Favorable conditions for heavy element nucleosynthesis in rotating proto-magnetar winds

The neutrino-driven wind cooling phase of proto-neutron stars (PNSs) follows successful supernovae. Wind models without magnetic fields or rotation fail to achieve the necessary conditions for production of the third r-process peak, but robustly produce a weak r-process in neutron-rich winds. Using 2D magnetohydrodynamic simulations with magnetar-strength magnetic fields and rotation, we show that the PNS rotation rate significantly affects the thermodynamic conditions of the wind. We show that high entropy material is quasi-periodically ejected from the closed zone of the PNS magnetosphere with the required thermodynamic conditions to produce heavy elements. We show that maximum entropy S of the material ejected depends systematically on the magnetar spin period P_ and scales as S ∝ P_-5/6 for sufficiently rapid rotation. We present results from simulations at a constant neutrino luminosity representative of ~ 1-2 s after the onset of cooling for P_ ranging from 5 ms to 200 ms and a few simulations with evolving neutrino luminosity where we follow the evolution of the magnetar wind until $10-14$ s after the onset of cooling. We estimate at magnetar polar magnetic field strength B₀=3× 10¹⁵ G, 10¹⁵ G, and 5× 10¹⁴ G that neutron-rich magnetar winds can respectively produce at least ~ 2-5× 10⁻⁵ M_, ~ 3-4× 10⁻⁶ M_, and ~ 2.5× 10⁻⁸ M_ of material with the required parameters for synthesis of the third $r-$process peak, within $1-2$ s, 10 s, and 14 s in that order after the onset of cooling. We show that proton-rich magnetar winds can have favorable conditions for production of $p-$nuclei, even at a modest B₀=5× 10¹⁴ G.