Twinkle twinkle dark star: Oscillating profiles from dark matter scalar solitons

TL;DR

This paper investigates observational signatures of oscillatons, time-periodic self-gravitating configurations of a real scalar field, by solving the Einstein–Klein–Gordon equations with a simple mass potential and a Fourier expansion in time to obtain the background spacetime. It analyzes timelike and null geodesics, showing oscillatory circular orbits at all radii and caustic/rainbow light deflection tied to the metric oscillations. It then computes accretion-disk emission using central, NT, and mixed profiles, revealing a breathing emission with period $T = pi/omega$ that drives transitions between central brightness and rings, a signature potentially detectable by the EHT for supermassive oscillatons. Overall, the work provides concrete, testable predictions for ultralight real scalar fields in strong gravity contexts and links near-horizon imaging to beyond-Standard-Model physics.

Abstract

Real scalar fields, e.g. the axion, cannot condensate into stationary solitonic configurations to form star-like structures, eventually either dispersing or collapsing. However, by relaxing the stationarity condition on the metric, it has been shown that oscillatory solitonic solutions -- known as oscillatons -- exist. Oscillatons share several properties with boson stars, including comparable compactness and mass ranges. However, their time-dependent nature can lead to potentially discriminating observable signatures. In this work, we explore the observational properties of oscillatons. We find that stable oscillatory circular orbits exist, extending down to the center of the configuration, supporting the possibility of accretion disk structures within the star. We compute the deflection of light rays and verify that it is largely insensitive to the time dependence of the metric. Despite this, the oscillatory behavior of the redshift factor has a strong effect on the observed intensity profiles from accretion disks, producing a breathing-like image whose frequency depends on the mass of the scalar field. In fact, their oscillation period may lie within the observational windows of the Event Horizon Telescope for Sgr A$^{*}$ and M87$^{*}$, suggesting the possibility that this ``twinkling" behavior could be tested via near-horizon imaging of these objects.

Figures (13)

• Figure 1: Sequence of oscillaton solutions. Left panel: Total mass $\mu M$ as a function of $\phi_c$. Right panel: Mass–radius relation for the oscillaton configurations. We can see that oscillaton shares many similarities with standard boson stars (see also Fig. 1 in Ref. Brito:2015yfh).
• Figure 2: Background metric and scalar field for the maximum-mass oscillaton. Darker shades of red correspond to including more terms in the series expansions \ref{['eq:A']}–\ref{['eq:phie']} (up to $N=2$). The dotted line indicates the corresponding Schwarzschild solution.
• Figure 3: Oscillatory patterns in the orbital frequency and radius of OCOs for $(r_0,L)=(1,0.12834)$ (left panel) and $(r_0,L)=(8,3.262266)$ (right panel).
• Figure 4: Minimum and maximum values of the angular frequency in Eq. (\ref{['eq:angvec']}) as a function of the average orbital radius of the OCO. The dotted black line corresponds to $(\tilde{A}_{0}'(r)/2r)^{1/2}$, which asymptotically approaches the Keplerian frequency.
• Figure 5: Slightly disturbed OCO orbit. For this orbital motion, we consider $(r_0,L)=(7.99,3.262266)$, so as to compare with the right-panel of Fig. \ref{['fig:circular']}. We see that there is an additional oscillatory pattern, reminiscent from the epicyclic modulation.