Modeling unresolved turbulence and star formation in galaxy simulations

During my PhD studies, my collaborators and I explored how to make star formation modeling in galaxy simulations more robust and physically motivated. Over the past decade, there was a substantial progress in the theory of star formation on small scales, and many analytical and numerical models exist that connect star formation to the properties of supersonic turbulence in star-forming regions (see Padoan et al. 2014 for a review). Galaxy formation simulations can benefit from such models, however, small-scale turbulence in such simulations cannot be resolved and thus it must be treated using subgrid models.

To explore this approach, I implemented a model for unresolved turbulence (Schmidt et al. 2014) into the galaxy formation code ART (Kravtsov et al. 2002). Such a methodology (known as Large Eddy Simulations) is actively used to model terrestrial turbulent flows in, e.g., aerospace engineering and climate simulations. We applied this model in idealized simulations of a disk galaxy and used the results of Padoan et al. (2012) simulations of star-forming regions to compute star formation efficiency in each computational cell.

Our galaxy simulations reproduce the observed turbulent velocities and star formation efficiencies on the scales of star-forming regions. In particular, star formation occurs only in dense cold gas with the average efficiency in agreement with the observational estimates of ~few % per freefall time. This agreement with observations is nontrivial because it is achieved without tuning the parameters of the turbulent star formation model: these parameters are calibrated against high-resolution simulations of turbulence and remain fixed when the model is applied in galaxy simulations. The model also predicts a strong variation of star formation efficiencies, which has important consequences for galaxy evolution. For example, high-efficiency regions lead to more clustered supernovae that can drive stronger outflows and remove gas from galaxies more efficiently.

Link to download this video

This video shows the evolution of a galaxy simulated with the explicit model for unresolved turbulence (shown in the rightmost panel). This is the fiducial galaxy simulation that we used in our papers on gas depletion times, and it nicely illustrates vigorous dynamic evolution of the interstellar medium when considered on the timescales of hundreds of millions of years. Panels from left to right:
1. recently formed stars (specifically, stars younger than 20 million years)
2. gas density; brighter color = higher density
3. gas temperature; blue is cold (less than 1000 K), red is hot (higher than 100000 K)
4. turbulent velocity; blue is few km/s, orange-yellow is more than 10 km/s

Isolated galaxy simulation with explicit modeling of unresolved turbulence. Predicted turbulent velocities on unresolved scales (3-rd panel) can be used to compute star formation efficiency in each computational cell (4-th panel). This approach is conceptually different from that used in almost all previous galaxy formation simulations which typically assume a constant efficiency in space and time.

Distribution of local star formation efficiency predicted in the above simulation. The turbulent star formation model naturally predicts a sharp density threshold with star formation occurring only in dense gas. Also, the model predicts the average value of efficiency of ~few % per freefall time which is similar to the values observed in real star-forming regions. The model also predict a strong variation of efficiency compared to a typically assumed constant efficiency in dense gas (illustrated by the red line).

For details see our paper:
Nonuniversal Star Formation Efficiency in Turbulent ISM