Hydrodynamical simulation of detonations in superbursts. I. The hydrodynamical algorithm and some preliminary one-dimensional results

TL;DR

This paper introduces a new second-order finite-volume hydrodynamical algorithm for astrophysical detonations, demonstrating its robustness and applying it to simulate carbon detonations relevant to superbursts on neutron stars, revealing their multiscale nature.

Contribution

The paper develops a novel hydrodynamical algorithm inspired by MUSCL, capable of accurately modeling multiscale astrophysical detonations without dimensional splitting.

Findings

The algorithm is robust and reliable for astrophysical detonation simulations.

Carbon detonations are multiscale phenomena with energy release scales much smaller than reaction lengths.

Multi-resolution methods can effectively handle the small reaction lengths in simulations.

Abstract

Aims. This work presents a new hydrodynamical algorithm to study astrophysical detonations. A prime motivation of this development is the description of a carbon detonation in conditions relevant to superbursts, which are thought to result from the propagation of a detonation front around the surface of a neutron star in the carbon layer underlying the atmosphere. Methods. The algorithm we have developed is a finite-volume method inspired by the original MUSCL scheme of van Leer (1979). The algorithm is of second-order in the smooth part of the flow and avoids dimensional splitting. It is applied to some test cases, and the time-dependent results are compared to the corresponding steady state solution. Results. Our algorithm proves to be robust to test cases, and is considered to be reliably applicable to astrophysical detonations. The preliminary one-dimensional calculations we have performed demonstrate that the carbon detonation at the surface of a neutron star is a multiscale phenomenon. The length scale of liberation of energy is $10^6$ times smaller than the total reaction length. We show that a multi-resolution approach can be used to solve all the reaction lengths. This result will be very useful in future multi-dimensional simulations. We present also thermodynamical and composition profiles after the passage of a detonation in a pure carbon or mixed carbon-iron layer, in thermodynamical conditions relevant to superbursts in pure helium accretor systems.