Prospects for detecting the Rossiter–McLaughlin effect of Earth-like planets: the test case of TRAPPIST-1b and c

Abstract

The Rossiter-McLaughlin effect is the principal method of determining the skyprojected spin-orbit angle (β) of transiting planets. Taking the example of the recently discovered TRAPPIST-1 system, we explore how ultracool dwarfs facilitate the measurement of the spin-orbit angle for Earth-sized planets by creating an effect that can be an order of magnitude more ample than the Doppler reflex motion caused by the planet if the star is undergoing rapid rotation. In TRAPPIST-1's case we expect the Rossiter-McLaughlin semi-amplitudes to be 40−50 m s −1 for the known transiting planets. Accounting for stellar jitter expected for ultracool dwarfs and instrumental noise, and assuming radial velocity precisions both demonstrated and anticipated for upcoming near-infrared spectrographs, we quantify the observational effort required to measure the planets' masses and spin-orbit angles. We conclude that if the planetary system is well-aligned then β can be measured to a precision of 10• if the spectrograph is stable at the level of 2 m s −1 . We also investigate the measure of ∆β, the mutual inclination, when multiple transiting planets are present in the system. Lastly, we note that the rapid rotation rate of many late M-dwarfs will amplify the RossiterMcLaughlin signal to the point where variations in the chromatic Rossiter-McLaughlin effect from atmospheric absorbers should be detectable.

A Review of Possible Planetary Atmospheres in the TRAPPIST-1 System

“…In parallel, large-aperture ground-based telescopes coupled to high-resolution spectrographs could be used to infer the properties of the TRAPPIST-1 system and the planetary atmospheres. Such observations could lead to (i) the detection of the Rossiter-McLaughlin effect (Rossiter 1924 ; McLaughlin 1924 ; Cloutier and Triaud 2016 ) to further constrain the orbital architecture of the system and confirm the 3.3 days rotation period of TRAPPIST-1, which is a crucial assumption in the stellar contamination model of Morris et al. 2018a .…”

“…In parallel, large-aperture ground-based telescopes coupled to high-resolution spectrographs could be used to infer the properties of the TRAPPIST-1 system and the planetary atmospheres. Such observations could lead to (i) the detection of the Rossiter-McLaughlin effect (Rossiter 1924;McLaughlin 1924;Cloutier and Triaud 2016) to further constrain the orbital architecture of the system and confirm the 3.3 days rotation period of TRAPPIST-1, which is a crucial assumption in the stellar contamination model of Morris et al 2018a. Hirano et al (2020 have very recently made a first potential detection of the Rossiter-McLaughlin effect with the Subaru-IRD spectrograph and derived a projected rotation velocity of TRAPPIST-1 of 1.49 +0.36 −0.37 km s −1 , which corresponds to a maximum stellar rotation period of 3.97 +1.32 −0.77 days, in agreement with the 3.3 days rotation period from the K2 light curves.…”

Evidence for Spin–Orbit Alignment in the TRAPPIST-1 System

“…We note, though, that our result for v sin i s is lower than the value of 6 ± 2 km s −1 reported by Reiners & Basri (2010), which we believe was mistaken. In fact, the high value of v sin i s reported earlier made the prospect of RM observations appear easier than it was in reality; for instance, Cloutier & Triaud (2016) predicted an RM amplitude of 40 − 50 m s −1 based on this larger v sin i s . To make sure that our measurement of λ is not vulnerable to v sin i s , we fitted the RV data with v sin i s being fixed at 1.8 km s −1 .…”

Probing Transit Timing Variation and its Possible Origin with Twelve New Transits of TrES-3b

“…We ensured here the efficient calculation of well sampled MCMC chain, since the estimated mean acceptance fraction of ∼ 0.44 was found to be consistent within the ideal range of 0.2-0.5 (see Foreman-Mackey et al 2013;Cloutier & Triaud 2016;Stefansson et al 2017). To assess the convergence of MCMC chain, we estimated the integrated autocorrelation time of the chain averaged across parameters (Goodman & Weare 2010;Foreman-Mackey et al 2013) and found its value to be 2018).…”