Rebrightenings of gamma-ray burst afterglows from an increasing magnetic inclination angle of a nascent magnetar

TL;DR

This work addresses how the magnetic inclination angle $\alpha$ of a nascent magnetar influences GRB afterglows by modulating the magnetar's energy-loss rate via magnetic-dipole radiation. By adopting an increasing-$\alpha$ evolution toward $90^{\circ}$, the model yields a rising energy-injection luminosity $L$ that naturally produces slight rebrightenings in afterglow light curves, without requiring special jet structures. The authors implement a coupled magnetar–jet framework with $L_{\rm dip}=\frac{B_{\rm p}^{2}R^{6}\Omega^{4}(1+\sin^{2}\alpha)}{6 c^{3}}$ and an evolving $\alpha(t)$, then fit X-ray light curves of GRB 170822A and GRB 230414B and optical data for GRB 230414B, finding good agreement. They show the rebrightenings are limited in amplitude (roughly a factor of two in $L$), consistent with observations, and discuss implications for the role of prolate toroidal-field-driven distortions and the negligible role of gravitational waves in typical cases. The framework suggests that early, mild rebrightenings across GRB afterglows may share a common origin in magnetar geometry evolution, with potential richer features for non-linear $\alpha$-evolution in future work.

Abstract

A nascent magnetar, accompanying a gamma-ray burst (GRB) explosion, releases enormous rotational energy via magnetic dipole radiation. The energy loss rate of the magnetar is determined by the strength of the magnetic field at the pole. We investigated the effect of the magnetic inclination angle on the energy loss rate. The released energy is injected into the GRB jet and shapes the light curves of GRB afterglow. Different evolutionary approaches lead to different curves shapes.A shallow decay phase in GRB X-ray afterglow may result from energy injection from a magnetar with a fixed inclination angle. A two-plateau phase may result from a decreasing inclination angle scenario. In this study, we considered an increasing inclination angle scenario. The energy loss rate of the magnetar increases as the magnetic inclination angle grows. Our analysis reveals that as the lost rotational energy injected into the GRB jet increases, rebrightening phases occur in the GRB afterglows. The rebrightening features are slight and short-lived. The observed afterglow rebrightening of GRB 170822A and GRB 230414B can be well explained within our framework. Some GRB X-ray afterglows that exhibit slight and early rebrightenings may result from an increasing magnetic inclination angle of a nascent magnetar.

Figures (3)

• Figure 1: Energy loss rate (energy injection luminosity) from nascent magnetar spin-down. Solid curve: evolving magnetic inclination angle ($\alpha$) from $\alpha_{\rm i} = 0.01$ rad to $\alpha_{\rm t} = \pi/2$ rad. Dashed gray curve: fixed inclination $\alpha \equiv \alpha_{\rm i} = 0.01$ rad. Dotted gray curve: fixed inclination $\alpha \equiv \alpha_{\rm t} = \pi/2$ rad.
• Figure 2: Observed X-ray afterglows of GRB 170822A (left) and GRB 230414B (right) with theoretical fits. Data points: Swift-XRT observations. Solid curve: magnetar model with an evolving magnetic inclination angle ($\alpha$ increasing from $\alpha_{\rm i} = 0.01$ rad to $\alpha_{\rm t} = \pi/2$ rad). Dashed gray curve: fixed $\alpha \equiv \alpha_{\rm i} = 0.01$ rad. Dotted gray curve: fixed $\alpha \equiv \alpha_{\rm t} = \pi/2$ rad.
• Figure 3: Optical afterglow light curves of GRB 230414B. Observational data (GCN circulars): circles and squares correspond to R-band and I-band (add 4 mag) photometry. Modeled light curves: solid and dashed curves correspond to R-band and I-band (add 4 mag) synthetic flux, respectively