Saturn’s Atmospheric Helium Abundance from Cassini Composite Infrared Spectrometer Data

We use thermal infrared data from the Composite Infrared Spectrometer, which was on board the Cassini orbiter, to retrieve the helium abundance in Saturn’s visible atmosphere. We find that the data is most consistent with a helium-to-hydrogen mole ratio in the range between 0.04 and 0.075, near the lower end of previous measurements, and implying a significant sequestration of helium in Saturn’s interior. The primary sources of uncertainty are in the spectroscopic parameters for H2–H2 collision induced absorption and the nonuniqueness of the spectral inverse problem.


Introduction
The atmospheric helium abundance provides an important constraint on the structure and evolution of the giant planets Jupiter and Saturn. They are expected to form with a bulk ratio of helium to hydrogen matching the protosolar nebula, and because their gravity is sufficient to preclude significant escape of helium or hydrogen, their bulk composition should retain the protosolar He/H 2 ratio. Early calculations of the phase diagram for H 2 -He mixtures indicated that a separation into helium-poor and heliumrich phases should occur at conditions in the interior of Saturn and possibly Jupiter (Stevenson 1975;Stevenson & Salpeter 1977a, 1977b, leading to "helium rain" and the sequestration of helium in Saturn's interior with a corresponding depletion of helium in the outer layers. Additionally, the energy generated by helium rain has been invoked to explain Saturn's current intrinsic luminosity (Stevenson & Salpeter 1977b;Hubbard et al. 1999;Fortney & Hubbard 2003), which is higher than predicted by thermal evolution models without an internal heat source. Measurements of the helium abundance in the atmosphere thus place observational constraints on the extent to which helium has been sequestered in Saturn's deeper interior and, in turn, on the models for the structure and evolution of the interior.
The first spacecraft measurement of Saturn's atmospheric helium abundance was by Orton & Ingersoll (1980), using a combination of thermal infrared observations from the Pioneer11 Infrared Radiometer (IRR) and temperature profiles from the Pioneer11 radio occultation experiment (RSS). Radio occultations give a profile of atmospheric refractivity as a function of altitude, from which a vertical temperature profile can be derived. The temperature profile depends upon the assumed atmospheric composition and is proportional to the inverse of the molecular weight of the atmosphere. The helium abundance can then be estimated by finding the composition for which calculations of the outgoing radiance from the radio occultation profile best matches the thermal infrared observations. Using this method, Orton & Ingersoll (1980) found a helium-to-hydrogen mole ratio of He/H 2 =0.11±0.03. Subsequently, Conrath et al. (1984) used the same method, combining data from the Voyager1 Infrared Interferometer Spectrometer (IRIS) and the Voyager2 RSS. They found a helium abundance of He/H 2 =0.034±0.024, indicating significant sequestration of helium in Saturn's interior. This value became the generally accepted helium abundance for the next decade.
However, the measurement of Jupiter's atmospheric helium abundance by the Helium Interferometer Experiment on board the Galileo probe (He/H 2 =0.157±0. 003;von Zahn et al. 1998) was outside of the error bars of the abundance determined from Voyager radio occultation and infrared data (He/H 2 = 0.110±0.032, Gautier et al. 1981;Conrath et al. 1984), suggesting that the radio occultation technique may have unknown systematic errors. This prompted Conrath & Gautier (2000) to reexamine Saturn's helium abundance, using only data from Voyager1 IRIS. Because H 2 -H 2 and H 2 -He collision induced absorption (CIA) have different spectral shapes, they were able to use spectroscopic inversion methods to retrieve temperature, hydrogen para-fraction and atmospheric helium abundance from several averages of Voyager1 IRIS spectra, finding a molar mixing ratio He/H 2 between 0.11 and 0.16, which is significantly larger than the abundance obtained using radio occultation data. Because of this large discrepancy between the results of Conrath et al. (1984) and Conrath & Gautier (2000), one goal of the Cassini mission to Saturn was an updated determination of Saturn's atmospheric helium abundance.
Two published estimates of Saturn's helium abundance from Cassini data currently exist. Sromovsky et al. (2016) analyzed data from the Cassini Visual and Infrared Mapping Spectrometer (VIMS) taken in the wake region of the 2010-2011 storm and found He/H 2 = -+ 0.055 0.015 0.010 , near the lower end of previous estimates. Koskinen & Guerlet (2018) combined stellar occultation measurements of atmospheric density as a function of altitude from the Ultraviolet Imaging Spectrograph (UVIS) with temperature profiles retrieved from Cassini Composite Infrared Spectrometer (CIRS) limb observations and found He/H 2 between 0.1 and 0.15 was needed to make the vertical density profiles as a function of latitude consistent between the UVIS and CIRS data, consistent with the results of Orton & Ingersoll (1980) and Conrath & Gautier (2000).
In this paper, we use thermal infrared spectra from the Cassini CIRS instrument to estimate the helium-to-hydrogen ratio in Saturn's visible atmosphere, using a retrieval procedure based on that of Conrath & Gautier (2000). A subsequent paper will discuss helium abundance retrieval from a combination of CIRS and Cassini radio science data, similar to the analysis of Conrath et al. (1984) from Voyager data. Section 2 describes the data set and analysis procedure, Section 3 presents the results of the retrievals, and Section4 gives a comparison with previous Saturn helium measurements and briefly discusses the implications for models of Saturn's interior and evolution.

Data Set
The data used is from focal plane 1 (FP1) of the CIRS instrument on board the Cassini spacecraft. FP1 is a single pixel detector with a circular field of view of~4.1 mrad diameter, with a nearly Gaussian spatial response with a full width at half maximum of 2.5 mrad, covering the spectral range from 20 to 600 cm −1 (16.7-1000 μm) with an apodized spectral resolution adjustable between 0.5 and 15.5 cm −1 . The FP1 data is supplemented with data from focal plane 4 (FP4), a 1-by-10 array of pixels with a square field of view of 0.27 mrad per pixel, which covers the spectral range from 1100 to 1500 cm −1 (6.7-9 μm). A full description of CIRS and its operation is given by Flasar et al. (2004) and Jennings et al. (2017).
We use data from a series of observations, called MIRMAPs and designed primarily for longitudinal temperature mapping, in which the CIRS fields of view were held fixed on the central meridian at a single latitude for 1-2 rotations of Saturn (11 or 22 hr), with periodic offsets to deep space for obtaining calibration data. During later parts of the mission, the latitude being observed was sometimes shifted by 10°midway through the two rotation MIRMAPs. In these cases, the data from each latitude pointing were analyzed as separate observations. The data were taken with a spectral resolution of 2.7 cm −1 ; the spatial resolution of FP1 during the observations varied between 5°and 10°of great circle arc. For each observation, all spectra at the targeted latitude are averaged to produce an averaged spectrum for each of FP1 and FP4. The standard deviation of the spectra in the average is used as an estimate of the noise level. To minimize potential errors in the hydrogen continuum, which is what contains the information on the helium abundance, we use the "local calibration" (Jennings et al. 2017, Section 7), which only uses deep space calibration spectra from times near the observation being calibrated. Because the original purpose of the observation required averaging only small numbers of spectra, the number of deep space spectra taken for calibration during the observations is substantially smaller than the number of data spectra. Thus, the uncertainty for the averaged spectrum is estimated by dividing the standard deviation of the averaged spectra by the square root of the number of deep space spectra used in calibration. Observations with fewer than 50 deep space spectra available for calibration are excluded from the analysis, as are observations with an emission angle greater than 55°. We also considered the "global calibration," which attempts to obtain at least 4000 deep space spectra by using deep space spectra taken up to several week from the time of the observation. This reduces the noise level of the spectra, at the expense of potentially decreased absolute radiometric accuracy (Jennings et al. 2017). We find that using the global calibration, the helium abundance from individual observations varies from the local calibration by an amount similar to the sensitivity of the retrievals to the instrument noise level. However, the mean of the retrieved helium abundance over all observations is nearly identical in both data sets, although the global calibration has a higher variance over the observations. Because the global calibration has potentially lower absolute radiometric accuracy, we present only the results using the local calibration. Details of the observations used are given in Table 1. Figure 1 shows the latitude and time coverage of the observations.

Retrieval Methodology
At wavenumbers between ∼220 and 600 cm −1 , the opacity of Saturn's atmosphere is dominated by CIA from H 2 -H 2 , H 2 -He, and H 2 -CH 4 pairs. The measured spectrum in this wavenumber range is sensitive to the upper tropospheric profiles of temperature and H 2 para-fraction (the ratio of parahydrogen to total hydrogen), as well as the abundances of helium and methane. At lower wavenumbers (longer wavelengths), absorption from the rotational lines of NH 3 and PH 3 becomes significant, and the measured spectrum also depends on the tropospheric NH 3 and PH 3 abundances.
Retrievals are performed using the constrained linear inversion method described by Conrath et al. (1998) and Conrath & Gautier (2000), updated to allow for retrievals of NH 3 and PH 3 . The algorithm is summarized in the Appendix. As discussed by Conrath & Gautier (2000), the retrieval problem is mathematically ill-posed in that there are multiple solutions that fit the data within the noise level. This occurs because the measured radiance is not sensitive to variations in atmospheric structure with vertical scale smaller than the width of the contribution function, which is roughly one pressure scale height for the temperature and hydrogen para-fraction; high spatial frequency variations can be added to the atmospheric profiles while keeping the modeled radiances within the noise level of the measurements. Thus, only a smoothed approximation of the atmospheric profiles can be retrieved, and high spatial frequency variations must be filtered out. This is done by constraining the solutions to be near the initial conditions and by low-pass filtering the difference between the retrieved and initial guess solutions, as described in the Appendix. We will see below that the sensitivity of the retrievals to the initial guess and to how strongly the solution is constrained to the initial guess are a significant contribution to the uncertainty in the retrieved helium abundance.
The forward model uses 200 layers equally spaced in logpressure between 5000 and 0.001 mbar. Collision induced absorption from H 2 -H 2 , H 2 -He, and H 2 -CH 4 pairs is calculated according to Borysow & Frommhold (1986) and Borysow et al. (1985Borysow et al. ( , 1988. We also consider the newer H 2 -H 2 CIA cross sections of Fletcher et al. (2018). Absorption from rotational lines of PH 3 and NH 3 is calculated using the correlated-k approximation (Goody et al. 1989;Lacis & Oinas 1991), with spectroscopic data as described by Fletcher et al. (2007a). The model allows for extinction, but not scattering, by haze or clouds but is not included in the default model, because the main cloud layers are deeper than the levels to which our data is sensitive and the 1-10 μm size tropospheric haze particles are expected to have negligible opacity at long IR wavelengths (Fletcher et al. 2007a(Fletcher et al. , 2007b. The potential consequences of this assumption will be discussed in Section 2.4.3. The initial guess atmosphere uses a temperature profile that is an average of observations taken during the approach to Saturn before Cassini orbit insertion (Flasar et al. 2005) and a para-fraction profile in thermodynamic equilibrium with the initial temperature profile. The PH 3 profile uses a mole fraction of 6.4×10 −6 for pressures greater than 550 mbar and decreasing exponentially at lower pressure with a scale height of 0.37 pressure scale height. The NH 3 profile assumes a deep abundance of 1.1×10 −4 , then follows the saturation vapor pressure curve from 1200 to 300 mbar, and decays exponentially with a scale height of 0.1 pressure scale height above 300 mbar. The CH 4 profile is taken from the photochemical model of Moses et al. (2000), scaled to a tropospheric volume mixing ratio of 4.7×10 −3 (Fletcher et al. 2009). A retrieval of the stratospheric temperature using FP4 data between 1250 and 1310 cm −1 is performed first and used as the initial temperature profile for retrievals from the FP1 spectrum. A full profile retrieval is performed for all atmospheric parameters being fit, except for the helium abundance that is assumed to be uniformly distributed. Figure 2 shows the sensitivity of the outgoing radiation to the helium abundance, as well as the temperature and hydrogen parafraction at 300 mbar, calculated for the initial guess atmosphere at an emission angle of 10°. The sensitivity of CIRS spectra to the helium abundance occurs primarily over the spectral range from 220 to 300 cm −1 . Unfortunately, this is also the spectral range most sensitive to the upper tropospheric temperature and hydrogen parafraction. In particular, the functional derivative of the measured radiance to the helium abundance is strongly anticorrelated with the functional derivative with respect to the upper tropospheric hydrogen para-fraction. Separating the effects of helium and hydrogen para-fraction thus requires using either wavenumbers greater than ∼350 cm −1 , where CIRS has a poor signal-to-noise ratio, and/or lower wavenumbers less than ∼200 cm −1 , where NH 3 and PH 3 absorption must then be included in the model.  To examine the ability of the CIRS spectra to distinguish the helium abundance from the upper tropospheric temperature and hydrogen para-fraction, we performed retrievals of the non-helium atmospheric parameters for a range of assumed helium abundances for two different spectral ranges: 230-600 cm −1 , where only H 2 -X CIA is important, and 80-600 cm −1 , where NH 3 and PH 3 must also be retrieved, with small gaps at the wavenumber ranges of known instrumental artifacts that are not completely suppressed in calibration-a feature at 191 cm −1 and a variable wavenumber feature (Jennings et al. 2017, Section 8c). Figure 3 shows the reduced chi-square residuals of the retrievals, as a function of the assumed helium-to-hydrogen volume mixing ratio, for the observation at 38°S latitude on 2005 February 23 (observation 003SA_MIRMAPA003 in Table 1). The reduced chi-square is defined as

Information Content of the Data
where N ν is the number of points in the spectrum, n I i ( ) is the measured radiance at wavenumber ν i , I f (ν i ) is the modeled spectrum, and σ i is the noise equivalent spectral radiance (NESR) at wavenumber ν i . We see that when using the 230-600 cm −1 spectral range, the quality of the fit is weakly sensitive to the helium abundance, with c N 2 decreasing slowly with decreasing helium abundance. Extending the spectral range to 80 cm −1 , the fits become more sensitive to the helium abundance, with a weak minimum in c N 2 near a helium-tohydrogen ratio of 0.045, and increase rapidly above ∼0.07. Figure 4 shows the spectral fits for three selected helium abundances (He/H 2 =0.01, 0.05, and 0.09), along with the deviation of the fits from the observed spectrum. The deviations of the fits are also shown smoothed by a 30 cm −1 boxcar to allow the effect of changing the helium abundance to be clearly seen. Figure 5 shows the retrieved temperature and hydrogen para-fraction profiles for the fits in Figure 4. When using only the 230-600 cm −1 range, the spectral fits at differing helium abundances are nearly identical except between ∼450 and 550 cm −1 , where the CIRS spectra have a poor signal-to-noise ratio (the NESR of CIRS is larger than that of Voyager IRIS at these wavenumbers), and are well below the noise level. For ν450 cm −1 , changes to the spectrum from varying the helium abundance between 0.01 and 0.09 are nearly completely compensated for by small changes in the temperature of less than 0.5 K and by changes in the hydrogen para-fraction of around 0.08.
When the spectral range of the fit is extended to 80 to 600 cm −1 , the spectral fits to different helium abundances show changes at all wavenumbers except between about 350 to 450 cm −1 and in particular at low wavenumbers where CIRS has its lowest NESR. The sensitivity of the retrieved temperatures are roughly a factor of four larger than with the more limited wavenumber range, and the structure of the retrieved hydrogen para-fraction profiles is very different. When including wavenumbers below ∼200 cm −1 , the retrieved para-fraction is nearly independent of the helium abundance at 300 mbar while the retrieved para-fraction around the tropopause becomes sensitive to the assumed helium abundance. We therefore find it necessary to use the wavenumber range from 80 to 600 cm −1 for helium retrievals from the full data set, despite the necessity of fitting the NH 3 and PH 3 rotational lines. Figure 6 shows the results of helium abundance retrievals for the 003SA_MIRMAPA003 observation shown in Figure 4, Figure 3. Reduced c N 2 for temperature and para-fraction retrievals from an observation at 38°S on 2005 February 23 as a function of assumed helium abundance. The circles are retrievals over the spectral range 230-600 cm −1 ; the squares are retrievals over the spectral range 80-600 cm −1 , for which NH 3 and PH 3 abundance is also retrieved.

Retrieval Parameters
using the spectral range from 80 to 600 cm −1 , as a function of the initial guess helium abundance, for three values of the retrieval parameter determining how closely the H 2 para-fraction is constrained to the initial guess (a p f in Equation (A6)). The values of a f p were chosen to represent the range over which the retrievals converge within 10 iterations without producing unphysical oscillations in the retrieved para-fraction profile. The error bars are an estimate of the sensitivity of the retrieved He/H 2 to instrument noise. We see that the retrieved helium abundances is weakly sensitive to the initial guess helium abundance, varying by an amount comparable to or less than the sensitivity of the retrieval to instrument noise. The slight discontinuities in the retrieved helium abundance and c N 2 as the initial guess is varied are accompanied by small, discontinuous changes in the para-fraction profiles, which is illustrative of the nonuniqueness problem with retrievals; small changes in the initial guess can result in the retrieval converging to a slightly different solution, and there are multiple solutions with nearly identical c N 2 . The sensitivity of the retrieved helium abundance to a f p is roughly a factor of three larger than the sensitivity to instrument noise. There is a similar sensitivity to how strongly the retrieved temperatures are constrained.
For our full set of retrievals, we adopt He/H 2 =0.11 as the initial guess helium abundance and use a = 0.03 f p . We use ±0.007 as an estimate of the sensitivity of the retrieved He/H 2 to the retrieval parameters. It should be noted that this value is not a formal error estimate but is only an estimate of the range of values consistent with the data given the instrument noise and the nonuniqueness of the retrievals.

Methane Abundance
Methane is sufficiently abundant in Saturn's atmosphere to affect the CIRS spectra in two ways: first through the contribution of H 2 -CH 4 CIA to the opacity and second through methane's contribution to the atmospheric mean molecular Figure 4. Fits to the zonal mean spectrum from observation 003SA_MIRMAPA003 from retrievals of temperature, H 2 para-fraction, NH 3 , and PH 3 for assumed He/H 2 mole ratios of 0.01 (green lines), 0.05 (red lines), and 0.09 (blue lines). The left column shows retrievals using the spectral range from 230 to 600 cm −1 , the right columns shows retrievals using the spectral range from 80 to 600 cm −1 . The top row shows the observed brightness temperature (black lines) and the modeled spectra from the retrieved profiles. The middle row shows the difference between the observed and modeled radiances; the black dashed lines are the NESR of the zonally averaged spectra. The bottom row shows the difference between the observed and modeled spectra averaged by a 30 cm −1 boxcar function. weight, which affects the CIA of all molecule pairs. Figure 7 shows the retrieved He/H 2 as a function of tropospheric methane mole fraction for observation 003SA_MIRMAPA003 around our nominal value of 4.7×10 −3 . The dashed line is a least-squares fit of a linear function to the retrieved He/H 2 and the gray box indicates the 1σ uncertainty in the tropospheric methane abundance from Fletcher et al. (2009) of ±2×10 −4 . For variations in the methane abundance on the order of its uncertainty, the retrieved He/H 2 is linear in the tropospheric methane abundance with a slope of 6.1, such that the uncertainty in the methane abundance creates a corresponding uncertainty in the retrieved He/H 2 of 0.0012.

Tropospheric Haze
Our retrievals assume that the tropospheric haze does not contribute to the opacity in the wavelength range of our data. Fletcher et al. (2007b) tested the effects of a tropospheric haze on temperature and para-fraction retrievals for several assumptions about haze composition, particle size, and vertical distribution and found that at four of the five latitudes examined, the inclusion of a tropospheric haze had no effect or worsened the fits, and in the case where the inclusion of haze improved the fit, the improvement was not statistically significant. To examine the possible effect of the tropospheric haze on the retrieved helium abundance, we added to our forward model a gray absorber with a uniform mass mixing ratio between 100 and 1000 mbar. Figure 8 shows the retrieved He/H 2 as a function of the optical depth of the gray absorber for the observation 003SA_MIRMAPA003, along with the c N 2 of the retrievals. We find that increasing the optical depth τ of the gray absorber lowers the retrieved helium abundance; each increase of 0.1 in the optical depth reduces the retrieved He/H 2 by ∼0.01. For haze optical depths 0.25, the c N 2 is within the range found in haze-free retrievals when the retrieval parameters are varied ( Figure 6). There is a weak minimum in the residuals at τ≈0.1; an F-test for the significance of including an extra term in the fit indicates that the reduction in c N 2 over the value for τ=0 is weakly significant, at about the 80% level (i.e., a 20% chance that the null hypothesis of no haze opacity is valid). Given that the haze opacity is poorly constrained by the CIRS data, we assume a haze-free atmosphere in our retrievals. If haze opacity is significant at the wavenumber range of CIRS FP1, our results will overestimate the helium abundance.

Hydrogen CIA Cross Sections
The H 2 -H 2 CIA of Borysow et al. (1985) used in our model includes only the free-free interactions between H 2 molecules, ignoring the bound-bound and bound-free contributions from dimers. The latest update to the CIA section of the HITRAN spectroscopic database (Karman et al. 2019) includes alternate H 2 -H 2 CIA data from Fletcher et al. (2018), which includes the effects of dimers. Fletcher et al. (2018) modeled Voyager spectra of the outer planets and found that using their updated CIA opacity instead of that of Borysow et al. (1985) had a nontrivial effect on the retrieved H 2 para-fraction in the upper troposphere. Since changes to the para-fraction have a significant effect on the retrieved helium abundance, we expect that the choice of H 2 -H 2 CIA will also effect the retrieved helium abundance. As we will see in the next section, using the H 2 -H 2 CIA of Fletcher et al. (2018) gives a retrieved He/H 2 that is ∼0.015 larger than when using the CIA of Borysow et al. (1985). Therefore, we   performed helium abundance retrievals for all of the observations using both H 2 -H 2 CIA models. Figure 9 shows the retrieved helium abundances for all observations in Table 1, as functions of the latitude, emission angle, and date of observation, for the H 2 -H 2 CIA coefficients of both Borysow et al. (1985;left column) and Fletcher et al. (2018;right column). Using the H 2 -H 2 CIA of Borysow et al. (1985), the mean and standard deviation of the retrieved helium abundance is He/H 2 =0.0515±0.0073; using the H 2 -H 2 CIA of Fletcher et al. (2018) gives He/H 2 =0.0624±0.0084. Although the standard deviation of the retrieved helium abundance is similar to our estimated uncertainty in the individual retrievals, the two largest identified sources of uncertainty are systematic and would have a similar effect on all data points, indicating that the random error is larger than our estimate of the effects of instrument noise. If we use the observed standard deviation of the retrievals as an estimate of the random uncertainty and add in quadrature with our estimates of the uncertainty due to the retrieval parameters and the methane abundance, we get estimates of He/H 2 of 0.041-0.052 using the Borysow et al. (1985) H 2 -H 2 CIA and 0.051-0.074 using the Fletcher et al. (2018) H 2 -H 2 CIA or an overall range for He/H 2 of 0.04-0.075, corresponding to a range for the mass fraction of helium relative to helium plus hydrogen of Y=0.075-0.13. Because of the nature of the sensitivity of the results to retrieval parameters, this range should not be considered as a formal uncertainty estimate but as a range over which the atmospheric helium abundance is consistent with the CIRS observations used to within the instrumental noise level.

Results
Examination of the latitudinal variation of the retrieved helium abundance (top row of Figure 9) shows a noticeable hemispheric asymmetry. Most of the southern hemisphere retrievals lie below the global mean, while the northern mid-latitude values are above the mean. Calculating separate mean He/H 2 for each hemisphere, using the Borysow et al. (1985) H 2 -H 2 CIA, the northern hemisphere mean is 0.053 6, while the southern hemisphere mean is 0.047 4. A t-test of the null hypothesis that the northern and southern hemisphere data are drawn from distributions with the same mean has a probability of 2×10 −5 , indicating that the hemispheric difference is statistically significant. There is also a small but noticeable slope to the retrieved helium abundance as a function of observation date. However, the variations in latitude and time are interrelated, as Figure 1 shows that most of the data in the last 4 yr of the mission were in the northern hemisphere. As neither a latitudinal nor temporal dependence of the helium abundance is physically realistic, there is likely an unidentified systematic error in the results. The most likely candidate for the unidentified systematic variation is in our assumption that haze opacity can be ignored. Many of the highest retrieved helium values occur at northern midlatitudes after the great 2010-2011 storm, which had a significant effect on the haze and cloud structure at northern midlatitudes (Sánchez-Lavega et al. 2019, and references therein). If haze opacity is nonnegligible in CIRS FP1 data, then our results will overestimate the helium abundance as discussed in Section 2.4.3. Table 2 summarizes the published retrievals of Saturn's atmospheric helium abundance from spacecraft observations. Our results indicate a moderately strong depletion of helium from the protosolar value, and from the helium abundance in Jupiter's atmosphere (0.157 ± 0.003, von Zahn et al. 1998), although it is not as depleted as indicated by the Voyager RSS/ IRIS analysis of Conrath et al. (1984). Our retrieved helium abundance is broadly consistent with the analysis of Cassini VIMS near-IR observations taken in the wake of the 2010-2011 storm (Sromovsky et al. 2016), although our uncertainties are somewhat larger. Despite the large uncertainties in our results, the CIRS observations used are clearly inconsistent with values of He/H 2 0.10, as can be seen from Figure 3. We are thus inconsistent with the helium abundances found from combining Pioneer IRR and RSS data by Orton & Ingersoll (1980), from a reanalysis of Voyager IRIS data by Conrath & Gautier (2000), and from combining Cassini CIRS and UVIS observations (Koskinen & Guerlet 2018).

Discussion and Conclusions
Given the significant difference between the helium abundance retrieved from Cassini CIRS and Voyager IRIS data using similar methodologies, we have reanalyzed one of the Voyager IRIS data sets used by Conrath & Gautier (2000), an average between 30°N and 40°N from the Voyager1 inbound north-south mapping sequence. We performed retrievals of the temperature and hydrogen para-fraction over a range of assumed helium abundances using the spectral range from 230 to 600 cm −1 using the same code and methodology as our retrievals from CIRS data, except that the Voyager2 ingress radio occultation temperature profile (Lindal et al. 1985) was used as the initial guess temperature. Extending the  Voyager data analysis to lower wavenumbers is not possible, because the IRIS wavenumber range did not extend below ∼200 cm −1 , although IRIS did have a better signal-to-noise ratio than CIRS at wavenumbers between 450 and 600 cm −1 . Figure 10 shows the resulting reduced c N 2 as a function of the assumed helium abundance for three values of the retrieval parameter a f p , determining how strongly the hydrogen para-fraction is constrained to the initial guess. For smaller values of a f p (stronger constraint), the minimum residual occurs for He/H 2 of around 0.10-0.11. As the constraint is loosened the retrieved helium abundance increases, becoming consistent with the results of Conrath & Gautier (2000) for a » 0.1 f p , and the minimum becomes shallower. Figure 11 shows the spectral fits for retrievals with a = 0.03 f p for assumed helium abundances of 0.07, 0.11, and 0.15. The fits are comparable to those found by Conrath & Gautier (2000, Figure 6). As found with the CIRS data, there are systematic deviations of the fit that are comparable to, or larger than, the sensitivity of the model spectrum to the helium abundance. A caveat in comparing our results with those of Conrath & Gautier (2000) is that Conrath & Gautier (2000) do not explicitly state what methane abundance they used, if any; as with the CIRS data, reducing the methane abundance increases the helium abundance needed to fit the spectrum. There is a clear discrepancy between the helium abundances inferred from the Voyager IRIS and Cassini CIRS data sets, indicating the presence of an unknown systematic error in one or both data sets.
Although the existing estimates of Saturn's atmospheric helium abundance cover a broad range of possible values, they all indicate a moderate to strong depletion of helium in Saturn's visible atmosphere relative to the protosolar value and also depletion relative to Jupiter's visible atmosphere. The data thus indicate that helium is being sequestered in Saturn's interior and that the sequestration of helium is larger on Saturn than on Jupiter. This is consistent with models for the hydrogen-helium phase diagram and the pressure-temperature profiles in the interiors of Jupiter and Saturn, which indicate that the region of helium separation should be larger in Saturn than in Jupiter (see, e.g., the review by Fortney et al. 2019, and references therein).
Modeling of the structure and evolution of both Jupiter and Saturn by Guillot (1999) and Hubbard et al. (1999) found that current values of the helium mass fraction in Saturn of 0.11Y0.21 (0.06He/H 2 0.13) were required to fit the current luminosity of Saturn along with its gravity field. The Saturn evolution model of Fortney & Hubbard (2003) was able to produce Saturn's current luminosity with atmosphere helium mass fraction Y=0.185 (mole fraction He/H 2 =0.114). Püstow et al. (2016) were able to construct Saturn evolution models leading to a wide range of current atmospheric helium abundances, with helium mass fractions between 0.06 and 0.22. However, many of their models require adjustments to the H 2 -He phase diagram that are inconsistent with the observed helium abundance on Jupiter, and the model presented that is consistent with Jupiter models had Y=0.18 (He/H 2 =0.11). All of these models are consistent with the lower end of the range of atmospheric helium abundances determined from Pioneer (Orton & Ingersoll 1980), Voyager IRIS (Conrath & Gautier 2000), and Cassini UVIS/CIRS (Koskinen & Guerlet 2018), and above the other available determinations. On the other hand, the recent model for the evolution of Jupiter and Saturn by Mankovich & Fortney (2020) required a helium mass fraction Y=0.07±0.01 (He/H 2 =0.036±0.006) to fit the observational constraints with a H 2 -He phase diagram consistent with Jupiter's observed atmospheric helium abundance.
The discrepancies between estimates of Saturn's atmospheric helium abundance from both modeling and remote sensing Figure 10. Reduced c N 2 for temperature and para-fraction retrievals from data averaged between 30°N and 40°N from the Voyager1 north-south mapping sequence (Conrath & Gautier 2000), as a function of assumed helium-tohydrogen mole ratio, for a f p of 0.01 (red circles), 0.03 (blue squares), and 0.1 (green diamonds). Figure 11. Fits to the zonal mean spectrum averaged between 30°N and 40°N from the Voyager 1 north-south mapping sequence, from retrievals of temperature and para-fraction over the spectral range 230-600 cm −1 , for assumed He/H 2 mole ratios of 0.07 (green lines), 0.11 (red lines), and 0.15 (blue lines). The top panel shows the observed brightness temperature (black lines) and the modeled spectra from the retrieved profiles. The bottom panel shows the difference between the observed and modeled radiances; the black dashed lines are the NESR of the zonally averaged spectra.