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.