$\begin{figure} \par\includegraphics[width=8.8cm,clip]{aaek042f2.eps} \end{figure}$

Figure 2: Time evolution of the polarization level P and position angle $\vartheta$ . Data for the first night are from Masetti et al. (2002c) and from Bersier et al. (2002).

In Fig. 2 we show the time evolution of the polarization level P and angle $\vartheta$ for GRB 020405, also including the measurements performed by Bersier et al. (2002) and by Masetti et al. (2002c). Because of the striking contrast between the observations of the first night, the question for variability cannot be firmly settled. However, no significant variation is found by looking at our data alone (second and third night). Our points are moreover fully consistent with the one of Masetti et al. (2002c).

A certain amount of (constant) polarization can be introduced by intervening dust along the line of sight, either in our Galaxy or in the host. The values reported in Table 1 are already corrected for the (low) Galactic contribution. If additional dust is present in the host galaxy, its presence should be revealed through spectral reddening. Since the induced polarization should not be larger than $P_{\rm max} = 9\%~E_{B-V}$ (Serkowski et al. 1975), a reddening $E_{B-V} \approx 0.2$ (in the host frame) would be required to explain our value $P \approx 2\%$ . This transforms into $A_V \sim 0.6 \div 1.1$ depending on the selective-to-total extinction coefficient R_V, that can be higher than the standard value $\sim$ 3.1 in star-forming regions (see e.g. Cardelli et al. 1989). X-ray data by Chandra (Mirabal et al. 2002) indeed reveal the presence of some material along the line of sight, with $N_{\rm H} = (4.7\pm3.7) \times 10^{21}$ cm^-2. Assuming a Galactic dust-to-gas ratio, this corresponds to $A_V = 2.8\pm2.2$ (Predehl & Schmitt 1995). The effect of dust on the polarization degree can therefore be significant. This shows that the study of polarization can yield important constraints about the medium surrounding the GRB progenitor.

In addition to the difficulty of assessing the intrinsic level of polarization of the OA, interpreting the polarization measurements within the framework of the proposed models is made difficult by the lack of a clear break in the power-law decay of the lightcurve. In fact, despite some claims of the possible presence of a jet break at early times ( $t_{\rm j} \sim1$ day, Price et al. 2002c), the data seem also compatible with a single power-law up to ten days after the burst (Masetti et al. 2002b).

In the framework of the patchy model (Gruzinov & Waxman 1999), a moderate-high level of polarization is expected. The level of polarization should monotonically decay as a function of time due to the increase of the visible surface of the fireball (and therefore to the increased number of visible patches). The position angle of the polarization vector should fluctuate randomly. Since the polarization predicted in this model is $P \sim 60\%~/\sqrt{N}$ , the inferred number of patches is $N \sim 1000$ .

In the case of collimated fireballs, Ghisellini & Lazzati (1999) and Sari (1999) proposed a model in which the polarized fraction has a more complex behaviour, with two peaks separated by a moment of null polarization that roughly coincides with the break time of the total flux lightcurve. Lacking a robust detection of a jet break and given the limited number of measurements, only a qualitative comparison can be performed. Again, the measurement of Bersier et al. (2002) cannot be reconciled with the model in any case and, if real, should be ascribed to some still unknown effect (see Bersier et al. 2002 for a comprehensive discussion).

In the case of a late time break ( $t_{\rm j}>10$ d), our measurements can be interpreted to belong to the first peak of the polarization curve (see Fig. 4 in Ghisellini & Lazzati 1999), with the moderate decay of the polarization being an indication that the break time is approaching. If the break were at early times ( $t_{\rm j}\le1$ d; see Price et al. 2002c), the absence of a rotation of $90\hbox{$^\circ$ }$ of the position angle that is predicted between the first and the second peak in the polarization time evolution (e.g. Ghisellini & Lazzati 1999; Sari 1999) would point either to a rapidly sideways expanding jet (Sari 1999) or to a structured jet (Rossi et al. 2002a,b).

3 Discussion