The recently-discovered Fundamental Metallicity Relation (FMR), which is the tight dependence of metallicity on both mass and SFR, proves to be a very useful tool to study the metallicity properties of various classes of galaxies. We have used the FMR to study the galaxies hosting long-GRBs. While the GRB hosts have lower metallicities than typical galaxies of the same mass, i.e., they are below the mass-metallicity relation, they are fully consistent with the FMR. This shows that the difference with the mass-metallicity relation is due to higher than average SFRs, and that GRBs with optical afterglows do not preferentially select low-metallicity hosts among the star-forming galaxies.
The gas-phase chemical abundance in galaxies is influenced by several effects: star formation and evolution, which reduce the amount of gas and increase the amount of metals, infall of metal-poor gas from the outer part of the galaxy and from the intergalactic medium, and outflow of enriched material due to feedback from SNe and AGNs. As a consequence, gas-phase metallicity is a fundamental test for all models of galaxy formation.
A fundamental discovery has been the relation between stellar mass M ⋆ (or luminosity) and metallicity (McClure & van den Bergh, 1968;Lequeux et al., 1979;Garnett, 2002;Lamareille et al., 2004;Pilyugin et al., 2004;Tremonti et al., 2004;Lee et al., 2006;Liang et al., 2006;Pilyugin & Thuan, 2007), with more massive galaxies showing higher Send offprint requests to: F. Mannucci metallicities. The origin of this relation is debated, and many different explanations have been proposed, including ejection of metal-enriched gas (e.g., Edmunds 1990;Tremonti et al. 2004), “downsizing”, which is a systematic dependence of the efficiency of star formation on galaxy mass (e.g., Brooks et al. 2007;Mouhcine et al. 2008;Calura et al. 2009), variation of the IMF with galaxy mass (Köppen et al., 2007), and infall of metal-poor gas (Finlator & Davé, 2008;Davé et al., 2010).
The evolution of the luminositymetallicity and mass-metallicity relations has been studied by many authors at z<1.5 (Contini et al., 2002;Kobulnicky et al., 2003;Maier et al., 2004;Liang et al., 2004; Fig. 1. Evolution of the mass-metallicity relation from local to high redshift galaxies from Mannucci et al. (2009). Data are from Kewley & Ellison (2008) (z=0.07), Savaglio et al. (2005) (z=0.7), Erb et al. (2006) (z=2.2) and Mannucci et al. (2009) (z=3-4). Cowie & Barger, 2008;Rodrigues et al., 2008;Hayashi et al., 2009;Lara-López et al., 2009;Lamareille et al., 2009;Pérez-Montero et al., 2009;Queyrel et al., 2009;Vale Asari et al., 2009;Thuan et al., 2010;Zahid et al., 2011) at z∼2-3 (Erb et al., 2006;Hayashi et al., 2009;Yoshikawa et al., 2010;Richard et al., 2011), and at z>3 (Pettini et al., 2001;Maiolino et al., 2008;Mannucci et al., 2009;Lemoine-Busserolle et al., 2010), finding a strong and monotonic evolution, with metallicity decreasing with redshift at a given mass (see Fig. 1). Both the shape and the normalization of the mass-metallicity relation are sensitive to the metallicity calibration used (Kewley & Ellison, 2008;Peeples & Shankar, 2011), which can differ significantly. Part of the differences is due to the secondary nature of nitrogen, whose abundance ratio with oxygen is expected and observed to vary during the galaxy lifetime. As several metallicity calibrations are based on the flux ratio of oxygen emission lines to the [NII]λ6584 line, this uncertainty also affects the oxygen abundance (e.g., Pilyugin et al. 2004;van Zee & Haynes 2006;Liang et al. 2006;Pérez-Montero & Contini 2009;Queyrel et al. 2009;López-Sánchez & Esteban 2010;Pilyugin & Thuan 2011;Thuan et al. 2010). This point will be addressed in a forthcoming paper (Maiolino et al., in preparation). Despite these problems, the evidence of evolution of the mass-metallicity relation is not affected by calibration uncertainties and is a very solid result.
Some authors (Erb et al., 2006;Erb, 2008;Mannucci et al., 2009) have studied the relation between metallicity and gas fraction, i.e., the effective yields. These results can be explained as a consequences of infall in high redshift galaxies. Also, Cresci et al. (2010) studied the metallicity maps of three star-forming galaxies at z>3, founding regions of low metallicity associated with the peak of starformation. This evidence can be explained assuming that some metal-poor infalling gas both fuels star formation and dilutes metallicity. If infall is at the origin of the star formation activity, and outflows are produced by exploding supernovae (SNe), a relation between metallicity and SFR is likely to exist. In other words, SFR is a parameter that should be considered in the scaling relations that include metallicity.
In Mannucci et al. (2010) we studied the dependence of metallicity on both mass and SFR in SDSS galaxies. As shown in Fig. 2, at constant stellar mass, metallicity anti-correlates with SFR, i.e., galaxies with higher SFRs also show lower metallicities. The dependence of metallicity on M ⋆ and SFR can be better visualized in a 3D space with these three coordinates, as shown in Fig. 3. In this space, SDSS galaxies appear to define a tight surface, named the Fundamental Metallicity Relation (FMR).
The introduction of the FMR results in a significant reduction of residual metallicity scatter with respect to the simple mass-metallicity relation. The dispersion of individual SDSS galaxies around the FMR is about ∼0.05 dex i.e, about 12%, and this scatter is consistent
The mass-metallicity relation of local SDSS galaxies. The grey-shaded areas contain 64% and 90% of all SDSS galaxies, with th
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