Bayesian Estimation of Spectroscopic Parameters: Application to the Atomic Nitrogen Bound-Bound System
Atomic nitrogen bound-bound radiation is a major component of the radiative heat flux on hypersonic vehicles entering nitrogen-dominated atmospheres, yet its prediction is limited by substantial parametric uncertainty in the published Einstein coefficients and Stark broadening coefficients. In the present study, these spectroscopic parameters are inferred and their uncertainty is quantified through Bayesian inversion of equilibrium spectral radiance measured in the NASA Ames Electric-Arc Shock Tube for two shots of the Test 62 campaign at shock speeds of 10.32 and 10.72 km/s. The inference is restricted to the post-shock equilibrium region, where the Boltzmann assumption closes the species population degree of freedom. The residual uncertainty in the post-shock temperature and species number densities is incorporated as a coupled nuisance parameter distribution. A hybrid principal component analysis and polynomial chaos expansion surrogate model and a likelihood formulated jointly over the two shots enable tractable Markov chain Monte Carlo sampling across multiple wavelength regions. Eighteen parameters in total, ten Einstein coefficients and eight Stark broadening coefficients, are inferred across eight wavelength regions, with posterior uncertainties significantly reduced relative to the prior literature bands. Forward propagation of the joint posterior through the stagnation-line flow field around a 3 m radius sphere at entry velocities of 10, 12, and 14 km/s demonstrates a reduction in the standard deviation of the predicted radiative heat flux by approximately a factor of five compared with the prior, in particular at 14 km/s, it drops from 10.4 to 1.94 W/cm$^{2}$.