# Evolution of newborn rapidly rotating magnetars: effects of r-mode and fall-back accretion

## TL;DR

This study explores how r-mode instabilities affect the spin evolution and gravitational wave emission of newborn rapidly rotating magnetars with fall-back accretion, highlighting the conditions for detectable signals.

## Contribution

It provides a detailed analysis of r-mode growth and magnetic damping in magnetars influenced by fall-back accretion, a novel aspect in magnetar evolution modeling.

## Key findings

- Gravitational waves from magnetars could be detectable within 1 Mpc by the Einstein Telescope.
- Maximum r-mode amplitude can reach ~0.001 with magnetic damping balancing growth.
- Growth of r-modes is primarily driven by accretion torque if the magnetar is not sufficiently spun up.

## Abstract

In this paper we investigate effects of the $r$-mode instability on a newborn rapidly-rotating magnetar with fall-back accretion. Such a magnetar could usually occur in core-collapse supernovae and gamma-ray bursts. We find that the magnetar's spin and $r$-mode evolution are influenced by accretion. If the magnetar is sufficiently spun up to a few milliseconds, gravitational radiation leads to the growth of the $r$-mode amplitude significantly. The maximum $r$-mode amplitude reaches an order $\sim 0.001$ when the damping due to the growth of a toroidal magnetic field balances the growth of the $r$-mode amplitude. If such a sufficiently spun-up magnetar was located at a distance less than 1\,Mpc, then gravitational waves would be detectable by the Einstein Telescope but would have an extremely low event rate. However, if the spin-up is insufficient, the growth of the $r$-mode amplitude is mainly due to the accretion torque. In this case, the maximum $r$-mode amplitude is of the order of $\sim 10^{-6}-10^{-5}$.