Merger of a White Dwarf-Neutron Star Binary to $10^{29}$ Carat Diamonds: Origin of the Pulsar Planets

Abstract

We show that the merger and tidal disruption of a C/O white dwarf (WD) by a neutron star (NS) binary companion provides a natural formation scenario for the PSR B1257+12 planetary system. Starting with initial conditions for the debris disk produced of the disrupted WD, we model its long term viscous evolution, including for the first time the effects of mass and angular momentum loss during the early radiatively inefficient accretion flow (RIAF) phase and accounting for the unusual C/O composition on the disk opacity. For plausible values of the disk viscosity $α\sim 10^{-3}-10^{-2}$ and the RIAF mass loss efficiency, we find that the disk mass remaining near the planet formation radius at the time of solid condensation is sufficient to explain the pulsar planets. Rapid rocky planet formation via gravitational instability of the solid carbon-dominated disk is facilitated by the suppression of vertical shear instabilities due to the high solid-to-gas ratio. Additional evidence supporting a WD-NS merger scenario includes (1) the low observed occurrence rate of pulsar planets ($\lesssim 1\%$ of NS birth), comparable to the expected WD-NS merger rate; (2) accretion by the NS during the RIAF phase is sufficient to spin PSR B1257+12 up to its observed 6 ms period; (3) similar models of `low angular momentum' disks, such as those produced from supernova fallback, find insufficient mass reaching the planet formation radius. The unusually high space velocity of PSR B1257+12 of $\gtrsim 326\,{\rm km\,s}^{-1}$ suggests a possible connection to the Calcium-rich transients, dim supernovae which occur in the outskirts of their host galaxies and were proposed to result from mergers of WD-NS binaries receiving SN kicks. The C/O disk composition implied by our model likely results in carbon-rich planets with diamond interiors.