Late-time X-ray afterglows of GRBs: Implications for particle acceleration at relativistic shocks

TL;DR

This paper tests PIC-derived predictions for the maximum synchrotron photon energy in GRB afterglows by analyzing six GRBs with late-time Swift/XRT detections. By accounting for equal-arrival-time surface effects and jet geometry, it refines the expected X-ray cutoff location and compares it to observed spectra, finding no compelling evidence for a cutoff in the 0.3–10 keV band at times around 10^6–10^7 s. The resulting 2σ lower limits on the cutoff energy constrain afterglow parameters and, for several bursts, are difficult to reconcile with standard PIC-based expectations unless extreme values hold for radiative efficiency, ambient density, or magnetic equipartition. The findings imply that electrons may be accelerated to higher energies than PIC simulations predict, with important implications for understanding particle acceleration at relativistic shocks and motivating future high-energy GRB observations to further probe these mechanisms.

Abstract

Particle-in-cell (PIC) numerical simulations are currently among the most advanced tools to investigate particle acceleration at relativistic shocks. Still, they come with limitations imposed by finite computing power, whose impact is not straightforward to evaluate a priori. Observational features are hence required as verification. energy electrons accelerated at external shocks, provides a testbed for such predictions. Current numerical studies suggest that in GRB afterglows the maximum synchrotron photon energy, which corresponds to the limit of electron acceleration, may fall within the $\sim$ 0.1--10 keV X-ray energy band at late times, $t\gtrsim 10^6 - 10^7$ s. To test this prediction, we analyzed the X-ray spectra of six GRBs with \emph{Swift}/XRT detections beyond $10^7$ s: our analysis reveals no clear evidence of a spectral cutoff. Using a model that accounts for the effect of the finite opening angle of the shock on the observed maximum synchrotron photon energy, we show that these observations are incompatible with PIC simulation predictions, unless one or more physical afterglow parameters attain values at odds with those typically inferred from afterglow modeling (small radiative efficiency, low ambient density, large equipartition fraction $ε_{\rm B}$ of the magnetic field). These findings challenge existing numerical simulation results and imply a more efficient acceleration of electrons to high-energies than seen in PIC simulations, with important implications for our understanding of particle acceleration in relativistic shocks.

Figures (6)

• Figure 1: Time evolution of the maximum synchrotron photon energy $h\nu_{\rm max} = \min \, [h\nu_{\rm syn}, \, h\nu_{\rm sat}]$ for different sets of afterglow parameters. The redshift is fixed at $z=0.2$, and the upstream magnetization parameter is fixed to be $\sigma_{\rm u} = 10^{-9}$. The gray shaded area indicates the energy band between 0.3 and 10 keV. Left panel: ISM case with $n_0 = 0.1$. Right panel: wind case with $A_{\star} = 1$. For $t_{\rm obs} \geqslant 10^6$ s, $h\nu_{\rm max}$ is set by $h\nu_{\rm sat}$ for all sets of parameters and can fall in the XRT energy band.
• Figure 2: Differential $dF_{\nu}/d\theta$ at $\nu/\mathcal{D} > \nu^{\prime}_{c}$ from different latitudes at the time $t = 3 \times 10^6$ s, adopting $p=2.2$ and $z=0.2$. The different line colors refer to different values of $E_{\rm k}$. The dashed vertical lines indicate the values of $\theta_{\rm c}$ and the gray shaded areas represent the typical range of values of the jet opening angle, $\theta_{\rm j} \in [0.05,0.3]$ radians. Left panel: ISM case with $n_{0} = 0.1$. Right panel: wind case with $A_{\star} = 1$.
• Figure 3: Comparison between the predicted maximum synchrotron photon energy along the line of sight (blue curve, from 2013ApJ...771...54S) and that obtained when considering EATS and a conical geometry of the outflow. All curves are computed assuming $z=0.2$, $\epsilon_{\rm B, -3} = 15$ and $\sigma_{\rm u,-9} = 3$. The black, green and red curves correspond to different jet break times $t_{\rm j}$. Solid and dashed curves of the same color share the same $t_{\rm j}$ but differ in $\theta_{\rm j}$ and $E_{\rm k , 54}/n_{0}$ (or $E_{\rm k, 54}/A_{\star}$ for the wind case) Left panel: ISM case with $n_{0} =1$. The solid curves correspond to $E_{\rm k,54} = 1$ and $\theta_{\rm j} = [0.05,\,0.1,\,0.15]$ rad, while the dashed curves correspond to $E_{\rm k,54} = 0.01$ and $\theta_{\rm j} = [0.09,\,0.18,\,0.27]$ rad. Right panel: wind case with $A_{\star} = 1$. The solid curves correspond to $E_{\rm k,54} = 1$ and $\theta_{\rm j} = [0.05,\,0.1,\,0.15]$ rad, while the dashed curves correspond to $E_{\rm k,54} = 0.01$ and $\theta_{\rm j} = [0.15,\,0.32,\,0.47]$ rad.
• Figure 4: Constraints on the parameter space for radiation with energy $h\nu_{\rm max} = 3$ keV observed at $10^6$, $3 \times 10^6$ and $10^7$ s (for a source redshift $z=0.2$). The gray shaded areas indicate the range of typical values of jet break times, $t_{\rm j} \in [10^4,10^6]$ s. Solid lines show the results in this work which accounts for the effect of EATS, while dotted lines reproduce the predictions of 2013ApJ...771...54S. Left panel: ISM case. Right panel: wind case.
• Figure 5: Constraints on the parameter space derived from the spectral analysis of the six selected GRBs. Each curve is built considering the prompt emitted energy $E_{\gamma}$ of the GRB (listed in Tab. \ref{['tab:E_gamma']}) and the lower limit on $h\nu_{\rm max}$ obtained from our spectral analysis at a given observational time $t_{\rm obs}$ (see text for details). The The gray shaded regions represent the typical range of the jet break time $t_{\rm j} \in [10^4, 10^6]$ s and the values of the $y$-axis correspond to representative values of the relevant parameters. Arrows indicate that the curves represent lower bounds on the allowed parameter space. Left panel: ISM case. Right panel: wind case. The three GRBs with low $E_{\gamma}$ - which, for standard values of the parameters, are in tensions with the predictions on $h\nu_{\rm max}$) - are marked with distinct symbols: $\star$ for GRB 190829A, $\bullet$ for GRB 161219B and $\blacktriangle$ for GRB 130702A.