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

By M. Cappellari. 2016

739 citations recorded by the source corpus.

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 $\sigma$ is smaller than the velocity sampling $\Delta V$, which is generally, by design, close to the instrumental dispersion $\sigma_{\rm inst}$. The standard approach consists of convolving templates with a discretized kernel, while fitting for its parameters. This is obviously very inaccurate when $\sigma<\Delta V/2$, 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 $\sigma$. This is important e.g. for spectroscopic surveys targeting galaxies with $\sigma\ll\sigma_{\rm inst}$, 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/97086ceb87bafa97f0ab5f7d0016cd2ad0ef0c3a

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Citations in the corpus

TDCOSMO IV: Hierarchical time-delay cosmography -- joint inference of the Hubble constant and galaxy density profiles (2020, methodology): “The lens galaxy 1D spectra were then extracted in two square apertures (R 0′′.6, 0′′.6 R 1′′.0), and processed with the Penalized PiXelFitting (ppxf) code presented in Cappellari & Emsellem (2004) and further upgraded in Cappellari (2017) to obtain velocity dispersions.”
Follow Up of GW170817 and Its Electromagnetic Counterpart by Australian-Led Observing Programmes (2017, methodology): “We use pPXF (Cappellari 2017) to fit the spectrum to 7 300 Å (the extent of the MILES spectral template library) to estimate the metallicity, age, r-band mass-to-light ratio, and velocity dispersion of stars in the region immediately surrounding AT2017gfo.”
Re-evaluating old stellar populations (2018, background): “Increasingly, such analyses are being complemented and superceded by pixel-by-pixel spectrophotometric fitting analyses, which provide increasingly precise matches between observations and templates (e.g. Cappellari 2017).”