A&A 617, A41 (2018) Astronomy https://doi.org/10.1051/0004-6361/201832868 & c ESO 2018 Astrophysics Measuring planetary atmospheric dynamics with Doppler spectroscopy Patrick Gaulme1,2,3 , François-Xavier Schmider4, and Ivan Gonçalves4 1 Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany e-mail: [email protected] 2 Department of Astronomy, New Mexico State University, PO Box 30001, MSC 4500, Las Cruces, NM 88003-8001, USA 3 Physics Department, New Mexico Institute of Mining and Technology, 801 Leroy Place, Socorro, NM 87801, USA 4 Laboratoire Lagrange, Université de Nice Sophia Antipolis, UMR 7293, Observatoire de la Côte d’Azur (OCA), Nice, France Received 21 February 2018 / Accepted 24 April 2018 ABSTRACT 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. Key words. planets and satellites: atmospheres – techniques: imaging spectroscopy – techniques: radial velocities – planets and satellites: individual: Venus – methods: observational 1. Introduction Express (VEx; Lellouch & Witasse 2008). The objective was to measure the atmospheric circulation using different spectral For dense atmospheres in the solar system, wind measure- ranges, to probe different altitudes in the Venus mesosphere. ments mostly come from the cloud tracking technique. The Significant results concerning the upper mesospheric dynam- method consists of following cloud features at specific wave- ics were obtained using mid-infrared heterodyne spectroscopy lengths taken on image pairs obtained at different times, to (Sornig et al. 2008, 2012) and millimeter and submillimeter retrieve the wind speed before cloud structures evolve or dis- wave spectroscopy (Clancy et al. 2008, 2012; Lellouch et al. appear (Sánchez-Lavega et al. 2008; Peralta et al. 2008, 2012; 2008; Moullet et al. 2012) but Doppler spectroscopy is more Moissl et al. 2009). This method has also provided results with challenging at shorter wavelength. Visible observations of so- spacecrafts that orbited or flew-by planets (e.g. Choi et al. 2007). lar Fraunhofer lines scattered by Venus clouds were per- Cloud tracking indicates the motion of large cloud structures formed by Widemann et al.(2007, 2008), Gabsi et al.(2008), (limited by spatial resolution), which is rather an indication of Gaulme et al.(2008b), Machado et al.(2012, 2014, 2017). the speed of iso-pressure regions, than the speed of the actual Regarding other planets, similar measurements were performed cloud particles. A complementary solution to access direct wind in the mm/submm domain for Mars (Lellouch et al. 1991; speed measurement is Doppler spectrometry, because it mea- Moreno et al. 2009) and Titan (Moreno et al. 2005), as well as sures the actual speed of cloud particles. So far, most obser- in the infrared with the 10-µm heterodyne observations of Titan vational efforts with Doppler measurements of dense planetary by Kostiuk et al.(2001, 2005, 2006, 2010). atmospheres have been dedicated to Venus and Jupiter, for two Secondly, the use of Doppler spectrometry for giant plan- distinct reasons. ets, Jupiter in particular, was inspired by its success with helio- Firstly, Doppler spectrometry was envisioned for Venus to seismology to probe the planets’ deep internal structures (e.g., understand its atmospheric circulation as it is a mostly feature- Appourchaux & Grundahl 2013). The principle relies on the de- less planet in the visible domain. First attempts based on visi- tection of global oscillation modes, whose properties are func- ble spectrometry were performed in the 1970s, but did not lead tions of the internal density profile. Giant planets being mostly to robust results (Traub & Carleton 1975; Young et al. 1979). In fluid and convective, their seismology is much closer to that of 2007, a significant international effort was organized to support solar-like stars than that of terrestrial planets. The basic prin- the atmospheric observations of Venus by ESA mission Venus ciple relies on monitoring the position of a spectral line that Article published by EDP Sciences A41, page 1 of 14 A&A 617, A41 (2018) probes an atmospheric level where the amplitude of acoustic modes is maximum. So far, resonant cell (Schmider et al. 1991; Cacciani et al. 2001) and Fourier transform spectrometry (FTS, e.g., Mosser et al. 1993; Schmider et al. 2007; Gonçalves et al. θ = 0 2016) have been considered. Two dedicated instruments were subsequently designed: the SYMPA instrument was an FTS θ = π/4 θ = -π/4 based on a Mach-Zehnder interferometer (Schmider et al. 2007) A which has provided the clearest observational evidence so far of Jupiter’s oscillations (Gaulme et al. 2011). Since then, the new O θ instrument JOVIAL/JIVE, inherited from SYMPA, has been de- θ = π/2 γ θ = -π/2 veloped and tested to perform both atmospheric dynamics of M dense atmospheres and seismic measurements of Jupiter and Sat- S urn (Gonçalves et al. 2016, 2018). In this paper, we first study the influence of two possi- bles sources of biases regarding Doppler spectroscopic mea- θ = 3π/4 θ = -3π/4 surements of planetary atmospheres. Firstly, we review and extensively revise the impact of the solar rotation on radial veloc- Fig. 1. Reference frame used to express the Young effect. The points S ity measurements, which was originally studied by Young(1975) and A are the subsolar and antisolar points respectively, O is the center in the case of Venus (Sect.2). Secondly, we consider the impact of the coordinates and M is a given point on the planet. In this frame, the of atmospheric seeing on both positioning on the planet and on angles of incidence γ and horizon inclination θ are uniform along par- radial velocity maps (Sect.3). In a third part, we focus on how allels and meridians respectively. The subpictures represent the radial to retrieve zonal and meridional components of atmospheric cir- velocity map of the Sun a seen with θ = [0; −π/4; −π/2]. The artificial θ culation from radial velocity maps (Sect.4). radial velocity is not observed along the meridian = 0, while it is maximum along θ = ±π/2. 2. Effect of the apparent diameter of the Sun Within this assumption, at a given point on Venus, the inten- sity of a ray coming from the Sun is proportional to the cosine 2.1. The Young effect of the incidence angle γ. Young(1975) was the first to point out that the apparent diameter Two factors drive the Young effect, both of which were men- of the Sun as seen from Venus causes an artificial radial veloc- tioned by Young himself, but only the first one was implemented. ity field on it. Indeed, rays from different parts of the Sun, which Firstly, the variation of incidence angle from different parts of the display different radial velocities, reach the planet with (slightly) Sun results in averaging regions with different radial velocities different incidence angles. Regions of the Sun that are closer to and intensities. Also, the center part of the Sun appears brighter Venus’ horizon contribute less to the reflected solar spectrum than the edge – limb darkening effect – which slightly counter- than regions closer to zenith. Thus, the radial velocity integrated balances the artificial Doppler signal, by giving more importance over the whole solar disk is not zero in a given point of Venus. to regions with low radial velocities. Secondly, the inclination of In other words, even if Venus would not be rotating, we would the solar rotation axis with respect to the horizon modulates the still measure a Doppler shift near the Venus terminator, and that Young effect. For example, near Venus’ poles, where the solar Doppler shift would mimic a retrograde rotation because the so- rotation axis is perpendicular to the horizon, both the blue and lar rotation is prograde. red sides of the Sun reach the surface in a symmetrical fashion Despite its pioneering aspect, Young(1975)’s analytical de- and average out. To the contrary, on Venus’ morning termina- scription of the artificial Doppler shift ∆VY on Venus was lim- tor, the blue side of the Sun rises first and the artificial Doppler ited to the equator. Out of the equator, the expression ∆VY ≈ signal is maximum (Fig.1). This second factor was not taken 3:2 tan γ, where γ is the solar-zenith angle, is no more valid.