Universal Fitting Formulae for the Peak Concentration of Dark Matter Halos

The prediction of the structural properties of dark matter halos is crucial for studies in modern cosmology and galaxy formation. Utilizing a comprehensive suite of N-body simulations spanning diverse cosmologies and box sizes, we derive a universal halo concentration prescription aligned with the excursion set theory framework. The halo peak-height parameter is revised to incorporate the linear growth factor at the halo formation epoch, enhancing its physical relevance to assembly history tracking. For fixed halo mass, we fit the distributions of the halo concentration and revised peak height to lognormal functions to extract their peak values. We find that these peaks follow a universal, tight relation invariant to redshift, box size, initial power spectrum, and cosmology, exhibiting remarkably small scatter. In particular, the relation flattens systematically with increasing revised peak height, approaching an asymptotic value of 2.54, consistent with previous reports of a concentration floor. The fitting formula consistently describes both the mass-concentration and peak height-concentration relations, easily quantifying how these relations depend on redshift and cosmological parameters. This universal framework enables robust prediction of the most probable (peak) halo concentration using our fitting formula or theoretical/semianalytical mass assembly histories. A software package for calculating peak concentrations is publicly available online.