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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.
 Winter '08
 Sargent,A

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