A variety of mechanisms can be invoked in order to explain the data presented in the previous section within a coherent picture of galactic chemical evolution. Unfortunately, the theoretical framework is, to a great extent, still lacking, since detailed modelling accounting for the gas-phase chemical abundances measured in the outer disks has not been developed yet. The relatively high metal enrichment observed in these H i-rich, low-star formation rate (SFR) regions of spiral galaxies suggests that some form of mixing mechanism, and perhaps more than one, should be responsible for the observed chemical abundance properties of the outer disks. This section presents some of the possible processes discussed in the literature that could redistribute metals produced in the main star-forming disk of spirals into their very outskirts, tens of kpc from the galactic centres. The effects of galaxy interactions and merging on the radial abundance gradients have already been introduced in Sect. 3.3, so that the focus will now be on mixing mechanisms that could affect, in principle, also isolated systems, but we should keep in mind that the chemical abundances in the outer disks could be sensitive to encounters that might have occurred in the distant past, as evidenced, for example, by the presence of warps in the H i envelopes.
The stellar radial migration process (Sellwood and Binney 2002; Roškar et al. 2008) does not affect the present-day abundance gradient of oxygen, since this element, whose abundance we trace with H ii region spectroscopy, is produced by massive stars, that do not have sufficient time to migrate radially before ending their lives (Kubryk, Prantzos and Athanassoula 2015). Older tracers of ionized gas metallicity, such as planetary nebulae, can have a different behaviour (Magrini et al. 2016).
5.1. Flattening the Gradients
While some of the processes discussed below can explain the flattening of the H ii region oxygen abundances observed in the outer disks, we start with the remark made by Bresolin et al. (2012), who suggested that the flat O/H distribution could simply be a consequence of relatively flat star formation efficiencies (Bigiel et al. 2010; Espada et al. 2011). Defining the star formation efficiency as SFE = ΣSFR / ΣHI (e.g., Bigiel et al. 2008), i.e., the ratio between the surface densities of star formation rate (inferred for example from far-UV observations) and H i mass, we can approximate the gas-phase oxygen abundance per unit surface area of the disk, neglecting effects such as gas flows and variable star formation rates, as
where t is the duration of the star formation activity, since the amount of oxygen produced per unit surface area and unit time is the product of the oxygen yield (by mass) yO and the star formation rate surface density. Then, according to (4) the flattened SFE radial profiles traced beyond the isophotal radius, relative to the behaviour in the inner disks, would result in a similarly flattened O/H radial gradient at large galactocentric radii, as observed. This appears to be consistent with the idea that the star formation activity at large galactocentric distances proceeds slowly enough for some metal mixing processes (discussed below) to efficiently erase or reduce chemical abundances inhomogeneities and large-scale gradients.
Equation (4) can also be used to estimate that, given the low star formation rates measured in the outer disks of spiral galaxies and the large H i content, the timescale necessary to reach the observed metal enrichment can be longer than the star formation timescale within an inside-out scenario for galaxy growth or even longer than a Hubble time, reinforcing the notion that the metallicities measured in outer disks exceed the values attainable by in situ star formation alone (see also Eq. 3 in Kudritzki et al. 2014 for an alternative calculation based on the closed box model, and leading to the same conclusion).
The link between SFE and O/H described above has been shown by recent tailored chemical evolution models to be able to reproduce the flattened gas-phase abundances in the outer disk of the Milky Way beyond 10 kpc from the centre (Esteban et al. 2013) and the flat oxygen abundance gradient in the outer disk of M83 (Bresolin et al. 2016, with an adaptation of the chemical evolution model by Kudritzki et al. 2015). This seems also to be consistent with chemical evolution models of the Milky Way in which the decreasing star formation efficiency with increasing galactocentric distance leads to a flattening of the metallicity gradients in the outer regions (Kubryk, Prantzos and Athanassoula 2015).
5.2. Bringing Metals to the Outer Disks
The transport of metals produced in the inner disks to large galactocentric radii appears to be necessary in order to explain the relatively high gas-phase metallicities observed in the extended disks of spiral galaxies. A number of different mechanisms have been discussed in the literature. The argumentation contained in the following section is rather speculative since, as already mentioned, a solid theoretical explanation for the chemical properties of extended disks is currently still missing. The mechanisms invoked can be broadly divided into two main categories: mixing and enriched infall. These are succinctly presented below, following in part Bresolin et al. (2009b), Bresolin, Kennicutt and Ryan-Weber (2012) and Werk et al. (2011), to which the reader is referred to for a more in-depth discussion.
Under this category we can include processes that can be effective in redistributing metals across galactic disks. Some examples are listed below.
5.2.2. Enriched Infall
The star formation and chemical enrichment histories of galaxies are profoundly affected by inflows and outflows of gas. Feedback-driven galactic winds eject a large portion of the metals produced in disk stars into the halos, the circumgalactic medium and the intergalactic medium (Kobayashi, Springel and White 2007; Lilly et al. 2013; Côté, Martel and Drissen 2015) out to distances of the order of 100 kpc (Tumlinson et al. 2011; Werk et al. 2013). These outflows are crucial to explain, for example, the existence of the mass-metallicity relation observed for star-forming galaxies (Tremonti et al. 2004; Finlator and Davé 2008).
The gas that has been metal-enriched by supernova explosions at early epochs and subsequently ejected from galaxies can later be re-accreted in a wind-recycling process (see, e.g., the models by Oppenheimer and Davé 2008; Davé, Finlator and Oppenheimer 2011). This re-accretion on the disk from the halo should take place preferentially in the outskirts, leading to an inside-out growth, on timescales on the order of a few dynamical times, ∼ 1 Gyr (Fu et al. 2013), necessary for the gas to cool down from the hot phase. Some evidence in support of this process has been presented recently by Belfiore, Maiolino and Bothwell (2016) from the spatially resolved metal budget in NGC 628.
Fu et al. (2013) estimated the gas-phase metallicity of the infalling gas to be around 0.4 × Solar for a Milky Way-type galaxy, which is in rough agreement with the observed metallicity of the extended disks. It is also worth pointing out that the metallicity of the circumgalactic medium at z < 1, as traced by Lyman limit systems, is bimodal, with a metal-rich branch peaking at a metallicity approximately 0.5 × Solar, as shown by Lehner et al. (2013). According to these authors this metal-rich branch could be tracing cool, enriched gas originating from galactic outflows and tidally stripped material.
The effects of an enriched infall process on galactic chemical evolution models have already been illustrated before. For example, Tosi (1988) showed how a metal-rich infall would affect the chemical composition of the outer parts of spirals, inducing a flattening of their abundance gradients, and estimated an upper limit for the infalling gas metallicity of 0.4 × Solar from comparisons with the chemical abundances observed in the Milky Way. Fig. 3 shows a model radial oxygen abundance gradient for the disk of M83, calculated with a galactic wind launched in the inner disk, following Kudritzki et al. (2015), but allowing for an inflow of metal-enriched gas with an oxygen abundance 12 + log(O/H) = 8.20 (equivalent to 0.32 × Solar). Such an enriched infall is required by the model to reproduce the gas metallicity observed in the extended disk of M83, with the flat distribution arising from the assumed constant star formation efficiency.
Figure 3. Model radial oxygen abundance gradient for the disk of M83 (continuous line), calculated including an enriched gas infall, compared with the H ii region metallicities (open circles) shown in Fig. 1 (Bresolin et al. 2016).
Minor mergers Minor merger activity, as a source of cold gas leading to mass growth in galaxies, has also been proposed to be effective at chemically enriching the outer disks (López-Sánchez et al. 2015), and is included in this section because its effects could resemble those described above for enriched infall. Given the low accretion rates of star-forming galaxies due to mergers with low-mass satellites measured in the local Universe (Sancisi et al. 2008; Di Teodoro and Fraternali 2014), this process is unlikely to be important for the chemical evolution of outer disks at the present time. However, higher merger rates in the past (around a redshift z ≃ 2) could have made this process a potential contributor to the accretion of metals in the outskirts of galaxies earlier on during their evolution (Lehnert, van Driel and Minchin 2016). Numerical simulations by Zinchenko et al. (2015) also indicate that the stellar migration process induced by minor merging in Milky Way-type spirals cannot generate the flattening of the metallicity observed in the outer disks.
Different mechanisms can be invoked to explain the chemical abundance properties of outer disks. Among these are various mixing processes, including turbulence, and metal-enriched infall of gas from the circumstellar medium.