I am working on a Type IIP supernova, for which I would like to estimate the plateau length. Note that this is a very handwavy analysis; I'm just building expectations and intuition and seriously abusing some models. A Type IIP light curve is powered by the recombination of shocked hydrogen in the ejected envelope of the star. Depending on the amount of hydrogen present, this mechanism can power a distinctive plateau (P) in the light curve for ~100 days.
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| Light curves of Type IIP and Type IIL supernovae. |
What I'm interested in is the following: if we've already settled onto the plateau, can we estimate how long the supernova is likely to maintain its plateau before dropping on the Ni-56 powered tail? Significant work has been invested in the theoretical study of IIP supernovae and their plateaus. In particular I turn to the following paper by Goldberg, Bildsten & Paxton:
We present advances in modeling Type IIP supernovae using MESA for evolution to shock breakout coupled with STELLA for generating light and radial velocity curves. Explosion models and synthetic light curves can be used to translate observable properties of supernovae (such as the luminosity at day 50 and the duration of the plateau, as well as the observable quantityET , defined as the time-weighted integrated luminosity that would have been generated if there was no56Ni in the ejecta) into families of explosions which produce the same light curve and velocities on the plateau. These predicted families of explosions provide a useful guide towards modeling observed SNe, and can constrain explosion properties when coupled with other observational or theoretical constraints. For an observed supernova with a measured56Ni mass, breaking the degeneracies within these families of explosions (ejecta mass, explosion energy, and progenitor radius) requires independent knowledge of one parameter. We expect the most common case to be a progenitor radius measurement for a nearby supernova. We show that ejecta velocities inferred from the Fe IIλ 5169 line measured during the majority of the plateau phase provide little additional information about explosion characteristics. Only during the initial shock cooling phase can photospheric velocity measurements potentially aid in unraveling light curve degeneracies.
Let's examine Figure 4:
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| Reproduced from Goldberg et al. |
Let's say we have constraints on the radius from shock cooling, which pins the progenitor radius to ~250 Rsun. We also have a day 50 luminosity of about ~ 6×1034 W ~ 6×1041 erg/s. From Figure 4, we are likely in something more similar to the right panel, with a small radius. This is on the low end based on the plot, but we may be affected by our smaller radius. The canonical IIP plateau luminosity (Podov) scales with progenitor radius; since our progenitor radius is ~40% smaller than the estimates here, that could have a significant effect. If we correct for this 40% effect (which is a significant oversimplification) it places us right in the middle of the spread (~1.5×1042 erg/s), with a mostly flat but slightly declining light curve (versus the severe dip). If we compare to our 50 day light curve, we don't observe a dip; this is a good sanity check that we're looking at roughly the right parameters. This narrows our range of possible plateau lengths quite a bit--we've gone from 90-150 days to 110-130 days. If we trust the corrected luminosity value too much, we're leaning a bit more to the 110 day models. Based on this, we could expect a plateau on the short side of 110 days; based on the time of peak, I'm anticipating a falloff sometime around the end of March/start of April.
Previously on this blog:
