Star-Planet Interactions: Observational Techniques and Methods

This chapter summarizes the techniques and methods used to study star-planet interaction (SPI) from the observational point of view. SPI can produce a wide range of observational signatures, from localized stellar activity enhancements to changes in planetary atmospheric escape and transmission spectra. This chapter reviews the main observational techniques used to detect and characterize SPI, emphasizing the methodological challenges involved in separating planet-induced signals from intrinsic stellar variability. We discuss radial-velocity diagnostics, including cross-correlation, template matching, line-by-line methods, and activity indicators, highlighting their sensitivity to line-profile distortions and chromatic variability. We then review precision photometry as a tool to search for orbit-locked variability, flare modulation, and active-region occultations during planetary transits. Chromospheric diagnostics, including Ca II, Halpha, He I, and Na II lines, are presented as tracers of magnetic variability at different atmospheric heights and as potential probes of intermittent SPI signatures. We also discuss transmission spectroscopy as a complementary approach, since planetary atmospheric tracers such as H I Lyalpha, Balmer lines, C II, and He I can encode information about the stellar high-energy environment, stellar wind, and magnetic coupling. In addition, radio observations provide a promising avenue to probe magnetic SPI directly through coherent emission mechanisms. Finally, we examine time-series analysis techniques commonly employed in SPI searches, including generalized Lomb-Scargle periodograms, rolling periodograms, harmonic analyses, and bootstrap-based significance estimation. (abridged)