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lecture notes9

There are two major circumstances where this is

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Unformatted text preview: ally since one sees a discrete jump in the continuum. The ratio of the continuum jump to the Balmer lines can thus be used to estimate nebular temperature. D. TWO PHOTON CONTINUUM Finally, we come to the hydrogen 2 ­photon continuum, which arises from the decay: H(2s) → H(1s) + γ + γ . The total energy of the two photons is hνLyα. We suppose that the energy is split in the ratio y:1 ­y with probability Π(y). This probability is normalized: € 4 1 ∫ Π( y )dy = 2, 0 since there are 2 photons emitted. The rate of 2 ­photon decays per unit volume per unit time is then: € Π( y ) jν (2γ ) = hν ∑ C(n' ' l' ',2s)α n'' l '' ne n p . ν Lyα n '' l '' Typically ~30% of the recombinations end at 2s, so the luminosity in the 2 ­photon decays is of the same order of magnitude as that in the Balmer lines. The continuum however ranges down to a€ inimum wavelength of 1216 Å, with half of the photons (and most of the m energy) emerging at λ < 2432 Å. Thus the 2 ­photon decay can be the dominant UV continuum emission mechanism. E. COLLISIONS Up until now, we have treated recombination as a process with one proton and one electron that form an atom that then decays in isolation. At high density, it is possible for the atom to undergo collisions before it decays. There are two major circumstances where this is possible: The 2s state is metastable, and its unusually long lifetime makes it more likely than other states to suffer a collision before it decays. The high ­n states are geometrically very large (~a0n2), and are often long ­lived (due to the low frequencies of the photons they emit when they decay). In the case of 2s, the lifetime is 0.1 s, the typical cross section of an atom is 10−15 cm2, and the typical...
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