White Dwarf Mergers on Adaptive Meshes I. Methodology and Code Verification

TL;DR

This paper introduces a new adaptive mesh refinement hydrodynamics code, CASTRO, for simulating white dwarf mergers, addressing the challenge of conserving energy in complex gravitational and rotational systems relevant to Type Ia supernovae.

Contribution

It presents the first detailed methodology and implementation of adaptive mesh refinement for simulating white dwarf mergers with energy conservation considerations.

Findings

Demonstrated the code's ability to model large mass advection over long timescales.

Validated the numerical methods with standard test problems.

Discussed improvements in energy conservation for gravitational and rotational coupling.

Abstract

The Type Ia supernova progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf merger scenario, which has the potential to naturally explain many of the observed characteristics of Type Ia supernovae. To date there have been relatively few self-consistent simulations of merging white dwarf systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.