A universal model for the accretion rates and formation times of dark matter halos

The formation histories of halos set the baseline rate at which galaxies accrete gas over cosmic time. While a number of models describe these histories and their derivative, the mass accretion rate (MAR), a simple and universal formula has remained elusive. Here we measure the median MARs and half-mass formation times of halos in dark matter-only and hydrodynamical simulations, in extremely different cosmologies ($\Lambda$CDM and Einstein-de Sitter), and across a wide range of redshifts ($z = 0$-$14$). We confirm that MARs increase with mass and redshift, and that they are virtually identical in hydrodynamical and dark matter-only simulations. We show that MARs are accurately described by a universal six-parameter function of three physical variables: the peak height $\nu$, the slope of the linear power spectrum $n_{\rm eff}$, and the effective linear growth rate $\alpha_{\rm eff}$. A complementary two-parameter fit for the formation redshift improves on the function of Lacey \& Cole by fixing one parameter to its physical value and adding a dependence on $n_{\rm eff}$. Our model is broadly consistent with some prescriptions from the literature but provides a larger range and higher accuracy at high redshifts and low masses. Our fitting functions are implemented in the publicly available \textsc{Colossus} toolkit.