Schematic view of the Doppler shift of a prograde rotating planet as seen from the THEMIS observatory. The Doppler effect measured in the visible on the reflecting cloud deck is the sum of the motion relative to the Sun and the Earth. Radial velocities are zero along the bisector meridian, located halfway in between the subsolar and subterrestrial meridian.

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... In the case of a non-zero phase angle, i.e., the angle Sun-planet-observer, the Doppler shifts cancel each other on the meridian located at the bisector of the subsolar and subterrestrial points (e.g., Gabsi et al. 2008). A retrogradely rotating zonal circulation therefore displays a blueshift in the morning and a redshift in the afternoon (Fig. 1). In our case, observations were performed during Earth morning elongation, which means that we were seeing the morning terminator of Venus. In Fig. 2, we represent theoretical RV maps of a solid-body rotator and a meridional circulation based on two Hadley cells at the phase angle corresponding to the 2009 campaign. On top of this, ...

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... Venus dayside and making one observation at a time per position to cover all positions. The whole scan of the dayside A82, page 4 of 19 hemisphere is then repeated once or twice, according to observing conditions. Centering and guiding is manually controlled with the help of a Venus template that is taped on the display of the guiding camera ( Fig. 1 of Machado et al. 2017). To compensate RV drifts of about 100 m s −1 , the spectrometer's wavelength calibrations were carried out using both Thorium-Argon (ThAr) lamps and a set of telluric lines following the standard protocol developed at CFHT ( Donati et al. 1997). Final RV measurements were corrected from the various motions ...

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... m s −1 at 10 • away from it. From the spectra obtained with the slit parallel to the rotation axis, they detected a slight asymmetry of zonal circulation by measuring that winds are faster by 6 ± 5 m s −1 in the southern hemisphere. The M-shaped latitudinal profile of mean zonal circulation is later compared with other published methods (e.g., Fig. 14 of Machado et al. ...

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... red curve indicates a fit of it with a third order polynomial. Figure 10 shows the mean RV that is measured on the sky. The variation of RV is much larger than that expected from the Earth's rotation (gray lines). ...

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... was not expected and surprised us is an RV drift in between the Earth's sky and Venus. In Fig. 11, we plot the difference of the Earth's sky RVs with the mean RV that is measured on Venus at each position. Since we are scanning the planet along the north-south axis (slit parallel to equator), we do not expect large variations of the average RV along the slit. It should display the meridional circulation on top of relative motions ...

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... motions of the planet with respect to the observatory and the Sun. Actually, it arises that whatever the direction of the scan (NS or SN), there is a spurious RV that increases monotonically at each step of the scan. For Fe spectra, the RV drift per scan reaches 2000 m s −1 per scan on September 14, while it is of 400 m s −1 three days later (Fig. 11). In 2008, we scanned the planet along the WE direction and found out this bias. This was particularly terrible as it overlapped and overwhelmed the zonal circulation of Venus. That made the observation taken in 2008 impossible to use scientifically. We thus decided to scan Venus in the perpendicular direction during A82, page 11 of 19 ...

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... correct the RV maps from this bias, we first flatten each individual RV map by fitting a tilted plane (2D linear polynomial) oriented along the NS axis (Fig. 12). Indeed, if the RV bias is pretty much stable from one scan to the next, it actually seems to diminish slightly with time. Therefore, by subtracting a tilted plane to the RV map is a way to include the amplitude variation of the bias. Subtracting a tilted plane affects any uniform pole-to-pole meridional RV field, but not ...

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... Fig. 12, we show the individual flattened RV maps and they appear to be very consistent from day to day and spectral line to line, although the data taken on September 14 are the only data that benefited from good observing conditions. From the photometric images, it clearly appears that the data taken on September 17 suffered from worse ...

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... caused by clouds, which is especially visible in the second half of the data taken on September 17. Conditions on September 16 were poor and allowed only for two scans (NS and SN). The error bars on Doppler velocity are about twice as bad as for the other two nights. For each day, all flattened RV maps were then averaged to get a final RV map (Fig. 13). For obvious observing condition differences, we only consider the data taken on September 14 to model the atmospheric circulation. However, it is worth noticing that despite significantly worse conditions and strong biases in some latitude ranges, the overall aspects of the September 16 and 17 RV maps are very consistent with the ...

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... this section, we aim to interprete the RV map obtained on September 14, 2009 (Fig. 13, upper panel). We first note that this map was computed by stacking data over about eight hours, which represents a little less than 10% of Venus' rotation at that altitude. We can therefore consider this map as an "instantaneous" Doppler snapshot of Venus. As far as we know, it is the first instantaneous optically resolved RV map of any planet of ...

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... which we alter according to the atmospheric seeing. The model is optimized with an MCMC routine that we developed to interpret these data. Such an approach, with respect to classical least-squares fitting, is a straightforward and reliable way to compute error bars on the estimated parameters. Two examples of outputs of the MCMC code are shown in Fig. 14. These examples correspond with two models that we comment on the next ...

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... κ is meant to take into account the fact that our measurements are not absolute. We introduce the subscript "0" in V z,0 to be consistent with other models (3-7), where more than one term is employed to describe the zonal circulation. However, fitting the map with a pure solid-body zonal circulation pattern plus a global RV offset (Model 1, see Fig. 15 and Table 2) appears to be rather unsatisfactory given the structure of the residuals (Fig. 15, top row, middle panel), and the large value of the reduced χ 2 at 6.14. To help evaluate the fitting quality, we also plot both data and model across the planet's equator in the third column of Fig. 15. The disagreement with a solid rotator ...

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... the subscript "0" in V z,0 to be consistent with other models (3-7), where more than one term is employed to describe the zonal circulation. However, fitting the map with a pure solid-body zonal circulation pattern plus a global RV offset (Model 1, see Fig. 15 and Table 2) appears to be rather unsatisfactory given the structure of the residuals (Fig. 15, top row, middle panel), and the large value of the reduced χ 2 at 6.14. To help evaluate the fitting quality, we also plot both data and model across the planet's equator in the third column of Fig. 15. The disagreement with a solid rotator is obvious. Furthermore, the residual map shows a symmetrical feature in both hemispheres at ...

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... pattern plus a global RV offset (Model 1, see Fig. 15 and Table 2) appears to be rather unsatisfactory given the structure of the residuals (Fig. 15, top row, middle panel), and the large value of the reduced χ 2 at 6.14. To help evaluate the fitting quality, we also plot both data and model across the planet's equator in the third column of Fig. 15. The disagreement with a solid rotator is obvious. Furthermore, the residual map shows a symmetrical feature in both hemispheres at mid-high latitudes, which recalls the Doppler signature of an equator-to-pole circulation peaking at mid-latitudes (Fig. 2, bottom panel). We then tested a second model composed of a solid-body zonal and ...

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... V m,0 is the speed of the meridional circulation at λ = 45 • . The results of model 2 are shown on the second row of Fig. 15. The residual map and reduced χ 2 (3.31) indicate a better agreement of the model with respect to the data, but a redshift bulb located in the equatorial region indicates that there are more terms to include in the model. Model 3 includes a variation of the zonal circulation as a function of longitude with either a maximum or a minimum ...

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... and σ z,1 is the standard deviation of the Gaussian function. Residuals are still present but are much less significant; i.e., ≈90% of the points within 2σ with respect to the model. This is illustrated by a much lower reduced χ 2 (1.42) and the cut along the equator, which shows a satisfactory agreement between the data and model. In Fig. 16 we represent the map of the zonal wind 5 deduced from the model 4, where it appears that zonal winds are larger than 200 m s −1 in the morning -and evening, by extrapolating -and get slower in the subsolar area, down to 70 m s −1 . These values are not considered as accurate values of the wind speed at noon or in the morning, but as ...

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... -in which winds are slower in the region where solar heating is maximum. That being said, the difficulty is to not overinterpret data that likely suffer from biases and were obtained in nonoptimal conditions. Is it possible to go further without interpreting noise? We make other three attempts to refine the atmospheric circulation model (Fig. 17). The first (model 5) lets the hot spot free to shift along the equator, instead of being centered around noon, ...

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... zonal wind asymmetry is smooth (0 at equator and maximum 5 We do not make a similar plot for meridional circulation as it is a simple equator to pole regime (sine curve from equator to pole), which is uniform as a function of the longitude. at 45 • ). Contrarily to models 5 and 6, model 7 improves the match between data and fit (red. χ 2 = 1.08, Fig. 18, Table 2). According to the results shown in Table 2, the zonal wind would be slightly larger in the northern hemisphere by about 18 × cos(π/4) ≈ 13 m s −1 at mid ...

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... poor observing conditions -even on September 14 the average seeing was 3 arcsec -we note a strong coherence of the RV maps (Fig. 13). Beyond biases on RVs, Doppler shifts vary 7 The maps obtained on September 16 and 17, 2009 are the result of integrating 2 and 3.5 h of data, respectively, which represent about 2.5 and 4.5% of the rotation period at the cloud-top ...

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... the same range from side to side (color scale are the same in Fig. 13), indicating a clear retrograde rotation. From a technical point of view, this paper makes use of an innovative method to measure and analyze the RVs of planetary atmosphere, following the recipes introduced by Gaulme et al. (2018) and applied in parallel to this work to observations of Jupiter ( Gonçalves et al. 2019). The main ...

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... 14, 2009 with a simple zonal plus meridional wind without taking account the biases on RVs caused by the atmospheric seeing. The model consists of an equator-topole meridional circulation (∝ | sin 2λ|) and a zonal wind whose amplitude is fitted for each band of latitude. The zonal wind profile as a function latitude obtained that way is shown in Fig. 19. We observe a (noisy) M-shaped profile where zonal winds peak at mid-latitudes with an amplitude of about 120 m s −1 and a local minimum around the equator at about 100 m s −1 , which is very similar to what is reported in the literature. This suggests that if atmospheric seeing and instrumental PSF were included in the previous ...

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... we average the zonal winds at a given latitude, we obtain that type of profile, with no wind at poles, a maximum amplitude at mid-latitudes and a local minimum in the equatorial region. Figure 19 also shows the zonal profile obtained by averaging the zonal wind along longitudes on the visible dayside of Venus: it shows that the observed M-shape can be the result of a hot spot structure. Such a regime recalls global circulation models that are proposed to explain light curves of stars hosting hot Jupiters. ...