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E the distribution of masses of stars that are formed

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Unformatted text preview: sily suppressed by collisions (lower ncr); an estimate of the density (coming next!) is thus also required. The single line may also be dominated by the hottest part of the nebula (due to its Boltzmann factor), hence one may overestimate the mean temperature. The Balmer continuum: As noted previously, the jump in the continuum at 3650Å is due to free ­bound emission as H+ ions recombine to H(n=2). The strength of the jump relative to the Balmer lines increases as we decrease T because more of the recombinations to n=2 come from very low ­energy electrons. Radio continuum: At low frequencies, the radio spectrum due to free ­free emission scales as Iν ∝ ν−0.15 (it is actually logarithmic in ν – see homework). However, at low frequencies (~100 MHz) the emitted radiation exceeds the blackbody spectrum at temperature T (∝ν2). The nebula then begins to absorb its own radiation and appear as a blackbody. B. DENSITY Diagnostics for the density include: Optical emission line ratios: Comparison of emission lines of the same ion and similar excitation energies but different critical density can be used to test for the electron density ne. Of particular use are the doublets where the excited level is fine structure split, e.g. [O II] 3726,3729Å. Fine structure lines: The ratio of IR to optical lines of the same ion (e.g. O III) can be used in a similar way. The optical/IR line ratios typically increase with temperature (Boltzmann again!) and density (since the fine structure excitations are longer ­lived and thus have a lower ncr). Measurement of multiple ratios can enable both T and ne to be computed. Radio recombination lines: Transitions such as H(n=110)H(n=109) give rise to lines in the radio part of the spectrum. If maser effects are small, their emissivity is proportional to nenp times combinations of the departure coefficients (with complicated depend...
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