# Mass transfer in white dwarf-neutron star binaries

## TL;DR

This study uses hydrodynamic simulations to analyze mass transfer stability in white dwarf-neutron star binaries, revealing that only systems with low-mass helium white dwarfs undergo stable evolution into ultra-compact X-ray binaries.

## Contribution

The paper introduces a detailed model of angular momentum loss via disc winds in WD-NS binaries, showing its impact on mass transfer stability and binary evolution.

## Key findings

- Only low-mass helium white dwarfs (<0.2 M_sun) undergo stable mass transfer.
- High-mass white dwarfs experience unstable transfer leading to disruption.
- Angular momentum loss is enhanced by disc winds at high mass-transfer rates.

## Abstract

We perform hydrodynamic simulations of mass transfer in binaries that contain a white dwarf and a neutron star (WD-NS binaries), and measure the specific angular momentum of material lost from the binary in disc winds. By incorporating our results within a long-term evolution model we measure the long-term stability of mass transfer in these binaries. We find that only binaries containing helium white dwarfs with masses less than a critical mass of $M_{\rm WD,crit}=0.2\,M_\odot$ undergo stable mass transfer and evolve into ultra-compact $X$-ray binaries. Systems with higher-mass white dwarfs experience unstable mass transfer, which leads to tidal disruption of the white dwarf. Our low critical mass compared to the standard jet-only model of mass loss arises from the efficient removal of angular momentum in the mechanical disc winds which develop at highly super-Eddington mass-transfer rates. We find that the eccentricities expected for WD-NS binaries when they come into contact do not affect the loss of angular momentum, and can only affect the long-term evolution if they change on shorter timescales than the mass-transfer rate. Our results are broadly consistent with the observed numbers of both ultra-compact $X$-ray binaries and radio pulsars with white dwarf companions. The observed calcium-rich gap transients are consistent with the merger rate of unstable systems with higher-mass white dwarfs.