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Observations and modeling of H_2 fluorescence with partial frequency redistribution in giant planet atmospheres

Partial frequency redistribution (PRD), describing the formation of the line profile, has negligible observational effects for optical depths smaller than ~10^3, at the resolving power of most current instruments. However, when the spectral resolution is sufficiently high, PRD modeling becomes essential in interpreting the line shapes and determining the total line fluxes. We demonstrate the effects of PRD on the H_2 line profiles observed at high spectral resolution by the Far-Ultraviolet Spectroscopic Explorer (FUSE) in the atmospheres of Jupiter and Saturn. In these spectra, the asymmetric shapes of the lines in the Lyman (v"- 6) progression pumped by the solar Ly-beta are explained by coherent scattering of the photons in the line wings. We introduce a simple computational approximation to mitigate the numerical difficulties of radiative transfer with PRD, and show that it reproduces the exact radiative transfer solution to better than 10%. The lines predicted by our radiative transfer model with PRD, including the H_2 density and temperature distribution as a function of height in the atmosphere, are in agreement with the line profiles observed by FUSE. We discuss the observational consequences of PRD, and show that this computational method also allows us to include PRD in modeling the continuum pumped H_2 fluorescence, treating about 4000 lines simultaneously.