Periodic gravitational lensing by oscillating boson stars

Abstract

We show that oscillating (real-scalar) boson stars can act as strictly periodic gravitational lenses and generically host an \emph{oscillating radial caustic}. Sources near this caustic cross it every half period, producing achromatic phase-locked photometric spikes synchronized with an astrometric wobble, providing a promising target for time-domain astronomy. Event-number estimation indicates a measurable discovery space with current astrometric and high-cadence photometric surveys. These predictions rely only on the dynamics of long-lived real-scalar condensates, therefore offering a clean test of self-gravitating quantum fields in curved spacetime. The framework extends naturally to self-interacting real scalars (including axion-like particles) and to ultralight vector bosons.

Figures (9)

• Figure 1: Deflection angle $\hat{\alpha}$ as a function of $\{\hat{t}, \hat{r}\}$ for the oscillating boson star with $\tilde{M}=0.5$.
• Figure 2: Schematic of periodic caustic-crossing lensing by an oscillating boson star. The gray disk marks the (unresolved) source; the black and red curves indicate the radial caustic and its corresponding radial critical curve, respectively. From top to bottom, the panels show successive phases over half an oscillation period as the caustic contracts. Phase 1 (top): the source lies entirely inside the caustic and three distinct images are produced. Phase 2: as the caustic moves inward, part of the source lies outside it and the image pair near the critical curve approaches and brightens. Phase 3: continued contraction further shrinks the image pair. Phase 4 (bottom): the source is entirely outside the caustic; the pair annihilates at the critical curve, leaving a single image.
• Figure 3: Time evolution of the image pair for two representative lensing configurations. The blue curve shows the mean magnification of the image pair (left blue axis), and the red curve shows the pair's maximum radial separation (right red axis).
• Figure 4: Schematic of type II periodic caustic-crossing lensing by an oscillating boson star. The gray disk marks the (unresolved) source; the black curve shows the radial caustic and the inner red curve is the corresponding radial critical curve; the outer red curve denotes the Einstein ring. Panels (left to right) show successive phases over half an oscillation period as the caustic contracts. Phase 1 (left): the source lies entirely inside the caustic; a bright Einstein ring and a central image are present. Phase 2: as the caustic moves inward, part of the source lies outside it and the image pair near the critical curve approaches and brightens. Phase 3: the radial caustic is fully contained within the source; the Einstein ring merges with the central image, producing two bright rings: the outer Einstein ring and the inner radial-critical ring. Phase 4 (right): the caustic vanishes ($\nu>1$); the bright rings disappear, leaving a single image with a bright central region.
• Figure 5: Reduced event number $\mathcal{N}$ for type I periodic caustic-crossing lensing as a function of model parameters.