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

I start by providing an updated summary of the penalized pixel-fitting (PPXF) method that 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 kinematics when the velocity dispersion is smaller than the velocity sampling V that is generally, by design, close to the instrumental dispersion inst . The standard approach consists of convolving templates with a discretized kernel, while fitting for its parameters. This is obviously very inaccurate when V /2, due to undersampling. Oversampling can prevent this, but it has drawbacks. Here I present a more accurate and efficient alternative. It avoids…