Can we detect the stellar differential rotation of WASP-7 through the Rossiter–McLaughlin observations?

ABSTRACT The Rossiter–McLaughlin (RM) effect is the radial velocity signal generated when an object transits a rotating star. Stars rotate differentially and this affects the shape and amplitude of this signal, on a level that can no longer be ignored with precise spectrographs. Highly misaligned planets provide a unique opportunity to probe stellar differential rotation via the RM effect, as they cross several stellar latitudes. In this sense, WASP-7, and its hot Jupiter with a projected misalignment of ∼90°, is one of the most promising targets. The aim of this work is to understand if the stellar differential rotation is measurable through the RM signal for systems with a geometry similar to WASP-7. In this sense, we use a modified version of soap3.0 to explore the main hurdles that prevented the precise determination of the differential rotation of WASP-7. We also investigate whether the adoption of the next generation spectrographs, like ESPRESSO, would solve these issues. Additionally, we assess how instrumental and stellar noise influence this effect and the derived geometry of the system. We found that, for WASP-7, the white noise represents an important hurdle in the detection of the stellar differential rotation, and that a precision of at least 2 m s−1 or better is essential.

LIE ALGEBROIDS AS SPACES

In this paper, we relate Lie algebroids to Costello’s version of derived geometry. For instance, we show that each Lie algebroid – and the natural generalization to dg Lie algebroids – provides an (essentially unique) $L_{\infty }$ space. More precisely, we construct a faithful functor from the category of Lie algebroids to the category of $L_{\infty }$ spaces. Then we show that for each Lie algebroid $L$, there is a fully faithful functor from the category of representations up to homotopy of $L$ to the category of vector bundles over the associated $L_{\infty }$ space. Indeed, this functor sends the adjoint complex of $L$ to the tangent bundle of the $L_{\infty }$ space. Finally, we show that a shifted symplectic structure on a dg Lie algebroid produces a shifted symplectic structure on the associated $L_{\infty }$ space.