TESS search for substellar companions through pulsation timing of $\delta$ Scuti stars. I. Discovery of companions around Chang 134 and V393 Car

Early-type main-sequence pulsating stars such as \ds{} variables are one of the least explored class of targets in the search for exoplanets. Pulsation timing (PT) is an alternative technique to the most effective search methods. It exploits the light-travel-time effect (LTTE) to infer the presence of additional massive bodies around a pulsating star by measuring a periodic phase modulation of its signal. PT has been extremely successful in discovering and characterizing stellar binaries when it was applied to high-precision light curves over long temporal baselines, such as those delivered by the Kepler mission. In favorable conditions, the sensitivity of PT can reach the planetary-mass regime; one such candidate has already been claimed. The advent of TESS, with its nearly full-sky coverage and the availability of full-frame images, opens a great opportunity to expand this field of research. In this work, we present a pilot study aimed to understand the potential of PT as applied to TESS data, which are considerably different from Kepler data in terms of photometric noise, sampling cadence, and temporal baseline. We focused on the most favorable class of \ds{}, that is, those showing strong pulsations and very simple frequency spectra. After the development of a customized pipeline, we were able to detect candidate companions for two targets in the (sub-)stellar mass regime: Chang~134 ($43\pm 5$~$M_\mathrm{jup}$, $P\simeq 82$~d) and V393 Car ($\gtrsim 100$~$M_\mathrm{jup}$, $P\gtrsim 700$~d). Our results also highlight the limiting factors of this technique and the importance of an accurate absolute time calibration for future missions such as PLATO.