Femtolensing: Beyond the semiclassical approximation

Abstract

Femtolensing is a gravitational lensing effect in which the magnification is a function not only of the positions and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of (10 −13 − 10 −16 M ⊙ ) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculations in general potentials. The physical-optics results presented here differ at low frequencies from the semi-classical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semi-classical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10 −11 solar masses, much larger than previously believed. Additionally, we discuss the possibility of a search for femtolensing of white dwarfs in the LMC at optical wavelengths.

Femtolensing and Picolensing by Axion Miniclusters

“…The minicluster has to be in the mass range, 10 Gould 1992;Ulmer & Goodman 1995) for femtolensing, or M mc < ∼ 10 −7 M (Nemiroff & Gould 1995) for picolensing.…”

Compact stars in the standard model - and beyond

“…After all, Popper's idea that we make progress by falsifying theories is not always true. By utilizing gamma-ray bursts (GRB) or white dwarfs in the large magellanic cloud as light sources, gravitational lenses with very small masses produce a diffraction signal in the spectrum, which might be observable [32,33,34,35]. For a lens with mass within the range 10 −16 M ⊙ ≤ M ≤ 10 −11 M ⊙ , the angular separation of images would be in the femto-arcsec range (femtolensing), and for more massive lenses, M ≤ 10 −7 M ⊙ , the angular separation is in the pico-arcsec range (picolensing).…”

“…This result was calculated with a physical-optics model, as described in [34]. In principle, the time dependent amplitude due to a single light pulse from the source was calculated, and then the power As mentioned in [8], preon stars could also form in the collapse of normal massive stars, if the collapse is slightly too powerful for the core to stabilize as a neutron star, but not sufficiently violent for the formation of a black hole.…”

Quasi-geometrical optics approximation in gravitational lensing

“…amplification of the wave amplitude by lensing in wave optics. It is important to derive the correction terms for the following two reasons: (1) the calculations in wave optics are based on the diffraction integral, but it is time-consuming to numerically calculate this integral, especially for high frequency (see e.g., Ulmer & Goodman 1995). Hence, it is a great saving of computing time to use the analytical expressions.…”