Importance of Time-dependence in the Rate Equations in SN Type II Atmosphere and Estimation of Recombination Time

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We address the issue of importance of time dependence in the rate equations in the atomospheres of Type II supernovae on the plateau. Recently, Utrobin and Chugai (2006) argued that time-dependence is required to obtain the correction ionization state. The showed that they could better reproduces the Balmer lines in SN 1987A by including time-dependent rate equations However, there are many degenerate ways to produce stronger Balmer lines on the plateau, for example, using a more complex density structure than just a single power-law. Utrobin and Chugai's argument that the recombination time is long compared to the age of the supernova is based on a two-level hydrogen atom model. However, supernova atmospheres include multilevel atoms and hence more lines and electron donors could affect the ionization state and hence the recombination time. We calculate the recombination time from our radiative transfer code PHOENIX from fundamental principles by just adding up the net continuum transitions for each bound state treated in NLTE. We treat H, He in NLTE to start with and then add other elements such as Fe (which are all present in LTE) into NLTE as we proceed. We compare this recombination time to a typical type II supernova on the plateau to access the importance of time dependence in rate equations.

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