Parametrizing superfluid dark matter with rational approximations

Abstract

We investigate how a spatially modulated real scalar background $φ(\vec{x})$ can modify phonon propagation in the context of Superfluid dark matter (SFDM). Using a simple toy model with quartic condensate and coupling $-gφ^2|Ψ|^2$, we derive the local equation of state and the effective sound velocity $c_s(\vec{x})$. For $g>0$, modulation tends to increase the effective mass of the condensate and make the medium less rigid, suppressing $c_s^2\propto m_{Ψ,\mathrm{eff}}^{-4}$ up to a ``dust-like'' regime, $c_s^2\to 0$. We implement this modulation for the background scalar field by imposing rational profiles, through Padé radial profiles, and show the corresponding variation of $c_s^2(r)$ for different $g$, discussing implications for the structure of SFDM cores and the possible formation of inhomogeneous regions of dark matter.

Figures (2)

• Figure 1: Increasing Padé profile for the scalar background $\phi(r)$: smooth interpolation between the central value and the outer plateau on scale $R_{SF}$. The graph legend shows the values of the parameters adopted as benchmarks.
• Figure 2: Profile of $c_s^2(r)$ with increasing Padé background for different values of $g$: as $g>0$ and $\phi(r)$ increase, suppression becomes stronger up to regions with $c_s^2\to 0$. The graph legend shows the values of the parameters adopted as benchmarks.