Diagnosing x-ray microlensing in the wave-optics regime

Develop a robust diagnostic methodology to identify and confirm gravitational microlensing events of x-ray pulsars by primordial black holes when wave-optics effects are important, i.e., when the photon wavelength is comparable to or larger than the Schwarzschild radius so that the magnification becomes frequency-dependent. The method should leverage multi-energy time-series data and instrument energy resolution to distinguish such chromatic microlensing signals from transient backgrounds and to enable inference of the lens mass and geometry despite finite-source and impact-parameter effects.

Background

The paper proposes a spectral diagnostic for confirming microlensing in the geometric-optics regime, where magnification is achromatic across energy bands. This enables distinguishing microlensing from transient backgrounds such as x-ray flares that are typically chromatic.

However, for lighter primordial black holes and/or lower photon energies, wave-optics effects become significant: the magnification becomes frequency-dependent, is suppressed for impact parameters larger than a scale set by the photon energy and lens mass, and exhibits chromatic behavior that is most pronounced near closest approach. These features, together with finite-source effects and detector energy resolution, complicate signal confirmation and parameter inference.

The authors therefore explicitly defer the task of constructing a practical, statistically sound diagnostic for the wave-optics regime, noting possible but challenging avenues (e.g., astrometric microlensing) and emphasizing the need for future work to establish a reliable analysis strategy.