Planet-star tidal interactions with precise transit timing

Theoretical calculation and some indirect observations show that massive exoplanets on the tightest orbits — so-called hot Jupiters — must undergo orbital decay due to tidal dissipation within their host stars. This orbital evolution could be observationally accessible through precise transit timing over the course of decades. Meter-class telescopes are recognised as excellent instruments for such follow-up observations. They usually provide photometric time series of millimagnitude or even sub-millimagnitude precision for stars brighter than ∼12 mag. Such observations allow us to determine individual mid-transit times with errors between 20 and 40 s, and when they are combined together, the averaged timing precision down to or even below 10 s can be achieved over time scales of months. The rate of planetary in-spiralling may not only help us to understand some aspects of evolution of planetary systems, but can also be used as a probe of the stellar internal structure. Since 2017 we have run a regular observing campaign aimed at transit timing for a sample of best candidates for in-falling planets. Among them there is WASP-12 b, transits of which exhibit a pronounced departure from a linear ephemeris. New observations allow us to confirm the rapid decay rate for that planet, and to place constraints on the tidal dissipation efficiency in other systems.