  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.
