3 Method: Reproducing the host galaxy photometry by means of synthetic and observed SED templates

The fit of the SEDs have been carried out using Hyperz (Bolzonella et al. 2000). Eight synthetic spectral types were used representing Starburst galaxies (Stb), Ellipticals (E), Lenticulars (S0), Spirals (Sa, Sb, Sc and Sd) and Irregular galaxies (Im). The time evolution of the SFR for all galaxy types is represented by an exponential model, i.e. SFR $\propto \exp(-t/\tau)$, where $\tau$ is the SFR time scale. Each galaxy type has a value of $\tau$ assigned. The SFR of Stb is simulated by an exponential decay in the limit when $\tau \rightarrow 0$, in other words an instantaneous SFR given by a delta function. The early type galaxy spectra (E, S0) are represented by values of $\tau$ between 1 and 2 Gyr. The Spiral galaxies (Sa, Sb, Sc and Sd) have $\tau$ values ranging from 3 to 30 Gyr. The SFR of Im galaxies are represented by a constant SFR ( $\tau \rightarrow \infty$).

Once the population of stars is generated following the time evolution given by the assigned SFR, the mass of the newly formed population is distributed in stars following an assumed Initial Mass Function (IMF). Three IMFs have been considered: Miller & Scalo (1979), Salpeter (1955), and Scalo (1986). These IMFs will be abbreviated hereafter as MiSc79, Sa55 and Sc86, respectively. In Sect. 5.1 we discuss the impact of the assumed IMFs in the determination of the photometric redshift.

The newly formed stars evolve depending on their mass and metallicity following stellar tracks. In each evolutionary stage the contribution of all the individual star spectra are added yielding an integrated galaxy SED which evolves with time. For each galaxy type the evolving SEDs can be tabulated and stored creating the so called SED libraries. Bruzual & Charlot (1993) have derived a SED library called GISSEL98 (Galaxy Isochrone Synthesis Spectral Evolution Library), which is the base of our SED fits.

In addition to the above mentioned evolutionary templates, four averaged templates (constructed grouping the SEDs of the observed local galaxies) from Coleman et al. (1980) were considered (hereafter named as CWW). These extra spectral templates work as a backup of the evolutionary fitting SEDs, and give an approximate hint of the galaxy type when synthetic SED fits fail. The observed CWW templates can be grouped in four sets: early galaxy types (E/S0), Sbc, Scd and Im.

Furthermore, the impact of considering different extinction laws has been studied. Four extinction laws have been taken into account for the determination of the photometric redshift and the physical conditions of the GRB 000210 host galaxy, namely Calzetti et al. (2000), Seaton (1979), Fitzpatrick (1986), and Prévot et al. (1984). Each of these laws determine the dependence of the extinction on the photon frequency and are the result of different physical conditions in the interstellar space in the hosts. Thus, Seaton (1979), Fitzpatrick (1986), and Prévot et al. (1984), are appropriate to describe the Milky Way (MW), Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) extinction laws, respectively. The Calzetti et al. (2000) extinction law is suitable for starburst regions. In Sect. 5.2 the effect of the adopted extinction law on the inferred host galaxy photometric redshift is discussed. In the SED fits a solar metallicity ( $Z= Z_{\odot} \simeq 0.02$, being Z the mass fraction of heavy elements in the interstellar gas) have been assumed.

We varied the GRB 000210 host galaxy redshift between z=0 and z=5with a redshift step of $\Delta z=0.01$. The host galaxy extinction was ranged in a $A_{\rm V}= 0-5$ interval with a step of $\Delta A_{\rm V}=0.005$ mag. Table 4 shows several inferred fit parameters for the assumed extinction law and IMFs: the fit confidence level ($\chi ^{2}/$dof), the photometric redshift z (and the associated asymmetric uncertainties), the best fitted template, the dominant stellar age, the extinction $A_{\rm V}$, the absolute B-band magnitude (M_B), and the host galaxy luminosity (in units of $L^{\star }$). As it is shown in Table 4 the resolution of our template grid is not able to make a distinction between most of the properties (Age, $A_{\rm V}$, M_B, $L/L^{\star }$) derived for the Sa55 and MiSc79 IMFs. Figure 2 shows the evolution of $\chi ^{2}/$dof as a function of the best fitted SED redshift, when a Sa55 IMF is assumed. The fit to the UBVRIZJsHK-band photometric points shows a clear minimum around $z \sim 0.85$ and has no other acceptable redshift solutions.