The Impact of Non-Gaussian Line Spread Functions on Stellar Kinematic Recovery: Consequences for Dynamical Models

The line spread function (LSF) of a spectrograph encodes the inherent broadening of a single spectral line. It is typically reported as a single number, the resolving power $R = \lambda/\Delta\lambda$ with $\Delta \lambda$ the FWHM of the LSF. In standard pipelines for extracting stellar kinematics the LSF is assumed to be a wavelength dependent Gaussian. However, detailed LSF measurements from real integral field spectrographs reveal a variety of shapes, some close to Gaussian, others with large wings or that appear boxy. I have studied the impact that these non-Gaussian LSF profiles have on the recovery of the stellar kinematics of a mock spectrum and find that even in the high dispersion case of 300 km s$^{-1}$, there is up to a 7 percent uncertainty in the dispersion due to non-Gaussian LSF profiles. Additionally, higher order Gauss-Hermite moments $h_3$ and $h_4$ can be biased by up to $\pm$0.1. To resolve this bias, I developed a method to match the LSF of the template spectra to the LSF of a target spectrum when the LSF of either one or both is non-Gaussian and show that it can reduce bias in the dispersion to less than a percent down to the instrumental resolution. A Python implementation of this method has been made publicly available.