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Accurate and Approximate Calculations of Raman Scattering in the Atmosphere of Neptune

Raman scattering by H$_2$ in Neptune's atmosphere has significant effects on its reflectivity for $λ<$ 0.5 $μ$m, producing baseline decreases of $\sim$ 20% in a clear atmosphere and $\sim$ 10% in a hazy atmosphere. Here we present the first radiation transfer algorithm that includes both polarization and Raman scattering and facilitates computation of spatially resolved spectra. New calculations show that Cochran and Trafton's (1978, Astrophys. J. 219, 756-762) suggestion that light reflected in the deep CH$_4$ bands is mainly Raman scattered is not valid for current estimates of the CH$_4$vertical distribution, which implies only a 4% Raman contribution. Comparisons with IUE, HST, and groundbased observations confirm that high altitude haze absorption is reducing Neptune's geometric albedo by $\sim$6% in the 0.22-0.26 $μ$m range and by $\sim$13% in the 0.35-0.45 $μ$m range. We used accurate calculations to evaluate several approximations of Raman scattering. The Karkoschka (1994, Icarus 111, 174-192) method of removing Raman effects from observed spectra is shown to have limited applicability and to undercorrect the depths of weak CH$_4$ absorption bands. The Wallace (1972, Astrophys. J. 176, 249-257) approximation produces geometric albedo values $\sim$5% low as originally proposed, but can be much improved by adding scattering contributions from the vibrational transition. The Pollack et al. (1986, Icarus 65, 442-466) approximation is inaccurate and unstable, but can also be improved greatly by several simple modifications. A new approximation provides low errors for zenith angles below 70°in a clear atmosphere, although intermediate clouds present problems at longer wavelengths.