Wind of change: retrieving exoplanet atmospheric winds from high-resolution spectroscopy

Abstract

Context. The atmosphere of exoplanets has been studied extensively in recent years, using numerical models to retrieve chemical composition, dynamical circulation or temperature from data. One of the best observational probes in transmission is the sodium doublet, due to its large cross section. However, modelling the shape of the planetary sodium lines has proven to be challenging. Models with different assumptions regarding the atmosphere have been employed to fit the lines in the literature, yet statistically sound direct comparisons of different models are needed to paint a clear picture. Aims. We will compare different wind and temperature patterns and provide a tool to distinguish them driven by their best fit for the sodium transmission spectrum of the hot Jupiter HD 189733b. We parametrise different possible wind patterns already tested in literature and introduce the new option of an upwards driven vertical wind. Methods. We construct a forward model where the wind speed, wind geometry and temperature are injected into the calculation of the transmission spectrum. We embed this forward model in a nested sampling retrieval code to rank the models via their Bayesian evidence.Results. We retrieve a best-fit to the HD 189733b data for vertical upward winds |v ver (mean)| = 40 ± 4 km s −1 at altitudes above 10 −6 bar. With the current data from HARPS, we cannot distinguish wind patterns for higher pressure atmospheric layers. Conclusions. We show that vertical upwards winds in the upper atmosphere are a possible explanation for the broad sodium signature in hot Jupiters. We highlight other influences on the width of the doublet and explore strong magnetic fields acting on the lower atmosphere as one possible origin of the retrieved wind speed.

Mass-loss rate and local thermodynamic state of the KELT-9 b thermosphere from the hydrogen Balmer series

“…Thus, for the rest of our study, we decided to ignore this effect in favor of the planetary rotation. We note that these two aspects have been previously explored in Seidel et al (2020). They were able to keep a 1D atmospheric structure at the price of several approximations in the atmospheric velocity patterns (pseudo-2D/3D).…”

“…We model the atmospheric structure ρ(r) with a hydrostatic or a hydrodynamic structure. For the hydrostatic solution, we have the base density ρ 0 (r = 1) as a free parameter, and consider that the pressure scale-height H = k B T/µg can change with the altitude according to T (r), µ(r), g(r) (see e.g., the π η code in Ehrenreich et al 2006;Pino et al 2018;Seidel et al 2020). In the hydrostatic case, we can estimate a lower limit to the mass loss rate, by computing the Jeans escape rate at the planetary Roche radius, r Roche (Eggleton 1983;Ridden-Harper et al 2016), or at the exobase radius, r exobase , if below (Lecavelier des Tian et al 2005;Salz et al 2016;Heng 2017):…”

“…When an element and its transitions are chosen (in our case the Hydrogen Balmer series), the opacity κ [cm 2 g −1 ] are computed in each layer of the atmosphere according to the line list of Kurucz (1979Kurucz ( , 1992, to the temperature, and to the number density n H I(n) . We do assume that the line intensity arises from photon absorption and from stimulated emission (Sharp & Burrows 2007). For the hydrogen Balmer transition from electronic level i to j, we have:…”

“…Within the previous two steps, our line profile can be broadened according to different atmospheric patterns (see Brogi et al 2016;Seidel et al 2020). First, we assume a solid body planetary rotation (perpendicular to the orbital plane).…”

“…In practice, for KELT-9b, for most of the mass loss rates (except for unphysical large rates), the upward velocity v(r) is smaller than 0.01-1 km s −1 in the probed layers (i.e., the sonic point r s , where the velocity becomes several km s −1 is far above the Roche radius). This leads to a negligible (much smaller than the instrumental resolution) parker wind broadening (though see Seidel et al 2020, for other possible scenarios). Thus, for the rest of our study, we decided to ignore this effect in favor of the planetary rotation.…”