Large-scale turbulent driving regulates star formation in high-redshift gas-rich galaxies

The formation of stars is a key process that has a major impact on the galactic evolution. Its efficiency and rate are influenced by many factors, and the relative importance of each of them is still poorly understood. One of the main reasons why it is so hard to fully understand star formation is that it involves scales ranging from a few astronomical units up to several kiloparsecs, with about nine orders of magnitude between them. As a consequence, self-consistent simulations of star formation in a galaxy are out of reach for now, and some possibly important factors have to be neglected or added through subgrid models (Dubois & Teyssier, 2008; Hopkins et al., 2011). Simulations of smaller regions of a galaxy are a useful complementary tool that enables the use of a higher resolution and the performance of parametric studies. An important challenge for this kind of numerical simulations is reproducing the Schmidt–Kennicutt (SK) law (Kennicutt, 1998; Kennicutt & Evans, 2012) that links the star formation rate (SFR) to the column density of gas. Previous results (Walch et al., 2015; Padoan et al., 2016; Iffrig & Hennebelle, 2017; Kim & Ostriker, 2017; Gatto et al., 2017) indicated that the magnetic field has a moderate effect on the SFR but that stellar feedback (namely H II regions and supernovae) can greatly reduce the SFR in Milky Way-like galaxies down to a rate consistent with the observed one. Colling et al. (2018) have shown that with a more comprehensive model of stellar feedback, including ionizing radiation as well as supernovae that explode after a delay corresponding to the stellar lifetime, the SFR typically lies a few times above the SK relation. However, they have shown that the galactic shear may be able, if it is strong enough, to reduce the SFR sufficiently to make it compatible with the SK law. In our work, we run simulations of a local region of a galactic disk within a kiloparsec cube box. We use a numerical setup that is very close to the one used by Colling et al. (2018). Our primary goal is to extend their results to galaxies with higher column densities with the aim to reproduce the SK law. The galaxies that we model have a stellar and dark matter potential similar to the Milky Way with a mean column density of gas $\Sigma_{0,\mathrm{gas}}$ that varies from $13$ to $155~\text{M}_{\astrosun}\cdot\mathrm{pc}^{-2}$, representative for Milky Way-like galaxies up to gas-rich galaxies at redshift $z=$ 1–3 (Genzel et al., 2008, 2010; Daddi et al., 2010). Since the total gravitational potential remains constant, so does the galactic shear, which is therefore not sufficient to regulate star formation (Colling et al., 2018). On the other hand, several recent studies have shown that injection of turbulence from galactic motions has to be taken into account in order to explain the observed velocity dispersion and SFR (Renaud et al., 2012; Krumholz et al., 2018; Meidt et al., 2020) as suggested by Bournaud et al. (2010). Possible source of turbulence include the orbital energy or even mass accretion onto the galaxies. The latter in particular requires a mechanism such as an instability to degrade this source of free energy. We test the effect of such injection of turbulence by adding a large-scale turbulent driving similar to the one used by Schmidt et al. (2009).

This Letter is organized as follows. In the section 2 we present our numerical setup and our simulations. In section 3 we investigate the relation between the SFR and the gas column density when only stellar feedback is at play. In section 4 we show the results of similar simulations when we add a turbulent driving. The necessity of the stellar feedback to quench star formation is investigated in section 5. Section 6 concludes the Letter.

In this section we study the SFR when only stellar feedback regulates star formation (without additional turbulent driving, group noturb). Figure 1 features edge-on and face-on column density maps of the simulations. In noturb simulations, the gas tends to form clumpy structures. Ejection of gas out of the disk plane due to supernovae explosions is clearly visible in the simulations with a high initial gas column density. Figure 2 shows the evolution of the total sink mass during the simulation for several initial column density going from $\Sigma_{\text{gas},0}=12.9~\text{M}_{\astrosun}\cdot\text{pc}^{-2}$ to $\Sigma_{\text{gas},0}=155~\text{M}_{\astrosun}\cdot\text{pc}^{-2}$. The dotted lines correspond to the expected stellar mass growth if the SFR was constant and scaled as in the SK law. For $\Sigma_{\text{gas},0}=12.9~\text{M}_{\astrosun}\cdot\text{pc}^{-2}$ (corresponding to a galaxy slightly heavier than the Milky way) the SFR is close to the observed one for similar galaxies. However, the stellar mass growth is considerably faster than expected in heavier galaxies, with SFR that can overpass the observation by more than one order of magnitude. Interestingly, the SFR also follows a star formation law $\Sigma_{\mathrm{SFR}}\propto\Sigma_{\mathrm{gas}}^{N}$ (see Figure 3a), but with an index $N=2.5$, which is much steeper than the $N=1.4$ determined by Kennicutt. This is unlikely to be due to an underestimation of the stellar feedback. First, all the main processes that may quench the star formation are included in the simulation, except stellar winds. Similar simulations with stellar winds shows that their effect on star formation are not completely negligible but modify it only by a factor of two (Gatto et al., 2017), and thus cannot explain the discrepancies we observe. Second, our FUV prescription (uniform heating proportional to the SFR) overestimates the heating because both absorption and the propagation delay are not well taken into account. Third, additional feedback effects strong enough to reduce star formation to the expected level for $\Sigma_{\text{gas},0}>25~\text{M}_{\astrosun}\cdot\text{pc}^{-2}$ would probably generate a too weak SFR for simulations with $\Sigma_{\text{gas},0}<20~\text{M}_{\astrosun}\cdot\text{pc}^{-2}$ which are already close to the observed SFR. Finally, Figure 3b shows that the expected turbulent power from stellar feedback is well below what is needed to quench star formation efficiently for high-redshift galaxies. The inefficiency of stellar feedback to quench star formation in gas-rich galaxies suggests that another phenomenon is likely at play.

In the previous section we have shown that a pure stellar feedback was not strong enough to quench star formation efficiently in galaxies with high column density. Figure 2 features the mass accreted by the sinks for several values of the initial gas column density $\Sigma_{0,\mathrm{gas}}$ with a turbulent forcing (with dominant solenoidal modes). We tested two scalings for the injected energy, $P_{\mathrm{inj}}\propto\Sigma^{2.5}$ and $P_{\mathrm{inj}}\propto\Sigma^{3.8}$. In both sets of simulations, the stellar mass has been reduced from the pure feedback model, and more powerful driving is more efficient at reducing star formation. The turb3.8 group has stellar mass curve compatible with a SFR matching the SK law.

Indeed, in Figure 3a the star formation law derived from this group has an index $N=1.5$, very close to the $N=1.4$ of the SK relation. Therefore, large-scale turbulent driving enables to reproduce a formation law close to the SK law when pure stellar feedback cannot.

Turbulent driving has a considerable influence on the shape of the galactic disk, as can be seen in Figure 1 representing the face-on and edge-on column density map of gas with and without turbulent driving. Pure feedback simulations show a lot of small-scale structures and clumps, and a lot of gas is blasted out of the disk plane by SNe. When turbulent driving is applied, the gas tends to organize within huge filaments, with fewer and bigger clumps. A significant bulk motion is triggered. The effects of turbulent driving are also clearly visible on the density probability distribution function (PDF) and on the density profile in Figure 6, in the Appendix. When applied, turbulent driving increases the fraction of gas within low-density regions and can move the position of the disk plane. In all cases the scale height of the disk increases for higher value of the column density as the strength of stellar feedback or turbulent driving also increase, but a disk structure is still clearly apparent. More energetic turbulent driving (or 3D turbulent driving) completely destroys the disks, which sets a limit on the turbulent energy that can be injected.

Previous studies (Bournaud et al., 2010; Renaud et al., 2012; Krumholz et al., 2018; Hopkins et al., 2011) suggest that both large-scale turbulence and stellar feedback are needed to match observations. Block et al. (2010) argue that stellar feedback is crucial to inject energy back to large scales. With our setup, we can carry out a simple experiment to see if stellar feedback is necessary to quench star formation. To investigate this, we rerun two simulations of the turb3.8 group, namely those with $n_{0}=1.5,f_{\mathrm{rms}}=2\times 10^{4}$ and $n_{0}=6,f_{\mathrm{rms}}=2\times 10^{5}$, with stellar feedback off (we switch off H II regions and SNe, and FUV heating is kept constant at solar neighborhood level), so that only the turbulent driving quenches star formation. On Figure 4, we can see that in such a configuration the SFR is higher than the one given by the Kennicutt law. For low gas column density, it is even higher than the one that we obtain with stellar feedback only. Thus, it appears that stellar feedback and large-scale turbulence are complementary to quench star formation, and that the relative importance of stellar feedback diminishes as the gas column density increase. This result is in good agreement with the conclusion reached from global galactic simulations (Bournaud et al., 2010).

We have presented simulations of kiloparsec cube regions of galaxies with and without stellar feedback and with and without turbulent driving (Table 1, figures 1,4). The simulated galaxies have a gas column density between $12.9$ and $155~\text{M}_{\astrosun}\cdot\mathrm{pc}^{-2}$. We reported the SFR in these simulations as function of the gas column density (Figure 2) and compared the obtained star formation law with the SK law (Figure 3a). Then we compared the power injected by the turbulent driving needed to reproduce the SK law with estimates of the turbulent power released by large-scale motions and stellar feedback (Figure 3b). Our main findings are as follows.

1. 1.

   Stellar feedback is able to explain the SFR in Milky Way–like galaxies.

2. 2.

   In high-redshift galaxies with high gas column densities, stellar feedback alone is too weak to quench star formation to a level consistent with the SK law: the obtained star formation law for the studied range of gas column densities is too steep compared to the SK law.

3. 3.

   The addition of a mainly solenoidal large-scale turbulent driving with a power injection $\overline{P_{\mathrm{inj}}}~\propto~\Sigma^{3.8}$ reduces considerably the SFR. The star formation obtained has an index $N=1.5$, which is close to the observed SK relation.

4. 4.

   The injected power is consistent with the power needed to maintain the disk at marginal stability (with a Toomre $Q\approx 1)$, which scales as $P_{\mathrm{LS}}~\propto~\Sigma^{4}$.

5. 5.
6. 6.

   Stellar feedback remains necessary, but its importance decreases as the gas column density increases.

Large-scale turbulent driving is therefore necessary when studying star formation in kpc-sized regions of galaxies, especially when the gas fraction is high. A key question that arises is what is the exact nature and origin of the turbulence that needs to be injected.