A Relativistic Radiative Hydrodynamic Framework for the Nuclear Impact Hypothesis: Implications for Proto-Stellar Ignition and Planetary Ejection

This manuscript delineates a relativistic radiative hydrodynamic framework underpinning the Nuclear Impact Hypothesis, which posits that a hypervelocity nuclear impactor (\( v_0 \gtrsim 10^3 \) km s\( ^{-1} \)) could precipitate proto-solar ignition and the ejection of nascent planetary embryos through asymmetric magnetocentrifugal thrust in a radiation-dominated proto-stellar milieu. The formulation integrates Poisson's equation for gravitational potentials, special relativistic momentum conservation, augmented Lorentz forces in magnetized plasmas, three-temperature radiation hydrodynamics, and relativistic Rankine-Hugoniot shock relations, extensible to heterogeneous stellar configurations. High-resolution simulations, leveraging cubic interpolation of helioseismically constrained Standard Solar Model profiles (deviations \( \lesssim 8\% \)), delineate penetration depths \( \delta \lesssim 0.05 R_\odot \) antecedent to electromagnetic disassembly and ablation-mediated fragmentation within neutral proto-stellar cores. The posited ejection paradigm, actuated by magnetocentrifugal thrust \( a_\mathrm{thrust} = \omega^2 r (B^2 / 4\pi \rho) \gtrsim 10^{-3} c^2 / R_\odot \) from proto-stellar rotation and magnetism, engenders egress from \( r_0 = 0.1 R_\odot \) at asymptotic velocities \( v_\infty \sim 40 \) km s\( ^{-1} \), consonant with orbital circularization and radiative equilibration timescales in archetypal systems. Variance-based global Sobol sensitivity analysis (\( N=2048 \)) underscores the preeminence of initial velocity (\( S_{v_0}=0.65 \)) and thrust (\( S_{a_\mathrm{thrust}}=0.58 \)), corroborated by Bayesian propagation affording \( \mu_\delta = 0.048 \pm 0.012 R_\odot \). Falsifiability anchors to anticipated Gaia DR4 transients and meteoritic isotopic disequilibria. Anchored in solar wind plasma diagnostics \citep{kasper2016sweap} and relativistic merger hydrodynamics \citep{hu2024energetic}, this rigorous construct hypothesizes shock-fostered thermonuclear ignition (\( \dot{E}_\mathrm{diss} \sim 10^{22} \) erg cm\( ^{-3} \) s\( ^{-1} \)) and density-discriminatory embryo expulsion (\( \rho > 10 \) g cm\( ^{-3} \)), proffering mechanistic insights into Solar System ontogeny and resilience paradigms for interstellar instrumentation.