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

Gamma-ray burst (GRB) central engines and jet production mechanisms are still open questions. Assuming that the shallow decay segments of canonical X-ray afterglowlightcurves of {\em Swift} GRBs are attributed to the magnetic dipole (MD) radiations of newly-born magnetars, we derive the parameters of the magnetarsand explore their possible relations to jet and MD wind emission. We show that the magnetarinitial 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 magnetarwith 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 limitsand contaminations of the bright jet afterglowscannot 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 magnetarsis presented.