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This distribution has a lower cutoff at 3288n2 thz

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Unformatted text preview: perature. For example, at ne = 100 cm−3 (see Table 4.4 of Osterbrock & Ferland): jHα/jHβ = 3.04 (T = 5000 K) … 2.75 (T = 20000 K). 3 In practice, this ratio is often used to estimate dust reddening. As one might expect, the Balmer lines become successively weaker as we move to higher order: Hα:Hβ:Hγ:Hδ ≈ 2.9:1:0.5:0.25 (T = 104 K). The Paschen line intensities are also weaker, jPaα/jHα ≈ 0.12 (although this is in part due to the lower energy per photon). C. FREE BOUND CONTINUUM Continuum radiation is emitted in recombination both via free ­bound transitions and two ­photon decay. We consider free ­bound transitions first. The number of direct recombinations to the nth shell per unit volume per unit time is αnnenp, where n −1 α n = ∑α nl . l= 0 The emissivity (in erg cm−3 s−1 Hz−1) is then € jν = hνα n n e n p Π(ν ) , where Π(ν) is the probability distribution for the frequency of the emitted photon. This distribution has a lower cutoff at 3288n−2 THz corresponding to emission from an electron € that recombines from zero velocity. It has a typical width of order the thermal energy of an electron, Δν~kT/h, and at higher frequencies (more than Δν above the cutoff) it declines exponentially. The total intensities ∫ jν dν of the Balmer, Paschen, etc. continua vary with temperature roughly in proportion to the recombination coefficients (~T−0.5), but their widths Δν are proportional to T. Thus the value of jν contributed by each continuum near its cutoff is proportional to T−1.5 (which makes sense since this is contributed by the slowest ­moving electrons). This continuum contribution can be measured spectroscopic...
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This document was uploaded on 03/08/2014 for the course AY 102 at Caltech.

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