Open Access
Issue
A&A
Volume 676, August 2023
Article Number A135
Number of page(s) 11
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/202142548
Published online 23 August 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

The recent claimed detection of 20± 10 ppbv of phosphine (PH3) in the cloud decks of Venus (Greaves et al. 2021a) based on disk-averaged observations at millimeter wavelengths has generated considerable discussion. Snellen et al. (2020) repeated the data analysis of Greaves et al. (2021a) and suggested a detection significance of only 2σ, which implied that instruments with a higher sensitivity are required. Thompson (2021) performed a bootstrapping analysis on the Greaves data, but was not able to recover a statistically significant signal for 20 ppbv PH3. Villanueva et al. (2021) and Lincowski et al. (2021) argued that the claimed PH3 signal could be reproduced by assuming plausible mesospheric SO2 abundances of around 10 ppbv or more. Akins et al. (2021) suggested, however, that the previously assumed 10 ppbv SO2 limit is unlikely to be detected by Atacama Large Millimeter Array (ALMA) data. Encrenaz et al. (2020) suggested that an upper limit of 5 ppbv PH3 is significant at the 3σ level based on disk-averaged observations at 10.5 µm. Trompet et al. (2021) suggested an upper limit of 0.4 ppb at 61 km for high latitudes and an upper limit of 6–8 ppb for equatorial regions. Greaves et al. (2020) recovered the PH3 signal in the Venus atmosphere with 5σ confidence and suggested planet-averaged abundances of PH3 of 1–4 ppb between 55 and 60 km. Most recently, Greaves et al. (2021b) concluded that the net abundances of PH3 are about 20 ppb from James Clerk Maxwell Telescope (JCMT) data and 7 ppb from ALMA data. A recent re-analysis by Greaves et al. (2022) of their millimeter wavelength data suggested low levels (~10%) of SO2 contamination in the PH3 signal. In anoxic terrestrial atmospheres, PH3 has been proposed as a potential biosignature (see Bains et al. 2019; Sousa-Silva et al. 2020). If the detection of PH3 with concentrations in the ppb level in the Venusian clouds is real, then Greaves et al. (2021a) and Bains et al. (2021) conclude that such large abundances of PH3 cannot be accounted for by currently known abiotic processes, suggesting a biological origin. Recently, Patel et al. (2022) showed that in the Venus clouds, a potential thermal and radiation habitable zone would extend from 59 to 48 km.

Possible abiotic source of PH3 have been investigated by various works. McTaggart (2022) simulated cosmogenic production of phosphorus in the atmosphere of Venus, but concluded that the amount of phosphorus produced is insufficient to explain the proposed concentrations of PH3. Truong & Lunine (2021) suggested that volcanic phosphides ejected into the clouds are a plausible abiotic source of the Venusian phosphine. However, Bains et al. (2022) argued that this mechanism requires an implausibly high eruption volume. Omran et al. (2021) proposed possible atmospheric abiotic pathways of PH3 from meteoritic and geological sources. They concluded that the detection of phosphine alone is likely not to be a decisive indicator of life. The photochemistry of phosphorus-bearing species in these environments is not well known (see e.g. Bains et al. 2021). Greaves et al. (2021a) and Bains et al. (2021) applied a detailed chemical network and used analogous nitrogen species reaction kinetics for several phosphorus-bearing chemical reactions with unknown rate coefficients. They suggested an abiotic upper limit of about 0.2 parts per quadrillion (ppq) (2×10−16) PH3 around 50 km.

In this work, we reassess the maximum chemical production of PH3 in the atmosphere of Venus by considering the uncertainties in its photochemical production pathways. Unlike previous works, we assume that phosphorus monoxide (PO) might be produced by destruction of tetraphosphorus hexoxide (P4O6), which was observed to be the main phosphorus-bearing gas on Venus with a mixing ratio of 2 ppmv below 25 km (see Krasnopolsky 1989). Section 2 describes the photochemical model and the scenarios. Section 3 shows results, and Sect. 4 provides some brief conclusions.

thumbnail Fig. 1

Input temperature profiles of modern Venus for latitudes below 35° (red line), 35–55° (orange line), 50–70° (green line), 70–80° (blue line) and 80–90° (purple line) taken from Haus et al. (2013) and a global average (black line).

2 Method

2.1 Model description

1D-TERRA is a one-dimensional global mean, cloud-free, stationary atmospheric convection-photochemical-climate model capable of simulating a wide range of atmospheric temperatures (100–1000 K) and pressures (0.01 Pa–103 bar) for different types of atmospheres such as those dominated by CO2, N2, H2, or H2O (Scheucher et al. 2020; Wunderlich et al. 2020). In the present study, we use only the chemistry module BLACKWOLF and employ observed temperature profiles for modern Venus taken from Haus et al. (2013), as shown in Fig. 1. BLACKWOLF features a chemical network with over 1000 reactions for more than 100 species, including sulphur, chlorine, and phosphorus chemistry (Wunderlich et al. 2020, 2021). A detailed description of BLACKWOLF can be found in Wunderlich et al. (2020).

2.2 Phosphorus photochemical network

For the present work, we extended the phosphorus reaction network presented in Wunderlich et al. (2021) to 79 reactions in total for 13 phosphorus-containing species. Our phosphorus photochemical network (PPN) was based on Greaves et al. (2021a) and Bains et al. (2021), but includes additional reactions such as the production of PO from PH and PH2. Appendix A shows the full list of PPN reactions, together with their rate coefficients and references. Reactions in Table A.1 marked with an asterisk indicate missing rate data and therefore use analogous rate coefficients in which phosphorus atoms present in reactant species are analogously replaced with nitrogen atoms for which rate data are available. Reactions for which the rate data are not available for temperatures below 750 K are indicated with a plus symbol in Table A.1. For all marked reactions, we calculated a log-normal uncertainty distribution as described in Appendix B.

2.3 Scenarios

We performed various scenarios simulating the atmosphere of modern Venus with our photochemistry module BLACK-WOLF (see Table 1). For all scenarios, we used a fixed volume mixing ratio, f, at the surface for , fOCS = 4 × 10−6, fCO = 2 × 10−5, and fHCl = 5 × 10−7, which provided model best fits to the observations. CO2 was used as a fill gas to make up the remainder of the atmosphere. For scenarios 1b and 2b, SO2 was fixed to 25 ppm at the surface, consistent with the VEGA 1 and VEGA 2 entry probes (Bertaux et al. 1996). For all other scenarios, SO2 at the surface was set to 130 ppm, consistent with measurements above 30 km (see e.g. Bézard et al. 1993; Pollack et al. 1993; Marcq et al. 2008). To match the observed decrease in SO2 mixing ratios above the clouds, we introduced an SO2 sink of magnitude 7.1 × 1012 molecules cm−2 s−1 in the cloud region in all scenarios except for scenarios 1b, 1c, 2b, and 2c.

In scenarios 1b and 2b, eddy diffusion coefficients were taken from Krasnopolsky (2007) below 47 km and from Krasnopolsky & Parshev (1981) above. All other scenarios used eddy diffusion coefficients below 47 km from Krasnopolsky (2012) and above 47 km from Krasnopolsky (2013). We used temperature profiles for modern Venus of five different latitudinal regions taken from Haus et al. (2013) and a weighted global mean temperature profile (see Fig. 1).

The phosphorus chemistry is introduced with the following three approaches. First, in scenarios 1a to 1h (termed “PH3 flux”), we used PH3 input fluxes in the cloud layer between 50 and 60 km, similar to the scenario with directly produced PH3 in the Venus clouds as performed by Greaves et al. (2020). All other phosphorus-containing species had zero input fluxes. Second, in scenarios 2a to 2h (termed “PO flux”), we used input fluxes of PO below 25 km. We assumed that PO is produced via P4O6 destruction. The other phosphorus-containing species had zero input fluxes. Third, in scenario 3 (termed “H3PO4 flux”), we used H3PO4 input fluxes in the cloud layer between 50 and 60 km, similar to the abiotic scenario of Greaves et al. (2020). All other phosphorus-containing species had zero input fluxes.

The main motivation behind scenarios 2 and 3 was to test whether the observed concentrations of PH3 could have arisen from atmospheric in situ chemical production via PO and H3PO4, respectively. P4O6 is suggested to be the main phosphorus species at 25 km (Krasnopolsky 1989) and could be destroyed into PO and PO2 via (1) (2)

In the lower atmosphere, the produced PO2 can react with H and form more PO (Bains et al. 2021). For the conditions in the Venus clouds, PO2 might not be present in the gas-phase state (see e.g. Haworth et al. 2002). Due to the lack of rate coefficient data for P4O6, we cannot include the above reactions into our network. Instead, we assumed a range of input fluxes of PO in the lower atmosphere of Venus, where P4O6 is likely to be destroyed quickly (Bains et al. 2021).

Table 1

Atmospheric scenarios for modern Venus.

2.4 MC simulations

We performed an MC analysis in which we randomly varied the coefficients of all reactions marked in the PPN (see Appendix A) within their log-normal uncertainty distribution (see Appendix B). We applied this technique to scenarios 1d-1h and 2d-2h with 200 MC runs for each scenario. Hence, the total number of MC runs of the PH3 flux scenarios and PO flux scenarios was 1000 each. A test was performed in which the number of MC runs was doubled, but this did not lead to significant changes in the main outcome. We therefore conclude that 1000 runs lead to robust results.

3 Results

3.1 Model validation

We used our photochemical model for the first time to simulate the atmosphere of modern Venus from the surface up to about 120 km. To validate the model, we compare in Fig. 2 the results for scenarios 1a–1d, 1f and 1h (see details in Table 1) with the observational ranges for several key species.

In scenarios 1a and 1c the mixing ratios of SO2 at the surface were fixed at 130 ppm, whereas in scenario 1b they are set to 25 ppm. For scenario 1a we added SO2 removal in the cloud region to compensate for a missing SO2 sink from cloud formation. Without this additional SO2 sink (scenario 1c), the model predicts mixing ratios of SO2 above 100 ppm from the surface up to 100 km. This leads to an overestimation of SO and OCS compared to the observations above 60 km. An assumed low-surface SO2 of 25 ppm leads to a decrease in SO2 above the clouds at around 70 km. Scenario 1a with its enhanced removal rate, as discussed in the scenarios section, reproduces the observed SO2 concentration profile; this suggests that the SO2 decrease in the clouds cannot be explained by known photochemical processes alone (see also Rimmer et al. 2021).

Most scenarios in Fig. 2 overestimate the water abundances between 60 and 80 km. The simulation using the mid-latitude temperature profile (Scenario 1f) matches the observed H2O concentrations in the middle atmosphere well. The concentrations of CO and HCl are less sensitive to both the choice of SO2 at the surface and the temperature profile, and all scenarios agree with the observed concentration range. The model underestimates the decrease in carbonyl sulfide (OCS) in the clouds. The steep decline in observed OCS abundances by around two orders of magnitude from 30 to 40 km altitude is discussed in Marcq et al. (2018) and Yung et al. (2009). The high SO2 scenarios with SO2 removal fit the OCS observations best.

In order to test the impact of the OCS vertical behaviour, we performed an additional run. Here, starting with scenario 1a, we introduced an additional sink for OCS of 2.3 × 1012 molecules cm−2 s−1 in the clouds, as shown in Figure 3. The results suggest that with this sink, OCS (dashed blue line) matches the observed decrease with altitude between 30 km and 60 km well. PH3 remained almost unaltered, whereas PO decreased quite considerably, suggesting that the production of PO from PH3 is weakened.

3.2 Phosphorus fluxes

Figure 4 shows the concentration of PH3 at 60 km with increasing input fluxes of PH3, PO, and H3 PO4. The observed global PH3 abundances of 1–4 ppb at 60 km shown in Greaves et al. (2020) are reached with a PH3 flux between 3 × 108 and 1 × 109 molecules cm−2 s−1. By comparison, on modern Earth, the global PH3 fluxes are not well determined, but are estimated to be around 4 × 107 kg yr−1 (Wang et al. (2022; =4.4 × 106 molecules cm−2 s−1). The production of PH3 from formation pathways via PO reaches a maximum of 0.04 ppb PH3 at 60 km for a PO flux of 1 × 1010 molecules cm−2 s−1 below 25 km. A higher PO flux leads to an enhanced production of O2 in and below the clouds and to weakened production of PH3 via PO pathways in the clouds (see Fig. 5).

Large abundances of O2 are not expected in the hot, reducing lower atmosphere of Venus, and early measurements by Oyama et al. (1979) that suggested around 43 ppm at 52 km disagree with photochemical models such as Krasnopolsky (2012) and Rimmer et al. (2021). However, our results suggest that these measurements would be consistent with simulations assuming a PO flux above 1 × 1010 molecules cm−2 s−1, which do not produce significant abiotic PH3. Above the clouds, photochemical models typically overestimate the upper limit O2 concentrations of 3 ppm that is uniformly mixed above 58 km, as suggested by Mills (1999). Consistent with Yung et al. (2009); Krasnopolsky (2012); Zhang et al. (2012); Rimmer et al. (2021) for example, we find an strong increase in O2 with concentrations higher than 10 ppm above 80 km.

An input flux of 5 × 106 molecules cm−2 s−1 H3PO4 between 50 and 60 km leads to a maximum in the PH3 concentration of 5 × 10−17 at 60 km. This result is comparable to the upper limit of abiotically produced PH3 of about 2 × 10−16 from H3PO4 destruction in the Venus clouds found by Greaves et al. (2021a). Fluxes higher than 5 × 106 molecules cm−2 s−1 H3PO4 lead to an increase in O2 below 60 km and subsequent lower concentrations of PH3 (not shown). Figures 4 and 5 suggest that the observed PH3 concentrations of 1–4· ppb cannot be reproduced abiotically. A caveat of this result, however, is that it has not considered uncertainties in the model boundary conditions and in the rate coefficients of phosphorus-containing reactions. We therefore consider these uncertainties in the following section.

thumbnail Fig. 2

Venus composition profiles for selected species predicted with our photochemistry model for scenarios 1a (solid blue line), 1b (dashed blue line), 1c (dotted blue line), 1d (dashed cyan line), 1f (dotted cyan line), and 1h (cyan dash-dotted line). For comparison, a range of observations is shown as solid, horizontal black lines. The observations of H2O, CO, OCS, and SO2 below the cloud top are taken from Svedhem et al. (2007) and Marcq et al. (2008). Observations of H2O and CO above the clouds are taken from Bertaux et al. (2007) and Krasnopolsky (2012). The OCS observational range at 65 km is taken from Krasnopolsky (2010) and the range at 33 km from Marcq et al. (2008). For the observational range of SO2 and SO above 60 km, we use data from Belyaev et al. (2012) and Sandor et al. (2010). Measurements of HCl above the cloud top are taken from Sandor & Clancy (2012) and Bertaux et al. (2007).

3.3 Uncertainties from the choice of boundary conditions

Figure 6 shows the dependence of PH3, PO, and H3PO4 on the choice of the SO2 below the clouds for scenarios 1a, 1b, 2a, and 2b. We do not show the results for scenarios 1c and 2c because the simulated concentrations of SO2, H2O, SO, and OCS above the clouds are not consistent with the concentrations that have been observed (see Sect. 3.1). The results suggest that the scenarios with low SO2 below the clouds feature stronger concentrations of PH3 and PO than the runs with high SO2. For scenario 1a, the mixing ratio of PH3 reaches a maximum of 3 ppb at around 55 km. Above 60 km, the predicted PH3 drops off rapidly. In scenario 1b, a maximum of 4 ppb for PH3 is reached at around 60 km, and the strong decrease in PH3 occurs at around 70 km. This very short lifetime of PH3 above the clouds is consistent with results from Greaves et al. (2021a).

In the cloud deck, the concentrations of PO are around 50 ppb for scenario 2a and 100 ppb for scenario 2b. The results for these scenarios suggest abiotically produced PH3 concentrations between 0.1 and 0.3 ppb below 60 km, about one order of magnitude below the value observed by Greaves et al. (2020). The mixing ratios of PO below 60 km are lower by more than six orders of magnitude for scenarios 1a and 1b than in scenarios 2a and 2b. Hence, the concentrations of PO are well separated for the scenarios in which PH3 originates from photochemistry and the scenarios in which PH3 is directly injected with a fixed input flux. Thus, results suggest that observations of PO might provide useful constraints on the origin of PH3.

The concentrations of H3PO4 increase from the surface to the top of atmosphere. The model predicts that H3PO4 is the dominant phosphorus species above 70 km (see also Bains et al. 2021). H3PO4 shows larger abundances for scenarios 2a and 2b than for scenario 1a and 2b. The maximum mixing ratios of H3PO4 are higher by about one order of magnitude for the scenarios with chemically produced PH3 than for the scenarios with a PH3 input flux. Hence, without considering the uncertainties from the input temperature profile and rate coefficients (see Sect. 3.4), the simulations suggest that a simultaneous detection of PH3 and H3PO4 might (similar to the PO result just discussed) provide information on the origin of PH3.

Figure 7 shows the simulated mixing ratios of PH3, PO, and H3PO4 as a function of height using different input temperature profiles for the simulations with PH3 fluxes (cyan lines) and PO fluxes (red lines). The choice of temperature profile below 60 km has little influence on the simulated concentrations of PH3, PO, and H3PO4 and other species for scenarios with a PH3 flux (see also Fig. 2). The PH3 concentrations at the cloud top show little dependence on the temperature profile for all scenarios.

For simulations with the PO flux, the concentration of PO is about two orders of magnitude lower when using the low-latitude temperature profile (scenario 2d) compared to scenarios 2f and 2h. The H3PO4 concentrations above the clouds is highest for the run with a PO flux using the high-latitude temperature profile (scenario 2h). When using the temperature profile for low-latitudes (scenario 2d), the volume mixing ratios of H3PO4 are similar to those in scenario 1h. Hence, when we consider the uncertainties from the temperature profile, the results suggest that it will be challenging to separate the scenarios with PH3 fluxes from the scenarios with PO fluxes based on H3PO4 observations.

thumbnail Fig. 3

As for Fig. 2, but comparing scenario 1a (solid blue line) with the same scenario, but with the additional sink for OCS in the clouds (see Sect. 3.1), (dashed blue line).

thumbnail Fig. 4

Concentrations of PH3 at 60 km for scenario 1a (blue dots and dashed line), scenario 2a (orange dots and dashed line), and scenario 3 (green dots and dashed line) with increasing input fluxes of PH3 between 50 and 60 km, PO below 25 km, and H3PO4 between 50 and 60 km, respectively. The observational range of PH3 is taken from Greaves et al. (2020).

thumbnail Fig. 5

Predicted volume mixing ratios of PH3, PO, H3PO4, and O2 against height for scenario 2a with three different PO input fluxes: 1 × 109 molecules cm−2 s−1 (red line), 1 × 1010 molecules cm−2 s−1 (orange line), and 1 × 1011 molecules cm−2 s−1 (purple line). We additionally show the observational ranges from Greaves et al. (2020, 2021b) and upper limits of Trompet et al. (2021).

thumbnail Fig. 6

Venus composition profiles for PH3, PO, and H3PO4 predicted with our photochemistry model for scenarios 1a (solid blue line), 1b (dashed blue line), 2a (solid orange line), and 2b (dashed orange line). We additionally show the observational ranges from Greaves et al. (2020, 2021b) and upper limits of Trompet et al. (2021).

thumbnail Fig. 7

As for Fig. 6, but showing the effect of varying the input temperature profile (see the legend).

thumbnail Fig. 8

Venus composition profiles for selected species predicted with our photochemistry model for scenario 1 (PH3 flux, solid blue line) and scenario 2 (PO flux, solid orange line). The shaded areas show the 99% ranges of the MC runs of scenario 1 (shaded blue) and scenario 2 (shaded orange). For comparison, a range of observations is shown with black lines. We additionally show the observational ranges from Greaves et al. (2020, 2021b) and upper limits of Trompet et al. (2021).

3.4 Uncertainties from rate coefficients

Figure 8 compares the chemical profiles of PH3, PO, and H3PO4 from scenario 1a (shown in blue), assuming a PH3 flux of 5 × 108 molecules cm−2 s−1 between 50 and 60 km with the results of scenario 2a (shown in orange), assuming a PO flux of 1 × 1010 molecules cm−2 s−1 below 25 km. The shaded blue and orange regions represent the 99% uncertainty range from the MC runs considering the uncertainties from using different temperature input profiles and the uncertainties of the PPN rate coefficients. The uncertainty range shows that up to 2 ppb PH3 at 50 km, 1.5 ppb PH3 at 55 km and 0.6 ppb PH3 at 60 km can be produced abiotically. Our abiotic uncertainty range includes the upper limit of Trompet et al. (2021) with 0.4 ppb at 61 km and agrees with the planet-averaged abundances of PH3 of 1–4 ppb between 55 and 60 km shown in Greaves et al. (2020). However, our abiotic upper limit is not consistent with the most recent estimate of 7 ppb PH3 above 55 km suggested in Greaves et al. (2021b).

As discussed in Sect. 3.3, the choice of the temperature profile has only little effect on the abiotic production of PH3. Figure 8 shows that the uncertainties from the estimated phosphorus rate coefficients are much larger. At 55 km, the range of the volume-mixing ratio of the abiotically produced PH3 spans almost six orders of magnitude. On the other hand, the rate coefficients for reactions that destroy PH3 are much better known. Hence, the uncertainty of PH3 for the PH3 flux scenarios is small, it ranges from 2.5 ppb to 3.8 ppb at 55 km.

The concentration ranges of PO for the runs considering a PH3 input flux and a PO input flux do not overlap below 55 km. Hence, observations of PO could help to constrain whether PH3 is produced by photochemistry or by other processes. Line lists and cross sections of PO have been computed by Prajapat et al. (2017) for instance. In this study, however, we limit our analysis to the photochemical response of high PO concentrations and do not investigate the potential detectability of PO in the atmosphere of Venus.

Similar to PO (see Fig. 8), our results suggest that the uncertainty ranges for PO2 (not shown) are separated for both sets of scenarios below 60 km. However, theoretical investigations suggest that PO2 may not exist in the gas phase for conditions in the Venus clouds (see e.g. Haworth et al. 2002). If we do not consider PO2 in our PPN, we find that the abundances of PO, H3PO4, and PH3 are similar to the results shown in Fig. 8. The uncertainty ranges for H3PO4 for the scenarios with PH3 input fluxes and PO input flux largely overlap. This suggests that a simultaneous detection of PH3 and H3PO4 would not reveal information about the origin of PH3.

4 Conclusions

We simulated the atmosphere of modern Venus with a sophisticated photochemical model including a new phosphorus reaction network in order to test the reproducibility of the observed concentrations of PH3. We considered three sets of scenarios: first with input fluxes of PH3 between 50–60 km, similar to the approach of Greaves et al. (2021a); second with input fluxes of PO below 25 km; and third with input fluxes of H3PO4 between 50–60 km. We considered the uncertainties of the temperature input profile and phosphorus reaction rate coefficients to compute a range of possible solutions with 200 MC runs for each of the scenarios. The main conclusions are listed below.

  • Our study suggests that a PH3 flux of 5 × 108 molecules cm−2 s−1 (4.1 Tg yr−1) between 50 and 60 km is needed to reproduce a PH3 mixing ratio of about 3 ppb at 60 km.

  • The choice of the temperature profile and the SO2 abundance in the lower atmosphere has little impact on the PH3 concentrations in the Venus clouds.

  • Varying H3 PO4 fluxes between 50 and 60 km led to a maximum PH3 mixing ratio of 5 × 10−17 at 60 km. This supports the results of Greaves et al. (2021a) and Bains et al. (2021) that a significant photochemical production of PH3 from H3PO4 pathways is unlikely.

  • We find that volume mixing ratios of PH3 between 1 × 10−15 and 2 × 10−9 might be produced abiotically at the height of the Venus clouds when assuming a PO input flux of 1 × 1010 molecules cm−2 s−1 (113 Tg yr−1) below 25 km.

  • The production of PO from destruction of PH3 is only weak (scenarios 1a–1h). Hence, the detection of large abundances of PO and PH3 might be an indicator for an abiotic production of PH3 via PO pathways.

Our main conclusion is that we can reproduce the lower estimates of about 1 ppb PH3 claimed by Greaves et al. (2020) in the Venus clouds with abiotic sources of PH3 alone when we take into account the uncertainties in the chemical rate coefficients.

Acknowledgements

The authors acknowledge the support of the DFG priority program SPP 1992 “Exploring the Diversity of Extrasolar Planets”.

Appendix A Phosphorus network

Table A.1

Phosphorus-containing reactions added to the original BLACKWOLF photochemical reaction scheme from Wunderlich et al. (2020).

Appendix B Uncertainty distribution

The uncertainties in the chemical rate coefficients are fitted to log-normal distributions for which the standard deviation is derived. The phosphorus-containing reactions shown in Table A.1 are grouped into three types as follows:

  1. Phosphorus reactions for which rate coefficient data are measured or valid for temperatures below 750 K (approximated surface temperature of Venus). For this type of reaction, we did not consider uncertainties in the rate coefficient data.

  2. Phosphorus reactions for which rate coefficient data are not valid for temperatures below 750 K. These reactions are marked with a plus in Table A.1, and the uncertainties in their rate coefficient data were considered.

  3. Reactions for which analogous rate coefficient data only exist for cases in which phosphorus is replaced with nitrogen. These reactions are marked with an asterisk in Table A.1, and the uncertainties in the rate coefficient data were considered.

For each MC run and each type 2 and type 3 reaction, we calculated a random factor inside the log-normal distribution and multiplied this factor with the rate coefficients of the reactions. The PPN used to simulate the phosphorus chemistry in this study includes type 2 reactions even when the observed rate coefficients are applied beyond their validity range for temperatures in the atmosphere of Venus. To estimate the uncertainty on extrapolating the coefficient data to Venus conditions, we collected all rate data from multiple studies over different reference temperature ranges. To be considered in our study, we specified that at least one of these data must be valid below temperatures of 750 K and at least one must be valid above 750 K. For the phosphorus-containing reactions R14, R16, and R27, rate coefficient data from Bolshova & Korobeinichev (2006) exist, in addition to the coefficients shown in Table A.1. To increase the number of members of the statistical analysis, we considered five nitrogen-containing reactions (analogue nitrogen reactions to R3, R5, R6, R21, and R53), where the rate data were taken from the National Institute of Standards and Technology (NIST, Mallard et al. 1994).

Note that datapoints in Fig. B.1 were constructed from the reactions in Table A.1 which are not marked with a plus. For these reactions, rate coefficient expressions exist which are valid below 750 K (as shown in Table A.1). Rate coefficient expressions also exist (see references in Table A.1) which are valid above 750 K. For every reaction, we calculated the coefficients between 200 and 750 K in 10 K steps. Then, for each reaction and temperature step, we divided the coefficients that are valid below 750 K () by the coefficients that are valid above 750 K (). The logarithm of the reaction coefficient quotients was then fitted to a normal distribution. Three-body and thermolysis reaction coefficients can be very small for low temperatures and the difference between and can be more than ten orders of magnitude. However, these reactions are not expected to significantly influence the photochemistry in and above the Venus clouds. Hence, in order to avoid an overestimation of the uncertainty range, we used only -10 < log10() < 10 for the fit.

The resulting distribution of log10 () is shown in Fig. B.1. The distribution in Fig. B.1 enables us to calculate a σ value as shown in the Figure. This value is then used to constrain the range over which the rate constants are varied in the Monte Carlo results shown in Fig. 8. The rate coefficients can be over- or underestimated when using rate coefficients that are not valid for temperatures below 750 K. The results suggest that it is more likely that the reaction rate would be underestimated when using (estimated coefficients) instead of (measured coefficients). However, due to the low number of statistics and the fact that both over- and underestimation of the coefficients is possible, we considered only the standard deviation, σ, to compute the log-normal distribution for the MC runs and assumed µ=0.

To compute the σ value for the type 3 reactions, we used the same procedure as for the type 2 reactions. Homologous nitrogen species reaction kinetics for unknown phosphorus species rate coefficients were compared in Bains et al. (2021). They showed that some rate coefficients of the analogue phosphorus and nitrogen reactions (CP and CN, respectively) agreed within about one order of magnitude. However, most of the phosphorus-containing reactions shown are only valid at a temperature above 1000 K. For the analogue reactions of PH3 and NH3, the difference between the rate coefficients is several orders of magnitude. We estimated the uncertainty when using this approach with 24 reactions, for which we found the corresponding CP and CN in the NIST (R1, R3, R5, R6, R8, R11, R12, R13, R14, R16, R18, R21, R22, R23, R24, R25, R26, R27, R28, R29, R31, R50, R51, and R53 in Table A.1).

Figure B.2 suggests that it is more likely that the reaction rate would be underestimated when using CN (estimated coefficient) instead of CP. However, both an over- and underestimation of the coefficients is possible. We only considered σ to compute the log-normal distribution for the MC runs and assumed µ to be zero.

thumbnail Fig. B.1

Histogram showing the ratio of measured to estimated rate coefficients of type 2 reactions () in blue. The fit of the data to a log-normal distribution with σ=4.118 and µ=0 is shown in black.

thumbnail Fig. B.2

Histogram showing the ratio of measured to estimated rate coefficients of type 3 reactions (CP/CN) in blue. The fit of the data to a log-normal distribution with σ=3.515 and µ=0 is shown in black.

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All Tables

Table 1

Atmospheric scenarios for modern Venus.

Table A.1

Phosphorus-containing reactions added to the original BLACKWOLF photochemical reaction scheme from Wunderlich et al. (2020).

All Figures

thumbnail Fig. 1

Input temperature profiles of modern Venus for latitudes below 35° (red line), 35–55° (orange line), 50–70° (green line), 70–80° (blue line) and 80–90° (purple line) taken from Haus et al. (2013) and a global average (black line).

In the text
thumbnail Fig. 2

Venus composition profiles for selected species predicted with our photochemistry model for scenarios 1a (solid blue line), 1b (dashed blue line), 1c (dotted blue line), 1d (dashed cyan line), 1f (dotted cyan line), and 1h (cyan dash-dotted line). For comparison, a range of observations is shown as solid, horizontal black lines. The observations of H2O, CO, OCS, and SO2 below the cloud top are taken from Svedhem et al. (2007) and Marcq et al. (2008). Observations of H2O and CO above the clouds are taken from Bertaux et al. (2007) and Krasnopolsky (2012). The OCS observational range at 65 km is taken from Krasnopolsky (2010) and the range at 33 km from Marcq et al. (2008). For the observational range of SO2 and SO above 60 km, we use data from Belyaev et al. (2012) and Sandor et al. (2010). Measurements of HCl above the cloud top are taken from Sandor & Clancy (2012) and Bertaux et al. (2007).

In the text
thumbnail Fig. 3

As for Fig. 2, but comparing scenario 1a (solid blue line) with the same scenario, but with the additional sink for OCS in the clouds (see Sect. 3.1), (dashed blue line).

In the text
thumbnail Fig. 4

Concentrations of PH3 at 60 km for scenario 1a (blue dots and dashed line), scenario 2a (orange dots and dashed line), and scenario 3 (green dots and dashed line) with increasing input fluxes of PH3 between 50 and 60 km, PO below 25 km, and H3PO4 between 50 and 60 km, respectively. The observational range of PH3 is taken from Greaves et al. (2020).

In the text
thumbnail Fig. 5

Predicted volume mixing ratios of PH3, PO, H3PO4, and O2 against height for scenario 2a with three different PO input fluxes: 1 × 109 molecules cm−2 s−1 (red line), 1 × 1010 molecules cm−2 s−1 (orange line), and 1 × 1011 molecules cm−2 s−1 (purple line). We additionally show the observational ranges from Greaves et al. (2020, 2021b) and upper limits of Trompet et al. (2021).

In the text
thumbnail Fig. 6

Venus composition profiles for PH3, PO, and H3PO4 predicted with our photochemistry model for scenarios 1a (solid blue line), 1b (dashed blue line), 2a (solid orange line), and 2b (dashed orange line). We additionally show the observational ranges from Greaves et al. (2020, 2021b) and upper limits of Trompet et al. (2021).

In the text
thumbnail Fig. 7

As for Fig. 6, but showing the effect of varying the input temperature profile (see the legend).

In the text
thumbnail Fig. 8

Venus composition profiles for selected species predicted with our photochemistry model for scenario 1 (PH3 flux, solid blue line) and scenario 2 (PO flux, solid orange line). The shaded areas show the 99% ranges of the MC runs of scenario 1 (shaded blue) and scenario 2 (shaded orange). For comparison, a range of observations is shown with black lines. We additionally show the observational ranges from Greaves et al. (2020, 2021b) and upper limits of Trompet et al. (2021).

In the text
thumbnail Fig. B.1

Histogram showing the ratio of measured to estimated rate coefficients of type 2 reactions () in blue. The fit of the data to a log-normal distribution with σ=4.118 and µ=0 is shown in black.

In the text
thumbnail Fig. B.2

Histogram showing the ratio of measured to estimated rate coefficients of type 3 reactions (CP/CN) in blue. The fit of the data to a log-normal distribution with σ=3.515 and µ=0 is shown in black.

In the text

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