Phosphine in Venus’ atmosphere: Detection attempts and upper limits above the cloud top assessed from the SOIR/VEx spectra

Context. Recent detection of phosphine (PH 3 ) was reported from James Clerk Maxwell Telescope and Atacama Large Millime- tre / submillimetre Array observations. The presence of PH 3 on Venus cannot be easily explained in the Venus atmosphere and a biogenic source located at or within the clouds was proposed. Aims. We aim to verify if the infrared spectral signature of PH 3 is present in the spectra of Solar Occultation at Infrared (SOIR). If it is not present, we then seek to derive the upper limits of PH 3 from SOIR spectra. Methods. We analyzed the SOIR spectra containing absorption lines of PH 3 . We searched for the presence of PH 3 lines. If we did not ﬁnd any conclusive PH 3 spectral signatures, we computed the upper limits of PH 3 . Results. We report no detection of PH 3 . Upper limits could be determined for all of the observations, providing strong constraints on the vertical proﬁle of PH 3 above the clouds. Conclusions. The SOIR PH 3 upper limits are almost two orders of magnitude below the announced detection of 20ppb and provide the lowest known upper limits for PH 3 in the atmosphere of Venus.


Introduction
In light of the recent publication of Greaves et al. (2020a) reporting on the detection of phosphine above the Venusian clouds, we decided to explore the Solar Occultation at Infrared (SOIR) database in search of a spectral signature of PH 3 in the infrared (IR) range. Greaves et al. (2020a) identified a phosphine line in spectra taken by two different instruments, James Clerk Maxwell Telescope (JCMT) and Atacama Large Millimetre/submillimetre Array (ALMA) in June 2017 and March 2019, respectively. They claim that it corresponds to 20 ppb of phosphine at an altitude of 53 to 61 km. In addition to the difficulties in understanding how phosphine can be present in Venus' atmosphere, this possible detection still needs confirmation and validation from other spectral lines of phosphine.
In this framework, Encrenaz et al. (2020) used a mid-IR (950 cm −1 ) spectrum from the Texas Echelon CrossEchelle Spectrograph (TEXES) instrument acquired on March 28, 2015. They could not detect any spectral signatures of phosphine and derived an upper limit of 5 ppb. Snellen et al. (2020) reprocessed the ALMA spectra and show that the apparent presence of a phosphine line might actually be a spurious feature from the calibration of the spectra. More recently, Villanueva et al. (2020) have concluded that the line in the JCMT spectra might be due to a SO 2 line and that the calibration of ALMA spectra used in Greaves et al. (2020a) might not have been correctly performed. Using updated and corrected ALMA data, Greaves et al. (2020b) revised their conclusion, confirming the detection of PH 3 but reducing the observed abundance to a 1 ppb global disk average.
The SOIR instrument has already proven to be very sensitive to the detection and quantification of trace gases (Wilquet et al. 2012;Vandaele et al. 2015;Mahieux et al. 2015a,b) thanks to its solar occultation measurements delivering spectra with a high signal-to-noise ratio (S/N). Providing that the species have a spectral signature in the SOIR instrument's spectral range, the SOIR dataset can corroborate the possible presence of trace gases in the atmosphere of Venus or, otherwise, help to constrain their upper limits.

SOIR description
The SOIR instrument (Nevejans et al. 2006) onboard the ESA Venus Express (VEx) spacecraft (Titov et al. 2006), which is an IR spectrometer sensitive from 2.2 to 4.3 µm, probed the atmosphere of Venus from June 2006 until December 2014. During this time, it performed more than 750 solar occultations of Venus' middle and upper atmosphere (∼60 to ∼180 km).
SOIR spectra have a resolution varying from 0.11 to 0.21 cm −1 (resolving power of 21500) with increasing wavenumber, the highest onboard VEx. SOIR combined an echelle grating to disperse the light in diffraction orders and an acousto-optical tunable filter (AOTF) as a diffraction order-sorting device. The echelle grating and the AOTF led to a division of the spectral range (2256 to 4369 cm −1 ) into 94 wavenumber domains corresponding to the diffraction orders, which are simply referred to as "orders" in the following. SOIR delivered height sets of spectra per solar occultation, each of them is referred to as "dataset" hereafter (see Appendix B for more details). We selected SOIR orders 105 to 110 (see Table 1 for the spectral range of each order) by considering the spectral signature of PH 3 in the SOIR spectral range. In this region, CO 2 and SO 2 also have a spectral signature and Fig. 1 shows the intensities of their theoretical lines.

Methods
The following two different methods were applied to try to detect phosphine in SOIR spectra: a radiative transfer algorithm dedicated to SOIR spectra retrievals named ASIMAT and a new machine learning algorithm. A third method computed the PH 3 detection limits for SOIR spectra.
ASIMAT is a Bayesian inversion algorithm using the approach developed by Rodgers (2000). It is set in an onion peeling frame, assuming a spherical symmetry of the atmosphere and fitting the logarithm of the number density of the targeted species. It accounts for the slit projected size at the impact point and for absorption line saturation (Mahieux et al. 2015a,c). ASIMAT successfully retrieved CO 2 , CO, HCl, HF, H 2 O, and SO 2 from the SOIR spectra. For this study, we implemented a specific scheme to distinguish between a real detection and an upper limit value. The approach is similar to what was done in Korablev et al. (2019) Fig. 2. Example of spectrum for orbit 108.1 order 108 bin 2 at a tangent altitude of 74 km. The SOIR spectrum subtracted by the ASIMAT CO 2 fit is plotted in orange. The synthetic spectrum of 20 ppb of PH 3 is plotted in blue.
error covariance matrix was computed as the sum of the covariance matrices of the smoothing error and the retrieval noise error (see Eq. (3.31) from Rodgers 2000). The square root of the diagonal of this matrix returned the retrieval detection limit at each altitude for a given species. We assimilated a retrieved number density lower than 3.2 times this value as a non-detection. We computed two inversions for each spectral set: the first one by considering CO 2 and PH 3 (and SO 2 for order 110), and the second one by considering only CO 2 . We compared the root mean square (rms) for each spectrum fit, and only kept the ones that have a lower rms when retrieving CO 2 + PH 3 + SO 2 than when only retrieving CO 2 + SO 2 .
An alternative attempt to detect PH 3 was carried out with a machine learning tool that had already been used to detect the CO 2 quadrupole and to infer the absence of methane in NOMAD-SO spectra (Schmidt et al. 2020). The method aims to summarize the dataset with statistical endmembers, hereafter "sources". First, data are pretreated to remove the baseline and converted into absorbance. The method consists of a linear blind source separation under positivity constraints and uses the probabilistic sparse Non-negative Matrix Factorization (psNMF) described in Hinrich & Mørup (2018). Appendix E provides more information on this analysis.
In addition to these detection methods, we determined the detection limits (DLs) of PH 3 in SOIR spectra in the volume mixing ratio (VMR). For each SOIR spectrum, we compared the measurement noise to a synthetic spectrum of PH 3 simulated by considering the SOIR instrumental function. We considered that a clear detection of a PH 3 line in SOIR spectra should be at least 3.2 times higher than the measurement noise. Appendix F contains a description of this method.

Results
Neither the radiative transfer algorithm nor the machine learning algorithm could infer any real detection of PH 3 lines for any of the orders selected. In orange, Fig. 2 shows an example of the residual of the SOIR spectrum at 74 km subtracted by the ASIMAT CO 2 fit for order 108. We see that several lines of the synthetic PH 3 spectrum (blue) are already much stronger than the residual. We see no clear presence of PH 3 lines in the SOIR spectrum. Figure 3 shows an example from the machine learning algorithm for order 106 where one of the sources is clearly identified as CO 2 (above panel), but no source could be identified as PH 3 . In the lower panel, the blue curve corresponds to a source with the highest contribution A PH 3 to a synthetic PH 3 spectrum (black curve).  Fig. 3. Example of source derived from the machine learning algorithm (in blue) compared to synthetic spectrum (in black) for order 106. The synthetic spectrum is rescaled with fitted linear contribution of CO 2 (A CO 2 ) and PH 3 (A PH 3 ). The correlation coefficient between source and synthetic spectra is noted corr. Above, the source is identified as CO 2 (significant A CO 2 > 0.5 and high corr > 0.3). Below the closest source (highest A PH 3 ) to the PH 3 synthetic spectrum is not coherent with its presence (A PH 3 < 0.5 and corr < 0.3).  The DLs were computed for two cases. The first case is a constant PH 3 VMR up to 190 km. The second case is a constant PH 3 VMR up to 68 km. The choice of this last case comes from the top panel of Fig. 9 from Greaves et al. (2020a) where 68 km corresponds to the highest altitude where the PH 3 VMR is higher than 0.1 ppb. Figure 4 shows the DL profiles for orders 105 to 110 for the first case. They have the typical shape expected for solar occultation measurements: from higher altitudes, they decrease with lower tangent altitudes until they increase again because of the progressive presence of clouds and hazes, which decreases the S/N along the whole spectra. The tangent altitude of lowest detection limit (ALDL) varies from one occultation to another depending on the latitude covered, the atmosphere variability, the cloud-deck height, and the strength of the PH 3 lines in the spectral order sounded.
The DLs for orders 109 and 110 are above 20 ppb, but those for orders 105 to 108 are well below 20 ppb. We expect some strong variations in the DLs with respect to the diffraction orders. The PH 3 line intensities are stronger in orders 105 and 106 and decrease in orders 107 to 110. Figure 4 clearly shows this variation in PH 3 lines intensities. The altitude of interest is closer to 60 km and thus a few kilometers below the typical ALDL. For order 108, the lowest DL is 3 ppb at 67 km and 4 ppb at 61 km (the lowest tangent altitude probed). For order 107, the lowest DL is 0.7 ppb at 67 km and 2 ppb at 61 km. For order 106, the lowest DL is 0.3 ppb at 69 km and 1 ppb at 65 km. For order 105, the lowest DL is 0.2 ppb at 69 km and 0.4 ppb at 61 km.
The DLs lower than 20 ppb and below 62 km corresponds to ten different datasets of SOIR and five different occultations. The DLs below 20 ppb and below 61 km correspond to six datasets from four different occultations.
The SOIR datasets presented here mostly cover latitudes above 60 • north. Still eleven datasets cover the latitudes below 60 • , corresponding to three different occultations. As seen in Fig. 5, they correspond to latitudes 6.67 • (orbit 108.1, orders 105 to 108), −30.96 • (orbit 446.1, order 108), and −9.11 • (orbit 591.1, order 105). For the dataset corresponding to orbit 446.1 order 108 bin 2, the ALDL is at 62 km with a detection limit of 8 ppb and at 61 km, and the DL is still 9 ppb. For orbit 108.1 order 107 bin 2, the DL at 62 km is 7 ppb.
ASIMAT also derives DLs and the results are the same as the ones shown in this section. The machine learning algorithm DL is estimated from those derived in Schmidt et al. (2020) for CH 4 lines at 3067.3 cm −1 , which are lost in dominant H 2 O lines in a realistic synthetic dataset, including nonlinear radiative transfer and an instrumental effect. In this case, the detection limit was with a noise variance of 0.001 between 500 ppt (mean absorption bands = 0.0092, S /N = 0.9) and 100 ppt (mean absorption bands = 0.00018, S /N = 0.1). Assuming the same behavior, we estimate that the machine learning algorithm PH 3 DL for SOIR spectra is thus 0.5 ppb. This value is similar to the lowest DL in Table 2.
For the second case (no PH 3 above 68 km), there are two orbits with DLs below 20 ppb: orbit 108.1 and 1250.1. Table 2 summarizes the DLs for a VMR of phosphine until 68 km (column DL2). For comparison, the corresponding DLs of the first case are also provided in column DL1.

Discussion and conclusions
We did not detect any phosphine in the SOIR spectra using the two completely different and independent detection methods described above. By considering a constant phosphine VMR, we derived SOIR DLs as low as 0.2 ppb at 69 km with still multiple DLs lower than 20 ppb from 60 to 95 km (see Fig. 4). For a more There is a difference in the time of measurements as SOIR datasets with DLs lower than 20 ppb extend from August 2006 until January 2010 and the spectra used by Greaves et al. (2020a) were recorded in June 2017 and March 2019. Another difference is that SOIR scanned a localized region of the Venus terminator, while the spectra from Greaves et al. (2020a) cover more than 15 • of latitude in the Venus disk, as seen from the Earth. These differences might be important if phosphine is really present in Venus' atmosphere and if the process producing phosphine is localized and varies in time.