Theoretical dark matter halo density profile

TL;DR

This paper derives a theoretical density profile for dark matter haloes using a modified secondary infall model that accounts for triaxiality, initial velocities, and inside-out growth, predicting an Einasto-like profile with a core.

Contribution

It introduces a novel analytical model for dark matter halo density profiles considering triaxiality and initial velocities, aligning with numerical simulations without relying on merger history.

Findings

Predicted halo profiles are well described by an Einasto profile with a core.

Inner density profiles are insensitive to the halo's formation history.

Model predictions match numerical simulations down to small radii.

Abstract

We derive the density profile for collisionless dissipationless dark matter haloes in hierarchical cosmologies making use of the Secondary Infall (SI) model. The novelties are: i) we deal with triaxial virialised objects; ii) their seeds in the linear regime are peaks endowed with {\it unconvolved} spherically averaged density profiles according to the peak formalism; iii) the initial peculiar velocities are taken into account; and iv) accreting haloes are assumed to develop from the inside out, keeping the instantaneous inner system unaltered. The validity of this latter assumption is accurately checked by comparing analytical predictions on such a growth with the results of numerical simulation. We show that the spherically averaged density profile of virialised objects can be inferred with no need to specify their shape. The {\it typical} spherically averaged halo density profile is inferred, down to arbitrarily small radii, from the power-spectrum of density perturbations. The predicted profile in the $\Lambda$CDM cosmology is approximately described by an Einasto profile, meaning that it does not have a cusp but rather a core, where the inner slope slowly converges to zero. Down to one hundredth the total radius, the profile has the right NFW and Einasto forms, being close to the latter down to a radius of about four orders of magnitude less. The inner consistency of the model implies that the density profiles of haloes harbour no information on their past aggregation history. This would explain why major mergers do not alter the typical density profile of virialised objects formed by SI and do not invalidate the peak formalism based on such a formation.