The water abundance in Jupiter's equatorial zone

Oxygen is the most common element after hydrogen and helium in Jupiter's atmosphere, and may have been the primary condensable (as water ice) in the protoplanetary disk. Prior to the Juno mission, in situ measurements of Jupiter's water abundance were obtained from the Galileo Probe, which dropped into a meteorologically anomalous site. The findings of the Galileo Probe were inconclusive because the concentration of water was still increasing when the probe died. Here, we initially report on the water abundance in the equatorial region, from 0 to 4 degrees north latitude, based on 1.25 to 22 GHz data from Juno Microwave radiometer probing approximately 0.7 to 30 bars pressure. Because Juno discovered the deep atmosphere to be surprisingly variable as a function of latitude, it remains to confirm whether the equatorial abundance represents Jupiter's global water abundance. The water abundance at the equatorial region is inferred to be $2.5_{-1.6}^{+2.2}\times10^3$ ppm, or $2.7_{-1.7}^{+2.4}$ times the protosolar oxygen elemental ratio to H (1$\sigma$ uncertainties). If reflective of the global water abundance, the result suggests that the planetesimals formed Jupiter are unlikely to be water-rich clathrate hydrates.

mixed occur much deeper (~10 bars) than what was predicted by an equilibrium thermochemical model. The concentration of water was subsolar and still increasing at 22 bars, where radio contact with the probe was lost, although the concentrations of nitrogen and sulfur stabilized at ~3 times solar at ~10 bars 9,10 . The depletion of water was proposed to be caused by meteorology at the probe location 8,11 . The observed water abundance was assumed not to represent the global mean water abundance on Jupiter, which is an important quantity that distinguishes planetary formation models [12][13][14][15][16] and affects atmospheric thermal structure 17,18 . The Juno mission was in part motivated by the necessity of determining the water abundance at multiple locations across the planet. Here we report on the initial analysis of the equatorial zone (EZ) defined as 0 to +4 degrees latitude, the first of Jupiter's regions analyzed.
We analyze the first eight of Juno's orbits around Jupiter (designated as PJ1, PJ3, PJ4, PJ5, PJ6, PJ7, PJ8 and PJ9), with each perijove probing a cross-section of Jupiter's atmosphere at a different longitude and spanning latitudes from the north pole to the south pole (no MWR data were obtained during PJ2). Dates and longitudes of each perijove are summarized in Supplementary Table 1. The raw data (antenna temperatures) were processed through a deconvolution algorithm (See Methods and Janssen et al. , 2017 19 ) that removes synchrotron radiation and microwave cosmic background radiation to recover calibrated atmospheric brightness temperatures whose emission angle dependence is parameterized by three coefficients with spatial resolution constrained by geometry and the antenna beam. The subset of nadir brightness temperatures thus obtained from PJ1 to PJ9 is displayed in Fig. 1. The spatial resolution is highest near the equator (~0.5 degree) and lowest toward the poles because the spacecraft is closer to the planet near the equator (~ 4000 km above 1 bar level) and further away near the poles. Despite an approximate 45-degree separation in longitude between each of the PJ1 to PJ9 orbits, the observed nadir brightness temperatures show extremely good consistency, especially at latitudes near the equator, at mid-latitudes, and at pressure levels larger than 10 bars. Compared to the simulated brightness temperatures of a reference adiabatic atmosphere, the observed nadir brightness temperatures are warmer than expected at all channels everywhere except within a narrow latitudinal range of a few degrees located near the equator.
Our new analysis has extended the latitudinal coverage to the poles, while our previous analysis based on PJ1 data 20 was confined to within 40 degrees of the equator. Fig. 1 shows that the values of the brightness temperature in the EZ are consistent with an ideal moist adiabat in which the temperature is moist adiabatic and the condensing species are well-mixed up to their condensation level. This is also in line with the lack of lightning observations in this region 21 because an ideal moist adiabatic temperature profile does not have enough convective available potential energy to produce lightning. A free inversion of the vertical distribution of ammonia gas using observed nadir PJ1 data 20,22 produced a nearly uniform distribution of ammonia gas, from ~100 bars to 1 bar within a few degrees of the equator, which further corroborates the observation that the ammonia gas in the EZ is mixed vertically to a greater degree than at other latitudes. The consistency between multiple perijoves confirms that the uniformity of ammonia in the EZ is independent of longitude. In addition, similar enrichment of ammonia gas in the EZ relative to the other latitudes was also found by the Cassini/CIRS retrievals 23 and VLA observations 24 although they were sensitive to only shallow levels and pressures less than a few bars. Thus, we identify the EZ as a unique region appropriate for deriving the water abundance assuming that the temperature profile follows a moist adiabat.
The MWR instrument measures the brightness temperature both at nadir and off-nadir angles. The precision of the angular dependence of the brightness temperature provides important additional information and a tight constraint on atmospheric structure beyond that available from the nadir brightness temperature alone. This is due to the fact that an absolute calibration uncertainty of about 2% does not affect the relative brightness at different angles 19 .
We define the limb-darkening parameter, ( ), as the fractional reduction of the brightness temperature when viewing off-nadir: Where * ( ) is the brightness temperature at emission angle . Fig. 2  For the gravity orbits, the spacecraft spin axis is oriented toward the earth, resulting in larger minimum emission angles as the orbit precesses. The consistency of multiple and different kinds of orbits and the absence of systematic correlation between the nadir brightness temperature and the limb-darkening in 0.6 -5.2 GHz channels indicate that nadir brightness temperature and limb-darkening are two independent measures of the thermal and compositional properties of the atmosphere. Nadir brightness temperature and limb-darkening have larger correlations in the 10 and 22 GHz channels because the limb-darkening is small in these channels due to narrower weighting functions and its estimation, by the deconvolution process, is influenced by the nadir brightness temperature.
Even though the EZ region is characterized by a greater degree of mixing, MWR data indicate possible departures from an ideal moist adiabat. MWR observations at the 5.2 and 10 GHz channels ( Fig. 1) measure slightly colder brightness temperatures (by ~ 5 K) than the ideal moist adiabatic model. The potential change in temperature due to ammonia condensation/vaporization at these levels is only NH + NH + / ,,H 2 ≈ 0.3 K -where NH + is the ammonia mole fraction, NH + is the latent heat of ammonia, and ,,. ! is the specific heat of H / at constant pressure -and therefore does not account for the observations. To account for the coldness, we allow the possibility that ammonia abundance is enriched by 10 to 15% (parameterized by the factor 0 in equation (3) with respect to the deep abundance near a few bars). Simulation of two-dimensional moist convection in Jovian atmospheres 25 suggests that the slight enrichment of ammonia in the subcloud layer is made possible by evaporated ammonia precipitation. The cold plumes of ammonia-rich precipitation sink into the atmosphere to a few bars, where they encounter stable layers due to an increase in the water abundance. This creates a local maximum in ammonia concentration -referred to as the enriched ammonia layer -that is consistent with the observations. As a result, the model for the ammonia distribution consists of five parameters: 1) the ammonia enrichment factor 0 , 2) the pressure of the enriched ammonia layer 1 , 3) its thickness Δ , 4) the deep ammonia abundance NH + , and 5) the deep water abundance H / O. Since we do not know the functional form of ammonia profile, ( ), in the enriched ammonia layer, we use an exponential profile that results from balancing the downward diffusive flux and upward advective flux. Its functional form in pressure coordinates is: where is pressure, 1 is the pressure level that the stable layer starts to develop, and Δ is its thickness in pressure. Two constants A and B are determined by matching the boundary conditions: which imply that the ammonia abundance is enriched by a factor of 0 with respect to the deep abundance at pressure levels less than 1 . The resulting ammonia profile is displayed in Fig. 4 where a small kink in the ammonia profile is visible.
We first examine qualitatively the sensitivity of limb-darkening to these parameters by show that the limb-darkening is not sensitive to the choices of 1 , Δ , and Θ. Therefore, the precise location, thickness and functional form of the ammonia-variable layer do not affect our retrieved deep ammonia abundance. For example, one may use a linear interpolation for the ammonia profile that starts at pressure level 1 and ends at pressure level ( 1 − Δ ); this does not change our result. Fig. 3(a) shows that the 1.25 GHz channel is most sensitive to the deep ammonia abundance. As demonstrated in Fig. 3(b) and in Janssen et al. (2017) 19 , the 2.6 GHz channel exhibits the most sensitivity to the water abundance because the limb-darkening value is largest when the water abundance changes significantly, which is at the water condensation level. Since the limb-darkening of this channel is also affected by 0 (Fig. 3e), there is a potential correlation between the estimation of the water abundance and the ammonia enrichment factor, a reason why 0 must be included in the forward model to allow a conservative estimate of the water abundance. But beecause the 10 GHz channel is more sensitive to 0 than the other channels, it can be used to determine 0 while the 2. we provide a simulation of results for the EZ using the 0.6 GHz channel assuming its opacity is well known, and we obtain a substantial improvement to our precision. The simulation shows that further laboratory data would be useful to constrain the water abundance beyond 30 bars.
All mixing ratios in this article are referred to molar mixing ratios and the Solar photospheric abundances are according to Table 1  They are also summarized in Supplementary Table 2.
A sample of thermal and compositional profiles explored by the sampler is displayed in   10 and is about a factor of two smaller than that suggested by the radio attenuation of the signal from the Galileo Probe (700 ± 100 ppm) 30 . We speculate that the discrepancy may be an overestimation of the radio attenuation due to signal loss by scintillation of the coherent signal The overall water abundance is 2.5 !4.6 %/./ × 10 + ppm, or 2.7 !4.7 %/.8 times solar with a long tail toward the larger values. The estimated ammonia and water abundance are negatively correlated because increasing either the ammonia abundance or the water abundance will reduce both the nadir brightness temperature and the limb-darkening (Fig. 6a). Ranges of water abundances as a function of ammonia abundance are summarized in Table 1. Although the centroid of the abundance values for water and ammonia expressed in terms of solar abundance lie on top of each other, we caution that both the magnitude of the error bars and their symmetry differ for the two determinations. In the case of ammonia, the error bars are small and symmetric; in the case of water, our error bars are larger with a tail toward higher values. The potential range of the enrichment ratios for water versus ammonia allows for water to be less enriched than ammonia (solar vs 2.6 times solar) or much more enriched (5 times solar vs 2.9 times solar).
Moreover, the quoted uncertainty range encompasses the 16 th to 84 th percentile of the probability space. A two-sigma (2.5 th to 97.5 th percentile) uncertainty of the water abundance is 2.7 !/.6 %8.9 times solar. Until we are able to utilize the 0.6 GHz channel data, we cannot definitively rule out zero water from fitting the MWR spectra. However, a lower limit of the deep water between 0 and the water abundance is shown in Fig. 6(b). 0 is positively correlated with the water abundance because a larger 0 leads to more limb darkening at the 2.6 GHz channel and so does a lesser water abundance. Since no previous studies have indicated the existence of such a region, the estimation of the water abundance is 1.7 !4./ %4.6 times solar given 0 = 1, and the corresponding probability density function is shown in Fig. 6(c).

Deconvolution methods
The brightness temperature at microwave channel , latitude , and emission angle = cos( ) is parameterized by a quadratic representation of the form where < ( ), different for each channel λ, is given by the ratio of the brightness temperature of a model atmosphere and a fit to that model atmosphere only over emission angles less than 53 degrees ( < 0.6). This ratio equals to one for angles less than 53 degrees but deviates from unity at larger angles. The idea is to fit small angles with a quadratic function but to assume some profile for large angles, which contribute only a small fraction to the antenna temperatures included in the measurement set. For this work, only emission angles less than 45 degrees are used. Therefore, the prefactor < ( ) is omitted in the main manuscript.
The performance of the fit was evaluated using an equilibrium cloud condensation model 1 , and it was found that the fits were not strongly dependent on the specific model atmosphere chosen to determine < ( ). It was found that a quadratic fit of the form given above ( = (?@A) ) was sufficient to fit the limb-darkening at 45 degrees (evaluated using a real radiative transfer program, = (CDEFG) ) for 1.25 -22 GHz channels to within an absolute error of 0.1% (Extended Fig.   E1) and the nadir brightness temperature to within a relative value of 0.1% (Extended Fig. E2) over all perijoves up to PJ9 and over a range of model atmospheres assuming both dry and moist adiabats for all latitudes and spanning ammonia abundances of 2.1 to 3.3 times solar, water abundances of 0.5 to 8 times solar, and half-bar reference temperatures of 130 K to 135.6 K. The maximum errors for 0.6 GHz channel, not included in this analysis, were about twice as large.
More details of the deconvolution algorithm, including the treatment of the synchrotron radiation will be summarized in a separate paper.
The measured antenna temperatures are a convolution of the antenna pattern for each channel with brightness temperatures that depend on both emission angle and spatial location.
To determine the brightness temperatures a deconvolution must be performed to negate the blurring induced by the instrument antenna pattern. Because the convolution is a linear operation, the set of measured antenna temperatures, H , can be represented as the product of a linear operator with a set of coefficients, , where the components of represent information regarding the angular dependence of the brightness temperature at different locations on Jupiter (the a I ( ), < ( ), < ( ) coefficients in equation (M1). Then we want to find the optimal solution * that minimize the cost function: which is: where L is an assumed prior, * is the measurement covariance matrix, H is a prior covariance, and H is the set of measured antenna temperatures, modified to estimate the contribution from synchrotron radiation. The covariance of * is a sparse matrix whose sparsity pattern is shown in Extend Fig. E3 for the 10 GHz channel. The other channels are similar. The deconvolution process is performed in two steps. First, a coarse grid of 1.2 degree spacing over the latitude range presented in this work for a and 2.4 degrees for b and c is used without any prior estimate L . This step is often sufficient to yield residuals that are within a small multiple of the instrument noise level. The coarse grid solution can then be used as prior estimate for a refined solution on a finer grid to reduce the χ 2 to a value close to 1.

Spectral inversion methods
Let the parameter vector = ( NH + , H / O, 0 , Δ , 1 , Θ) K and the measurement vector = ( 4 , 4 , 4 , / , / , / … , ; , ; , ; ) K , where , and are brightness temperature coefficients introduced in equation (M1) and their subscripts are channel numbers. We accounted for the limb-darkening via the use of these coefficients. The sensitivity study in the previous section has demonstrated that the 2.6 GHz channel best constrains the water abundance, which is the main objective of this article. We use a Markov Chain Monte Carlo (MCMC) sampler 2 to assess the joint probability of the parameter given the observation . Bayes' theorem states that: where ( ) is the prior distribution of the parameter, ( | ) is the probability of observing Y given , and ( | ) is the probability of the parameter given the observation . We assume the prior probability of Θ is a Gaussian distribution with a mean of 132.1 K and a standard deviation of 2 K 3 . The prior probabilities of other parameters are uniformly distributed. Denoting the forward model as ( ) and assuming Gaussian statistics, ( | ) is: where = 15 is the dimension of the observation vector , and Σ is the formal covariance matrix estimated from the deconvolution process. Σ is a block diagonal matrix with each block of size 3 × 3 because the five channels are independent of each other. The magnitude of the elements in Σ is illustrated by the error bars in Fig. 7. The MCMC sampling algorithm uses 24 Markov chains with 6,000 states in each chain to fit the measurement vector.
The thermal profile is obtained by integrating the moist adiabatic temperature gradient