Power spectrum of radiation from a Gaussian source microlensed by a point mass: analytic results

TL;DR

This paper derives analytical formulas for the power spectrum of electromagnetic radiation from a Gaussian source microlensed by a point mass, accounting for wavelength dependence and source size effects.

Contribution

It provides new analytical expressions for the microlensed power spectrum, including closed-form and series solutions, for extended sources under gravitational lensing.

Findings

Closed-form power spectrum expression for aligned source, lens, and observer

Series expansion for general source and lens positions

Approximate formulas for large sources and high frequencies

Abstract

Gravitational lensing deals with general-relativistic effects in the propagation of electromagnetic radiation. We consider wavelength-dependent contributions in case of a (micro)lensing of an extended Gaussian source by a point mass under standard assumptions about the incoherent emission of different source elements. Analytical expressions for the power spectrum of a microlensed radiation, which are effective in case of a large source, are obtained. If the source center, the mass, and an observer are on a straight line, the power spectrum is found in a closed form in terms of a hypergeometric function. In the case of general locations of the lens and the source, the result is presented in the form of a series. Approximate analytic expressions for the power spectrum in the case of a large source and high frequencies are obtained.