A.1 Validity of the Model
4.2 A Fundamental Metallicity Relation?
By comparing the histograms in Figures 4.5 and 4.8, it is clear that the lensed galaxies presented here typically have much lower SFR than in other spectroscopic surveys at similar redshift, but only slightly smaller masses. This may explain the higher metallicities seen in the lensed galaxies (Figure 4.10), since evolution in the mass-metallicity relation is generally attributed to higher gas fractions (and hence higher SFR) at increasing redshift (e.g., Erb et al. 2006). If this is indeed the case, selecting objects of lower SFR would counteract this effect and explain the deviation of our sample towards slightly higher metallicity.
Recently, Mannucci et al. (2010) have proposed to include the SFR as a third component of the mass-metallicity relation, which would explain its evolution in redshift. They find that a mass- metallicity-SFR relation is able to predict the metallicity of local galaxies in SDSS with a scatter of onlyσ= 0.05 dex, somewhat more accurate than the traditional mass-metallicity relation which has σ= 0.08 dex. Of much greater interest, however, is their discovery that a single mass-metallicity- SFR relation is able to reproduce the observed metallicities of all galaxies at all redshifts from 0 < z <2.5. This “fundamental metallicity relation” (FMR) is most easily expressed in terms of
12 + log O/H
z=0.07 z=2.2
10 8 10 9 10 10 10 11
M * (M sun )
12 + log O/H
z=0.07
z=3.5
Figure 4.10: The relation between gas-phase metallicity and stellar mass as a function of redshift. This is based on the diagram presented by Maiolino et al. (2008), with their measurements of galaxies atz∼3.5 shown as grey points. The local mass-metallicity relation is shown as a dotted line forz= 0.07, while their best fits atz ∼2.2 and z ∼3.5 are shown as solid lines in the top and bottom panels respectively. The lensed galaxies are shown as blue diamonds and separated into redshift bins of 1.5< z <2.5 (top panel) and 2.5< z <3.5 (bottom panel). Values derived from the two composite spectra (see§2.2.5) are shown as red points in the left panel.
the quantity
x= logM∗−0.32 log SFR−10 (4.3)
where metallicity is given by
12 + logO/H= 8.90 + 0.47x (4.4)
for the casex <0.2, which applies to the entire lensed galaxy sample. We computed the expected metallicity for the lensed galaxies using Equation 4.4 and find that on average, measured metallicities are in better agreement with the FMR than with the redshift-dependent mass-metallicity relation.
Figure 4.11 shows the difference ∆ log O/H between measured metallicity and that predicted by the FMR. Measured metallicities are slightly lower than predicted, with average ∆ log O/H = −0.14 dex and a standard deviation of 0.30 dex. Considering sample statistics, the mean difference is
−0.14±0.06 dex such that our measurements are compatible with the FMR at a 2σlevel.
One of the most important caveats of the proposed fundamental metallicity relation is that galax- ies observed at different redshifts probedifferent regionsof the mass-SFR plane. This is partly due to the trend of specific SFR increasing at higher redshifts, but largely imposed by instrumentation limits. In practice, emission lines needed for metallicity measurements can only be detected in the most actively star forming galaxies at high redshift (e.g., SFR>∼10 M⊙yr−1atz≃2), whereas such high SFR is rare in the local universe. Hence, galaxies used to constrain the fundamental metallicity atz >1 are disjoint from those atz≃0 in the sense that the range of SFR in these two samples does not overlap. Therefore, previous surveys do not actually provide any evidence for a fundamental relation which does not evolve with time.
Thanks to the lensing selection which enables us to measure metallicity in a significant sample of galaxies with SFR<10 M⊙yr−1, we are uniquely able to constrain whether the proposed FMR is truly time-invariant over 0 < z < 2.5, a period of 11 Gyr. Four lensed galaxies in our sample (A2218 Ebbels, MACS0451, CL0949, and MACS0712) have stellar mass and SFR within the range of SDSS galaxies from which Mannucci et al. (2010) determine the FMR. Hence, these sources provide a direct measurement of FMR evolution. Figure 4.11 shows that all four have metallicity lower than predicted by the locally-determined FMR. These galaxies have redshifts 2.0< z <2.65 with mean z= 2.4. On average, their metallicities are lower than SDSS galaxies at fixed stellar mass and SFR by ∆ log O/H =−0.44±0.11 dex. Formally, time invariance of the FMR is therefore ruled out with 4σsignificance, however we caution that this is a very small sample and could suffer from systematic errors. In particular, high redshift galaxies selected to haveM∗ and SFR comparable to samples in the SDSS will have lower specific SFR than typical galaxies at similar redshift. This selection will therefore be biased to include galaxies with measurement errors in the sense that M∗ is higher (or SFR is lower) than the true value. Both of these biases will result in a higher predicted metallicity and hence this may explain the observed discrepancy. Of course, it is also likely that the FMR is
not time invariant, as suggested by our data. One possible explanation for the observed increase in gas-phase metallicity at lower redshifts is that gas accreted from the intergalactic and circumgalactic media is more highly enriched at later times, for example by “galactic fountain” processes (e.g., Werk et al. 2011; Dav´e et al. 2011).
In summary, the lensed galaxies are in better agreement with the FMR proposed by Mannucci et al. (2010) than with the mass-metallicity relation. We have made the first direct measurement of time evolution of the FMR, and find a significant evolution in metallicity at fixed stellar mass and SFR in the sense that metallicity increases at lower redshifts. Although we caution that this result is based on only four galaxies and may suffer from systematic errors, these data suggest that the FMR is nota fundamental relation in that it does not adequately describe galaxies at all redshifts.