Exact and approximate expressions of energy generation rates and their impact on the explosion properties of Pair Instability Supernovae

TL;DR

This paper derives exact and approximate energy generation expressions for pair instability supernovae, demonstrating their significant impact on explosion properties and implications for observational detection rates.

Contribution

It provides the first derivation of exact energy conservation expressions for PISNe and compares their effects with approximate formulas used previously.

Findings

Exact expressions differ notably from approximate ones in simulations.

Explosion properties like Ni-56 yield are sensitive to the energy generation formula.

Results influence estimates of PISN detection rates in observations.

Abstract

Energetics of nuclear reaction is fundamentally important to understand the mechanism of pair instability supernovae (PISNe). Based on the hydrodynamic equations and thermodynamic relations, we derive exact expressions for energy conservation suitable to be solved in simulation. We also show that some formulae commonly used in the literature are obtained as approximations of the exact expressions. We simulate the evolution of very massive stars of ~100-320 Msun with zero- and 1/10 Zsun, and calculate further explosions as PISNe, applying each of the exact and approximate formulae. The calculations demonstrate that the explosion properties of PISN, such as the mass range, the 56Ni yield, and the explosion energy, are significantly affected by applying the different energy generation rates. We discuss how these results affect the estimate of the PISN detection rate, which depends on the theoretical predictions of such explosion properties.