Oscillatons in Scalar-Field Dark Matter from a Full Fourier Expansion of an Exponential Potential

TL;DR

This paper develops a comprehensive Fourier-based framework to analyze oscillating scalar-field configurations called oscillatons, which are potential dark matter candidates, including effects of various self-interactions and their observable properties.

Contribution

It introduces a unified Fourier approach to model oscillatons with exponential self-interactions, enabling detailed numerical analysis of their structure and dynamics.

Findings

Oscillatons exhibit only even harmonics of the fundamental frequency.

Radial flux oscillates mainly at twice the fundamental frequency.

Negative instantaneous pressures are due to coherent oscillations and are analyzed via energy conditions.

Abstract

Real, time-dependent scalar fields can form oscillating, self-gravitating configurations-oscillatonsthat are viable candidates for scalar-field dark matter (SFDM). We revisit oscillatons with an exponential self-interaction and develop a full Fourier (Jacobi{Anger) treatment that resums the time dependence of both the metric and the potential, thereby unifying quadratic, quartic, and higher-order interactions within a single framework. After fixing the small-amplitude normalization V0 = m2 {\Phi}=({\lambda}2k0), we derive a closed, dimensionless boundary-value problem for the radial profiles and solve it numerically via Bessel-series truncation with controlled convergence. We compute time-resolved and time-averaged observables energy density, radial energy flux, radial/tangential pressures, and total mass and map their dependence on the coupling {\lambda} and central amplitude. The geometry exhibits only even harmonics of the fundamental frequency, while composite observables inherit a DC part plus even harmonics; the radial flux oscillates predominantly at 2!. Apparent negative instantaneous pressures arise from coherent oscillations and are assessed consistently through classical energy-condition diagnostics (WEC/NEC/SEC). Our formulation provides a reproducible and extensible baseline for stability analyses and observational constraints on SFDM oscillatons