Improving the full spectrum fitting method: accurate convolution with Gauss-Hermite functions

Michele Cappellari

doi:10.1093/mnras/stw3020

paper

Improving the full spectrum fitting method: accurate convolution with Gauss-Hermite functions

arXiv:1607.08538 · doi:10.1093/mnras/stw3020

Abstract

I start by providing an updated summary of the penalized pixel-fitting (pPXF) method, which is used to extract the stellar and gas kinematics, as well as the stellar population of galaxies, via full spectrum fitting. I then focus on the problem of extracting the kinematic when the velocity dispersion $σ$ is smaller than the velocity sampling $Δ V$ , which is generally, by design, close to the instrumental dispersion $σ_{inst}$ . The standard approach consists of convolving templates with a discretized kernel, while fitting for its parameters. This is obviously very inaccurate when $σ < Δ V /2$ , due to undersampling. Oversampling can prevent this, but it has drawbacks. Here I present a more accurate and efficient alternative. It avoids the evaluation of the under-sampled kernel, and instead directly computes its well-sampled analytic Fourier transform, for use with the convolution theorem. A simple analytic transform exists when the kernel is described by the popular Gauss-Hermite parametrization (which includes the Gaussian as special case) for the line-of-sight velocity distribution. I describe how this idea was implemented in a significant upgrade to the publicly available pPXF software. The key advantage of the new approach is that it provides accurate velocities regardless of $σ$ . This is important e.g. for spectroscopic surveys targeting galaxies with $σ ≪ σ_{inst}$ , for galaxy redshift determinations, or for measuring line-of-sight velocities of individual stars. The proposed method could also be used to fix Gaussian convolution algorithms used in today's popular software packages.

14 pages, 4 figures, LaTeX. Accepted for publication in MNRAS. The upgrade to the pPXF method described in this paper is available at http://purl.org/cappellari/software

Improving the full spectrum fitting method: accurate convolution with Gauss-Hermite functions

Abstract

References in corpus (13)

Cited by in corpus (24)