The Saturn’s Atmosphere

Ben Wei Peng Lew

May 2, 2017

1 Introduction

Saturn is 9.5 AU away from the Sun. Given a radius of 58000 km (0.84 RJup) and mass of5.68 ×1026kg (0.28MJup), the surface gravity is around 11 kgms−2. It is tilted 26.73 degreeto the orbit with 10 h 32 min 45 s ± 46s rotation period based on the gravitational fieldand oblateness (Helled et al., 2015). The hue yellow color seen in Saturn’ chromosphere ispossibly caused by spectrally featureless hydrocarbon (West et al., 2009). Saturn’s effectivetemperature is around 125 K at 9.5 AU orbital distance from the Sun.The correspondingscale height is kT/µg=43km, where µ ≈ 2 for hydrogen dominated atmosphere.

2 Composition

The 5 most abundant gases in Saturn atmosphere are hydrogen, helium (8% , Fletcheret al. (2007a)), methane (0.45%, Courtin et al. (1984)), ammonia (NH3) (0.05%, Briggs& Sackett (1989)) and ethane (C2H4) (0.0003 %, Courtin et al. (1984)) . The composi-tion of Saturn atmosphere are mainly estimated based on radio occultation and infraredspectroscopy. Radio occultation measures the refractivity of atmospheres as a functionof altitude. Based on the measured refractive index, assumed atmospheric composition(as well as mean molecular mass) and ideal gas law (p= ρkbµ T ), we can know the T(p)profile and corresponding infrared spectra from radiative transfer model. The assumedatmospheric composition is revisited if the estimated infrared spectra does not match withthe observation. The helium to hydrogen mixing ratio that measured by Voyager is under-estimated because of the instrumental systematics. A self-consistent helium-to-hydrogenmixing ratio is measured by Cassini, giving volume mixing ratio [He]/[H2]=0.08 (mass frac-tion of 0.13, or a mole fraction of 0.07) (Gautier et al., 2006) by only considering H2,Heand CH4 (Assume[CH4]/[H2]= 4.86 × 103) in the atmosphere.

The abundance of trace gases is more uncertain due to incomplete understanding ofclouds. By using a series of possible mixing ratio of gases, including continuous absorptioncaused by clouds or haze and pressure-broadened spectral lines, forward radiative transfer

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Figure 1: The infrared spectra calculated based on the T/µ profile measured from radiooccultation method by Cassini.Dougherty et al. (2009)

modeling was used by Courtin et al. (1984) to obtain the best fit of methane, ammonia,ethane, phosphine and other trace gasses’ composition.

3 Temperature Profile

Both radio occultation and thermal infrared spectra can provide indirect measurement ofSaturn’s temperature profile. Thermal infrared spectra of Saturn atmosphere that coversfrom 10 to 1400 cm−1 (1000 to 7 µm) is observed by using Composite Infrared Spectrometer(CIRS) on Cassini. The molecular absorption features that are sensitive to temperatureand pressure are used to infer the temperature at certain pressure level. The most usefulIR features and pressure sensitivities are listed as below (Fletcher et al., 2007a):

• Collision induced continuum features that span from 1-500 cm−1(see also figure 1)that is sensitive to pressure until around 800mbar. In order to get the temperature,the fraction of para-hydrogen has to be known as well.

• Mid-IR (600-680 cm−1) has higher spatial resolution and is used to fine-tune thetemperature profile in 60-200mbar region.

• By assuming methane volume mixing ratio of qCH4 = 4.5×10−3 (Flasar et al., 2005),the blended pseudo-continuum of CH4 emission line in 1250-1350 cm−1 region is usedto update the temperature at around 1mbar region.

Assuming the aerosol (ammonia) haze is evenly distributed from 80 to 1800 mbar witha standard size distribution of 1.0 ± 0.2µm and using pre-tabulated collision-induced ab-sorption (CIA) coefficients of H2 −H2, H2 −He,H2 − CH4, CH4 − CH4 pairs, (Fletcher

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Figure 2: The Saturn and Jupiter Spectra measured by CIRS Cassini (Burrows & Orton,2009)

et al., 2007a) used radiative transfer and non-linear optimal estimation algorithm (Rodgers,1976; Irwin et al., 2004)1 to retrieve the temperature and fraction of para-hydrogen as afunction of pressure. The retrieval method also assumed that the upper limit of lapse rateis the dry adiabat (around −0.78Kkg−1km−1). The temperature profile is relaxed to thea priori(initial guess) of retrieval model whenever no information is provided.

4 Clouds and Haze

[!h] The composition and properties of clouds are normally obtained by fitting spectra orimage with theoretical cloud models, which are highly depend on the assumed number ofcloud layers, particulates size distribution and particle properties. In previous section, theretrieved temperature and composition is mainly from (Fletcher et al., 2007a) based onCassini radio occultation and thermal spectra (CRIS). They compare and explore differentsimple haze layers in their model and concluded that haze model does not have significanteffect to their result (see section 4.3.3 in (Fletcher et al., 2007a)).

Here I choose the latest work done by Sromovsky et al. (2013), which fits the Visualand Infrared Mapping Spectrometer (VIMS) spectra outside of storm of Saturn with 3 lay-

1This algorithm minimize the ”cost function”, which is sum of difference between model and data andthe difference between model parameter and initial guess (a priori):φ = (y − F(x))TS−1

ε (y − F(x)) + (x− a)TS−1x (x− a)

where y is the measured spectrum; F(x) is the spectrum from forward modeling; Sε is a covariance matrix,consist of measurement and modeling errors; x is a state vector, consist of a set of model parameters; ais a priori state vector, consist of the initial guess for forward modeling; Sx is a priori covariance matrix,consist of the assumed error range for each parameter.

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Figure 3: The a priori used for retrieval model from (Fletcher et al., 2007b). The assumedcomposition other than H2, He is shown. They assume He/H2 ratio is 0.135.

Figure 4: The T-P profile retrieved by Fletcher et al. (2007a) based on spectra fromComposite Infrared Spectrometer (CIRS Composite Infrared Spectrometer (CIRS).

ers cloud model. The first two layers are assumed to be formed via condensation process,though the exact composition of cloud layer is not clear. The third layer is stratospherichaze, which is optically thin and thought to be formed via similar process as suggested forJupiter (see Figure 2). Again, (Sromovsky et al., 2013) used slightly different temperature(i.e. Lindal et al. (1985) and composition (e.g., H/He2ratio, CH3D,PH3, NH3) assump-

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Figure 5: The volume mixing ratio used for (Sromovsky et al., 2013). Note that the PH3

mixing ratio decrease slower compare to figure 3

tion. I also include the calculated result at similar pressure level from (Fouchet et al., 2009)and (Perez-Hoyos et al., 2005) for comparison.

4.1 Particulates in upper troposphere

The first two cloud layers suggested by Sromovsky et al. (2013): (i) An optically thick,deep cloud layer obscure most of thermal radiation from deeper layer but still thin enoughto allow 5µm radiation. Cloud model fitting from citetfletcher2011 based on nightside4.1-5 µm VIMS spectra suggest that cloud base resides at 2.5-2.8 bar level globally andadvection raise the cloud base to higher altitude at equator. The composition of cloud ishighly uncertain because of the strong opacity from the gases like PH3 and the overlayingstratospheric aerosol layer.

(ii) A middle cloud layer that extend from around 100-800mbar and have optical depthof 3.5-8.2 at 2 µm. The particulates in this layer are around 0.6µm in radius with refractiveindex of 1.4+0.0i.

Where are ammonia-ice clouds?

Thermodynamics model predict that ammonia ice should exist in Saturn atmosphere (seeFigure 7) but the corresponding spectral feature at 9.4 and 24 µm is not seen in Saturnatmosphere globally but only in giant storm where clouds are freshly formed. Severalfactors could partly explain this, including the overlapping absorption from methane andhydrogen gas, effect caused by non-spherical particulates, broaden and shallow line profile

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Figure 6: The cloud model used by (Sromovsky et al., 2013). The cloud model in text isthe Model C, which gives the best fit to VIMS data.

Figure 7: Thermodynamics model predict that ammonia ice cloud should exist in Saturn’satmosphere. The cloud concentration is the upper limit in gram per liter. Schematicdiagram is adopted from (Atreya & Wong, 2005)

due to larger particle size, or contamination from upper or lower layers. However, Westet al. (2009) reject all the later three factors. Fouchet et al. (2009) suggest it is actuallydiphosphine(P2H4) haze that contribute to the significant opacity at deep layer, but noexamination can be done without measuring the refractive index of diphosphine in lab first.

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4.2 Particulates in stratosphere

(iii) Spectroscopic signatures for hydrocarbon haze, mainly at 3.4 µm, is observed at middlelatitude via stellar occultation method by using Cassini VIMS (Nicholson et al. 2006). Inpolar region, benzene or polycyclic aromatic hydrocarbon (PAHs) could be more abundant.

One of the most important properties of the stratospheric haze is the scattering phasefunction. The particle scattering phase function of Saturn at mid-latitude belt, measuredby Pioneer 11Tomasko & Doose (1984), matches with the lab measurement of scatteringangle of ammonia crystal, suggesting that the size of haze particle must be larger thanvisible wavelength. Strong forward scattering seen from polarization function Tomasko &Doose (1984) also indicates that the haze particle is not spherical but linear shape.

Low UV reflectivity at large reflection angle near the limb of Saturn from Hubble SpaceTelescope (HST) indicates that the haze particle must extend to few millibar otherwiseRayleigh scattering at 10mbar level will cause Saturn’s limb to be brighter than observedvalue (West et al., 2009). Perez-Hoyos et al. (2005) used HST to measure the absolutereflectivity from center to limb in UV and near-IR wavelength region and fitted with two-layer haze models. They concluded that the stratospheric haze particle size is around0.1-0.15 µm, assuming they are spherical (note: this is actually contradict with observedstrong forward scattering) with refractive index of 1.4-1.5. The haze particle is opticallythin, with optical depth ranges from 0.05 at around 0.9µm and 0.7 at 0.2µm.

Figure 8: The photochemical network for the formation of stratospheric aerosols on Jupiter.Similar formation mechanism is seen expected on Saturn except NH3, NH2, N2H4 arePH3, PH2, P2H4 instead respectively.

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5 Spatial and Time Variation of T-P profile

There is significant variation in latitudinal distribution of haze. At polar region (> 70 deg),the UV absorption of haze particle is stronger, implying smaller particle size relative toother region (latitude < 70 deg). The image of equatorial region, especially at wavelengthwhere methane has strong absorption, is seen to be darker than higher latitude region, sug-gesting that haze layer is thicker at lower latitude (West et al., 2009). Using ten years ofHST images, Perez-Hoyos et al. (2005) found that optical thickness of haze at short wave-length (255nm) ,which is most sensitive to stratospheric haze, is positively correlated withthe insolation but the dependance varies at different latitudes. On the shorter timescale(months to 1-2 years) , they noted optical thickness of haze layer can varies at a factor of2, which likely attributed to atmospheric circulation.

Figure 9: Interesting surface feature on Saturn: Upper left: False color image of DragonStorm at 35 deg S in near-infared continuum and methane band filters from Cassini ISSin 2004. Red color is lower cloud tops, blue shades is higher cloud tops and white color isoptically thick haze and clouds. Right: The Great White Storm from HST in 1994. Lower:False color images of a convective storm, which is looked like a inverse question mark, in2008. Figures from Dougherty et al. (2009)

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