Time dependent models of accretion disks 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 disks produced by the tidal disruption of a white dwarf (WD) by a binary neutron star (NS) companion. Nuclear reactions in the disk midplane burn the WD matter to increasingly heavier elements at sequentially smaller radii, releasing substantial energy which can impact the disk dynamics. A model for disk outflows is employed, by which cooling from the outflow balances other sources of heating (viscous, nuclear) in regulating the Bernoulli parameter of the midplane to a fixed value $\lesssim 0$. We perform a comprehensive parameter study of the compositional yields and velocity distributions of the disk outflows for WDs of different initial compositions. For C/O WDs, the radial composition profile of the disk evolves self-similarly in a quasi-steady-state manner, and is remarkably robust to model parameters. The nucleosynthesis in helium WD disks does not exhibit this behavior, which instead depends sensitively on factors controlling the disk midplane density (e.g. the strength of the viscosity, $\alpha$). By the end of the simulation, a substantial fraction of the WD mass is unbound in outflows at characteristic velocities of $\sim 10^9~{\rm cm~s}^{-1}$. The outflows from WD-NS merger disks contain $10^{-4}-3 \times 10^{-3} M_\odot$ of radioactive $^{56}$Ni, resulting in fast ($\sim$ week long) dim ($\sim10^{40}~{\rm erg~s}^{-1}$) optical transients; shock heating of the ejecta by late time outflows may increase the peak luminosity to $\sim 10^{43}~{\rm erg~s}^{-1}$. The accreted mass onto the neutron star is probably not sufficient to induce gravitational collapse, but may be capable of spinning up the NS to periods of $\sim 10~{\rm ms}$. This is a new possible channel for forming isolated recycled pulsars.