Analysing spectral lines in Gaia low-resolution spectra

With its third data release, European Space Agency's Gaia mission publishes for the first time low resolution spectra for a large number of celestial objects. These spectra however differ in their nature from typical spectroscopic data. They do not consist of wavelength samples with associated flux values, but are represented by a linear combination of Hermite functions. We derive an approach to the study of spectral lines that is robust and efficient for spectra that are represented as a linear combination of Hermite functions. For this purpose, we combine established computational methods for orthogonal polynomials with the peculiar mathematical properties of Hermite functions and basic properties of the Gaia spectrophotometers. Particular use is made of the simple computation of derivatives of linear combinations of Hermite functions and their roots. A simple and efficient computational method for deriving the position in wavelength, the statistical significance, and the line strengths is presented for spectra represented by a linear combination of Hermite functions. The derived method is fast and robust enough to be applied to large numbers of Gaia spectra without high performance computing resources or human interaction. Example applications to hydrogen Balmer lines, He I lines, and a broad interstellar band in Gaia DR3 low resolution spectra are presented.