Early supernova emission -- logarithmic corrections to the planar phase

TL;DR

This paper revises the understanding of early supernova emission by showing the diffusion wave propagates logarithmically into the envelope, significantly affecting the predicted temperature and luminosity during the planar phase.

Contribution

It introduces a self-similar solution revealing a logarithmic correction to the diffusion wave propagation, challenging previous fixed-mass coordinate assumptions in supernova early emission models.

Findings

Luminosity originates from regions with higher density than previously thought.

The observed temperature decreases by two orders of magnitude during the planar phase.

The model predicts out-of-thermal-equilibrium emission for blue supergiant and Wolf-Rayet supernovae.

Abstract

When the shock wave generated in a supernova explosion breaks out of the stellar envelope, the first photons, typically in the X-ray to UV range, escape to the observer. Following this breakout emission, radiation from deeper shells diffuses out of the envelope as the supernova ejecta expands. Previous studies have shown that the radiation throughout the planar phase (i.e., before the expanding envelope has doubled its radius) originates in the same mass coordinate, called the `breakout shell'. We derive a self-similar solution for the radiation inside the envelope, and show that this claim is incorrect, and that the diffusion wave propagates logarithmically into the envelope (in Lagrangian sense) rather than remaining at a fixed mass coordinate. The logarithmic correction implies that the luminosity originates in regions where the density is $\sim 10$ times higher than previously thought, where the photon production rate is increased and helps thermalization. We show that this result has significant implications on the observed temperature. In our model, the radiation emitted from blue supergiant and Wolf-Rayet explosions is still expected to be out of thermal equilibrium during the entire planar phase, but the observed temperature will decrease by two orders of magnitude, contrary to previous estimates. Considering the conditions at the end of the planar phase, we also find how the temperature and luminosity transition into the spherical phase.