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Gas inflows impact galaxy metallicities on a wide range of timescales and spatial scales, and through a variety of processes that we associate either with Mergers, Galactic Fountains, or Environment. In this section, we summarize observational and theoretical progress in understanding these processes.

2.1. Mergers

Both observations and theory indicate that mergers are not the dominant way in which fresh gas is delivered to galaxies (Papovich et al., 2011, Behroozi et al., 2013). However, on timescales comparable to a dynamical time, mergers can cause relatively unenriched gas that has previously settled in a galaxy's outskirts to plummet into the central 100–1000 parsecs (pc), simultaneously suppressing the central gas metallicity and boosting the central star formation rate.

This effect arises naturally in hydrodynamic simulations of galaxy mergers. Torrey et al. (2012) found that interactions suppress the nuclear metallicity of gas-poor galaxies (gas fractions of ≤ 20%) by an amount that fluctuates depending on which merger stage the galaxies are observed in, but is typically ≈ 0.07 dex. Gas-rich galaxies, by contrast, can experience nuclear metallicity boosts during interactions although this effect is not expected in typical SDSS galaxies owing to their generally low gas fractions. A similar result was presented by Rupke et al. (2010a), who found that the suppressed metallicities were associated with the period between the first and second pericenter passages of a merger event.

Does this mean that metallicities can be used to detect mergers? In fact, the statistical signature of nuclear inflows has been identified observationally in galaxy pairs from the Sloan Digital Sky Survey (SDSS). In particular, Scudder et al. (2012), Scudder et al. (2013) showed that star-forming galaxies have suppressed central metallicity (by 0.02–0.3 dex) and enhanced central SFR (by 60%) if they are separated from a paired galaxy by a projected separation of ≤ 80 kpc h−1 (see also Rupke et al. (2010b)). It is also possible that galaxy mass and merger mass ratio modulate this effect: Splitting the merging SDSS galaxies by stellar mass, Michel-Dansac et al. (2008) have argued that mergers systematically boost the metallicity of low-mass galaxies while suppressing the metallicity of massive ones. The different behavior reflects a competition between dilution and enrichment, and is qualitatively expected based on the results presented by Rupke et al. (2010a) if low-mass galaxies are relatively gas-rich while massive ones are gas-poor.

While the ability of mergers to drive nuclear flows has been identified both in simulations and in observations, these flows have yet to be invoked as a rigorous constraint on galaxy evolution models. As a first step in this direction, Grønnow et al. (2015) asked whether a small but robust population of galaxies whose metallicities were lower than expected for their combination of stellar mass and star formation rate (Mannucci et al., 2010) could be interpreted as ongoing mergers or merger remnants. They developed a simple analytical model invoking the known halo merger rate along with the assumption that mergers boost SFR and suppress metallicity for a set time and showed that this model's parameters can be tuned to yield excellent agreement with the observed outlier population. They found that post-merger galaxies must exhibit diluted nuclear metallicities for 1.568−0.027+0.020Gyr, and the average dilution for mergers with mass ratios of 1:1–1:5 was 0.114 dex. Encouragingly, these inferences are within a factor of two of expectations from numerical simulations and observations.

A caveat to analyses of SDSS metallicities is that the SDSS spectroscopic fibers subtend a diameter of 3 arcsec, hence they capture only the central 5 kpc of galaxies at the typical redshift of SDSS galaxies (z = 0.1). While this makes them ideal for studying nuclear metallicities, it leaves unanswered the question of how mergers effect the metallicity at larger radii. Rupke et al. (2010a) showed that the same interaction-triggered flows that dilute central metallicities also flatten overall gas metallicity gradients. This effect has likewise been observed in ongoing mergers (Kewley et al., 2010). Unfortunately, it is difficult to use the physics of ongoing mergers to test galaxy formation models because results are so sensitive to details of the merger such as gas fractions, mass ratio, and orbital parameters (Torrey et al., 2012).

Fortunately, the tendency for mergers to flatten metallicity gradients and to build up central bulges does leave an observable signature: Galaxies that are more massive or have larger (classical) bulges should have flatter gas metallicity gradients. Fu et al. (2013) have shown that this effect is strong observationally, and can readily be reproduced by their semi-analytical model (their Figure 12). However, they did not explore which of the assumptions underlying their merger model are required to yield the good agreement. Moreover, they address only local observations, and suggest that extending the work to higher redshifts would be a useful next step. We will return to this point in Section 4.2.

2.2. Outflows and Galactic Fountains

The way in which galactic inflows modulate metallicities and metallicity gradients depends critically on galactic fountains. Observations indicate that vigorous star formation is inevitably associated with outflows that eject gas from galaxies at a rate that is comparable to the star formation rate (Veilleux et al., 2005). Observations and models both suggest that they carry away most of the metals that are generated in core-collapse supernovae (Martin et al., 2002, Fu et al., 2013). The gas is expected to re-accrete on a dynamical timescale, particularly in massive galaxies (log(M* / M) > 10.5) and at relatively late times (z < 1; Oppenheimer et al. (2010), Henriques et al. (2013)). The gas that a central galaxy re-accretes contains contributions both from its progenitor and from satellite systems, while satellite systems probably do not accrete much gas. Importantly, while the ejected gas has predominantly low angular momentum, it picks up angular momentum from the halo and re-accretes at generally larger radii than where it was ejected (Brook et al., 2012, Christensen et al., 2016). This has a number of observational consequences.

2.2.1. Galaxy-averaged quantities

First, re-accreted metals boost the central galaxy's metallicity with respect to models with unenriched inflows (or, viewed from a different perspective, they suppress dilution). If the metallicity of inflowing gas varies with mass, then recycled gas must affect the slope of the mass-metallicity relation. In particular, if low-mass galaxies accrete predominantly pristine material while inflows into massive galaxies are pre-enriched (Ma et al., 2016, Brook et al., 2014), then this differential pre-enrichment steepens the slope of the mass-metallicity relation.

If pre-enrichment levels vary with redshift, then they furthermore contribute to the evolution of the normalization of the mass-metallicity relation (Davé et al., 2011). For example, if inflows are pristine at early times and enriched to roughly the same level as the ISM at z=0, then they are more effective at diluting gas reservoirs at high redshift, driving stronger evolution in the normalization of the mass-metallicity relation. The normalization of the MZR is observed to increase (Maiolino et al., 2008, Faist et al., 2016), which could be explained in this way. The observational challenge is to disentangle this factor from other influences that could also evolve with redshift (or mass) such as the initial mass function (van Dokkum, 2008, Davé, 2008).

It is instructive to compare this interpretation of how the MZR's normalization evolves upwards to that presented in Ma et al. (2016). In the latter work, high-resolution simulations were used to show that the relationship between gas metallicity and stellar mass fraction f* (that is, the stellar mass divided by the baryonic mass) is nearly that of a closed-box throughout z = 3 → 0 when averaged over the entire halo rather than just the central galaxy. In this view, growth in the MZR's normalization tracks growth in f*. While this is a suggestive insight, it does not directly address growth in galaxy metallicities, which are far more readily observable. It is not hard to imagine, for example, that gas flows might hide metals within the halo at high redshifts but then shift progressively more of them into observability at late times. In other words, galaxy metallicities may evolve to become an increasingly unbiased probe of the halo metallicity, which in turn tracks closed-box expectations. A more detailed study of the evolving relationship between halo-averaged and ISM-averaged metallicity is probably indicated. For the present, however, it is clear that pre-enriched inflows have the potential to drive MZR evolution.

2.2.2. Radial Metallicity Gradients

If inflows deposit gas that has relatively uniform metallicity over a range of radii as expected theoretically (Brook et al., 2012, Christensen et al., 2016), then they flatten radial metallicity gradients because the metallicity at any point is driven by the inflowing gas, washing out other influences such as radial gradients in star formation efficiency or wind characteristics, or radial flows that escort low-metallicity in from the galaxy's outskirts. This raises the possibility of using observed metallicity gradients to constrain inflows.

At low redshift, it has long been known observationally that star-forming galaxies have slowly-declining metallicity gradients (Zaritsky et al., 1994), and recent analyses have confirmed these results (Fu et al., 2013, Carton et al., 2015, Ho et al., 2015). Fu et al. (2013) used a semi-analytical model of galaxy formation to interpret observations. They showed that inflows can readily dominate metallicity gradients (their Figure 6), while the effect of radial flows is probably relatively weak. They further found that it was necessary to assume that 80% of all newly-formed metals are launched into the halo in order to match observed metallicity gradients, qualitatively consistent with inferences from X-ray observations of local outflows (Martin et al., 2002). In their model, the tendency for ejected metals to re-accrete over a range of radii makes the baryon cycle into an efficient method for redistributing metals.

Carton et al. (2015) interpreted locally-observed metallicity gradients using a simpler model that assumes a local equilibrium between inflows, star formation, and outflows (Section 4.2). In their model, radial flows are ignored, and inflows are assumed to be uniform across the disk. Hence the observed metallicity gradient is driven by the radial dependence of the mass-loading factor (that is, the ratio of the outflow to star formation rates), with weaker outflows yielding higher metallicity in the center and stronger outflows suppressing it toward the disk edge. This model requires inflows in order to balance ongoing enrichment (Lilly et al., 2013), but that does not mean that the data require strong inflows. In fact, it is not even possible to use the Carton et al. (2015) model to measure inflow rates or metallicities owing to degeneracies. For example, a high observed metallicity could reflect a high metal yield and unenriched inflows, or a low metal yield and highly-enriched inflows.

The model explored by Ho et al. (2015) leads to a different interpretation, tying locally-observed metallicity gradients to gradients in gas fraction. These authors relax the assumption that all regions of a galaxy are in local enrichment equilibrium, but assume that the mass-loading factor and the ratio of inflow to star formation rates dot{M}g, in / SFR are all constant. In this case, metallicity decreases with radius because more diffuse regions have higher gas fraction, implying that they are chemically less mature. They also find that their models fit observations if they assume that both inflows and outflows are weak, indicating nearly closed-box chemical evolution for systems with low gas fraction.

The Ho et al. (2015) and Carton et al. (2015) studies both leverage high-quality measurements of radial trends in metallicity and gas fraction, but their modeling efforts lead to different conclusions regarding the flow of gas into and out of the galaxy because they invoke different assumptions. Which model is more correct? More theoretical insight into how observables connect to the underlying physics would certainly help. At the same time, it is to be hoped that future studies that leverage measurements on halo metallicities or inflow rates (from, for example, absorption-line campaigns) will eventually break the underlying degeneracies.

Fu et al. (2013) indicated that the evolution of metallicity gradients to high redshift is a complementary constraint on star formation and gas flows. This echoes Pilkington et al. (2012), who analyzed how the radial and vertical gradients evolved in 25 cosmological simulations of Milky Way analogs from several groups as well as two independent analytical models. They found that, although all models roughly reproduce the Milky Way's current radial gradient, some predicted dramatically steeper gradients at earlier times while others did not. They concluded that steep gradients in metallicity reflect steep gradients in star formation efficiency and noted that strong feedback can wash out metallicity gradients. However, their discussion did not consider the possible role of inflows in balancing enrichment.

Observationally, the high-redshift story is far from clear. An early integral field study of three star-forming galaxies at z ∼ 3 uncovered inverted metallicity gradients (i.e., the gas-phase metallicity is lower in the center; Cresci et al. (2010)). The authors interpreted their findings as evidence that inflows deliver pristine gas preferentially to the center of high-redshift galaxies, although in fact this is not expected to produce inverted gradients generically (Pilkington et al., 2012).

Over the following years, detailed analyses of a few strongly-lensed high-redshift systems yielded steeply declining metallicity gradients (Yuan et al., 2011, Jones et al., 2013) as predicted in Pilkington et al. (2012). These results seemed to indicate that strong inflows do not flatten or invert metallicity gradients at high redshifts.

Most recently, however, a study of a large sample of unlensed systems indicated that metallicity gradients are flatter than in the local Universe or even absent at higher redshifts (Wuyts et al., 2016). As noted in Wuyts et al. (2016), it is not obvious why lensed systems should show strong gradients while unlensed ones do not, particularly given that the samples overlap in stellar mass. Wuyts et al. (2016) consider a number of effects such as beam-smearing, AGN, or shocks that could artificially suppress the intrinsic metallicity gradient in unlensed systems, but conclude that they would have detected strong gradients if they were there. Hence while further work is needed to control biases, current observations support the idea that strong inflows flatten high-redshift metallicity gradients, as qualitatively suggested by some (but not all) models (Brook et al., 2012, Fu et al., 2013).

2.2.3. Future Work

At a technical level, the pioneering study of re-accretion presented in Oppenheimer et al. (2010) deserves to be re-visited in the context of more recent numerical models for two reasons. The less important of these is that galactic outflow models have grown more realistic owing to high-resolution simulations (Muratov et al., 2015) as well as to increasingly detailed comparison with measurements (Mitra et al., 2015). The more important reason is that simulations now incorporate significantly improved hydrodynamic solvers and dynamic range, which are critical for resolving the complicated interaction between outflows and the circumgalactic medium (Nelson et al., 2015). Relatedly, improved cross-fertilization of insights regarding outflows and enriched inflows between hydrodynamic simulations and semi-analytical models would be helpful both for distilling insight from the numerical models and for exploring its implications within a more flexible framework.

With an improved understanding of the baryon and metal cycles, a straightforward next step would be to review the hypothesis presented in Davé et al. (2011) that pre-enriched inflows drive the MZR's shape and evolution. A detailed budgeting of how galaxies distribute their baryons and metals within the ISM and halos would be necessary for this step, and would inform the next generation of measurements of the CGM, which has become a very active field over the past few years.

In the specific case of merger-induced inflows, it is not to soon to ask whether simulations can accommodate the rich set of observations of how interactions trigger nuclear flows driving star formation, gas dilution, as well as AGN activity (cf. the “Galaxy Pairs in the Sloan Digital Sky Survey” paper series by S. Ellison and collaborators); this would test the hypothesis that mergers can be identified based on their suppressed nuclear metallicities (Grønnow et al., 2015).

Finally, the effective use of metallicity gradients for constraining gas inflows in a cosmological context will require further development both in models and in observations. An improved understanding of what drives the metallicity gradients that are predicted by numerical simulations, a converged picture for the observed evolution of metallicity gradients to higher redshift, and the continued development of techniques for using observations to test models (for example, accounting for biases associated with sample selection and and strong-line abundance indicators) will yield further insight into the baryon cycle.

2.3. Environment

At fixed stellar mass, galaxies that live in richer environments are observed to have slightly higher metallicities (Mouhcine et al., 2007, Cooper et al., 2008), although the effect is weak and not always observed (Hughes et al., 2013). A qualitatively similar relationship occurs in cosmological simulations (Davé et al., 2011), suggesting that it may in fact be real. If so, it could reflect systematic variation in the basic properties of the baryon cycle. For example, it is easy to imagine that weaker outflows, more efficient re-accretion of previously-ejected gas, or enriched inflows could boost the metallicities in overdense regions. Indeed, analytical models have been used to argue that enriched inflows are a viable explanation for the offset (Peng & Maiolino, 2014).

In reality, it may be that none of these is the correct explanation. A detailed study of galaxies in the Illustris simulations (Genel, 2016) recently traced the metallicity-environment correlation to two causes. First, at a given stellar mass, satellite galaxies (which dominate richer environments) tend to form earlier than centrals, draining their gas reservoirs and boosting their metallicities. Second, satellites' disks tend to be truncated and more centrally-concentrated such that observations are weighted toward their metal-rich cores. Combining these effects essentially accounts for the the entire simulated offset.

Genel (2016) notes that the CGM around satellite galaxies is more enriched than around centrals of the same stellar mass, and in fact the offset is comparable to offset in the galaxies' metallicities. However, he argues that this does not dominate the dependence of metallicity on environment because centrals and satellites with similar stellar mass and star formation history have nearly the same metallicity—despite the apparently higher metallicity of the gas around satellites.

Future work disentangling the metallicity of inflowing and outflowing gas may be needed in order to understand how a more enriched CGM does not drive higher galaxy metallicities. For the present, however, it seems that the tendency for metallicity to increase in rich environments does not relate to inflows.

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