Towards the Reconstruction of a Unified Dark Matter Halo: a Phenomenological Approach

TL;DR

This paper develops a method to map standard dark matter density profiles to unified dark matter models using scalar fields, preserving observed galaxy rotation curves within a relativistic framework.

Contribution

It introduces a systematic approach to reconstruct UDM models from known CDM profiles, ensuring physical viability and observational consistency.

Findings

Successfully maps NFW, Burkert, and other profiles to UDM models.

Reproduces flat rotation curves without separate dark matter and dark energy.

Ensures stability and energy conditions in the reconstructed models.

Abstract

We investigate static, spherically symmetric halo configurations within Unified Dark Matter (UDM) scalar-field models, developing a systematic mapping between standard cold dark matter (CDM) density profiles and their UDM counterparts. Exploiting the equivalence-class structure of UDM models, we show that, in principle, different Lagrangian realisations can share the same weak-field rotation curve while exhibiting distinct field properties. We reconstruct the effective energy density, radial and tangential pressures from a phenomenological circular velocity profile, ensuring the absence of ghosts and instabilities and the preservation of the Null Energy Condition (NEC). Applying our procedure to several commonly used CDM halo profiles -- including Persic, Salucci \& Stel, NFW, and Burkert models -- we demonstrate that their phenomenological success can be retained within a relativistic UDM framework, reproducing the observed flatness of rotation curves without introducing separate dark matter and dark energy components.