Parametrizing superfluid dark matter with rational approximations

TL;DR

This paper explores how rational profile modulations of a scalar field in superfluid dark matter affect phonon propagation and the effective sound speed, with implications for dark matter structure formation.

Contribution

It introduces a method using Padé rational profiles to model scalar field modulations and analyzes their impact on the sound speed in superfluid dark matter.

Findings

Modulation can suppress the effective sound speed, approaching a dust-like regime.

Rational profiles allow controlled variation of the sound speed within the superfluid.

Implications for the formation of inhomogeneous dark matter regions.

Abstract

We investigate how a spatially modulated real scalar background $\phi(\vec{x})$ can modify phonon propagation in the context of Superfluid dark matter (SFDM). Using a simple toy model with quartic condensate and coupling $-g\phi^2|\Psi|^2$, 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 $c_s^2\propto m_{\Psi,\mathrm{eff}}^{-4}$ 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 Pad\'e 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.