Analytical Galaxy Profiles for Photometric and Lensing Analysis

TL;DR

This paper introduces a new family of analytical galaxy profiles based on incomplete Bessel functions, which accurately model galaxy light and mass distributions and are computationally efficient for photometric and lensing analyses.

Contribution

The paper presents a novel family of analytical functions that approximate Sersic profiles, with simple Fourier transforms, enabling improved modeling of galaxy profiles for lensing and photometry.

Findings

Functions accurately fit galaxy light profiles over a wide range of parameters.

They enable efficient convolution with PSF for lensing analysis.

High S/N lensing measurements can recover distortions even with large PSF.

Abstract

This article introduces a family of analytical functions of the form x^{\nu} K_{\nu}(x), where K_{\nu} is the incomplete Bessel function of the third kind. This family of functions can describe the density profile, projected and integrated light profiles and the gravitational potentials of galaxies. For the proper choice of parameters, these functions accurately approximate Sersic functions over a range of indices and are good fits to galaxy light profiles. With an additional parameter corresponding to a galaxy core radius, these functions can fit galaxy like M87 over a factor of 100,000 in radius. Unlike Sersic profiles, these functions have simple analytical 2-dimensional and 3-dimensional Fourier transforms, so they are easily convolved with spatially varying point spread function and are well suited for photometric and lensing analysis. We use these functions to estimate the effects of seeing on lensing measurements and show that high S/N measurements, even when the PSF is larger than the galaxy effective radius, should be able to recover accurate estimates of lensing distortions by weighting light in the outer isophotes that are less effected by seeing.