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

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.

Figures (7)

• Figure 1: In this Figure we show a suitable parametrisation of the rotation curve of a spiral galaxy.
• Figure 2: Pressure and energy density of a UDM model reconstructed from a phenomenological circular velocity profile.
• Figure 3: Rotation curve, general case defined in Eq. (\ref{['eq:general_case']}), with $\alpha=2$, $\beta=0.01$ and $\delta=3$.
• Figure 4: Energy density and pressure profile of a UDM model reconstructed from the rotation curve defined in Eq. (\ref{['eq:general_case']}), with $\alpha=2$, $\beta=0.01$ and $\delta=3$.
• Figure 5: Energy density and pressure profiles of a UDM model and matter density profile of a CDM halo, reconstructed from the BT-URC rotation curve profile.