[Paper Review] Method for detecting a boson star at Sgr A* through gravitational lensing

Amitai Y. Bin-Nun|arXiv (Cornell University)|Jan 8, 2013

Astrophysical Phenomena and Observations3 citations

TL;DR

This paper proposes using strong gravitational lensing of S-stars near Sgr A* to detect a boson star, a hypothetical compact object made of scalar particles. By modeling the lensing effects of a boson star’s extended mass distribution, the study shows that secondary images formed via radial caustics would be significantly brighter than those from a black hole of similar mass, with magnification peaks exceeding K=18—well within reach of upcoming instruments like GRAVITY and MICADO.

ABSTRACT

Observations of the Sgr A* region in the galactic center confirm the presence of a large amount of matter in a small volume, leading to the consensus that a black hole exists there. However, dynamical observations cannot rule out the presence of a boson star, a compact object made up of scalar particles, as both objects are far more compact than the scale of current observational constraints. While a boson star in the galactic center is disfavored for a number of theoretical considerations, we outline the first test that can directly observe a boson star. We accomplish this by studying the strong gravitational lensing of S stars resulting from the assumption of a boson star in the Galactic Center. Boson stars have an extended mass distribution and are transparent to electromagnetic radiation, giving rise to a radial caustic curve. We calculate the brightness of images formed by stars crossing these radial caustics and show that a boson star would give rise to much brighter images than a black hole with a similar mass and that those images would be easily bright enough to be detected with upcoming instruments.

Motivation & Objective

• To develop a direct observational test distinguishing a boson star from a black hole at the Galactic Center, where dynamical constraints alone cannot differentiate the two.
• To investigate how the extended mass distribution of a boson star produces radial caustics that enhance image magnification during stellar flybys.
• To quantify the brightness of secondary images formed by lensing of S-stars, particularly focusing on detectability with upcoming high-sensitivity instruments.
• To assess the feasibility of detecting boson star lensing events through photometric and astrometric measurements despite unresolved image separation.

Proposed method

• Modeling the spacetime of a boson star using the Einstein-Klein-Gordon equations with a self-interacting scalar field potential, assuming spherical symmetry and a time-harmonic ansatz for the scalar field.
• Solving the resulting system of differential equations to determine the metric coefficients and mass distribution of the boson star, parameterized by central density and self-interaction strength.
• Calculating the deflection angle and image positions for stars orbiting Sgr A* under the influence of a boson star lens, identifying radial caustics arising from the extended mass profile.
• Simulating light curves for S-stars (e.g., S27, S6) crossing these radial caustics, computing magnification factors (K) as a function of impact parameter and stellar radius.
• Assessing detectability by comparing predicted image brightness (K-magnitude) to the sensitivity thresholds of upcoming instruments such as GRAVITY and MICADO.
• Evaluating the distinguishability of boson star lensing from Kerr black hole lensing, noting that the latter’s caustics are too close to the black hole to be crossed by known S-stars.

Experimental results

Research questions

• RQ1 Can strong gravitational lensing of S-stars produce detectable secondary images that differ significantly in brightness between a boson star and a black hole of similar mass?
• RQ2 How does the extended mass distribution of a boson star generate radial caustics that enhance image magnification compared to a black hole?
• RQ3 What is the predicted peak magnification (K-magnitude) of secondary images formed by lensing of S-stars by a boson star, and is it within the sensitivity range of upcoming instruments?
• RQ4 Can the absence of expected secondary images for a black hole lens, or their unexpected brightening, serve as unambiguous evidence for a boson star?
• RQ5 How does the size of the source star (e.g., R⊙ vs. 10R⊙) affect the sharpness and detectability of caustic crossing events?

Key findings

• Boson star lensing produces radial caustics due to its extended mass distribution, leading to significantly enhanced secondary image magnification compared to black hole lensing.
• For a boson star with a self-interaction-dominated potential, secondary images can reach peak magnification factors (K) exceeding 18, with some cases surpassing the black hole’s maximum of K=20.7.
• The brightest secondary image from a black hole lens is K=20.7, but a boson star can produce images brighter than K=18, making them detectable with instruments like GRAVITY and MICADO.
• Smaller stellar sources (e.g., R=0.1R⊙) produce sharper, more dramatic magnification peaks during caustic crossings, increasing detectability for compact objects like white dwarfs.
• The separation between the two brightest secondary images during caustic crossing is less than 10 μas, making them unresolved by current and near-future instruments, but photometric detection remains feasible.
• A caustic crossing event with unexpected brightening beyond black hole predictions—or the absence of a predicted secondary image—would provide strong evidence for a boson star-like object at Sgr A*.