Time-dependent models of accretion discs with nuclear burning following the tidal disruption of a white dwarf by a neutron star

We construct time-dependent one-dimensional (vertically averaged) models of accretion discs produced by the tidal disruption of a white dwarf (WD) by a binary neutron star (NS) companion. Nuclear reactions in the disc mid-plane burn the WD matter to increasingly heavier elements at sequentially smaller radii, releasing substantial energy which can impact the disc dynamics. A model for disc outflows is employed, by which cooling from the outflow balances other sources of heating (viscous, nuclear) in regulating the Bernoulli parameter of the mid-plane to a fixed value ≲0. We perform a comprehensive parameter study of the compositional yields and velocity distributions of the disc outflows for WDs of different initial compositions. For C/O WDs, the radial composition profile of the disc evolves self-similarly in a quasi-steady-state manner, and is remarkably robust to model parameters. The nucleosynthesis in helium WD discs does not exhibit this behaviour, which instead depends sensitively on factors controlling the disc mid-plane density (e.g. the strength of the viscosity, α). By the end of the simulation, a substantial fraction of the WD mass is unbound in outflows at characteristic velocities of ~10⁹ cm s^-1. The outflows from WD-NS merger discs contain 10^-4-3 × 10^-3 M_⊙ of radioactive ⁵⁶Ni, resulting in fast (~ week long) dim (~10⁴⁰ erg s^-1) optical transients; shock heating of the ejecta by late-time outflows may increase the peak luminosity to ~10⁴³ erg s^-1. The accreted mass on to the NS is probably not sufficient to induce gravitational collapse, but may be capable of spinning up the NS to periods of ~10 ms, illustrating the feasibility of this channel in forming isolated millisecond pulsars.