Gravitational redshift determination in the Sun and other stars

Large telescopes with increased light-collecting power have alleviated the photon-noise limitation to high precision spectroscopy and prompted the need for a more precise calibration source. A collaboration between ESO, MPQ, Menlo GmbH, IAC, UFRN has been studying the capabilities of laser frequency combs (LFC) as a calibration source for high-resolution astronomical spectrographs. The LFC attached to the ultra-stable spectrograph HARPS (designed to detect exoplanets using the radial velocity technique; Mayor et al. 2003), has been demonstrated to be a very accurate calibration system, achieving short-term repeatability at the cm/s level (Wilken et al. 2012; Probst et al. 2020). One interesting application is the empirical determination of the gravitational redshift (GRS) of the Sun from accurate measurements of wavelength positions of spectral lines, as predicted from the General Theory of Relativity (Einstein 1916). The high accuracy of the LFC calibrated HARPS spectra of solar system objects allowed recently to measure the solar gravitational redshift as a test of the general theory of relativity (González Hernández et al. 2020). Additional efforts in trying to measure the GRS in other stars have been also carried out in different types of stars, while dealing with their relative motions with respect to the Sun. In this talk I will try to summarize these attempts and the prospects for additional more accurate measurements of the gravitational redshift