1. The BPT diagram and mass-metallicity relation at z~2.3: Insights from KBSS-MOSFIRE Steidel et al. (2014) - Strong nebular line ratios in the spectra of z=2-3 star-forming galaxies: First results from KBSS-MOSFIRE - arXiv:1405.5473 Obtained rest-frame optical spectroscopy of 251 emission-line galaxies between 2.0 < z < 2.6 from Keck. 8.6 < log(M * /M ʘ ) < 11.42 < SFR [M ʘ /yr] < 2007.9 ≤ Z g (O3N2) ≤ 8.6 The star-forming sequence on the BPT diagram at z~2.3 is shifted upwards with respect to that at z=0. This is due to a) higher ionisation parameter, b) harder ionising radiation field (i.e. higher T eff ), and c) higher N/O. The mass-metallicity relation (MZR) at z~2.3 is lower than that at z=0 by ~0.32 dex, at all stellar masses. The dependence of Z g on SFR is much weaker than at z=0, suggesting no FMR extension to these redshifts. Fig. 1 Fig. 2 1

2. The BPT diagram at z~2.3: Fig. 3 High-z galaxies (symbols) lie above the z=0 relation from SDSS (grey points). See also Brinchmann+08, Kewley+13b. The scatter around the best fit (orange line) is similar to that at z=0 (~0.1 dex). This shift away from the local relation implies that locally calibrated strong- line diagnostics will give inconsistent values of Z g at higher redshift. This is because galaxies no longer lie on the expected 1D relations (red curves)… BPT diagram at z=0: Can be used to distinguish star- forming galaxies (along main ridge, e.g. red lines) from AGN hosts (high [OIII]/Hβ and high [NII]/Hα). See e.g. Kewley+01, Kauffmann+03c. Also tells us about metallicity distribution, as Z g for SF galaxies increases to the bottom-right of the plot. 2 Increasing Z g

3. The BPT diagram at z~2.3: …for example, the N2 diagnostic provides a higher Z g than the O3N2 diagnostic at z~2.3, even when calibrated to the same low-z sample of T e galaxies (Pettini & Pagel 04). Therefore, conversions between different diagnostics calibrated at z=0 (e.g. Kewley & Ellison 08) are not applicable at higher z (see also Cullen+14). This is a problem for studies of MZR and FMR evolution (e.g. Maiolino+08; Mannucci+10). Fig. 4 3 Using photoionisation models, Steidel+14 found that both higher ionisation parameter, Γ, and higher T eff are required to reproduce observations at z~2.3 (i.e. match Figs. 3 and 4). n e =1000 cm -3, -2.9 < log(Γ) < -1.8, and T eff ~50000 K are required. However, note the small dependence of BPT position on Z g at fixed Γ in Fig. 5… Are strong- line diagnostics mainly tracing Γ and/or T eff at high-z? Fig. 5 Z/Z ʘ = 0.2 Z/Z ʘ = 1.0

4. O/H dependence on N/O: There is evidence that O/H is nearly independent of N/O at high z, unlike the positive correlation assumed at low z. When assuming no N/O dependence in the photoionisation models, the sensitivity of the N2 diagnostic to Z g is weakened (Fig. 7). The stronger N/O-dependence of the N2 diagnostic causes the over-estimate of Z g at high z relative to the O3N2 diagnostic. Recalibrations of the low-z diagnostics specifically for high z give good correspondence with T e -based metallicities. 4 Fig. 6 Fig. 7

5. The MZR at z~2.3: 5 Assuming that the (locally calibrated) O3N2 diagnostic is better (as it has a weaker N/O dependence and closer correspondence to the few T e metallicities available), the MZR at z~2.3 is plotted (Fig. 8). An offset of around -0.32 dex in Z g from the z=0 MZR is found, similar to the average offset found by Erb+06a using N2. However, no clear mass-dependence in the Zg offset is seen (see also Moustakas+11). This is in contradiction to the ‘chemical downsizing’ claimed by other works using other diagnostics, e.g. locally-calibrated N2 and R23 (e.g. Maiolino+08, Zahid+13b). Compared to Erb+06a metallicities: a) Lower Z g at high M * due to weaker N/O dependence. b) Higher Z g at low M * due to better correspondence with T e metallicities (i.e. higher SNR). Fig. 8

6. The MZR at z~2.3: The scatter in the z~2.3 MZR is remarkably small (σ sc ~0.10 dex), similar to that at z=0. Note that the diagnostic used (even when calibrated to be optimal at high-z) has a larger scatter (σ O3N2 ~0.14 dex). This suggests that there should be an even tighter correlation between M * and line intensity (therefore, Γ) than between M * and Z g … Also, there is no clear dependence of Z g on SFR at fixed mass in the MOSFIRE sample (Fig. 9). This suggests the FMR doesn’t hold at these high redshifts/SFRs… Zahid+14 Moustakas+11 6 Is chemical downsizing really occurring in galaxies?... Fig. 10 Fig. 11 Fu+12 Maiolino+08 See also Aumer+13 Fig. 12 Fig. 9

7. Conclusions: 7 Very young stellar populations, or very top-heavy IMF are not required to reproduce shifted BPT diagram at high redshift. Instead, binarity and fast rotation of low-metallicity, massive stars provide the conditions needed (i.e. high ionisation parameter and high T eff, and increased primary N production). Eight AGN hosts (determined by their far-UV, mid-IR, and X-ray properties) do not lie within the star-forming sequence of the BPT diagram at z~2.3. Therefore, this diagram can still be used to distinguish AGN optically. Strong-line diagnostics are likely tracing ionisation parameter more than Z g at high redshift. However, the O3N2 diagnostic (re-calibrated at z=0) appears to be the most accurate available currently, due to weaker N/O dependence and closer correspondence to T e -method metallicities. Metallicites from strong-line diagnostics differ from each other in different ways at low and high redshift. Therefore, conversions between diagnostics calibrated at z=0 won’t work at high redshift. No mass-dependent MZR evolution from z~2.3 to z=0 found. Previous high-z metallicity estimates using N2 and R23 are likely to be less accurate than the O3N2 diagnostic used here (which, in turn, is worse than an ‘ideal’ high-z-calibrated diagnostic, or T e metallicities). Uncomfortably small scatter in the MZR at all redshifts (compared to the error in the metallicity diagnostics used) suggests that a) a low range of T eff should be present at each epoch, and b) there should be a more fundamental, monotonic relation between M* and Γ. The fundamental metallicity relation (FMR) does not match the distribution of the z~2.3 sample in M * -SFR- Z g space. Nor does this projection onto this space reduce the scatter compared to the MZR (see also Cullen+14). T e -based metallicites, using either weak optical lines or rest-UV intercombination lines (e.g. Erb+10), and high- z calibrations of strong-line ratios from them, are the best ways forward for studying Z g at high redshift.