lecture notes9

The geometry and velocity structure of the system are

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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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