Analysing spectral lines in Gaia low-resolution spectra

Context. With its third data release, European Space Agency’s Gaia mission has published the first set of low-resolution spectra for a large number of celestial objects. However, these spectra differ in their nature from typical spectroscopic data, as they do not consist of wavelength samples with associated flux values. Instead, they are represented by a linear combination of Hermite functions. Aims. We derive an approach to studying spectral lines that is robust and efficient for spectra that are represented as a linear combination of Hermite functions. Methods. For this purpose, we combined established computational methods for orthogonal polynomials with the peculiar mathematical properties of Hermite functions and basic properties of the Gaia spectrophotometers. In particular, we made use of simple computatios for the derivatives of linear combinations of Hermite functions and their roots. Results. A simple and efficient computational method for deriving the position in wavelength, statistical significance, and 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 the need for high-performance computing resources or human interference. We present example applications to hydrogen Balmer lines, He I lines, and a broad interstellar band in Gaia DR3 low-resolution spectra.