Analytical galaxy profiles for photometric and lensing analysis

This article introduces a family of analytical functions of the form x ^υK_υ(x), where K_υ 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 10⁵ in radius. Unlike Sersic profiles, these functions have simple analytical two-dimensional and three-dimensional Fourier transforms, so they are easily convolved with spatially varying point-spread function (PSF) 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 affected by seeing.