1 Introduction

Almost all the $\gamma$-ray bursts (GRBs) detected so far are associated with a transient X-ray afterglow (Lazzati et al. 2002a). This afterglow is supposed to be due to the early deceleration of the fireball by the interstellar medium (Meszaros & Rees 1997) and its radiation produced by non-thermal synchrotron. Such an interpretation is corroborated by spectral (van Paradijs et al. 2002) and polarimetric (Covino et al. 1999) observations.

More recently, several X-ray afterglows observed by Newton-XMM had a spectrum that can be better fit by an optically thin thermal bremsstrahlung model (Watson et al. 2002) rather than with an absorbed power-law (even though the latter model cannot be unambiguously ruled out on purely statistical grounds). In particular, several high ionization emission lines were detected in the early afterglow of GRB 011211 (Reeves et al. 2002, hereafter R02) which can be accounted for, together with the observed continuum, by a moderately enriched thermal plasma.

The possibility of a thermal origin of the X-ray lines detected in several afterglows was first discussed in Lazzati et al. (1999; see also Vietri et al. 1999; Kumar & Narayan 2002), who pointed out how a 10 times solar enriched plasma may produce a Fe K$_\alpha$ line with the observed large luminosity and equivalent width. In this paper we derive more rigorously the conditions for the environment and the heating mechanism that must be satisfied in order to observe line and continuum emission with the prescribed luminosities, equivalent widths (EWs) and variability time scales.