A spherical scalar-tensor galaxy model

We build a spherical halo model for galaxies using a general scalar-tensor theory of gravity in its Newtonian limit. The scalar field is described by a time-independent Klein-Gordon equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. Our model, by construction, fits both the observed rotation velocities of stars in spirals and a typical luminosity profile. As a result, the form of the new Newtonian potential, the scalar field, and dark matter distribution in a galaxy are determined. Taking into account the constraints for the fundamental parameters of the theory (lambda,alpha), we analyze the influence of the scalar field in the dark matter distribution, resulting in shallow density profiles in galactic centers.

💡 Research Summary

The paper presents a spherical halo model for spiral galaxies derived from the Newtonian limit of a general scalar‑tensor theory of gravity. In this limit the gravitational potential Φ obeys the usual Poisson equation, while an additional scalar field φ satisfies a static Klein‑Gordon (Yukawa) equation that is sourced by the same matter density ρ. The two equations read

 ∇²Φ = 4πG ρ, (∇² – λ⁻²)φ = –α 4πG ρ,

where λ is the Compton wavelength (or range) of the scalar field and α quantifies the coupling strength between the scalar and ordinary matter. Because the equations are linear, their solutions can be expressed with Green’s functions: the Newtonian potential retains its 1/r form, whereas the scalar contribution is a Yukawa term φ(r) = –α (GM/r) e^{–r/λ}. For distances r ≪ λ the scalar field either enhances (α > 0) or weakens (α < 0) the effective gravity; for r ≫ λ the Yukawa term is exponentially suppressed and the theory reduces to standard Newtonian gravity.

To confront the model with observations the authors adopt realistic baryonic mass distributions. The stellar component is inferred from the observed surface‑brightness profile using an exponential disk (and a de Vaucouleurs bulge where appropriate) together with a mass‑to‑light ratio M/L. The gaseous component is taken from HI data. These baryonic densities ρ_b(r) are combined with the scalar‑tensor field equations to compute the total potential Φ_tot(r) = Φ(r) + φ(r). The circular velocity follows from V_th(r) = √