Relativistic Superfluid Turbulence in Neutron Star Crusts: A Comprehensive Analytical Framework for Understanding Pulsar Glitch Phenomena

This Thesis presents a comprehensive analytical framework for understanding pulsar glitch phenomena through the lens of relativistic superfluid turbulence in neutron star crusts, synthesizing established theoretical foundations from nuclear physics, general relativity, and quantum fluid dynamics with observational data from 537 recorded glitch events across 189 pulsars, including detailed case studies of the Vela pulsar (PSR B0833-45) with twenty glitches since 1969 exhibiting fractional frequency increases Δν/ν ranging from 1. 2 × 10⁻⁷ to 3. 1 × 10⁻⁶ and the Crab pulsar (PSR B0531+21) with twenty-five glitches showing Δν/ν ≈ 10⁻⁸, drawing upon continuous monitoring from the Jodrell Bank Observatory, Parkes 64-meter radio telescope, and the now-decommissioned Arecibo Observatory. The microphysical structure of neutron star crusts, extending from the outer crust at densities below 10¹¹ g/cm³ through the inner crust at densities up to 2 × 10¹⁴ g/cm³ where neutron superfluid coexists with nuclear lattices, provides the physical setting for quantized vortex lines with circulation κ = h/2mₙ = 2. 0 × 10⁻³ cm²/s and equilibrium surface density nᵥ = 2Ω/κ ≈ 10¹⁷ lines for typical 10 Hz pulsars, with inter-vortex spacing dᵥ ≈ 3 × 10⁻³ cm and pinning forces from nuclear clusters calculated at 10¹⁵ to 10¹⁶ dyn/cm based on Hartree-Fock-Bogoliubov calculations with Skyrme interactions. The general relativistic framework employs the Tolman-Oppenheimer-Volkoff equation dp/dr = -G (ρ + p/c²) (m + 4πr³p/c²) / (r² (1 – 2Gm/rc²) ) for hydrostatic equilibrium in curved spacetime, yielding compactness parameters 2GM/Rc² = 0. 2 to 0. 4 for canonical 1. 4 solar mass neutron stars, with the covariant Gross-Pitaevskii equation □gΨ + (mₙ²c²/ħ²) Ψ + λ|Ψ|²Ψ = 0 describing the superfluid condensate in the metric derived from TOV solutions.