Merger of white dwarf-neutron star binaries: Prelude to hydrodynamic simulations in general relativity

TL;DR

This paper models white dwarf-neutron star binaries in Newtonian gravity to predict their evolution, gravitational wave signals, and possible outcomes like collapse or planet formation, informing future relativistic simulations.

Contribution

It constructs equilibrium models of WDNS binaries, analyzes their evolution paths, and estimates their gravitational wave signals and fates, guiding future relativistic studies.

Findings

Binaries terminate at the Roche limit with potential stable or unstable mass transfer.

Estimated number of LISA-resolved binaries undergoing different mass transfer modes.

Possible outcomes include collapse, disk formation, or planet formation from debris.

Abstract

White dwarf-neutron star binaries generate detectable gravitational radiation. We construct Newtonian equilibrium models of corotational white dwarf-neutron star (WDNS) binaries in circular orbit and find that these models terminate at the Roche limit. At this point the binary will undergo either stable mass transfer (SMT) and evolve on a secular time scale, or unstable mass transfer (UMT), which results in the tidal disruption of the WD. The path a given binary will follow depends primarily on its mass ratio. We analyze the fate of known WDNS binaries and use population synthesis results to estimate the number of LISA-resolved galactic binaries that will undergo either SMT or UMT. We model the quasistationary SMT epoch by solving a set of simple ordinary differential equations and compute the corresponding gravitational waveforms. Finally, we discuss in general terms the possible fate of binaries that undergo UMT and construct approximate Newtonian equilibrium configurations of merged WDNS remnants. We use these configurations to assess plausible outcomes of our future, fully relativistic simulations of these systems. If sufficient WD debris lands on the NS, the remnant may collapse, whereby the gravitational waves from the inspiral, merger, and collapse phases will sweep from LISA through LIGO frequency bands. If the debris forms a disk about the NS, it may fragment and form planets.