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The previous section drew attention to our imperfect understanding of how galaxies and halos grow together. A specific problem related to this question is the “dwarf galaxy conundrum”, or the suite of observational clues that galaxies with stellar masses below 1010 M do not grow at the same specific rate as their host halos (for example, Weinmann et al. (2012)). This behavior is very difficult for conventional galaxy evolution models to accommodate (White et al., 2015, Somerville & Davé, 2015): generically, the strong outflows that seem required in order to bring the predicted stellar mass function at z = 0 into agreement with observations lead to metallicities and gas fractions that are under-predicted at low redshifts. Conversely, adopting weaker outflows at low masses in order to match MZR observations yields too many stars in low-mass halos at z = 0.

The problem clearly points to the need for a qualitatively new physical mechanism that retards gas processing in low-mass systems. This raises the question of whether that process operates in the IGM/CGM, or in the ISM. In a creative analytic model, Bouché et al. (2010) argued for a CGM-based solution, showing that forbidding halos less massive than 1011 M from cooling their gas onto galaxies improves agreement with measurements of star formation and stellar mass growth. They unfortunately did not address metallicities. Lilly et al. (2013) also addressed this problem. They found that, under the assumption that enrichment and dilution balance exactly (Section 4), the fraction of galaxy gas that is converted to stars can be inferred directly from the MZR, and the resulting scaling matches the requirement that is implied by the stellar mass function. In this argument, the dwarf galaxy conundrum can be resolved by processes that occur within the ISM, although inflows are required.

In order to assault the problem using a more comprehensive suite of observables, White et al. (2015) implement several galaxy-slowing mechanisms (both galaxy-based and CGM-based) into a semi-analytical model. They show that two changes to the fiducial model can improve agreement: in their “preferential reheating” model, low-mass galaxies eject systematically more gas in outflows per unit of stellar mass formed at higher redshift. In their “parking lot” model, ejected gas is not permitted to re-accrete for a delay time that depends on halo mass (see also Henriques et al. (2013)). By manipulating the parameters governing these processes, they found improved agreement with measurements of cold gas fractions, specific star formation rates, and ISM metallicities

In the context of numerical simulations, Ma et al. (2016) have shown that accounting more realistically for the physical processes that occur within the interstellar medium (ISM) tends naturally to decouple the growth of low-mass galaxies from their host halo, leading to improved agreement with observations of the MZR evolution (see also Hopkins et al. (2014)). Their findings are qualitatively consistent with the inferences that White et al. (2015) draw from semi-analytical models, but it is difficult to draw robust conclusions owing to the small number of halos that have been simulated at high resolution. For example, is the bottleneck that retards gas processing located in the ISM, in the CGM, or both? Ongoing efforts to distill their results into scalings that can be implemented into cosmological simulations and semi-analytical models will generate further insight (Davé et al., 2016).

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