Prediction of multi-wavelength emissions associated with X-ray flare and extended emission of GRBs

TL;DR

The paper tackles the origin of X-ray flares and extended emissions in GRBs by modeling broadband synchrotron emission from nonthermal electrons in relativistic jets. It uses a one-zone leptonic framework across a grid of dissipation radii $r_{ m diss}$ and jet Lorentz factors $\Gamma$, solving transport equations with AMES to predict UV and VHE observability and to delineate the $r_{ m diss}$–$\Gamma$ parameter space. Key findings show that simultaneous UV and VHE emission can occur in several regimes, with CTAO capable of detecting VHE flares for certain cases and redshift horizons, while SSA and $\gamma\gamma$ absorption shape detectability. The work provides a practical pathway to constrain jet dissipation scales and Lorentz factors through multi-wavelength observations and highlights future prospects for coordinated follow-ups with Swift/UVOT, SVOM/VT, Fermi-LAT, and CTAO.

Abstract

Gamma-ray bursts (GRBs) are one of the most extreme transients in the universe, but their explosion and emission mechanism remains unclear. To investigate the nature of GRB jets, here we focus on X-ray flares (XFs) and extended emissions (EEs), which are X-ray emissions that occur 100 to 1000 seconds after the main burst. They can be observed by recently developed multi-wavelength facilities. In this paper, we calculate emissions across multi-wavelengths associated with XFs and EEs under the hypothesis that XFs and EEs are optically-thin synchrotron emissions from nonthermal electrons in relativistic jets. Considering ranges of the dissipation radius $r_{\rm diss}$ and the Lorentz factor $Γ$ of the jet, we determine the parameter space in which a detectable emission can be produced at each wavelength. We found that simultaneous ultraviolet and very-high-energy gamma-ray emission associated with XFs or EEs can be detected by Swift/UVOT, SVOM/VT, and CTAO approximately every three years. The detection and non-detection rates for each detector are key to determining the uncertain yet essential values necessary for understanding the physics of GRB jets.

Figures (7)

• Figure 1: Spectra for cases (A)–(E) and (a)-(c). Right panels is for $F_\nu$, and left panels is for $\nu F_\nu = \varepsilon_\gamma F_{\varepsilon_\gamma}$. The top panels show cases (A)–(C). The dotted–dashed blue line, solid light-orange line, and dashed orange line represent cases (A), (B), and (C), respectively. The middle panels show cases (a)–(c). The dotted–dashed blue line, solid light-orange line, and dashed orange line represent cases (a), (b), and (c), respectively. The bottom panels show cases (D) and (E). The dashed red line, solid purple line correspond to cases (D) and (E), respectively. The horizontal gray lines in right panels ($\varepsilon_\gamma F_{\varepsilon_\gamma}$ plots) indicate the typical luminosity of XFs and EEs, $3\times10^{48}$ erg/s. Thin lines indicate the detection limits for 300-second transients: the dashed red lines are for SVOM/VT Atteia2022_SVOM, the solid blue lines are for Swift/UVOT Gehrels2004_swift, the dotted black lines are for SVOM/MXT Atteia2022_SVOMGotz2014MXTsensitivity, the solid black lines are for Swift/XRT Gehrels2004_swiftBurrows2005XRTsensitivity, and the dashed black lines are for CTAO Hofmann2023_CTAO, and the dotted-dashed black lines are for MAGIC Aleksic2016MAGICFioretti2019MAGICsensitivity. The CTAO and MAGIC sensitivity lines end at 250 GeV in our plots following Figure 22 in Hofmann2023_CTAO and Fioretti2019MAGICsensitivity, but actually it extends to 100 TeV.
• Figure 2: Detectabilities on the $r_{\rm diss}$–$\Gamma$ plane. The blue region indicates that UV emission associates with XFs or EEs but no VHE gamma-ray emission. The orange region indicates that both UV (Swift/UVOT) and VHE (CTAO) emissions associate with XFs or EEs. The red region indicates that neither UV nor VHE emission associates with XFs or EEs. The purple region indicates that VHE emission associates with XFs or EEs but no UV emission. The black shaded region is where the photon index at the X-ray band is too hard for the XFs and EEs. The gray region is not considered because the Thomson optical depth exceeds unity and the emission there is subphotospheric. The thin white dotted line represents where the $\delta t = r_{\rm diss}/(2\Gamma^2 c)$ is constant.
• Figure 3: Spectrum of the flare in GRB 060926 at $T - T_0 \sim 10^{2.5}$ s. The thick solid blue line and thick dashed orange line show the spectra for cases 1 and 2 in Table \ref{['tab:param_case']}, respectively. The thin dashed line shows the spectrum for case 2 at $z = 2$. The triangular and circular points represent the observed data from Swift/XRT and UVOT, respectively. The thin dashed black line indicates the detection limit of CTAO same as in Figure \ref{['fig:spectra']}Hofmann2023_CTAO.
• Figure 4: Same as Figure \ref{['fig:r-Gamma']} but for the magnetized jet.
• Figure 5: Same as Figure \ref{['fig:spectra']} but for the soft electron injection case ($p=2.5$).