The Rossiter‐McLaughlin Effect and Analytic Radial Velocity Curves for Transiting Extrasolar Planetary Systems

TLDR

Transiting exoplanets block starlight across the stellar disk, and stellar rotation causes asymmetric line‑profile distortions that produce the Rossiter‑McLaughlin radial‑velocity anomaly. We derive analytic expressions for the Rossiter‑McLaughlin anomaly that incorporate limb darkening. Using simulated radial‑velocity curves for HD 209458, we show that these analytic templates, combined with high‑resolution spectra from 8–10 m telescopes, markedly improve constraints on V sin I_s and λ. The Rossiter‑McLaughlin effect will be a key probe for understanding the angular‑momentum origins of exoplanetary systems.

Abstract

A transiting extrasolar planet sequentially blocks off the light coming from the different parts of the disk of the host star in a time dependent manner. Due to the spin of the star, this produces an asymmetric distortion in the line profiles of the stellar spectrum, leading to an apparent anomaly of the radial velocity curves, known as the Rossiter - McLaughlin effect. Here, we derive approximate but accurate analytic formulae for the anomaly of radial velocity curves taking account of the stellar limb darkening. The formulae are particularly useful in extracting information of the projected angle between the planetary orbit axis and the stellar spin axis, λ, and the projected stellar spin velocity, V sin I_s. We create mock samples for the radial curves for the transiting extrasolar system HD209458, and demonstrate that constraints on the spin parameters (V sin I_s, λ) may be significantly improved by combining our analytic template formulae and the precision velocity curves from high-resolution spectroscopic observations with 8-10 m class telescopes. Thus future observational exploration of transiting systems using the Rossiter - McLaughlin effect is one of the most important probes to better understanding of the origin of extrasolar planetary systems, especially the origin of their angular momentum.