# Magnetar as Central Engine of Gamma-Ray Bursts: Central Engine-Jet Connection, Wind-Jet Energy Partition, and Origin of Some Ultra-Long Bursts

## TL;DR

This paper investigates the connection between magnetar properties and gamma-ray burst (GRB) jet and wind emissions, revealing correlations that suggest faster magnetars produce more energetic GRBs and proposing explanations for ultra-long GRBs and their potential gravitational wave signals.

## Contribution

It introduces a model linking magnetar initial spin periods to jet and wind energies, supported by observational data and simulations, and offers explanations for ultra-long GRBs and their possible gravitational wave counterparts.

## Key findings

- Magnetar initial spin period correlates with jet energy.
- Jet and wind energies are nearly proportional.
- Ultra-long GRBs may be orphan magnetar wind emissions.

## Abstract

Gamma-ray burst (GRB) central engines and jet production mechanisms are still open questions. Assuming that the shallow decay segments of canonical X-ray afterglow lightcurves of {\em Swift} GRBs are attributed to the magnetic dipole (MD) radiations of newly-born magnetars, we derive the parameters of the magnetars and explore their possible relations to jet and MD wind emission. We show that the magnetar initial spin period ($P_0$) are tightly correlated with the jet energy ($E_{\rm jet}$), which is almost proportional to the wind energy ($E_{\rm wind}$). Our least square fits yield $P_0\propto E^{-0.36\pm 0.03}_{\rm jet}$ and $E_{\rm wind}\propto E^{0.91\pm 0.07}_{\rm jet}$. These relations may imply that a magnetar with faster rotating speed can power a more energetic GRB, and energy partition between the jet and wind may be quasi-universal. Although the $P_0-E_{\rm jet}$ relation is driven by a few sub-energetic GRBs in our sample, our Monte Carlo simulation analysis shows that sample selection biases from instrumental flux limits and contaminations of the bright jet afterglows cannot make this correlation. Within this jet-wind paradigm, we propose that GRB 101225A-like ultra-long GRBs, whose prompt gamma-ray/X-ray lightcurves are featured as a long-lasting plateau with a sharp drop, may be the orphan MD wind emission being due to misalignment of their jet axis to the light of sight. Brief discussion on the orphan MD wind emission and its association with the gravitational wave radiation of newly-born magnetars is presented.