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Register a new userThe fundamental metallicity relation emerges from the local anti-correlation between star formation rate and gas-phase metallicity existing in disk galaxies
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The fundamental metallicity relation (FMR) states that galaxies of the same stellar mass but larger star formation rate (SFR) tend to have smaller gas-phase metallicity (<Zg>). It is thought to be fundamental because it naturally arises from the stochastic feeding of star-formation from external metal-poor gas accretion, a process extremely elusive to observe but essential according the cosmological simulations of galaxy formation. In this letter, we show how the FMR emerges from the local anti-correlation between SFR surface density and Zg recently observed to exist in disk galaxies. We analytically derive the global FMR from the local law, and then show that both relations agree quantitatively when considering the star-forming galaxies of the MaNGA survey. Thus, understanding the FMR becomes equivalent to understanding the origin of the anti-correlation between SFR and metallicity followed by the set of star-forming regions of any typical galaxy. The correspondence between local and global laws is not specific of the FMR, so that a number of local relations should exist associated with known global relations.
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Using a representative sample of 14 star-forming dwarf galaxies in the local Universe, we show the existence of a spaxel-to-spaxel anti-correlation between the index N2 (log([NII]6583/Halpha)) and the Halpha flux. These two quantities are commonly employed as proxies for gas-phase metallicity and star formation rate (SFR), respectively. Thus, the observed N2 to Halpha relation may reflect the existence of an anti-correlation between the metallicity of the gas forming stars and the SFR it induces. Such an anti-correlation is to be expected if variable external metal-poor gas fuels the star-formation process. Alternatively, it can result from the contamination of the star-forming gas by stellar winds and SNe, provided that intense outflows drive most of the metals out of the star-forming regions. We also explore the possibility that the observed anti-correlation is due to variations in the physical conditions of the emitting gas, other than metallicity. Using alternative methods to compute metallicity, as well as previous observations of HII regions and photoionization models, we conclude that this possibility is unlikely. The radial gradient of metallicity characterizing disk galaxies does not produce the correlation either.
The fundamental metallicity relation (FMR) is a postulated correlation between galaxy stellar mass, star formation rate (SFR), and gas-phase metallicity. At its core, this relation posits that offsets from the mass-metallicity relation (MZR) at a fixed stellar mass are correlated with galactic SFR. In this Letter, we quantify the timescale with which galactic SFRs and metallicities evolve using hydrodynamical simulations. We find that Illustris and IllustrisTNG predict that galaxy offsets from the star formation main sequence and MZR evolve over similar timescales, are often anti-correlated in their evolution, evolve with the halo dynamical time, and produce a pronounced FMR. In fact, for a FMR to exist, the metallicity and SFR must evolve in an anti-correlated sense which requires that they evolve with similar time variability. In contrast to Illustris and IllustrisTNG, we speculate that the SFR and metallicity evolution tracks may become decoupled in galaxy formation models dominated by globally-bursty SFR histories, which could weaken the FMR residual correlation strength. This opens the possibility of discriminating between bursty and non-bursty feedback models based on the strength and persistence of the FMR -- especially at high redshift.
We study the relations between gas-phase metallicity ($Z$), local stellar mass surface density ($Sigma_*$), and the local star formation surface density ($Sigma_{rm SFR}$) in a sample of 1120 star-forming galaxies from the MaNGA survey. At fixed $Sigma_{*}$ the local metallicity increases as decreasing of $Sigma_{rm SFR}$ or vice versa for metallicity calibrators of N2 and O3N2. Alternatively, at fixed $Sigma_{rm SFR}$ metallicity increases as increasing of $Sigma_{*}$, but at high mass region, the trend is flatter. However, the dependence of metallicity on $Sigma_{rm SFR}$ is nearly disappeared for N2O2 and N2S2 calibrators. We investigate the local metallicity against $Sigma_{rm SFR}$ with different metallicity calibrators, and find negative/positive correlations depending on the choice of the calibrator. We demonstrate that the O32 ratio (or ionization parameter) is probably dependent on star formation rate at fixed local stellar mass surface density. Additional, the shape of $Sigma_*$ -- $Z$ -- $Sigma_{rm SFR}$ (FMR) depends on metallicity calibrator and stellar mass range. Since the large discrepancy between the empirical fitting-based (N2, O3N2) to electronic temperature metallicity and the photoionization model-dependent (N2O2, N2S2) metallicity calibrations, we conclude that the selection of metallicity calibration affects the existence of FMR on $Sigma_{rm SFR}$.
Using a sample of dwarf galaxies observed using the VIMOS IFU on the VLT, we investigate the mass-metallicity relation (MZR) as a function of star formation rate (FMR$_{text{SFR}}$) as well as HI-gas mass (FMR$_{text{HI}}$). We combine our IFU data with a subsample of galaxies from the ALFALFA HI survey crossmatched to the Sloan Digital Sky Survey to study the FMR$_{text{SFR}}$ and FMR$_{text{HI}}$ across the stellar mass range 10$^{6.6}$ to 10$^{8.8}$ M$_odot$, with metallicities as low as 12+log(O/H) = 7.67. We find the 1$sigma$ mean scatter in the MZR to be 0.05 dex. The 1$sigma$ mean scatter in the FMR$_{text{SFR}}$ (0.02 dex) is significantly lower than that of the MZR. The FMR$_{text{SFR}}$ is not consistent between the IFU observed galaxies and the ALFALFA/SDSS galaxies for SFRs lower than 10$^{-2.4}$ M$_odot$ yr$^{-1}$, however this could be the result of limitations of our measurements in that regime. The lowest mean scatter (0.01 dex) is found in the FMR$_{text{HI}}$. We also find that the FMR$_{text{HI}}$ is consistent between the IFU observed dwarf galaxies and the ALFALFA/SDSS crossmatched sample. We introduce the fundamental metallicity luminosity counterpart to the FMR, again characterized in terms of SFR (FML$_{text{SFR}}$) and HI-gas mass (FML$_{text{HI}}$). We find that the FML$_{text{HI}}$ relation is consistent between the IFU observed dwarf galaxy sample and the larger ALFALFA/SDSS sample. However the 1$sigma$ scatter for the FML$_{text{HI}}$ relation is not improved over the FMR$_{text{HI}}$ scenario. This leads us to conclude that the FMR$_{text{HI}}$ is the best candidate for a physically motivated fundamental metallicity relation.
Recent results have suggested that the well known mass-metallicity relation has a strong dependence on the star formation rate, to the extent that a three dimensional `fundamental metallicity relation exists which links the three parameters with minimal scatter. In this work, we use a sample of 4253 local galaxies observed in atomic hydrogen from the ALFALFA survey to demonstrate, for the first time, that a similar fundamental relation (the HI-FMR) also exists between stellar mass, gas-phase metallicity, and HI mass. This latter relation is likely more fundamental, driving the relation between metallicity, SFR and mass. At intermediate masses, the behaviour of the gas fundamental metallicity relation is very similar to that expressed via the star formation rate. However, we find that the dependence of metallicity on HI content persists to the highest stellar masses, in contrast to the `saturation of metallicity with SFR. It is interesting to note that the dispersion of the relation is very low at intermediate stellar masses (9< log(M*/Msun) <11), suggesting that in this range galaxies evolve smoothy, in an equilibrium between gas inflow, outflow and star formation. At high and low stellar masses, the scatter of the relation is significantly higher, suggesting that merging events and/or stochastic accretion and star formation may drive galaxies outside the relation. We also assemble a sample of galaxies observed in CO. However, due to a small sample size, strong selection bias, and the influence of a metallicity-dependent CO/H2 conversion factor, the data are insufficient to test any influence of molecular gas on metallicity.
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