Early supernova emission -- logarithmic corrections to the planar phase

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.

After first referee report

References in corpus (8)

• Modules for Experiments in Stellar Astrophysics (MESA)
• An optical supernova associated with the X-ray flash XRF 060218
• A neutron-star-driven X-ray flash associated with supernova SN 2006aj
• From Shock Breakout to Peak and Beyond: Extensive Panchromatic Observations of the Type Ib Supernova 2008D associated with Swift X-ray Transient 080109
• The metamorphosis of Supernova SN2008D/XRF080109: a link between Supernovae and GRBs/Hypernovae
• Early-Time Photometry and Spectroscopy of the Fast Evolving SN 2006AJ Associated with GRB 060218
• Relativistic Radiation Mediated Shocks
• SN 2006aj Associated with XRF 060218 At Late Phases: Nucleosynthesis-Signature of A Neutron Star-Driven Explosion

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• The circumstellar material around the Type IIP SN 2021yja
• Revisiting GRB 060218: new insights into low-luminosity gamma-ray bursts from a revised shock breakout model
• Shock Breakout from Stellar Envelopes: The relativistic limit
• An unexplored regime of shock breakout with a distinct spectral signature