On the wave optics effect on primordial black hole constraints from optical microlensing search

Abstract

Microlensing of stars, e.g. in the Galactic bulge and Andromeda galaxy (M31), is among the most robust, powerful method to constrain primordial black holes (PBHs) that are a viable candidate of dark matter. If PBHs are in the mass range M PBH < ∼ 10 −10 M , its Schwarzschild radius (r Sch ) becomes comparable with or shorter than optical wavelength (λ) used in a microlensing search, and in this regime the wave optics effect on microlensing needs to be taken into account. For a lensing PBH with mass satisfying r Sch ∼ λ, it causes a characteristic oscillatory feature in the microlensing light curve, and it will give a smoking gun evidence of PBH if detected, because any astrophysical object cannot have such a tiny Schwarzschild radius. Even in a statistical study, e.g. constraining the abundance of PBHs from a systematic search of microlensing events for a sample of many source stars, the wave effect needs to be taken into account. We examine the impact of wave effect on the PBH constraints obtained from the r-band (6210Å) monitoring observation of M31 stars in Niikura et al. (2019), and find that a finite source size effect is dominant over the wave effect for PBHs in the mass range M PBH [10 −11 , 10 −10 ]M . We also discuss that, if a densercadence (10 sec), g-band monitoring observation for a sample of white dwarfs over a year timescale is available, it would allow one to explore the wave optics effect on microlensing light curve, if it occurs, or improve the PBH constraints in M PBH < ∼ 10 −11 M even from a null detection.

Updated constraints on asteroid-mass primordial black holes as dark matter

“…Here, we note that the previous microlensing constraints show no appreciable difference between wave and geometric approaches when the finite size effect is taken into account [5,6]. This is because during a real observation, the diffraction term in Eq.…”

“…This means that for extended sources, the peak magnification is significantly lower than in the point source case. We recalculate the magnification, taking into account the finite size effects following [11] and [6]. The effect on amplification including both finite-source and wave effects for different source size and wavelength is shown in Fig.…”

“…[4] showed that GRB femto-lensing constraints, after correction for finitesize effects, do not presently constrain PBH as DM candidates; Ref. [5] (see also [6]) realized their original constraints from optical observations of M31 had been vastly over-estimated because finite-source-size effects had originally not been accounted for. Ref.…”

Gravitational microlensing by dark matter in extended structures

“…Lenses much smaller than this have u 1. 34 1 everywhere, viz., behave like pointlike lenses. The 30 R (300 R ) nfw subhalo is slightly more (less) efficient than point-like lenses everywhere in the lensing tube.…”

“…Lenses cannot be more compact than black holes, hence their sizes are bounded from below by their Schwarzschild radius ∝ M . Moreover, the microlensing geometric setup breaks down for lens sizes much smaller than the photonic wavelength spectrum of the telescope, since the effects of wave optics greatly suppress the magnification [34]. In Fig.…”