Imprints of gravitational waves from magnetar spindown in GRB X-ray afterglows

TL;DR

This work addresses the problem of identifying gravitational-wave signatures in GRB X-ray afterglows by modeling a nascent magnetar whose spindown is initially dominated by $r$-mode GW radiation and magnetic-distortion GW, then by magnetic distortion GW, and finally by magnetic dipole EM radiation. The authors apply this magnetar spindown framework to GRB 130603B, performing an MCMC fit to the four-segment X-ray plateau and extracting physical parameters: an initial spin period $P_0 \approx 5.3\times10^{-4}$ s, an effective dipole field $B_{ m eff} \approx 5.2\times10^{14}$ G, an ellipticity $\epsilon \approx 1.3\times10^{-4}$, and an $r$-mode amplitude $a \approx 3.3\times10^{-2}$. The inferred GW strains are $h^{\epsilon} \sim 10^{-25}$ and $h^{r} \sim 10^{-26}$ at 1 Mpc, below current detectors but potentially detectable with third-generation observatories, providing an indirect probe of neutron-star physics through EM observations. This approach offers a path to constrain NS interior properties and the role of GW processes in GRB engines, with significant implications for future GW and EM joint studies.

Abstract

Given that newborn magnetars are considered potential central engines of gamma-ray bursts (GRBs), there is strong motivation to identify gravitational wave (GW) signatures within GRB samples. If the X-ray afterglow of a GRB is powered by a magnetar, and the initial spindown of the magnetar is dominated by the GW radiation induced by $r$-mode instability or magnetic-field-induced deformation, the decay of the X-ray flux would record the information of the GW radiation. We find that GRB 130603B potentially represents a rare and precious case where the spindown of the central magnetar is dominated in-turn by $r$-mode and magnetic distortion-induced GW radiation. By fitting the X-ray light curve of GRB 130603B in this model, we obtain the initial spin period of magnetar $\sim 5.3\times 10^{-4}$ s, the effective dipole magnetic field strength $\sim 5.2\times 10^{14}$ G, the ellipticity of the magnetar $\sim 1.3\times 10^{-4}$, and the amplitude of $r$-mode oscillation $\sim3.3\times 10^{-2}$. It may serve as a reliable approach for investigating neutron star physics by comparing the parameters estimated using the method presented in this manuscript with those obtained from future GW observations.

Figures (3)

• Figure 1: Schematic diagram of the X-ray afterglow of GRB contributed by magnetar spindown. The first two parts are dominated by $r$-mode oscillation, the third part is dominated by magnetic distortion process, and the fourth part is dominated by magnetic dipole radiation. Here $\tau_{\rm gw,r}$ is the GW spindown timescale. The time $\tau_{\rm \star1}$ marks the transition where the spindown luminosity is no longer dominated by $r$-mode GWs but by GWs from magnetic distortion, while $\tau_{\rm \star2}$ marks the subsequent transition to dominance by magnetic dipole radiation.
• Figure 2: Left panel: Fitting of the X-ray light curve of GRB 130603B with multi power-law functions. The green dashed lines indicate the corresponding break times. The evolution indices of the four segments are: $\sim 0.09, \sim 0.71, \sim 1.23, \sim 2.50$, respectively. Right panel: MCMC fitting on the unabsorbed luminosity of GRB 130603B with magnetar model based on the Equation (\ref{['7']}).
• Figure 3: Corner plot of the posterior probability distributions of the magnetar parameters: the initial period $P_0$, the ellipticity $\epsilon$, the amplitude of the oscillation from $r$-mode $a$, and the effective magnetic field $B_{\rm eff}$.