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Unformatted text preview: here is a cross section at line center of: 3λ2 α ALyα
σ (ν ) = Ly/ 2
= 6 × 10−14 T4−1 / 2 cm2 . 3
8π Δν D
This is ~4 orders of magnitude larger than the photoionization optical depth at threshold, so we expect a typical H II region to have an optical depth in Lyman
α of τLyα ≈ 104. Thus €
we confirm our expectation that a Lyman
α photon will scatter in the nebula many times (as will other low
order Lyman lines, although it is possible that Lyman
π et al will escape). It is important to note that for Galactic objects, the intervening neutral ISM scatters Lyman
α photons out of the line of sight. Such objects can be observed if they have high
velocity Lyman
α emission (Doppler
shifted away from the absorption). Thus most of our interest in the appearance of Lyman
α radiation is associated with extragalactic (redshifted) objects or with ISM absorption itself. In the presence of such a large optical depth, one can imagine several ways to lose the photon. In principle, it could random
walk through the nebula to the exterior. Since the mean free path is 10−4 of the size of the nebula, roughly ~108 scatterings would be required to random walk to the edge. When it gets there, of course, there is a neutral region so the photon still does not escape. Rather the photon random
walks in frequency space, i.e. its frequency ν is redistributed at each scattering. There is a probability of order 10−4 that a given scattering occurs off a fast
moving atom that kicks the photon out to a frequency offset with exp(−Δν2/ΔνD2)~10−4. Then the photon sees an optical depth of only τ~1 and escapes the nebula. The frequency at which the photon emerges is ν = ν Lyα...
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 Winter '08
 Sargent,A

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