# Are pulsars spun up or down by SASI spiral modes?

## TL;DR

This study uses 2D simulations to explore how stellar rotation influences hydrodynamic instabilities like SASI and corotation in supernovae, affecting the resulting pulsar spins, with implications for understanding pulsar birth properties.

## Contribution

The paper provides a systematic analysis of how rotation affects SASI and corotation instabilities, revealing conditions under which pulsars are spun up or down during supernova explosions.

## Key findings

- Faster rotation enhances SASI spiral modes if the shock-to-neutron star radius ratio is large.
- Corotation instability develops at high rotation rates, significantly impacting dynamics.
- Rapid progenitor rotation modestly spins down pulsars, suggesting limited hydrodynamic influence in most cases.

## Abstract

Pulsars may either be spun up or down by hydrodynamic instabilities during the supernova explosion of massive stars. Besides rapidly-rotating cases related to bipolar explosions, stellar rotation may affect the explosion of massive stars in the more common situations where the centrifugal force is minor. Using 2D simulations of a simplified setup in cylindrical geometry, we examine the impact of rotation on the Standing Accretion Shock Instability (SASI) and the corotation instability, also known as low-T/|W|. The influence of rotation on the saturation amplitude of these instabilities depends on the specific angular momentum in the accretion flow and the ratio of the shock to the neutron star radii. The spiral mode of SASI becomes more vigorous with faster rotation only if this ratio is large enough. A corotation instability develops at large rotation rates and impacts the dynamics more dramatically, leading to a strong one-armed spiral wave. Non-axisymmetric instabilities are able to redistribute angular momentum radially and affect the pulsar spin at birth. A systematic study of the relationship between the core rotation period of the progenitor and the initial pulsar spin is performed. Stellar rotation rates for which pulsars are spun up or down by SASI are estimated. Rapidly spinning progenitors are modestly spun down by spiral modes, less than $\sim 30\%$, when a corotation instability develops. Given the observational constraints on pulsar spin periods at birth, this suggests that rapid rotation might not play a significant hydrodynamic role in most core-collapse supernovae.