Numerical simulation of oscillatons: extracting the radiating tail

TL;DR

This paper uses spectral numerical methods to analyze oscillatons, revealing that their radiating tail prevents them from being truly localized and causing gradual mass loss in physical solutions.

Contribution

It provides a precise numerical study of oscillatons, quantifies their radiating tail, and estimates the mass loss rate of physical oscillatons, connecting numerical and analytical results.

Findings

Oscillating tails are very small but non-zero, preventing perfect localization.

Physical oscillatons lose mass over time due to scalar radiation.

Numerical results agree with analytical small-amplitude approximations.

Abstract

Spherically symmetric, time-periodic oscillatons -- solutions of the Einstein-Klein-Gordon system (a massive scalar field coupled to gravity) with a spatially localized core -- are investigated by very precise numerical techniques based on spectral methods. In particular the amplitude of their standing-wave tail is determined. It is found that the amplitude of the oscillating tail is very small, but non-vanishing for the range of frequencies considered. It follows that exactly time-periodic oscillatons are not truly localized, and they can be pictured loosely as consisting of a well (exponentially) localized nonsingular core and an oscillating tail making the total mass infinite. Finite mass physical oscillatons with a well localized core -- solutions of the Cauchy-problem with suitable initial conditions -- are only approximately time-periodic. They are continuously losing their mass because the scalar field radiates to infinity. Their core and radiative tail is well approximated by that of time-periodic oscillatons. Moreover the mass loss rate of physical oscillatons is estimated from the numerical data and a semi-empirical formula is deduced. The numerical results are in agreement with those obtained analytically in the limit of small amplitude time-periodic oscillatons.