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Theoretically, inflows happen. The classical and perhaps most famous motivation for this view is the failure of the “closed-box” model (Schmidt, 1963, Tinsley, 1980) to account for the observed paucity of low-metallicity G and K stars (Pagel & Patchett, 1975, Casuso & Beckman, 2004), a discrepancy that persists even with the most recent measurements of stars throughout the Milky Way disk (Schlesinger et al., 2012). The closed-box model has other problems such as its inability to account for the slow decline in galaxy gas fractions (Tacconi et al., 2013) and the cosmic abundance of neutral hydrogen (Wolfe et al., 2005). Likewise, it cannot account for the weak observed evolution in galaxy metallicities during the interval z = 2 → 0 (Erb et al., 2006), an epoch during which most of the present-day stellar mass formed.

More importantly, however, galaxy growth without inflows is theoretically incompatible with the current ΛCDM paradigm. In this picture, galaxies are viewed as condensations of cold baryons within dark matter halos. The dark matter halos themselves grow via a sequence of mergers that is decoupled from baryon physics and straightforward to compute using either analytic (White & Rees, 1978, White & Frenk, 1991) or numerical methods (Springel et al., 2005). As the halos grow, they accrete gas directly from the intergalactic medium (IGM). The vast majority of this gas accretes in a smooth fashion; that is, it does not arrive having previously condensed into an interstellar medium (ISM; Nelson et al. (2013)). Halos that are more massive than the cosmic Jeans mass are expected to acquire a mass of baryons that is of order (Ωb / ΩM) × MDM, where MDM is the halo's total mass (Gnedin, 2000, Okamoto et al., 2008, Christensen et al., 2016). Roughly half of this material collapses from the halo onto the central galaxy (Christensen et al., 2016), driving further star formation.

The expected thermal history of collapsed gas prior to its arrival in the central galaxy remains a topic of active study. It was originally assumed that all gas is shock-heated to the virial temperature and then cools in a spherically-symmetric way (White & Rees, 1978). This was challenged a decade ago by numerical calculations, which found that much of the gas accretes directly onto the central galaxy without ever being heated, particularly at masses below 1012 M (Kereš et al., 2005, Dekel & Birnboim, 2006). The most recent calculations that include significantly improved hydrodynamic solvers contradict those results, attributing the lack of shock-heating and the inefficient cooling of the hot gas in previous calculations to numerical problems (Nelson et al., 2013). The new calculations indicate that the majority of gas at all halo masses is heated to the virial temperature before accreting onto the halo. However, it does not accrete in a spherically-symmetric fashion as originally envisioned (White & Rees, 1978). Instead, it tends to concentrate in coherent structures that connect to large-scale intergalactic medium (IGM) filaments. The upshot is that, one way or another, gas readily accretes efficiently enough in ΛCDM to form the observed galaxy populations, with most gas arriving in the form of smooth inflows.

Once the gas condenses to densities of ∼1 atom per cm−3,gravitational instability triggers the formation of molecular clouds and eventually stars. Feedback energy from the young stars limits the efficiency of star formation and regulates the ISM's structure in a number of ways. For our purposes, the most important of these is the generation of galactic outflows, which are inevitably observed wherever there is vigorous star formation (Veilleux et al., 2005). Theoretical models consistently predict that the mass of material that is ejected is comparable to or greater than the mass of stars that form (Murray et al., 2005, Muratov et al., 2015, Christensen et al., 2016). This enriched material then becomes available for re-accretion after a few dynamical times (Oppenheimer et al., 2010, Henriques et al., 2013, Christensen et al., 2016).

Outflows thus give rise to two conceptually distinct gas accretion channels, “Primordial Gas” and “Recycled Gas”. Primordial gas dominates inflows at early times and low masses (Oppenheimer et al., 2010, Ma et al., 2016), and it dilutes galaxies' gas-phase metallicities. Recycled gas becomes increasingly important at late times and high masses. It is pre-enriched, and therefore less effective at dilution.

To summarize, in the era of ΛCDM, galaxy growth driven by ongoing inflows is unavoidable. The central conceit of this chapter is that measurements of galaxy metallicities may be used to test models of those inflows. To motivate our discussion of how they do so, we list the observational probes that have been deployed:

Stellar metallicity distributions have historically been an important indicator that inflows occur, but they are only available for the Milky Way and a handful of its satellite galaxies (Kirby et al., 2011). For this reason, we will not discuss them further. Rather, we will focus on extragalactic diagnostics where larger samples are available. We also note that, throughout this discussion, we will focus on the oxygen metallicity as it is the most widely-observed tracer of the overall gas-phase metallicity. In Section 2, we review the physical processes through which inflows modulate galaxy metallicities. In Section 3, we discuss the extent to which galaxy growth tracks the host halo growth. In Section 4, we introduce the Equilibrium Model, which is the simplest way for relating observables to inflows. In Section 5, we discuss departures from equilibrium growth. Finally, in Section 6 we summarize.

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