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

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.