THE GALAXY POPULATION HOSTING GAMMA-RAY BURSTS

The first gamma-ray burst (GRB) ever discovered was in the year 1967 (Klebesadel et al. 1973), but it took 30 more years to finally identify these sources as extragalactic and cosmologically distributed (Metzger et al. 1997). As of 2008 September 22, the total number of GRBs with known redshift⁴ is 154, half of which are at z > 1.4, and 69% were discovered by the dedicated space mission Swift (Gehrels et al. 2004) after 2005 January.

Although the GRB population with redshift is rather small, studies dedicated to the hosting galaxies are often deep and can cover the wavelength range from the radio, to mid-IR, to optical, and UV in imaging and spectroscopy (e.g., Bloom et al. 2002; Le Floc'h et al. 2006; Priddey et al. 2006; Prochaska et al. 2006; Berger et al. 2007b; Ovaldsen et al. 2007). The typical nature of GRB hosts is of a faint star-forming galaxy, dominated by a young stellar population (Christensen et al. 2004), detected at any redshift from 0 to 6.3 (Berger et al. 2007b). Luminosities are generally low (Chary et al. 2002; Le Floc'h et al. 2003), indicating low masses and low metallicities (Gorosabel et al. 2005b; Wiersema et al. 2007a; Kewley et al. 2007). New cosmological simulations suggest that hosts associated with long GRBs are representative of the whole galaxy population (Nuza et al. 2007).

Many hosts are fainter than the observational limits achieved today by the typical galaxy survey at high redshift (see for instance Cimatti et al. 2002; Abraham et al. 2004; Reddy et al. 2006; Noeske et al. 2007). In fact, the bright optical GRB afterglow often facilitates obtaining a spectroscopic redshift and the mere presence of a GRB encourages deeper photometric and spectroscopic observing campaigns than in conventional galaxy surveys. It is not clear yet whether this faint population is stand-alone and characterized by the association with a GRB event (Stanek et al. 2006; Fruchter et al. 2006), or whether we see many faint galaxies simply because these are the most common galaxies in the universe. Wolf & Podsiadlowski (2007) showed that there is no dramatic difference between GRB hosts and what is expected for a galaxy population tracing star formation.

This paper is dedicated to the study of the largest possible sample of GRB host galaxies. In the past, many different tools applied to individual or a few GRB hosts led to very heterogeneous results, not always easy to compare. We used a compilation of GRB hosts to measure a large number of galaxy parameters in a robust and consistent way, and try to establish the role of GRB hosts in the cosmological scenario of galaxy formation and evolution.

The sample is selected by requiring that optical and/or near-IR (NIR) photometry (available in the literature) have allowed the host identification. For a better stellar mass estimate, the important observable is the galaxy photometry redward of the 4000 Å break (Glazebrook et al. 2004), which restricts our search to (mainly) GRBs with z ≲ 3. The total number of GRB hosts for which the stellar mass is estimated is 46 (Figure 1). For a subsample of 33, rest-frame optical emission-line fluxes from spectra are also available In the past, the stellar mass for several GRB hosts was derived by Chary et al. (2002), Castro Cerón et al. (2006), and Michałowski et al. (2008).

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Throughout the paper, we distinguish between the subsamples of galaxies originating in short GRBs, which are associated with neutron star/black hole mergers possibly in evolved stellar populations, or long GRBs, associated with core-collapsed SNe and more abundant in young stellar populations (Woosley 1993). It has been argued by different authors that the hosts of the two classes are substantially different, the former in early- as well as late-type galaxies, the latter mainly in young star-forming galaxies (e.g., Prochaska et al. 2006; Berger et al. 2007c). Long GRB hosts are the vast majority (seven out of eight), as the long duration allows an easier identification of the afterglow, whereas the detection of short afterglows is very recent (Gehrels et al. 2005).

Our group created a public database, where many GRB-host observed parameters, available from the literature, are classified and stored. The database, the largest of its kind, is called GRB Host Studies (GHostS) and is accessible at the Web site www.grbhosts.info. GHostS is an interactive tool offering many features. It also incorporates Virtual Observatory services, in particular Sloan Digital Sky Survey (SDSS) and Digital Sky Survey (DSS) sky viewing.

The paper is organized as follows: in Section 2, we describe the sample selection; in Section 3, multiband photometry and emission lines are used to derive galaxy parameters; results are given in Sections 4 and 5; the discussion and summary are presented in Sections 6 and 7. Throughout the paper we adopt an h ≡ H_o/100 = 0.7, Ω_M = 0.3, Ω_Λ = 0.7 cosmology (Spergel et al. 2003).

The sample selection is based on the requirement that multiband photometry is available for the GRB host, mainly optical and NIR photometry. Some mid-IR detections from Spitzer are also included in our analysis (Le Floc'h et al. 2006). The sample is listed in Table 1, for which we report redshift, the type of GRB (short or long), and the morphological classification, as given by Conselice et al. (2005) and Wainwright et al. (2007). The Galactic color excess E_G(B − V) for each object (Table 1) is estimated using the reddening maps by Schlegel et al. (1998), and is less than 0.15 for 83% of the cases. All measurements reported in this work are corrected for the Galactic extinction (Cardelli et al. 1989). Figure 1 shows the number of objects in the sample per redshift bin and the comparison with the total sample of GRBs with measured redshift.

We compare observed parameters, with the same parameters measured in field galaxies, observed at different redshifts. In particular, we use results from the 0.4 < z < 2 Gemini Deep Deep Survey (GDDS; Abraham et al. 2004), the Lyman break galaxies (LBGs; Erb et al. 2006; Reddy et al. 2006), and the local dwarf galaxies (Lee et al. 2006). The GDDS is an ultra-deep NIR-selected survey (K < 20.6, I < 24.5) targeting galaxies in the "redshift desert" (0.8 < z < 2). GDDS is designed to find the most massive galaxies up to z = 2. The limit in K gives very high sensitivity to low-mass galaxies at z = 1 (e.g., Savaglio et al. 2005). LBGs are UV-selected (observed ${\cal R}<25.5$) high-z galaxies (1.4 < z < 2.6). Dwarfs in the local universe (distance D < 5 Mpc) have absolute magnitudes at 4.5 μm in the interval −19.9 < M_[4.5] < −13.3.

Measurements from GDDS and the GRB hosts are treated in the same way, in particular in the modeling analysis we use the initial mass function (IMF) proposed by Baldry & Glazebrook (2003). A correction for the different IMFs, generally Salpeter is assumed, is necessary for the other samples.

The GRB-host sample studied here contains 46 objects (30% of all GRBs with measured redshift). Six of these are associated with short GRBs, all at redshift z < 0.7, with a mean redshift z = 0.38 (Table 1). The mean and median redshift of the long-GRB sample is z = 1.05 and z = 0.84, respectively, with 88% being at z ⩽ 1.60, when the universe was 4 Gyr old (i.e., 29% of the age today).

We note that the GRB hosts that are considered have relatively low redshift, in comparison with the mean and median values for the total GRB population with known redshift (z = 1.79 and z = 1.32, respectively). This is because GRB hosts are faint and hard to detect for z > 2, and also because redshifts in the pre-Swift era were mainly determined from strong optical emission lines, redshifted in the more difficult NIR regime for z > 1.5. Most GRBs (∼70%) in our sample belong to the pre-Swift era. This can potentially bias the results that we discuss in this paper. For instance, GRBs are associated with regions of star formation. As the star formation rate (SFR) density in the universe is a strong function of the galaxy stellar mass (Juneau et al. 2005), it might be that GRB hosts at low and high redshifts are associated with less and more massive galaxies, respectively.

From the multiband photometry, we derive a "pseudophotometry" to create a homogeneous sample, as described in Section 2.1 (Table 2). Thirty-three out of 46 hosts have detected optical emission lines, indicating ongoing star formation (Table 3). This is partly an observational bias, as the redshift of a GRB is often determined from the emission lines in the host. The bluest of these lines is the [O ii] at λ = 3727 Å. As many hosts are spectroscopically observed in the optical, the highest redshift of the sample is marked by the [O ii]λ3727 line, at z ∼ 1.6 (Figure 1). Details are given in Section 2.2.

2.1. The Photometric Sample

The photometry of the sample is mainly covering the observed optical (including the U band) and NIR bands. For a subsample, mid-IR detections or upper limits are also available (Le Floc'h et al. 2006; Berger et al. 2007b). Only GRB hosts detected in at least two bands are included in the sample, the reddest of which has to be above the 4000 Å break. This means mainly z ≲ 3.4 hosts, the only exception being the host of GRB 050904 at z = 6.3, for which only optical and mid-IR upper limits are available (Berger et al. 2007b). The total number of GRBs with z ≲ 3.4 is 109, two fifths of which are in our sample. The rest were not considered, because optical–NIR photometry is not available either because observations were never attempted or not deep enough.

The detection of the host above the 4000 Å break is necessary to determine one of the galaxy key parameters, the total stellar mass. Parameters derived from only UV photometry are very uncertain because the mass-to-light ratio in the UV can vary by a very large factor in young stellar populations and due to the presence of dust.

The main difficulty of dealing with the photometric sample of GRB hosts is that it is very heterogeneous and sparse. For instance, the data taken by different groups are treating Galactic dust extinction or aperture corrections in different ways. Moreover, heterogeneous filters are often used. In a few cases the GRB host is observed in the same band with different telescopes, and results differ by more than the observational uncertainties.

To reduce the confusion, from the observed multiband photometry we have derived a "pseudophotometry," which is a homogeneous photometry for a reduced set of filters. Magnitudes for the pseudophotometry in the AB system, corrected for Galactic extinction, are reported in Table 2.

The principle of "pseudophotometry" is to first define a large set of commonly used filters including SDSS, Hubble Space Telescope (HST), Bessel, Johnson, and IRAC filters. Then, we reduce this set of filters to the filters which are necessary to represent all the photometric points involved in the available GRB-host observations. To do so, we use a criterion |log λ₁ − log λ₂| < log(1 + 300/5000), or maximum wavelength difference of 300 Å at 5000 Å: the effective wavelengths λ₁ of the filters involved in the real photometry must be close enough to one of the effective wavelengths λ₂ included in the reduced set of filters. We thereby build a small set of 16 filters, ranging from the U band to IRAC 8 μm band, which we use in practice for our spectral energy distribution (SED) fitting. All the GRB-host SEDs are therefore described with this set of filters. The effect of using the reduced set of filters instead of the exact bibliographic filters is small for our study: the offset in effective wavelengths is typically less than 200 Å. For each GRB host, we checked with Monte Carlo simulations that random shifts of this order on the filters wavelengths produce small errors on the mass estimates. We note that not all observed magnitudes are in Table 2. For more details on the observed photometry, see the GHostS database.

The R_AB and K_AB magnitudes for the sample are shown in Figure 2. The comparison with the GDDS K_AB < 22.5 galaxies shows that GRB hosts are generally faint galaxies, with about half being fainter than R_AB = 23.5 and K_AB = 22.5. All short-GRB hosts are at z < 0.7. This could be a selection effect, as short afterglows are harder to detect than long afterglows (Gehrels et al. 2005). In Figure 3, we show the apparent colors of the sample. The comparison with a complete sample of GDDS galaxies, and the predicted colors assuming different stellar populations (E/S0, Sbc, irregulars, and starbursts), indicates that GRB hosts are generally blue star-forming galaxies (see also Berger et al. 2007a). The short-GRB hosts are still too few to conclude anything about their stellar population from their colors.

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2.2. The Spectroscopic Sample

The stellar properties of GRB hosts in the sample have been studied using the observed multiband photometry. Following the procedure of Glazebrook et al. (2004), we model the stellar population using PÉGASE.2 (Fioc & Rocca-Volmerange 1997, 1999) and PÉGASE-HR (Le Borgne et al. 2004). In order to avoid distorted mass-to-light ratios from young burst components superimposed on older stars, we represent the stellar population by two components, with SFR ∝exp^−t/τ, where t is time and τ is the e-folding time. The first component is one of 10 alternate SEDs, each characterized by a different discrete value of τ (from starburst to constant SFR), covering a range of star formation histories (SFHs). The primary stellar component is coupled with a secondary component representing a star-bursting episode, with τ = 0.1 Gyr, and a total stellar mass in the range from 1/10,000 up to two times the mass of the primary component. The age of the stellar population is also constrained by the age of the universe at the observed galaxy redshift. The attenuation of the stellar emission, due to dust, is a free parameter and can vary in the range 0 < A_V < 2 (the Calzetti law is used). The same for the metallicity, in the range 0.0004 ⩽ Z ⩽ 0.02. The modeling also includes an emission-line nebulosity component which we include as it can have small effects on the photometry near bright lines. We use the standard PÉGASE prescription for this and note that this is only used in the SED modeling and not in the interpretation of real galaxy emission-line spectra.

The IMF used to estimate stellar masses is that which is derived by Baldry & Glazebrook (2003). This more realistic IMF gives a total stellar mass which is generally 1.8 and 1.3 times lower than that derived by using Salpeter (1955) and Kroupa (2001) IMF, respectively. The full distribution function of allowed masses was calculated by Monte Carlo resampling the photometric errors. The Monte Carlo error approach is to (1) apply a scaled Poisson error distribution of the fluxes and flux errors (this is superior to using a Gaussian distribution as fluxes come from photon counting detectors); (2) create a new SED by flux and Poisson realization (flux error) and refit the masses; and (3) iterate N times to make a distribution. The resulting mass distribution then samples the range of SFHs consistent with the error distribution of the photometry. The final masses and errors are the mean and standard deviation of the Monte Carlo mass distribution.

Our code is more general than most in the literature because we include a secondary burst component. This is advantageous as it allows for possible mass biases associated with young bursts superimposed on old stellar populations to be explored (by turning off the burst term). In general we find that masses are robust to turning on/off bursts, and varying metallicities and dust, and are good to the 0.2–0.3 dex level. With this code then the mass of GRB hosts with poor photometry (e.g., few data points or photometry not sampling redder rest frame wavelengths) is poorly constrained, and this is reflected correctly as large error bars in Table 5.

The requirement that one or more photometric detections above the 4000 Å Balmer break is known, and that at least two photometric bands are used, provides a reasonably robust total stellar mass determination. At λ>4000 Å, the SEDs are far less affected by younger stellar populations and uncertain dust modeling.

Figure 4 shows the best fit to the observed SED. The stellar mass-to-light ratio in the K band, M_*/L_K, and the stellar mass for each GRB host are listed in Table 5, together with the absolute K and B magnitudes. The age of the last episode of star formation, the metallicity, the SFR, and dust extinction in the stellar component are also calculated. However, these parameters are more uncertain due to the well-known degeneracy, according to which the colors of metal-rich stellar populations are indistinguishable from those of old or dusty stellar populations (Worthey 1994).

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Our method is more general than previous work which make assumptions which speed up the calculation (for example, by assuming a single simple SFH or a single metallicity). In contrast with the method adopted by Christensen et al. (2004), our metallicity is given by the best fit, and not assumed to be solar. Moreover, Christensen et al. (2004) assume a single episode of star formation and do not derive the total stellar mass.

3.1. Stellar Masses

For the stellar mass fitting, we have utilized a very robust code which has been applied and tested in the literature extensively (e.g., Glazebrook et al. 2004; Baldry et al. 2008).

Stellar masses and AB absolute K and B magnitudes are shown in Figure 5 and Table 5. Magnitudes are corrected for dust attenuation in the host (a Calzetti law is assumed). In Figure 5 we show the comparison with field galaxies, from the GDDS (Glazebrook et al. 2004) and LBGs (Reddy et al. 2006). The GRB-host median stellar mass is 10^9.3  M_☉, and is much lower than in the GDDS, by about one order of magnitude. For short-GRB hosts, the median mass is higher, ∼10^10.1M_☉. More objects are necessary to conclude that the typical mass of short-GRB hosts is larger than that of long GRB hosts. The curves in the upper plot of Figure 5 represent the stellar mass as a function of redshift of a galaxy with AB K observed magnitude m_K = 24.3, in the case of a old simple stellar population or a young stellar population with constant SFR.

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In general, the sample is too small and inhomogeneous to study the mass function of the GRB-host population. Nevertheless, we inspected the fraction of GRB hosts per stellar mass bin. In Figure 6, we compare this with that of the high-z LBG sample (Reddy et al. 2006), after normalizing it to the GRB-host sample for galaxy stellar mass M_* > 10¹⁰M_☉, where the LBG sample is less affected by incompleteness. From the GRB-host stellar mass histogram (which drops for M_* < 10^9.2 M_☉), it is clear that galaxies similar to the typical GRB host are under-represented in high-z spectroscopic galaxy surveys.

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As already described before, the stellar mass of galaxies is better represented by the observed fluxes redward of the Balmer break at 4000 Å. The rest-frame K-band luminosity is generally well correlated with the galaxy stellar mass. This correlation is also shown by GRB hosts (Figure 7), and can be expressed by

$$\begin{equation} \log M_\ast = -0.467 \times M_K - 0.179, \end{equation} \tag{ 1 }$$

where M_K is the dust-corrected K-band absolute magnitude. This relation can be used to estimate the stellar mass of GRB hosts, provided that the SED is known redward of the Balmer break. The dispersion of the sample in Figure 7 around Equation (1) is about a factor of 2, and gives the minimum error on the stellar mass that one obtains by using this procedure. Such an error does not take into account systematic uncertainties on the modeling of the stellar mass and errors on the measured photometry.

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We note that on average GRB hosts have higher K-band luminosities than field galaxies (from GDDS) with the same stellar mass (Figure 7). This means that M_*/L_K is lower, which is expected from younger galaxies (Glazebrook et al. 2004), suggesting an intrinsic difference between the two galaxy populations.

We compared our results with the stellar masses derived for seven hosts by Chary et al. (2002) and another seven hosts by Castro Cerón et al. (2006). We find a weak correlation in the former, and no correlation at all in the latter, although the sample is too small to draw any conclusion.

Optical emission lines⁵ detected in a subsample of 33 GRB hosts (redshift range 0.009 < z < 1.31) are used to estimate SFRs, metallicities, and dust extinction in the gas component. These are all (but one) long GRB hosts. The exception is the host of the short GRB 051221 (Soderberg et al. 2006b). Stellar absorption and slit-aperture flux loss (Table 4) are taken into account to estimate the total emission flux. The dust extinction in the hosts is obtained as described below, and is used when measuring SFR and metallicity. The final adopted SFRs for GRB hosts are listed in the eighth column of Table 6. It is the value measured from Hα when available, or [O ii] otherwise. If no emission line is detected, UV luminosities at 2800 Å are used. Details are in Sections 4.2 and 4.3.

4.1. Dust Extinction

4.2. Star Formation Rates from Emission Lines

Traditionally, the best SFR indicator available for the optical-UV is the Hα luminosity, corrected for dust extinction and stellar absorption. Otherwise, the more uncertain [O ii] or Hβ can be used instead. The conversions derived by Kennicutt (1998) are the most commonly used. Moustakas et al. (2006) also provided conversions, valid for local star-forming galaxies.

We used the dust-corrected [O ii], Hβ, and Hα luminosities. A mean visual extinction 〈A_V〉 = 0.53 corresponds to an SFR correction for [O ii], Hβ, and Hα fluxes of a factor of 2.1, 1.8, and 1.5, respectively (for MW extinction law), is applied when the Balmer decrement is not measured. The Balmer stellar absorption correction is on average 4% and 10% of the observed flux, for Hα and Hβ, respectively (Table 4). The slit-aperture flux loss (up to a factor of 5, Table 3) is also taken into account.

To derive SFR from Hα, we used the prescription given by Kennicutt (1998). We only correct for the different IMF adopted, which gives an SFR a factor of 1.8 lower, going from Salpeter to the more realistic IMF proposed by Baldry & Glazebrook (2003). This gives

$$\begin{equation} {\rm SFR}_{\rm H\alpha } = 4.39\times 10^{-42} \frac{L(\rm H\alpha)_{\rm corr}}{\rm erg\; s^{-1}}\; M_\odot \; {\rm yr}^{-1}, \end{equation} \tag{ 2 }$$

where L(Hα)_corr is the Hα luminosity corrected for stellar absorption and dust extinction.

Equivalently, the SFR from Hβ can be expressed by

$$\begin{equation} {\rm SFR}_{\rm H\beta } = 12.6\times 10^{-42} \frac{L(\rm H\beta)_{\rm corr}}{\rm erg\; s^{-1}}\; M_\odot \; {\rm yr}^{-1}, \end{equation} \tag{ 3 }$$

where L(Hβ)_corr is the dust and stellar absorption corrected Hβ luminosity, and the multiplicative constant 12.6 is the one in Equation (2) multiplied by 2.86 (the recombination factor assuming T = 10⁴ K; Osterbrock 1989).

The advantage of using Hβ instead of [O ii] to estimate SFR is that, to first order, it does not depend on metallicity. However, the stellar Balmer absorption is generally uncertain, and important for old stellar populations. On the other hand [O ii] is generally stronger and easier to detect than Hβ, but it is more affected by an at times undetermined dust extinction. Moreover, the [O ii] flux depends on metallicity and ionization level (Kewley et al. 2004).

Moustakas et al. (2006) found that the mean dust-corrected [O ii]-to-Hα flux ratio in local star-forming galaxies is about 1, with negligible dependence from the galaxy luminosity. SFRs based on the observed [O ii] luminosity are 0.4 dex uncertain. The metallicity⁶ dependence is weak −0.1 < log([O ii]/Hα) < 0.2 in the metallicity range 12 + log(O/H) = 8.2–8.7, and becomes linear (in log–log scale) for 12 + log(O/H) < 8.2, down to 12 + log(O/H) = 7.5, where log([O ii]/Hα) ∼ −1.0. For galaxies with relatively high metallicity, the [O ii] SFR is rather robust.

In nine GRB hosts the dust-corrected ratio is relatively low, in the range −0.6 < log([O ii]/Hα) < 0.0, which can be explained by the generally low metallicities (see Section 5). Metals are an important source of radiative cooling, which gives the relation between metallicity and [O ii]/Hα (Kewley et al. 2001). We note the different mean redshift for the GRB hosts and the Moustakas et al (2006) sample (z = 0.23 and z ∼ 0, respectively). However, this is likely too small to sensibly affect the results.

We derived an [O ii]–SFR relation valid for GRB hosts by considering the subsample with simultaneous [O ii] and Hα detection. The [O ii]–SFR best conversion is empirically derived by determining the best concordance between the SFRs estimated from Hα and [O ii] (Figure 8). This is given by

$$\begin{equation} {\rm SFR}_{[{\rm O}\,\hbox{\scriptsize {\sc {ii}}}]} = 5.54\times 10^{-42} \frac{L([{\rm O}\,\hbox{\sc {ii}}])_{\rm corr}}{\rm erg\; s^{-1}}\; M_\odot \; {\rm yr}^{-1}, \end{equation} \tag{ 4 }$$

where L([O ii]_corr is the dust-corrected [O ii] luminosity. The dispersion in Figure 8 is 0.22 dex (a factor of 1.7). Equation (4) is proposed as a valuable tool to estimate SFRs for GRB hosts when Hα or Hβ are not detected. Equation (4) gives an SFR which is a factor of 1.39 lower than the same relation proposed by Kennicutt (1998), after converting to the same IMF.

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To check the validity of our [O ii] SFR conversion, we studied the sample of 18 GRB hosts with simultaneous measurement of [O ii] SFR and Hβ SFR (Figure 9). The correlation is very good, and is basically indistinguishable from the best-fit linear correlation. The dispersion in this sample is 0.26 dex (a factor of 1.8).

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When Hα is not measured, we estimated SFR from [O ii] using Equation (4) (Table 3). SFR from Hβ is also estimated for a subsample of GRB hosts (Table 3). The slit-aperture correction is not necessary when deriving SFR relations, but it is required when estimating the total SFR. This correction is uncertain, because it depends on the galaxy size and how the star-forming H ii regions are distributed in the galaxy. All SFRs derived from emission lines (Table 6) are corrected for aperture-slit loss (given in Table 3).

4.3. Star Formation Rates from the UV Luminosity

For 13 GRB hosts, there is no information on emission-line luminosities from H ii regions. This is because either the redshift of the GRB is too high, so significant emission lines are shifted to the NIR (where observations are much harder), or lines are intrinsically too weak, or simply the host was never spectroscopically observed. The UV luminosity can be used instead to estimate SFR, as this is a tracer of almost instantaneous conversion of gas into stars. However, we should say that residual UV emission can still be detected even in the absence of star formation, for instance from blue horizontal branch stars.

UV luminosities were used several times in the past to study the SFR history of the universe (Madau et al. 1998; Glazebrook et al. 1999; Meurer et al. 1999; Erb et al. 2006; Moustakas et al. 2006). The conversion often used is the one provided by Kennicutt (1998) at 1500 Å. Moustakas et al. (2006) use the U-band luminosities at 3600 Å, as this is less affected by dust.

We derived relations between UV luminosities and SFR more suitable for GRB hosts, using the same empirical approach as for [O ii]. We compare SFRs derived from emission lines, with UV luminosities obtained from the best fit of the observed SED (Figure 4). We obtain

$$\begin{equation} {\rm SFR}_{1500} = 1.62\times 10^{-40} \frac{L_{1500,{\rm corr}}}{\rm erg\; s^{-1}\; \AA^{-1}}\ M_\odot \; {\rm yr}^{-1} \end{equation} \tag{ 5 }$$

$$\begin{equation} {\rm SFR}_{2800} =4.33\times 10^{-40} \frac{L_{2800,{\rm corr}}}{\rm erg\; s^{-1}\; \AA^{-1}}\ M_\odot \; {\rm yr}^{-1} \end{equation} \tag{ 6 }$$

$$\begin{equation} {\rm SFR}_{3600} = 5.47\times 10^{-40} \frac{L_{3600,{\rm corr}}}{\rm erg\; s^{-1}\; \AA^{-1}}\ M_\odot \; {\rm yr}^{-1} \end{equation} \tag{ 7 }$$

for dust-corrected rest-frame 1500 Å, 2800 Å and 3600 Å luminosities, respectively. Results for 33 GRB hosts are shown in Figure 10 and given in Table 6 (for SFR₂₈₀₀ only). The dispersions of the points around the three relations are 0.49, 0.41, and 0.40 dex, respectively. This is relatively small, given the large interval spanned by the SFRs (3.5 orders of magnitude) and the uncertainties of the UV–SFR relations (Glazebrook et al. 1999). The dispersion found by Erb et al. (2006), who derived SFRs using Hα and UV at 1500 Å and the Kennicutt (1998) conversion, is 0.34 dex. Moustakas et al. (2006) used the UV luminosities at 3600 Å, on the subsample of galaxies with B absolute magnitude M_B < −18.3. When converted to take into account the different IMF and the monochromatic luminosity, the constant in our Equation (7) is a factor of 2.0 larger than theirs. This factor is 1.5 if dwarf galaxies only are considered (M_B > − 18.3). Meurer et al. (1999) estimated an SFR conversion in local starbursts using UV luminosities at 1600 Å. After correcting for the same IMF, Equation (5) gives SFRs which are 2.7 times higher than theirs. These differences can be explained by variations in SFH, dust attenuation, and redshift among the samples (effectively, different sample selections). Equations (5)–(7), proposed for GRB hosts, can be used to estimate SFR when no emission lines are detected, likely for low SFRs or z > 1.6.

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The good agreement between SFRs from emission lines and SFR₃₆₀₀ is surprising as one expects these longer continuum wavelengths to be increasingly affected by older stellar populations (Madau et al. 1998). The fact that the dispersion is still small indicates again that GRB galaxies are dominated by young stellar populations. We note that 3600 Å is much less affected by dust than 1500 Å, but likely marginally affected by UV photons from older stars. The best measure of SFR, on balance, might be that derived at 2800 Å.

In Figure 11, we show SFR₂₈₀₀ and SFR derived from emission lines, as a function of redshift. UV luminosity are very useful to estimate SFRs at z > 1.6, and in general are more sensitive to low SFRs. In the same figure also SFRs from GDDS galaxies and LBGs (Erb et al. 2006).

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An interesting finding is a possible correlation between the SFR and the stellar mass (Figure 12). This has not been seen before in high-redshift or local galaxy samples. If confirmed, it might be peculiar to the GRB-host sample, and suggest an approximately constant specific SFR (SSFR). Whether or not it has physical significance needs to be determined from more extensive data.

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4.4. Specific Star Formation Rates

The SFR by itself does not tell how active the galaxy is. Another parameter to consider is the SSFR, that is the SFR normalized to the total stellar mass of the galaxy. The SSFR has been studied in galaxies at low redshift (Pérez-González et al. 2003; Brinchmann et al. 2004) and high redshift (Juneau et al. 2005; Bauer et al. 2005; Noeske et al. 2007).

In Figure 13 we show the SSFR as a function of stellar mass, investigated for the first time for a large sample of GRB hosts. These are compared with SSFRs of star-forming galaxies of the GDDS in the redshift interval 0.4 < z < 1.7 (Juneau et al. 2005; Savaglio et al. 2005) and LBGs at 1.3 ≲ z ≲ 3 (Reddy et al. 2006). Field galaxies of the AEGIS at 0.70 < z < 0.85 cover a similar region in the SSFR–M_* plot as the GDDS (Noeske et al. 2007). The SSFRs in GRB hosts tend to show properties different from field galaxies in the GDDS, with lower masses and higher SSFRs. The median SSFR for the GRB hosts is 0.8 Gyr⁻¹, similar to LBGs, but the mean stellar mass is six times lower, 10^9.3 M_☉ for the former and 10^10.1M_☉ for the latter.

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The inverse of the SSFR is called the growth timescale ρ_*. It defines the time required by the galaxy to form its observed stellar mass, assuming that the measured SFR has been constant over the entire galaxy history. In Figure 14, we show ρ_* (left y-axis) or SSFR (right y-axis) as a function of redshift. The symbol size is bigger for larger stellar masses. For all but one GRB host with detected emission lines, ρ_* is smaller than the age of the universe (Hubble time) at the observed redshift. This is true for four more GRB hosts, with SFR estimated from UV luminosities. For the total sample of 46 hosts, the median value is ρ_* = 1.3 Gyr, and for 2/3 ρ_* < 2 Gyr. It is also apparent that the growth timescale is longer for more massive galaxies. This is different than what has been observed in other galaxy samples, which have a large fraction of quiescent galaxies (ρ_* larger than the Hubble time). When ρ_* is <1 Gyr, true for about 2/5 of the GRB-host sample, the galaxy is in a "bursty mode." For instance, a galaxy with a stellar mass of a few times 10⁹ M_☉ (the stellar mass of the LMC) and SFR = 5 M_☉ yr⁻¹ (10 times larger than LMC) is a starburst, with ρ_* ∼ 500 Myr.

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Metallicity in H ii regions is typically measured using detected emission lines. At redshift z > 0.2, the spatial resolution of the data is generally too low to derive metallicity in small regions, so what is measured from integrated fluxes is an optical luminosity-weighted mean value in the galaxy. This is the case for most GRB hosts analyzed here, as 85% of the spectroscopy sample is at z > 0.2. For low-z hosts, like that of GRB 060505 at z = 0.089 studied in great detail by Thöne et al. (2008), we use integrated fluxes over the entire galaxy to treat it as the rest of the sample.

Metallicities can be derived from different emission-line sets, according to the spectral coverage, redshift, and galaxy properties. The numerous methods, developed in the last few years, have complicated the effort of having a tool for a realistic estimate. Each method is affected by systematic errors that are not easy to determine (for a review, see Kewley & Ellison 2008).

A direct estimate is possible through a measurement of the electron temperature T_e (Izotov et al. 2006), possible when several lines of the same element with very different ionization levels are detected (Bresolin 2007). For instance, these could be the generally weak auroral line [O iii]λ4363 and the nebular lines [O iii]λλ4959, 5007. For its definition, the T_e method is sensitive to low-metallicity systems. As this is based on the generally weak [O iii]λ4363 line, it is very hard to measure in small and distant galaxies.

Other calibrators are easier to measure, but give more systematically uncertain results. The O3N2 calibrator, which uses a combination of [O iii]λ5007, [N ii]λ6583, Hβ, and Hα lines (Alloin et al. 1979), needs NIR spectroscopy when exceeding redshift z = 0.5.

For higher redshift and relatively low spectral sensitivity, the very popular R₂₃ calibration (Pagel et al. 1979) and its refinement, the P-method (Pilyugin 2000), both requiring Hβ, [O ii], and [O iii] fluxes, can be used up to redshift z ≃ 1. The R₂₃ calibration is notoriously problematic. First, it gives two solutions (lower and upper branch), which are not easy to disentangle. Moreover, the upper branch solution, when applied to integrated fluxes, is affected by systematic errors which could be as large as a factor of 3 (Kewley & Dopita 2002; Kennicutt et al. 2003; Stasińska 2005; Bresolin 2006). A value of log(N ii]/[O ii]) < −1.2 can point to the lower branch solution (Kewley & Dopita 2002). Despite the difficulties, the R₂₃ calibrator is an important resource because it is easier to measure than other methods.

Our choice for the final metallicity is done as follows: the T_e metallicity is preferred, measurable for four GRB hosts with detected [O iii]λ4363. When this is not detected, we give priority to the O3N2 metallicity, available for five GRB hosts, and use the prescription given by Pettini & Pagel (2004).

For all other GRB hosts, we used the R₂₃ calibrator, available for a total of 18 hosts. Recently, Kewley & Ellison (2008; hereafter KE08) derived conversion relations between different methods. Following their prescriptions, we used the R₂₃ calibrators given by Kewley & Dopita (2002) and Kobulnicky & Kewley (2004), for the lower and upper branch solutions, respectively. We converted R₂₃ metallicities into O3N2 metallicities using the relations proposed by KE08. These are tested for metallicities in the ranges 8.05 < log 12 + log(O/H) < 8.3 and 8.2 < log 12 + log(O/H) < 8.9, for the lower and upper branch solution, respectively. For metallicities outside these ranges, we use the recently tested R₂₃–metallicity relation proposed by Nagao et al. (2006, hereafter N06).

The hosts for which we could measure metallicity are all at z < 1. For z > 1, no NIR spectra of GRB hosts are good enough to measure metallicity. In the following subsections, we list measurements for different methods.

5.1. The T_e Metallicities

5.2. O3N2 Metallicities

The O3N2 method, originally proposed by Alloin et al. (1979), was updated by Pettini & Pagel (2004). In the new formulation, the metallicity is given by

$$\begin{equation} 12+\log (\rm O/H) = 8.73-0.32\times O3N2, \end{equation} \tag{ 8 }$$

where O3N2 = log{([O iii]5007/Hβ)/([N ii]6583/Hα)}. This method is useful only for −1 < O3N2 < 1.9, and much more uncertain for O3N2 ≳ 2.

This metallicity can be measured in five GRB hosts, and in two additional objects an upper limit is set (Table 8). Derived values are low, with a mean metallicity of 1/3 solar.

Table 8. O3N2 Metallicities

GRB	z	O3N2a	12 + log(O/H)
980425	0.0085	1.94	8.1 ± 0.5
990712	0.434	> 1.29	<8.3
020903	0.251	2.39	8.0 ± 0.5
030329	0.168	> 1.81	<8.2
031203	0.1055	2.07	8.1 ± 0.5
060218	0.03345	1.87	8.13 ± 0.25
060505	0.0889	0.92	8.44 ± 0.25

Notes. Quantities are all corrected for dust extinction and stellar absorption. The uncertainties on metallicities are ±0.25 dex for −1 < O3N2 < 1.9, and 0.5 for larger O3N2 values (Pettini & Pagel 2004). ^aO3N2 = log{([O iii]5007/Hβ)/([N ii]6583/Hα)}.

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5.3. R₂₃ Metallicities

The R₂₃ calibrator uses the following combination of [O ii], [O iii] and Hβ lines:

$$\begin{equation} \log R_{23} = \log \left(\frac{\rm [O\,\hbox{\sc {ii}}]\lambda 3727+[O\,\hbox{\sc {iii}}]\lambda \lambda 4959,5007}{\rm H\beta }\right), \end{equation} \tag{ 9 }$$

and the O₃₂ parameter:

$$\begin{equation} \log O_{32} = \log \left(\frac{\rm [O\,\hbox{\sc {iii}}]\lambda \lambda 4959,5007}{\rm [O\,\hbox{\sc {ii}}]\lambda 3727}\right), \end{equation} \tag{ 10 }$$

which takes into account different ionization levels of the gas. In Figure 15 we show R₂₃ and O₃₂ for GRB hosts, and comparison with galaxies of the GDDS and Canada France Redshift Survey (CFRS; Lilly et al. 2003) at 0.4 < z < 1, before dust-extinction correction (the dust extinction in GDDS and CFRS galaxies is not measured). GRB hosts tend to have higher R₂₃ values, which could be due to low metallicity or/and lower dust extinction.

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To measure R₂₃ metallicities, we followed the prescriptions given by KE08. Namely, we used Kewley & Dopita (2002) and Kobulnicky & Kewley (2004) for the lower and upper branch solutions, respectively. Then we used the relations given by KE08 to convert to O3N2 metallicities. These relations are valid for 8.05 < 12 + log(O/H) < 8.3 and 8.2 < 12 + log(O/H) < 8.9 only (for the input metallicity). See Section 5.4 for more R₂₃ metallicities.

The R₂₃ and O₃₂ values used are corrected for dust extinction, and are reported in Table 9, together with the derived metallicities.

Table 9. GRB-Host Metallicities

			12 + log(O/H)
GRB	log R23	log O32	Lower KD02a	Upper KK04b	Lower N06c	O3N2d	Tee	Adoptedf	log ([N ii]/[O ii])	log ([N ii]/Hα)
980425	0.960	0.550	...	...	∼8.1	8.1	8.16	8.16	−1.06	−1.21
980703	0.840	−0.529	...	8.14	7.6	...	...	7.6/8.14	...	...
990712	0.932	0.302	...	...	∼8.1	<8.3	...	8.1	<−0.66	<−0.66
991208	0.330	0.491	...	8.73	<7.4	...	...	<7.4/8.73	...	...
010921	0.857	−0.064	...	8.15	8.0	...	...	8.0/8.15	...	...
011121	0.566	−0.429	7.50	8.64	...	...	...	7.50/8.64	...	...
020405	0.759	0.279	7.78	8.44	...	...	...	7.78/8.44	...	...
020903	0.957	0.508	...	...	∼8.1	8.0	8.22	8.22	−1.55	−1.67
030329	0.820	0.430	7.97	8.33	...	<8.2	...	7.97	<−1.08	<−1.25
030528	0.935	0.179	...	...	∼8.1	...	...	8.1	...	...
031203	0.965	1.067	8.25	...	...	8.1	8.02	8.02	−0.68	−1.27
050223	0.536	−0.135	...	8.66	7.5	...	...	7.5/8.66	...	...
050416	0.741	−0.029	7.97	8.44	...	...	...	7.97/8.44	...	...
051022	0.556	0.186	...	8.65	7.5	...	...	7.5/8.65	...	...
051221	0.614	−0.336	...	8.59	7.6	...	...	7.6/8.59	...	...
060218	0.927	0.396	...	...	∼8.1	8.13	7.29g	8.13	−1.15	−1.22
060505	0.770	−0.292	...	8.37	7.8	8.44	...	8.44	−0.88	−0.75

Notes. Quantities are corrected for dust extinction in the host. No solution was found for the host of GRB 040924, so this is not included in the table. ^aDerived using the R₂₃ lower branch solution, as defined by Kewley & Dopita (2002), and converted to O3N2 metallicity, according to Kewley & Ellison (2008). ^bDerived using the R₂₃ upper branch solution, as defined by Kobulnicky & Kewley (2004), and converted to O3N2 metallicity, according to Kewley & Ellison (2008). ^cDerived using the R₂₃ lower branch solution, as defined by Nagao et al. (2006), and converted to O3N2 metallicity, as described in Section 5.4. ^dDerived using the O3N2 prescription of Pettini & Pagel (2004). Uncertainty is 0.25 or 0.5, for 12 + log(O/H)>8.1 or 12 + log(O/H) ⩽ 8.1, respectively. ^eDerived using the electron temperature T_e prescription of Izotov et al. (2006). ^fFinal adopted metallicity. For a subsample of GRB hosts, both the lower and upper branch solutions are considered. ^gThis value is likely a lower limit, due to the dubious detection of the [O iii]λ4363 line.

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5.4. More R₂₃ Metallicities

For metallicities outside the intervals 8.05 < 12 + log(O/H) < 8.3 and 8.2 < 12 + log(O/H) < 8.9 we used the R₂₃–metallicity relation provided by N06. This is described by a best-fit polynomial, whose coefficients are in Table 6 of N06. Six GRB hosts have R₂₃ in the turnover region, for which 12 + log(O/H) ∼ 8.1 (Table 9). For the other GRB hosts, in the case of the lower branch part of the relation, we estimated the correction from N06 to KE08, by comparing results for those hosts with metallicity calculated with both calibrations. The conversion relation from N06 to KE08 is given by

$$\begin{equation} 12+\log (\rm O/H)_{KE08} = 0.8885\times [12+\log (\rm O/H)_{N06}] +1.177, \end{equation} \tag{ 11 }$$

valid in log 12 + log(O/H) = 7.2–8.1 for the N06 metallicity. Results for the lower branch metallicities, after applying Equation (11), are given in the sixth column of Table 9.

The upper branch solution of N06 is not used, as this does not add anything to our analysis.

5.5. The Electron Density

5.6. AGN Contamination

Figure 16 shows the location of GRB hosts, in the diagrams that use line ratios to distinguish galaxies with bright H ii regions from AGN dominated galaxies. For comparison, we also show GDDS and CFRS star-forming galaxies at high redshift, and local metal-poor galaxies (Izotov et al. 2006).

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The [O iii]/Hβ versus [N ii]/Hα relations proposed by Kewley et al. (2001) and Kauffmann et al. (2003) are relatively robust diagnostics and generally used in galaxy surveys. The [O iii]/Hβ versus [O ii]/Hβ relation is more uncertain (Lamareille et al. 2004). However, this is easier to measure at z > 0.5, when NIR spectra are not available.

From Figure 16, we conclude that the AGN contamination in GRB hosts is likely not significant. The [O iii]/Hβ versus [N ii]/Hα plot indicates that GRB hosts behave like local metal-poor galaxies, i.e. with high values of [O iii]/Hβ. In fact, the majority of galaxies in the local universe from the SDSS have [O iii]/Hβ < 1 (Stasińska et al. 2006).

The main goal of this work is to characterize the galaxy population hosting GRBs. In the past, several authors conducted studies over a small sample of GRB hosts and concluded that this population is not representative of the bulk of all galaxies as a function of cosmic time (Fruchter et al. 1999; Le Floc'h et al. 2003; Christensen et al. 2004; Berger et al. 2003, Tanvir et al. 2004; Fruchter et al. 2006; Le Floc'h et al. 2006). In fact, they are on average bluer, younger, and fainter than the field galaxy population. However, we consider that faint, blue, and young galaxies are by far the most common galaxies that existed in the past. Galaxies can only get bigger over time and not smaller, through merging and star formation processes. Nevertheless, they are the most elusive to find in the distant universe. Through a GRB event, our capabilities of digging deeper in terms of galaxy mass and distance is considerably increased.

Fruchter et al. (2006) showed that long GRBs happen much more in the brightest regions of their host galaxies than type II SNe, suggesting that GRBs are associated with different galaxies. This result is not confirmed by Kelly et al. (2008), who considered SN Ic hosts and found that SN Ic occur in an environment similar to that of GRBs. Indeed, some nearby GRBs are associated with SN Ic, a subclass of core-collpase supernovae (Galama et al. 1998; Stanek et al. 2003; Hjorth et al. 2003; Modjaz et al. 2006).

The connection between GRB events and the nature of their hosts is advocated by Modjaz et al. (2008), who found that five GRB hosts are significantly more metal poor than sample of SN Ic hosts in a similar luminosity range in the B band. However, SN discoveries are observationally biased toward luminous (and hence on average more metal rich) galaxies.The result of Modjaz et al. (2008) is affected by the small number statistics. Prieto et al. (2008) found in a statistically significant sample a much larger metallicity spread, and a significant mass–metallicity relation which would include GRB hosts. Moreover, one should consider that the B-band absolute luminosity in galaxies is weakly correlated with mass. The K-band luminosity would instead better represent the galaxy stellar mass (Figure 7), and this would better support the special nature of GRB hosts. Wolf & Podsiadlowski (2007) quantitatively showed that any GRB rate dependence on galaxy mass (or ultimately metallicity) is at best small.

To better understand the impact of GRB hosts on our knowledge of galaxy formation and evolution, we have analyzed the properties of the largest possible sample, 46 GRB hosts, using multiband photometry and optical spectroscopy. Relevant parameters are summarized in Table 11. The median redshift, K-band absolute magnitude, stellar mass, dust extinction, metallicity, SFR, and SSFR are reported at the bottom of the table.

The ultimate goal is to understand whether GRB hosts are special galaxies, related to the occurrence of a GRB event, or just normal galaxies, but small and metal poor because these are the most common galaxies in the universe. Due to the large redshift interval spanned by the sample, 0 < z < 6.3, different populations likely coexist. The one at low redshift is different from that at high redshift because of the intrinsic evolution of galaxies with time, and because of the redshift dependence of the selection effects.

From the colors of the sample, we confirm that GRB hosts tend to be blue galaxies. The best-fit SED can constrain the fraction of stars involved in the burst phase, which in our sample is generally less than 10% of the total mass. A reliable estimate of the K-band absolute magnitudes is provided. Due to observational limits, at high redshift only bright galaxies are detected. GRB hosts below z = 0.4 have −24 < M_K < −16. Most galaxies (83%) have stellar masses in the range 10^8.5 M_☉ to 10^10.3M_☉. The stellar mass completeness limit of the typical present day high-redshift galaxy survey is higher than 10^10.3M_☉. For M_* < 10^9.2 M_☉, the GRB-host sample is highly incomplete. For the six short-GRB hosts the median stellar mass is M_* ≃ 10^10.1 M_☉, indicating that the association of short GRBs with elliptical, more massive galaxies needs a larger sample to be proven. We provide a relation between stellar mass and absolute magnitude K (Equation (1)), which is based on the finding of a nearly constant stellar mass-to-light ratio in the K band, of the order of M_*/L_K = 0.1 (M/L_K)_☉.

The SFRs derived from emission lines, after dust-extinction, aperture-slit loss, and stellar Balmer absorption correction, are the best approximation to the true total SFR. When emission lines are not measured, we propose an SFR relation which uses the UV luminosity at 2800 Å. SFRs in the total sample span three and a half orders of magnitudes (SFR = 0.01–36 M_☉ yr⁻¹). Two out of six short-GRB hosts have high SFRs, more than 10 M_☉ yr⁻¹. The SFR normalized by the stellar mass SSFR, or its inverse, the growth timescale ρ_* indicate that GRB hosts are active and young systems, which is expected given the generally low mass of the hosts, the high redshifts, and the fact that redshifts are often found trough the detection of emission lines.

Berger et al. (2003) and Le Floc'h et al. (2006) have claimed much higher SFRs, based on radio and mid-IR detections. The host of GRB 980613 looks involved into a merger of several subcomponents (Hjorth et al. 2002; Djorgovski et al. 2003). Our SFR estimate refers to component A that hosted the GRB. The high SFR derived by Le Floc'h et al. (2006) refers to component D, which is more than 30 kpc away from component A. Regarding GRB 980703 and GRB 000418, Le Floc'h et al. (2006) commented that AGN contamination would explain the high radio emission and no Spitzer detection. However, the existence of two GRB hosts with AGN on a relatively small sample observed in the radio is hard to explain (Michałowski et al. 2008). If the radio is associated with SF, then the nondetection in the mid-IR would imply a strong absorption by the silicates around 10 μm (E. Le Floc'h, 2008 private communication). The blue optical colors for some of the GRB hosts can be explained if large regions of these galaxies are totally obscured by dust. Optical light might be dominated by relatively less obscured stars outside star-forming regions, leading to blue colors (Michałowski et al. 2008).

We further investigate the relation between GRB hosts and other galaxies, by analyzing the mass–metallicity (MZ) relation. This is the correlation between the stellar mass of galaxies and their metallicity (Lequeux et al. 1979; Tremonti et al. 2004; Savaglio et al. 2005). In the MZ plot of Figure 17, we compare GRB hosts with local dwarf galaxies (Lee et al. 2006), and GDDS and CFRS galaxies at 0.4 < z < 1 (Savaglio et al. 2005). The local sample metallicities are estimated using the T_e method. Since the T_e or O3N2 metallicities are not measured for GDDS galaxies and GRB hosts, proper conversions are applied, as explained in Section 5. In the left and right panels of Figure 17, we show the lower and the upper branch solutions for metallicity in a subsample of nine GRB hosts. The picture is not very clear, and we do not detect an MZ relation in the GRB hosts of any kind, especially because for nine hosts the metallicity is poorly constrained. However, we can say that there is no indication that GRB hosts have metallicity lower than expected, given their stellar mass (Stanek et al. 2006). GRB hosts are not a special class of galaxies. Given the redshift and the stellar mass, the lower branch metallicity is favored for the nine GRB hosts with double solution (the right hand side of Figure 17),

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As regards the redshift evolution, we compare GRB-host metallicities, with the metallicities measured in 11 damped Lyman-α systems through afterglow spectroscopy (GRB-DLAs; Savaglio 2006) at redshift z > 2 (Figure 18). Again, the situation is not very clear. GRB-DLAs indicate that metallicities of the order of half solar are expected at z < 1. This is actually observed in the subsample of six GRB hosts whose metallicity (determined with the T_e or O3N2 calibration) is better constrained. However, for the rest of the sample, the lower branch solution suggests no redshift evolution in 0 < z < 6.3, an interval of more than 13 Gyr. Any conclusion needs more and deeper observations, to break the degeneracy in those objects already observed, or to study new objects. For instance, the O3N2 calibrator can be detected using NIR spectroscopy for the brightest objects at 1 ≲ z ≲ 1.6.

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The typical GRB host is a small starforming galaxy with likely subsolar metallicity, but a nonnegligible dust extinction (Table 11). It is in some regards similar to a young LMC, observed at redshift z ∼ 0.7, when it was more active than now, with an SFR which is five times higher than today. We still do not know whether hosts associated with short GRBs are considerably different from those associated with long GRBs.

We have presented a complete study of the largest sample of galaxies hosting GRBs, 46 objects, distributed along the redshift interval 0 < z < 6.3. GRB hosts can be used as important probes of the cosmic history of galaxy formation and evolution. Most GRBs are associated with the death of young massive stars, which are more common in star-forming galaxies. Therefore, GRBs are an effective tool to detect star-forming galaxies. As shown by recent studies (Glazebrook et al. 2004; Juneau et al. 2005; Borch et al. 2006), the star-formation density in the z < 1 universe is carried out by small, faint, low-mass star-forming galaxies, similar to the typical GRB host. Moreover, in the z ∼ 5 universe, GRB hosts observed with Spitzer are ∼3 times fainter than the typical spectroscopically confirmed galaxy in the Great Observatories Origins Deep Survey (GOODS; Yan et al. 2006), suggesting that not all star-forming galaxies at these redshifts are detected in deep surveys (Chary et al. 2007; Yüksel et al. 2008). We consider however, that our view of GRB hosts is still partial, as we mainly detect those at z < 1.5. Hosts at higher redshift are harder to observe. It is possible that high-z GRB hosts are more massive than those at low redshift, because star formation could be carried by more massive galaxies in the remote universe Future, deeper multiband observations of high-z hosts are mandatory to help solve this issue.

In summary, our conclusions are (Table 11) as follows:

• 1.  
  GRB hosts are generally small star-forming galaxies. The mean stellar mass is similar to the stellar mass of the LMC, M_* ∼ 10^9.3 M_☉. About 83% of the sample has stellar mass in the interval 10^8.5–10^10.3 M_☉). The median SFR = 2.5 M_☉ yr⁻¹ is five times higher than in the LMC.
• 2.  
  To estimate SFR, we derived new relations, suitable for GRB hosts. These give the total SFR when Hα is not detected, but [O ii] or UV are detected. Our SFRs span an interval of more than three orders of magnitudes, from 0.01 M_☉ yr⁻¹ to 36 M_☉ yr⁻¹.
• 3.  
  The dust extinction in the visual band is on average A_V = 0.53. The Balmer stellar absorption is generally small, but not negligible. Dust extinction, Balmer absorption, and slit-aperture flux loss are considered when measuring SFR.
• 4.  
  The median SFR per unit stellar mass (SSFR) is ∼0.8 Gyr⁻¹, with a small scatter, such that SFR ∝M_*, a somewhat surprising result. The median SSFR is about five times higher than in the LMC. A large fraction of GRB hosts are the equivalent of local starbursts.
• 5.  
  Metallicities derived from emission lines in the host galaxies at z < 1 are relatively low, likely in the range 1/10 solar to solar.
• 6.  
  Metallicities measured from UV absorption lines in the cold medium of GRB hosts at z > 2 (GRB-DLAs) are in a similar range. Combining this with the results for z < 1 GRB hosts, we see no significant evolution of metallicity in GRB hosts in the interval 0 < z < 6.
• 7.  
  The subsample of six short-GRB hosts have stellar masses 10^8.7 M_☉ < M_* < 10^11.0 M_☉ and SSFRs in the range 0.006–6 Gyr⁻¹. The suggestion that short-GRB hosts are large quiescent galaxies requires a larger sample to be confirmed.
• 8.  
  There is no clear indication that GRB host galaxies belong to a special population. Their properties are those expected for normal star-forming galaxies, from the local to the most distant universe.

Our investigation will continue, and results will be made public in the GHostS public database. In the final sample, we plan to include all GRB hosts detected with Swift, for a total of a few hundred objects. This will give a more complete picture on the nature of GRB hosts and their relation with all other galaxies.

We thank Avishay Gal-Yam, Emeric Le Floc'h, Lisa Kewley, Maryam Modjaz, John Moustakas, Daniele Pierini, Gra$\dot{\rm z}$yna Stasińska, and Christian Wolf for stimulating discussions. We are indebted to the anonymous referees for the many valuable comments. We also acknowledge the inspiring collaboration with Tamás Budavári, the programmer behind the GHostS database. Gerhardt Meurer is acknowledged for constant scientific support.