Modelling supernova line profile asymmetries to determine ejecta dust masses: SN 1987A from days 714 to 3604

The late-time optical and near-IR line profiles of many core-collapse supernovae exhibit a red-blue asymmetry as a result of greater extinction by internal dust of radiation emitted from the receding parts of the supernova ejecta. We present here a new code, DAMOCLES, that models the effects of dust on the line profiles of core-collapse supernovae in order to determine newly formed dust masses. We find that late-time dust-affected line profiles may exhibit an extended red scattering wing (as noted by Lucy et al. 1989) and that they need not be flux-biased towards the blue, although the profile peak will always be blueshifted. We have collated optical spectra of SN 1987A from a variety of archival sources and have modelled the Ha line from days 714 to 3604 and the [O I] 6300,6363 angstrom doublet between days 714 and 1478. Our line profile fits rule out day 714 dust masses >3 x 10(-3) M-circle dot for all grain types apart from pure magnesium silicates, for which no more than 0.07 M-circle dot can be accommodated. Large grain radii (>= 0.6 mu m) are generally required to fit the line profiles even at the earlier epochs. We find that a large dust mass (>= 0.1 M-circle dot) had formed by day 3604 and infer that the majority of the present dust mass must have formed after this epoch. Our findings agree with recent estimates from spectral energy distribution fits for the dust mass evolution of SN 1987A and support the inference that the majority of SN 1987A's dust formed many years after the initial explosion.