The Scale-dependent Energy Transfer Rate as a Tracer for Star Formation in Cosmological N-Body Simulations

We investigate the energy release due to large-scale structure formation and the subsequent transfer of energy from larger to smaller scales. We calculate the power spectra for the large-scale velocity field and show that the coupling of modes results in a transfer of power predominately from larger to smaller scales. We use the concept of cumulative energy to calculate the amount of energy deposited into small scales during the cosmological structure evolution. To estimate the contribution due to the gravitational interaction only, we perform our investigations by means of dark matter simulations. The global mean of the energy transfer increases with redshift ~(z + 1)3; this can be traced back to the similar evolution of the merging rates of dark matter halos. The global mean energy transfer can be decomposed into its local contributions, which allows us to determine the energy injection per unit mass into a local volume. The obtained energy injection rates are at least comparable to other energy sources driving interstellar turbulence, e.g., supernova kinetic feedback. On that basis, we make the crude assumption that processes causing this energy transfer from large to small scales, e.g., the merging of halos, may contribute substantially to the driving of interstellar medium turbulence, which may eventually result in star formation on much smaller scales. We propose that the ratio of the local energy injection rate to the energy already stored within small-scale motions is a rough measure for the probability of local star formation, applicable within cosmological large-scale N-body simulations.