In the following we explain how to derive the atomic oxygen gas mass from prompt emission level population. To estimate the mass of oxygen gas we consider the excitation of atomic oxygen to its first fine structure level in the absence of a collisional partner. This situation happens in very low density environments such as debris discs. The main mechanism involved is the so-called prompt emission and fluorescence. The prompt emission involves the absorption of a photon from the star or from the dust at the precise wavelength of the atomic emission, and subsequent re-emission. To model the emission, we assume that the ground state is the most populated. The population at steady-state for level is given by: (B.1)Assuming that only the first two levels are populated (n = n0 + n1), (B.2)since g0B01 = g1B10 and B10 = (c2/2hν3)A10, the fractional population is (B.3)For OI we have g0 = 5, g1 = 3. J10 is computed using the distance-dilluted stellar flux in the Rayleigh-Jeans regime at 63 μm: (B.4)where R is the distance to the star and R∗ the stellar radius. We obtain J10 = 2.273 × 10-13 × (1 AU/ R(AU))2 erg s-1 cm-2 Hz-1 sr-1, and the fractional population is thus: x = 8.67 × 10-5
The effect of including additional excitation paths is negligible. We compare this with a situation when the emission is produced at 1 AU from the star. For example, if we include all main fluorescence pumping paths ( → → , → → , and → → → ), the final mass of oxygen is M([OI] ) = 0.0247 M⊕, compared to M([OI] ) = 0.025 M⊕ obtained when we only include the main excitation path.
© ESO, 2012