A Differentiable Model of the Evolution of Dark Matter Halo Concentration

We introduce a new model of the evolution of the concentration of dark matter halos, c(t). For individual halos, our model approximates c(t) as a power law with a time-dependent index, such that at early times, concentration has a nearly constant value of c=3-4, and as cosmic time progresses, c(t) smoothly increases. Using large samples of halo merger trees taken from the Bolshoi-P and MDPL2 cosmological simulations, we demonstrate that our 3-parameter model can approximate the evolution of the concentration of individual halos with a typical accuracy of 0.1 dex for t>2 Gyr for all Bolshoi-P and MDPL2 halos of present-day mass greater than 10^11.5 Msun. We additionally present a new model of the evolution of the concentration of halo populations, which we show faithfully reproduces both average concentration growth, as well as the diversity of smooth trajectories of c(t), including capturing correlations with halo mass and halo assembly history. Our publicly available source code, Diffprof, can be used to generate Monte Carlo realizations of the concentration histories of cosmologically representative halo populations; Diffprof is differentiable due to its implementation in the JAX autodiff library, which facilitates the incorporation of our model into existing analytical halo model frameworks.