# Astrophysics Research Centre

## School of Mathematics and Physics

In Jerkstrand+2014 a method to estimate the O mass from [O I] 6300, 6364 and [O I] 5577 is outlined. One can apply this method once the oxygen lines have begun transitioning to become optically thin (the 6364 component should be distinctly weaker than the 6300 component).

1. Determine the [O I] 6300, 6364 luminosity
2. Determine the [O I] 5577 luminosity by a two-component fit ([Fe II] 5528 needs consideration, see Fig 3).
3. Estimate the temperature range from Eq. 2, using the constraint beta1/beta2 = 1-2 (if the 6300/6364 ratio is clearly in the 3:1 limit use 1, otherwise 1.5)
4. Estimate the O I mass from Eq. 3, with beta_6300 = 0.5 (or other value determined from the 6300/6364 ratio).

The formula asssumes LTE which according to typical IIP models holds to around ~250d post explosion (the upper level of 5577 then starts falling out of LTE). After that time, the mass obtained with the formula is an upper limit only (but this is often quite useful).

The multi-zone model best fitting the [O I] lines in 2012aw has an (optically emitting) O mass of 0.3 Msun. The analytic formula gave instead an O mass of 0.6pm 0.2 Msun. It is desirable that some degree of consistency between the two methods emerges and here it is better than factor 2. However: a multizone model could have a wrong O mass with a wrong distribution and still give match the observed lines (or vice versa if something in the spectral formation physics is wrong). The analytic formula could indicate an incorrect value if its assumption of uniform and homogenous emission of the oxygen is not a good approximation (and the necessary beta value settings introduces errors too).