# A Comparison of Grid-Based and SPH Binary Mass-Transfer and Merger Simulations

## TL;DR

This study compares grid-based and SPH simulations of binary star mergers, analyzing their outcomes, differences in evolution times, and effects of different energy equations on the stability and dynamics of the systems.

## Contribution

It provides a detailed comparison of two numerical methods for simulating binary mergers, highlighting their agreement and differences under various initial conditions and physics assumptions.

## Key findings

- Agreement in final outcomes and intermediate stages when initial conditions are matched.
- SPH tends to produce higher mass transfer rates and faster evolution.
- The ideal gas equation of state destabilizes binaries more than the polytropic one, especially in grid simulations.

## Abstract

Currently there is great interest in the outcomes and astrophysical implications of mergers of double degenerate binaries. In a commonly adopted approximation, the components of such binaries are represented by polytropes with an index n=3/2. We present detailed comparisons of stellar mass-transfer and merger simulations of polytropic binaries that have been carried out using two very different numerical algorithms --- a finite-volume "grid" code and a smoothed-particle hydrodynamics (SPH) code. We find that there is agreement in both the ultimate outcomes of the evolutions and the intermediate stages if the initial conditions for each code are chosen to match as closely as possible. We find that even with closely matching initial setups, the time it takes to reach a concordant evolution differs between the two codes because the initial depth of contact cannot be matched exactly. There is a general tendency for SPH to yield higher mass transfer rates and faster evolution to the final outcome. We also present comparisons of simulations calculated from two different energy equations: in one series we assume a polytropic equation of state and in the other series an ideal gas equation of state. In the latter series of simulations an atmosphere forms around the accretor which can exchange angular momentum and cause a more rapid loss of orbital angular momentum. In the simulations presented here, the effect of the ideal equation of state is to de-stabilize the binary in both SPH and grid simulations, but the effect is more pronounced in the grid code.