Measuring planetary atmospheric dynamics with Doppler spectroscopy

Doppler imaging spectroscopy is the most reliable method of directly measuring wind speeds of planetary atmospheres of the solar system. However, most knowledge about atmospheric dynamics has been obtained with cloud-tracking technique, which consists of tracking visible features from images taken at different dates. Doppler imaging is as challenging (motions can be less than 100 m s^-1) as it is appealing because it measures the speed of cloud particles instead of large cloud structures. A significant difference between wind speed measured by cloud-tracking and Doppler spectroscopy is expected in case of atmospheric waves interfering with cloud structures. The purpose of this paper is to provide a theoretical basis for conducting accurate Doppler measurements of planetary atmospheres, especially from the ground with reflected solar absorption lines. We focus on three aspects which lead to significant biases. Firstly, we fully review the Young effect, which is an artificial radial velocity field caused by the solar rotation that mimics a retrograde planetary rotation. Secondly, we extensively study the impact of atmospheric seeing and show that it modifies the apparent location of the planet in the sky whenever the planet is not observed at full phase (opposition). Moreover, the seeing convolves regions of variable radial velocity and photometry, which biases radial-velocity measurements, by reducing the apparent amplitude of atmospheric motions. Finally, we propose a method to interpret the data: how to retrieve zonal, meridional, vertical, and subsolar-to-antisolar circulation from radial velocity maps, by optimizing the signal-to-noise ratio.