School of Physics - Theses
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ItemNon-Equilibrium Processes in Neutron Stars and Ultracold Gases( 2023-06)From the booms and busts of the economy to the schooling of fish, non-equilibrium phenomena are ubiquitous and appear at all scales. However, non-equilibrium systems have proven infamously difficult to model and understand. In this thesis we present two different of non-equilibrium systems, one classical and one quantum mechanical, and thoroughly investigate their behaviour: (i) the repeated localised mechanical failure of the crust of a spinning down neutron star, and (ii) the dynamics of quenched few-body quantum systems. As an isolated neutron star spins down the centrifugal force weakens but the gravitational force doesn't change. This results in the crust changing shape and accruing mechanical strain to the point of failure. Mechanical failure locally deforms the crust and dissipates and redistributes strain. This can result in avalanches of further failures as one region of the crust failing may prompt a neighbouring region to fail. The evolving crust is a classical far-from-equilibrium system capable of avalanche behaviour like the classic sandpile model. The statistics of crustal failure events are of much interest due to their suggested relevance to transient phenomenon such as glitches or fast radio bursts. We present a cellular automaton designed to describe the evolution of the crust over spin down and the effects of local failure. This automaton describes when and where crustal failures occur and how large they are. Additionally this automaton describes the failure-induced change in the shape of the crust. Using this automaton we find that the star needs to be born spinning over \approx 750 Hz to accumulate sufficient strain to fail at all, that the waiting-times between subsequent events are distributed as a power-law spanning seven orders of magnitude, and that the ellipticities of isolated neutron stars are in the range 10^{-13} to 10^{-12}, among many other results. It has been suggested that the mechanical failure of the crust is the cause (or result) of a variety of transient phenomena such as glitches or gamma ray bursts. This model provides predictions of the statistical behaviour of crustal failure which can be compared to the observed behaviour of these transients. Additionally, the model describes the shape of the crust and the rotational frequency at all times which allows for the wave strain of emitted gravitational waves to be calculated with implications for searches for continuous gravitational wave sources. Cold quantum gases have attracted a great deal of experimental and theoretical interest thanks to the high degree of experimental control possible over them which makes them excellent testing grounds of quantum theory. Additionally, they are excellent tools for the study of quantum thermalisation. We consider a few interacting particles initially in some equilibrium state and suddenly change (quench) the interaction strength which kicks the system away from equilibrium. Specifically, we consider systems of two and three bodies of arbitrary mass and various particle symmetries interacting via a contact interaction in an isotropic three-dimensional harmonic trap. We take particular interest in quenching between the weakly and strongly interacting regimes and the following far-from-equilibrium post-quench evolution. We describe the non-equilibrium post-quench evolution of the system by analytically and semi-analytically calculating two observables: the Ramsey signal and the particle separation. We are able to calculate these quantities for the two-body system with arbitrary particle masses for any quench in interaction strength. Additionally, we extend these calculations to three-body systems of two identical fermions and a distinct particle or three identical bosons where the quench is between the strongly and weakly interacting regimes. In the two-body case we find when quenching from weak to strong interactions the particle separation oscillates periodically between \approx0.85a_{\mu} and \approx1.15a_{\mu}, where a_{\mu} is the simple harmonic oscillator length-scale. For the same quench in the three-body case the particle separation varies depending on the specifics of the system. For the fermionic case the particle separation oscillates periodically, peaking at \approx 2.18a_{\mu} with the mass ratio of the two species determining the minimum separation. For the bosonic case the oscillation is aperiodic. Both the maximum and minimum particle separation are determined by a quantity called the three-body parameter, but particle separation generally oscillates between \approx a_{\mu} and \approx 2a_{\mu}. However, in all cases when quenching from strong to weak interactions the calculations of the particle separation do not converge. This divergence is present whatever the initial state, mass ratio, particle symmetry, etc. and is present only for this particular quench from strong to weak interactions. We investigate possible sources of this divergence and future avenues of research into its causes. Finally, we note that these theoretical predictions of Ramsey signal and particle separation are experimentally testable with current techniques.
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ItemSpin-down signatures of young neutron stars( 2022)The spin down of neutron stars has been invoked to explain a wide variety of electromagnetic and gravitational-wave signals. This thesis explores two different signals associated with the spin down of neutron stars, one electromagnetic signal and one gravitational-wave signal. Binary neutron star coalescences, confirmed as the progenitor of at least some short Gamma-ray bursts (sGRBs) in 2017, are predicted to form either a black hole or a highly magnetized neutron star. Up to 20% of sGRBs observed by the Neil Gehrels Swift telescope display prolonged X-ray emission, sometimes called a ``canonical'' afterglow, consisting of three phases: an initial power-law luminosity decay; a 'plateau', lasting between 10 s and 105 s, during which the X-ray luminosity is approximately constant; and a final power-law decay. Previous authors have noted that the evolution of the canonical light curve is broadly consistent with the expected spin-down luminosity of a neutron star. Key ideas from analytic, one-zone models of plerions (also called pulsar wind nebulae) can be used to model the evolution of a synchtrotron nebula fuelled by the the spin-down luminosity of a neutron star formed in an sGRB. An analytic expression for time-dependent, spatially-averaged electron energy distribution in the nebula is found and used to calculate the light curve and the point-in-time spectra. The light curves predicted by the plerionic model are consistent with the shape and luminosity of the X-ray light curves and reproduce the observed correlation between plateau duration and luminosity (i.e. brighter plateaux end sooner). Furthermore, Bayesian parameter estimation comparing the point-in-time spectra to time-averaged spectra of six Swift sGRBs with canonical X-ray afterglows and of known redshift allows estimation of the parameters of the neutron-star central engine, including its poloidal field strength Bp and its rotation period P0 at birth, and injection parameters within the shock, including the energy range of the relativistic electrons and their power-law index. All six sGRBs favour a neutron star with Bp ~ 1011 T and P0 ~ s, consistent with the prediction the neutron star should be highly magnetized and rapidly spinning. We also apply the point-in-time spectra to four time-averaged spectra taken at four separate epochs in the X-ray afterglow of GRB130603B and infer the evolution of the magnetic field in the synchrotron bubble B. We find the evolution of B is slower than the expected evolution of the far-field limit of the stellar magnetic field. Rotating, non-axisymmetric neutron stars spin down via the emission of continuous gravitational waves which may be detectable by current terrestrial interferometers such as the advanced Laser Interferometric Gravitational-wave Observatory (LIGO) and advanced Virgo. Young core-collapse supernova remnants are likely hosts of young neutron stars and are common targets for wide-band directed searches for continuous gravitational waves targeting non-pulsating neutron stars. In this work, we present the results for two searches for continuous waves from neutron stars in young supernova remnants using a hidden Markov model (HMM). The HMM tracking scheme models the frequency evolution as a random walk with secular spin down and remains sensitive in the presence of stochastic spin wandering similar to that observed in pulsar timing observations. A search targeting twelve neutron stars in young supernova remnants in the second observing run (O2) of advanced LIGO using an HMM tracking scheme identifies 1012 potential candidates, 18 of which survive a series of standard vetoes. Further assessment of the 18 survivors based on their dependence on sky position and Doppler modulation confirms they are all consistent with terrestrial noise. A second search, conducted with the the LIGO-Virgo-KAGRA (LVK) collaboration, targets fifteen neutron stars in young supernova remnants in the first half of the third observing run (O3a) of advanced LIGO and advanced Virgo using three search pipelines, including an HMM tracking scheme, and reports no candidates consistent with an astrophysical origin after a rigorous veto and follow-up process. The HMM tracking scheme sets the first 95% confidence limits on gravitational-wave strain, h095%, for these targets with a random-walk signal model, reaching a sensitivity of h095% = 2.64 x 10-25 at 172 Hz for G353.6-0.7. The constraints on h095% are converted to upper limits on neutron-star ellipticity below 10^-5 above 150 Hz and constrain the maximum amplitude of internal r-mode oscillations below 10^-3 above 150 Hz.