Revisiting early afterglows of gamma-ray bursts with finite-thickness ejecta: Implications from XRF 080330 and GRB 080710

Abstract

We revisit the physical origin of the achromatic peaks and breaks observed several thousand seconds after the burst in the multi-wavelength afterglows of XRF 080330 and GRB 080710. Using a numerical afterglow model that consistently incorporates finite ejecta thickness and a generalized external density profile, we perform Bayesian inference to estimate model parameters describing these events. Our analysis shows that the gradual rise and achromatic temporal features in both events are more naturally explained by jet dynamical evolution with finite shell thickness rather than by off-axis viewing effects. The inferred initial radial width of the ejecta is of order $10^{13}$ cm for both bursts, implying a central engine activity timescale significantly longer than that suggested by the prompt gamma-ray duration alone. Taken together, these results demonstrate that early afterglow light curves are strongly influenced by transition dynamics when finite ejecta thickness is properly taken into account, thereby providing a physical link between the prompt and afterglow phases and highlighting limitations of simply applying the thin-shell approximation when interpreting early-time afterglows. Furthermore, Bayesian model comparison favors a generalized circumburst density profile over the canonical uniform or steady-wind models, suggesting that fixing the external density structure to idealized profiles a priori may obscure crucial information about the progenitor's pre-burst activity.

Figures (4)

• Figure 1: Multi-wavelength afterglow observations of XRF 080330 (data points) together with posterior predictive light curves (100 faint solid lines). From top to bottom, the bands are the $K$-band (black), $H$-band (yellow), $J$-band (red), $i$-band (green), $r$-band (purple), $g$-band (blue) and the X-ray at 3 keV (cyan). The X-ray data were down-weighted by inflating their quoted uncertainties.
• Figure 2: Posterior probability distributions obtained from the Bayesian inference applied to the observational afterglow data of XRF 080330. The diagonal panels show the one-dimensional posterior distributions of each parameter, and the off-diagonal panels show the corresponding two-dimensional joint posterior distributions. The black dashed lines show the medians and the 95% credible intervals, and the red solid lines mark the maximum a posteriori (MAP) values; $E_0 = 1.6\times 10^{54}~\mathrm{erg}$, $\Gamma_0=4.9\times 10^2$, $\Delta_0= 8.6\times 10^{12}~\mathrm{cm}$, $n_0 = 6.0~\mathrm{cm^{-2.14}}$, $k = 0.86$, $\theta_\mathrm{j} = 0.08~\mathrm{rad}$, $\theta_\mathrm{obs} = 0.03~\mathrm{rad}$, $p = 2.11$, $\epsilon_e = 0.12$, $\epsilon_B = 1.4\times 10^{-6}$, and $f_\mathrm{e} = 0.89$.
• Figure 3: Multi-wavelength afterglow observations of GRB 080710 (data points) together with posterior predictive light curves (100 faint solid lines). From top to bottom, the bands are the $z$-band (blue), $r$-band (red) and the X-ray at 3 keV (green).
• Figure 4: Posterior probability distributions for GRB 080710, shown in the same format as Figure \ref{['fig:080330_result_corner']}. The maximum a posteriori (MAP) values, shown as red solid lines, are $E_0 = 2.1\times10^{54}~\mathrm{erg}$, $\Gamma_0=42$, $\Delta_0=1.3\times10^{13}~\mathrm{cm}$, $n_0=1.1\times10^{2}~\mathrm{cm^{-2.95}}$, $k=0.06$, $\theta_\mathrm{j}=0.15~\mathrm{rad}$, $\theta_{\rm obs}=0.01~\mathrm{rad}$, $p=2.05$, $\epsilon_e=2.2\times10^{-3}$, $\epsilon_B=7.4\times10^{-2}$, and $f_\mathrm{e}=0.85$.