5 Discussion

   
5.1 The impact of the assumed IMF on the photometric redshift

As shown in Table 4 the spectroscopic redshift is consistent (within the 99% percentile error range) with the inferred three photometric redshifts. Thus the effect of the assumed IMF is not crucial to confirm the spectroscopic redshift of the GRB 000210 host galaxy. However, among the assumed three IMFs the MiSc79 and Sa55 IMFs are the only ones providing a photometric redshift consistent within 1$\sigma$ with the spectroscopic redshift. Thus, we consider the Sc86 IMF as the less appropriate one to describe the predominant stellar population of the GRB 000210 host galaxy.

According to Bolzonella et al. (2000) the Sa55 IMF produces an excess of bright blue stars yielding an UV flux excess. On the other hand the Sc86 IMF generates an excessive number of solar mass stars, making the spectrum too red to reproduce the observed SEDs. Intensive photometric redshift studies have shown that the MiSc79 IMF is a good compromise between both tendencies (Bolzonella et al. 2002).

In the particular case of the blue SED of the GRB 000210 host, the potential excess of massive stars given by the Sa55 IMF is not an inconvenient at all. The prominent UV flux predicted by Sa55 can easily reproduce the blue part of the observed SED. On the contrary, the excess of solar mass stars given by the Sc86 IMF is not able to reproduce the blue SED part unless the host galaxy redshift is slightly accommodated. Thus, the expected impact of the three IMFs (Bolzonella et al. 2002) is in agreement with the photometric redshifts displayed in Table 4.

   
5.2 The effect of the adopted extinction law on the photometric redshift

The host galaxy restframe SED flux density (in a $F_{\lambda}$representation as the one of Fig. 4) increases from 3000 to 2000 Å (corresponding to the observed SED between the U and the Vband). The detection of this ionising UV continuum implies a very low extinction in the host. Given the low extinction derived for the host (see the values of $A_{\rm V}$ in Table 4) the inferred photometric redshift is basically independent of the adopted extinction law for the three IMFs. The results displayed in Table 4 for Sa55 and MiSc79 IMFs remain unchanged if the Calzetti et al. (2000) extinction law is replaced by another reddening law, as the ones given by Seaton (1979), Fitzpatrick (1986), or Prévot et al. (1984). The values of the photometric redshift derived assuming a Sc86 IMF changes slightly from z=0.757 to z=0.783, depending on the extinction law.

Therefore, in the particular case of the GRB 000210 host galaxy, the impact of the adopted extinction law on the inferred redshift is negligible and has to be considered as a second order parameter in comparison to the assumed IMF.

   
5.3 Is the GRB 000210 host a subluminous galaxy?

A subluminous galaxy is determined for having a luminosity below the knee of the luminosity function given by $L^{\star }$ (Schechter 1976). The characteristic luminosity $L^{\star }$ can be associated to a characteristic AB-system B-band absolute magnitude, $M^{\star}_B(AB)$, which ranges from -20.8 to -23.0 depending on the rest-frame colour of the galaxy (Lilly et al. 1995). In a more simplified approximation to the luminosity function, Schechter (1976) reports an unique value of $M^{\star}_{B}=-20.6$ (in the Vega system) for all galaxy types.

The restframe (U-V) colour of the host galaxy is ( U-V)=-0.54, which in the AB system corresponds to ( U-V)_AB=0.15 (see the AB offsets given in Table 2). According to Table 1 of Lilly et al. (1995) this ( $U-V)_{\it AB}$ colour implies a value of $M^{\star}_B(AB)=-21.40$ (given for a cosmology defined by $\Omega_{\Lambda} = 0$, $\Omega_{M} = 1$ and H₀= 50 km s^-1 Mpc^-1) for the redshift bin corresponding to the host. This B-band AB-system magnitude corresponds to a B-band absolute magnitude of $M^{\star}_B=-21.33$ in the Vega system (see Table 2).

The absolute B-band magnitude of the host galaxy for MiSc79 and Sa55 IMFs ( $M^{\star}=-20.16$ see Table 4), when rescaled to the cosmology used by Lilly et al. (1995), corresponds to $M^{\star} = -20.18$. Given that $M^{\star}_B=-21.33$, then $L=0.35\ L^{\star}$. The corresponding value of L derived for a Sc86 IMF is 0.27 $L^{\star }$ (see last column in Table 4).

The values of L, obtained using Schechter (1976), basically double (see the eighth column in Table 4) those obtained when Lilly et al (1995) is considered. Therefore, considering an averaged value of $L = 0.5 \pm 0.2\ L^{\star}$ for the host, we conclude that the host is very likely a subluminous galaxy. This luminosity value is consistent with the one ( $L \approx 0.5\ L^{\star}$) derived by Piro et al. (2002).

5.4 Estimation of the star formation rate

The redshifted spectra of the GRB 000210 host galaxy have the restframe UV continuum in the observed optical range. The UV continuum emission with ongoing star formation is dominated by bright, short-lived, main-sequence O and B stars. According to Kennicutt (1998), for a Sa55 IMF (consistent with our host galaxy SED, see Table 3), the SFR in a galaxy is directly proportional to the rest frame UV luminosity; SFR $_{\rm UV} = 1.4 \times 10^{-28}~L_{\nu}$, where $L_{\nu}$ indicates the emitted energy per unit frequency around 2800 Å, measured in ergs s^-1 Hz^-1. SFR$_{\rm UV}$ gives the amount of stellar mass (measured in solar masses) created in the host galaxy in a restframe year. The method of deriving the SFR from the UV continuum flux (named SFR$_{\rm UV}$ in the present paper) is one of several diagnostic methods used in the literature to measure SFRs in galaxies (see Kennicutt 1998 for a comprehensive review). Obviously, if there is dust-enshrouded star formation then this UV-based method will only provide a lower limit to the actual SFR.

At z=0.8463 the 2800 Å region is redshifted to 5169.6 Å, so it is bracketed between the B and V bands. Assuming a power law SED stretch between both bands, a flux density of $0.70 \pm 0.07~\mu$Jy is estimated at 5169.6 Å. This flux density corresponds to a restframe 2800 Å luminosity of $L_{\nu} = 1.53 \pm 0.15 \times 10^{28}$ ergs s^-1 Hz^-1, and therefore to a SFR$_{\rm UV}$ of $2.1 \pm 0.2 \ M_{\odot}$ yr^-1. The SFR$_{\rm UV}$ derived to date for GRB host galaxies range from 1 to 55 $M_{\odot}$ yr^-1 (see Berger et al. 2003, Table 3). Thus the SFR$_{\rm UV}$ of the GRB 000210 host galaxy is in the low end of the distribution for the studied hosts. The SFR$_{\rm UV}$ per unit luminosity (considering $L \sim 0.35\ L^{\star}$ based on the Sa55 IMF results of Table 4) is similar to that of other host galaxies.

As detailed in Kennicutt (1998) the above given SFR$_{\rm UV}$ estimate is more adequate for galaxies with continuous star formation (over time scales of 10⁸ years or longer), and provides an upper limit for younger populations such as young starburst galaxies with ages below 10⁸ years. For the estimated stellar population age of the host galaxy (0.181 Gyr, see Table 4), we consider that the SFR$_{\rm UV}$ expression gives still an acceptable approximation to the actual SFR$_{\rm UV}$. Kennicutt (1998) estimates that the internal uncertainty of this method is $\sim$30%. This value is far from the SFR derived by Berger et al. (2003) based on the tentative sub-millimeter detection of the host galaxy (SFR $_{\rm smm} \approx 500 \ M_{\odot}$ yr^-1). The apparent discrepancy between SFR $_{\rm smm}$ and SFR$_{\rm UV}$can not be explained by the internal uncertainties inherent to the SFR$_{\rm UV}$ or SFR $_{\rm smm}$ methods.

If the tentative detection of sub-mm emission from the host galaxy of GRB 000210 is real, as opposed to noise or emission from another source along the line of sight, we need to conclude that the host of GRB 000210 has two separate populations of massive stars. One is traced by the rest frame UV/optical light and shows no sign of extinction and the other is completely obscured by dust and is only detectable at sub-mm wavelengths. A possible way to explain this apparently odd configuration is if the host has a clumpy and opaque ISM with no thin absorbers, which is able to completely hide part of the massive stellar population, but does not significantly affect the UV flux of the not hidden massive stars. This scenario would be consistent with the significant line of sight column density inferred from the afterglow X-ray spectrum ( $N_{\rm H} = (5 \pm 1) \times 10^{21}$ cm^-2, Piro et al. 2002). It would also naturally explain the lack of optical afterglow emission if the progenitor was a member of the enshrouded population.

Based on the flux of the [O II] line and assuming several reasonable hypotheses Piro et al. (2002) deduced a SFR $_{\mbox{[O{\sc II}]}}$ of $\sim$ $3 M_{\odot}$ yr^-1. Given the impact of their assumptions (they calibrated the GRB 000210 [O II] flux relative to the one of the GRB 970828 host galaxy) and the intrinsic scatter of the SFR$_{\rm UV}$ method ($\sim$30% according to Kennicutt 1998), we consider that our SFR$_{\rm UV}$ estimate is in agreement with the SFR $_{\rm [O{\sc II}]}$ determined by Piro et al. (2002). Thus, the [O II] line and the UV continuum originate from the same unextincted blue stellar component.

5.5 Implications of the fitted SED on the GRB progenitor

The fitted SED assuming a MiSc79 or a Sa55 IMF is consistent with a Stb, independently of the extinction law used. The Stb template is characterized by a value of $\tau \rightarrow 0$, so the SFR can be expressed by a delta function. In this scenario, the star formation is instantaneous, and occurs at the same time for all the stars, independently of their masses. Thus all the stars should have the same age. The local birth places in a host galaxy (even in the same star forming region) show different physical conditions and, besides, they would be causally separated from each other, so an instantaneous star formation is physically inviable. Therefore, this description should be considered only as an idealisation of a quasi-simultaneous starburst episode occurred around 0.181 Gyr ago (measured in the restframe) in the host galaxy. Several alternatives are possible to explain a GRB progenitor with an age of $\sim$0.181 Gyr. The first alternative would be a progenitor made up of a binary merging system. The life time of such systems is $\sim$0.1-1 Gyr, i.e. compatible with the host galaxy dominant stellar age (Eichler et al. 1989). Thus, the $\gamma$-bright (but optically dark) GRB 000210 would come from the collapse of a compact binary system. This interpretation would support a connection between dark GRBs and binary merging systems, which would not necessarily invoke a circumburst dense region and an extinction mechanism to explain the lack of optical emission (Castro-Tirado et al. 2002). However, a binary merging origin shows several problems. Piro et al. (2002) derived a column density of $N_{\rm H} = (5 \pm 1) \times 10^{21}$ cm^-2 along the line of sight to the burst. It is not obvious to conceive such binary systems located within a high density ( $N_{\rm H} > 10^{21}$ cm^-2) region. Each of the components of such systems is the result of an asymmetric collapse of stellar cores, providing in the instant of the explosion kick off velocities up to 900 km s^-1 to the newly formed compact object (Frail et al. 1994; Nazin & Postnov 1997). Thus the binary systems tend to be located far from their birth places, as they have 0.1-1 Gyr to travel before the binary collapse episode occurs. However, Belczynski et al. (2002) have recently shown that, although far from the star forming regions, the binary systems should occur inside the host galaxies. Besides they find that such systems are more numerous than previously thought.

In principle a collapsar with an age of $\sim$0.181 Gyr is not easy to accommodate. The age of a 8 $M_{\odot}$ star when it explodes as a type II SN is $\sim$0.05 Gyr (see for instance Portinari et al. 1998). More massive stars, as the progenitors suggested in the collapsar scenario (Paczynski 1998; MacFadyen & Woosley 1999), have even shorter lifetimes.

The clumpy ISM scenario would be able to reconcile the difference between the age derived from the SED ($\sim$0.181 Gyr) and the age expected for a collapsar (the lifetime of a $\sim$100 $M_{\odot}$ progenitor is $\sim$0.003 Gyr, according to Portinari et al. 1998). In such scenario the hidden population of young stars would be able to generate a collapsar but not contribute to the host galaxy SED.