetic plasma simulations with the GRZeltron code, and general relativistic resistive magnetohydrodynamics simulations with the BHAC code. We show that a dipole magnetic field on the event horizon opens into a split-monopole and reconnects in a plasmoid-unstable current-sheet. The plasmoids are ejected from the magnetosphere, or swallowed by the black hole. The no-hair theorem is satisfied, in the sense that all components of the stress-energy tensor decay exponentially in time. We measure the decay time of magnetic flux on the event horizon for plasmoid-dominated reconnection in collisionless and collisional plasma.

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For the past several decades, mass estimates for supermassive black holes hosted by active galactic nuclei (AGN) have been made with the reverberation mapping (RM) technique. This methodology has produced consistent results and has been used to establish several relations that link the characteristics of the host galaxy to the mass of the central black hole. Despite this success, there are less than 50 AGN with black hole masses derived from RM. This low number is generally attributed to the difficulties in coordinating large blocks of telescope time for making simultaneous photometric and spectroscopic observations. Spectroscopic observations also generally require several months of nightly observations with moderate to large size telescopes as the signal-to-noise ratio is too low for smaller telescopes. We have made photometric observations of NGC 5548 in four filters (a custom-made Hα10 filter, the Strömgren y filter, the Johnson/Cousins V filter and the Johnson/Cousins R filter) in order to evaluate a photometric methodology for determining the lag time between the variations observed in the continuum and the Hα emission from the broad-line region (BLR) gas. This time delay represents the mean light travel time to the BLR and is therefore a measurement of the mean BLR radius. Multiple JAVELIN analyses of the three continuum light curves (y, V, and R), relative to the light curve from the Hα10 filter yields a value for τ = 3.3 ± 0.1 days. Adopting a value of f = 5.5, along with a single-epoch spectroscopic measurement from Park et of Δv = 4354±25 km/s, enables us to estimate a black hole mass of M_BH = 67.2±2.2x10^6 M_sun.

We present a method for solving the Einstein-Maxwell equations in a five dimensional, asymptotically flat, black hole spacetime with three commuting Killing vector fields. In particular, we show that by reducing the dimension of the Einstein-Maxwell equations in a Kaluza-Klein like manner we can determine the components of the metric and vector potential which lie in the direction of the Killing vector fields. These components are determined by nine scalar fields each of which satisfy a partial differential equation in two variables. These equations take the form of an elliptic operator set equal to a nonlinear source. We find evidence that particular combinations of these fields satisfy Dirichlet boundary conditions, and are well suited to numerical solution using Green functions. Using this method we generate numerical solutions to the 4+1 Einstein-Maxwell equations corresponding to charged generalizations of the Myers-Perry solution. We also discover symmetry relations among the scalar equations which constrain their functional forms and posit the existence of two rigidity-theorem-like relations for electrovac spacetimes and sketch how their use generalizes our method to N+1 dimensions.

Charged or rotating black holes possess an inner horizon beyond which determinism is lost. However, the strong cosmic censorship conjecture claims that even small perturbations will turn the horizon into a singularity beyond which the spacetime is inextendible, preventing the loss of determinism. Motivated by this conjecture, this dissertation studies free scalar quantum fields on various black-hole spacetimes to test whether quantum effects can lead to the formation of a singularity at the inner horizon in cases where classical perturbations cannot. The starting point is the investigation of the behaviour of real-scalar-field observables near the inner horizon of Reissner-Nordström-de Sitter spacetimes. Using semi-analytical methods, we find that quantum effects can indeed uphold the censorship conjecture. Subsequently, we consider charged scalar fields on the same spacetime and observe that a first-principle calculation is essential to accurately describe the quantum effects at the inner horizon. As a first step towards an extension of these results to rotating black holes, we rigorously construct the Unruh state for the real scalar field on slowly rotating Kerr-de Sitter spacetimes. We show that it is a well-defined Hadamard state and can therefore be used to compute expectation values of the stressenergy tensor and other non-linear observables.:1 Introduction 7 2 An introduction to quantum fields and black holes 13 2.1 Notations and conventions . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 A brief introduction to AQFT . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 An introduction to microlocal analysis . . . . . . . . . . . . . . . . . . . 24 2.4 An introduction to black-hole spacetimes . . . . . . . . . . . . . . . . . 28 2.4.1 The Reissner-Nordström-de Sitter spacetime . . . . . . . . . . . 28 2.4.2 The Kerr-de Sitter spacetime . . . . . . . . . . . . . . . . . . . . 32 2.5 Free scalar fields in black-hole spacetimes . . . . . . . . . . . . . . . . . 37 3 Computing the energy flux of the real scalar field 43 3.1 Strong cosmic censorship on RNdS . . . . . . . . . . . . . . . . . . . . 43 3.2 The Klein-Gordon equation on RNdS . . . . . . . . . . . . . . . . . . . 45 3.3 Extension to the charged scalar field on RNdS . . . . . . . . . . . . . . . 52 3.4 The energy flux at the Cauchy horizon . . . . . . . . . . . . . . . . . . . 53 4 The charged scalar field in Reissner-Nordström-de Sitter 63 4.1 The Unruh state for the charged scalar field . . . . . . . . . . . . . . . . 65 4.2 The renormalized current . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.3 The current in the Unruh state - numerical results . . . . . . . . . . . . . 80 4.4 The charged scalar field at the inner horizon . . . . . . . . . . . . . . . . 86 5 The Unruh state on Kerr-de Sitter 97 5.1 Null geodesics in the Kerr-de Sitter spacetime . . . . . . . . . . . . . . . 98 5.2 The Unruh state on Kerr-de Sitter . . . . . . . . . . . . . . . . . . . . . . 107 5.3 The Hadamard property of the Unruh state . . . . . . . . . . . . . . . . . 120 5.3.1 The Hadamard condition in O . . . . . . . . . . . . . . . . . . . 123 5.3.2 The Hadamard condition on M\O . . . . . . . . . . . . . . . . . 128 6 Summary and discussion 139 A Bibliography 143

The astrophysical origins of the rapid neutron-capture process (r-process), which gives rise to roughly half of the elements heavier than iron, has remained a mystery for almost 70 years. The likely violent events, which seed the r-process abundances in our solar system and galaxy, remain uncertain to this day. This is in part due to nuclear physics uncertainties associated with the r-process itself, but mainly due to uncertainties in astrophysics modeling. The discovery of the radioactively-powered kilonova emission from the neutron star merger event GW170817 confirmed the violent deaths of neutron stars as one key site of the r-process in the universe. However, other evidence appears to favor an additional r-process channel that more promptly follows star formation in the universe, such as core-collapse supernovae (CCSNe), i.e. the brilliant births of neutron stars. The two viable sites for the r-process are (1) core-collapse supernovae (CCSNe), which are explosions of massive stars at the end of their lives and (2) compact object mergers, which are violent collisions of stellar remnants formed at the endpoints of stellar evolution. Chapters 2 and 3 of this dissertation present general relativistic magnetohydrodynamic simulations of one potential r-process site associated with CCSNe: the neutrino-driven wind. These outflows are launched from the hot proto-neutron star (PNS) remnant by neutrino-heating above their surfaces, within seconds after the collapse of a massive star. However, previous work has shown that spherically symmetric winds from non-rotating PNS fail to achieve the requisite conditions for a robust r-process. Chapter 2 explores for the first time the combined effects of rapid rotation and strong gravity of the PNS on the wind properties. Chapter 3 explores the impact of a dynamically strong ordered magnetic field on the properties of non-rotating PNS winds. The wind in both cases is simulated in a controlled environment rather than as a part of a self-consistent global CCSNe simulation, to assess the viability of r-process nucleosynthesis as a function of PNS properties (neutrino energies/luminosities, rotation rate, magnetization). We find that rapid rotation allows for outflows that are ~10% more neutron-rich in the equatorial region, where the mass loss rate is roughly an order of magnitude higher than that of otherwise equivalent non-rotating models. The birth of very rapidly spinning neutron stars may thus be a site for the production of light r-process nuclei (38 < Z < 47). For PNSs with sufficiently strong magnetic fields (such that magnetic pressure exceeds gas pressure above the PNS surface), we find that equatorial outflows are trapped by the magnetic field in a region near the surface, and therefore receive additional neutrino heating relative to a freely-expanding unmagnetized wind. This allows a modest fraction of the wind material to achieves entropies high enough to synthesize 2nd peak r-process elements via an alpha-rich freeze-out mechanism. The final chapter explores the interplay between the r-process and the dynamics of compact object merger ejecta. Gravitational wave observatories are expected to detect several additional binary neutron star (BNS) and black hole-neutron star (BHNS) mergers in current and future observing runs, some of which may be accompanied by electromagnetic counterparts such as kilonovae. However, distinguishing more distant BNS from BHNS mergers based on their associated gamma-ray bursts (GRB), has proven tricky. This chapter presents a calculation of the effects of r-process heating on the dynamics of tidal ejecta from BNS and BHNS mergers. In particular we explore whether late-time fall-back of weakly bound debris created during the merger to the central black hole remnant, can explain the temporally extended X-ray emission observed following several merger GRB on timescales of several seconds to minutes. As a result of the different impact that r-process heating has depending on the composition of the ejecta and the mass of the black hole, a method to differentiate BHNS from BNS mergers, based on their extended X-ray emission, is proposed.

In this thesis, we consider three aspects of black holes. First, we examine a black hole boosted through a uniform magnetic field. We find that it can acquire an electric charge, just as a spinning black hole in an ambient magnetic field can, though the gravito-electrodynamics upstage naive arguments about screening electric fields in determining the value of the charge accrued. We study the chaotic behavior of the charged particles via their fractal basin boundaries. Second, we study the vanishing of Love numbers for black holes from a geometric perspective and connect it to the existence of quasinormal modes in de Sitter space. Behind each phenomenon is a ladder structure with a geometric/representation-theoretic origin which makes it possible to connect the asymptotic behavior of solutions at different boundaries. Third, we model the formation of a black hole in dRGT massive gravity in a de Sitter background with a collapsing homogeneous and pressureless ball of dust or ``star''. We focus on several choices of parameters corresponding to models of interest. We compute the position of the apparent horizon where it crosses the surface of the star, the Ricci curvature at the boundary, and the finite correction to the curvature of the apparent horizon due to the graviton mass. We argue that our collapsing solutions cannot be matched to a static, spherically symmetric vacuum solution at the star's surface, providing further evidence that physical black hole solutions in massive gravity are likely time-dependent.

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