Measuring Sub-Kelvin Variations in Stellar Temperature with High-Resolution Spectroscopy

The detection of stellar variability often relies on the measurement of selected activity indicators such as coronal emission lines and non-thermal emissions. On the flip side, the effective stellar temperature is normally seen as one of the key fundamental parameters (with mass and radius) to understanding the basic physical nature of a star and its relation with its environment (e.g., planetary instellation). We present a novel approach for measuring disk-averaged temperature variations to sub-Kelvin accuracy inspired by algorithms developed for precision radial velocity. This framework uses the entire content of the spectrum, not just pre-identified lines, and can be applied to existing data obtained with high-resolution spectrographs. We demonstrate the framework by recovering the known rotation periods and temperature modulation of Barnard star and AU Mic in datasets obtained in the infrared with SPIRou at CHFT and at optical wavelengths on $\epsilon$ Eridani with HARPS at ESO 3.6-m telescope. We use observations of the transiting hot Jupiter HD189733\,b, obtained with SPIRou, to show that this method can unveil the minute temperature variation signature expected during the transit event, an effect analogous to the Rossiter-McLaughlin effect but in temperature space. This method is a powerful new tool for characterizing stellar activity, and in particular temperature and magnetic features at the surfaces of cool stars, affecting both precision radial velocity and transit spectroscopic observations. We demonstrate the method in the context of high-resolution spectroscopy but the method could be used at lower resolution.