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The study of the degree of linear polarisation of light reflected by Titan is the subject of original work presented in this thesis (see Section 6.2.5).

Iapetus is Saturn’s third largest moon. Its bulk density of 1.150 _± 0.004 g/cm3 indicates that it is mostly composed of ice material. The rotation of Iapetus is synchronised to the orbital period of Saturn, hence the moon is tidally locked to its parent planet. An interesting observation of Iapetus is that the leading and trailing hemispheres have an albedo contrast from 0.04 on the dark leading hemisphere to 0.39 on the trailing hemisphere [Spencer & Denk, 2010]. There are several theories as to how this albedo di↵erence has arisen. Spencer & Denk [2010] suggest that deposition of material from Saturn’s outer retrograde satellites has resulted in the leading hemisphere having a darker albedo, hence increasing its temperature and sublimation rates of water-ice.

Ejeta et al. [2012] observed the bright side of Iapetus at five di↵erent phase angles, carrying out spectropolarimetry over the wavelength range 400-800 nm, in order to assess the light scattering behaviour of any potential surface water-ice present on Iapetus. The degree of linear polarisation was found to increase with phase angle, from -0.9% at 0.77 to -0.3% at 5.2 . The polarimetric phase function was found to be in agreement with previous studies, and with other solar system bodies with a high albedo, such as the icy Galilean satellites and certain types of asteroid. The study provides an additional line of evidence for the way small solar system bodies with high surface albedos and/or surfaces rich in water ice scatter light.

Enceladus is the sixth-largest moon of Saturn. It has the highest albedo of any object in the solar system, reflecting almost 100% of sunlight incident upon it. This was measured by the Voyager missions in 1981, which established that the high geometric albedo is consistent with snow or ice. In 2005, the Cassini spacecraft completed three close flybys of the moon, and the onboard instruments gathered data indicating that Enceladus is geologically active [Spencer et al., 2006].

The only record of polarimetric study of Enceladus, Rhea, and Dione is from observa- tions carried out from 2010 in theRfilter. The data are presented in Rosenbush et al.

[2015]. The phase curves for Enceladus and Rhea can be seen in Figure 1.4, with each body displaying a negative polarisation branch fairly typical for atmosphere- less bodies at small phase angles. The phase curve of Dione is limited to phase angles of less than 2 , and displays a steeper branch of negative polarisation [see Rosenbush et al., 2015]. Polarimetric studies of Enceladus at higher phase angles would be especially interesting due to the possibility of detecting polarised light resulting from scattering by cryovolcanic ejecta.

Titan is the largest moon of Saturn, and a unique moon of our solar system, because it is the only one with a sizeable atmosphere. When observed polarimetrically from Earth-based telescopes (and thus at small phase angles like for Saturn) the polarisa- tion is positive, whereas other low albedo solid bodies have a negative polarisation in the same phase angle range [West et al., 2015]. This is due to the atmosphere of Titan, inferred by Kuiper [1944] who concluded that Titan must have an atmosphere based on finding gaseous methane in its spectra.

Veverka [1973] found positive polarisation from Titan, and from this result also inferred the presence of an atmosphere, consisting of a thin molecular layer overlying an absorptive cloud deck. The high polarisation was attributed to the overlying molecular layer, which would cause incident light to undergo Rayleigh scattering, resulting in a relatively high degree of linear polarisation. Measurements from space missions have also confirmed these findings from data taken at higher phase angles, but the strong polarisation is thought to be caused by scattering from cloud and haze particles rather than molecules. HST polarimetric observations from 220 nm to 2000 nm have been shown to be consistent with those polarimetric measurements taken at higher phase angles by space instruments [Bazzon et al., 2014].

Pioneer 11 was the first spacecraft to observe Titan’s strong linear polarisation near a phase angle of 90 first reported by Tomasko [1980], followed with a detailed analysis by Tomasko & Smith [1982]. It was found that to account for the observed results the polarisation of the haze particles resulting from single scattering had to be 95% or higher at 90 phase angle at red wavelengths, including photons that were multiply-scattered (which would usually lower overall polarisation). It was noted by Tomasko & Smith [1982] that a vertically homogenous atmosphere consisting of spherical aerosol particles of any refractive index could not account for the high polarisation at any of the observed wavelengths. Attempts were made over the few years that followed to model the optical properties of the haze, but a close enough solution could not be found. Tomasko & Smith [1982] proposed that the di↵erences between red and blue wavelengths could be due to particle sizes increasing with

atmospheric depth.

Following Pioneer 11, the cameras on the two Voyager missions took data for larger phase angles than for Pioneer 11, near 160 . The intensity at these phase angles was found to be too high (known as forward scattering) to be explained by particles of a small enough size to be able to produce high polarisation [Rages & Pollack, 1981]. At these phase angles the intensity is most sensitive to the uppermost layer of aerosol particles, thus photons scattered by particles residing in deeper layers are not registered. Tomasko & Smith [1982] considered this and proposed a model that had larger haze particles at the very top of the haze layer, with radius 0.25µm, overlying smaller particles that produced high polarisation at smaller phase angles. This model atmosphere configuration was found to account for both the high polarisation and high forward scattering, but a microphysical process producing such a particle distribution is thought to be unlikely [West et al., 2015].

West et al. [1983] found the same problem of matching strong polarisation near a 90 phase angle and strong forward scattering when computing models. A more detailed look into possible types of non-spherical particles was made, but none of the non-spherical particle types described in the literature at the time provided a means to account for the observations. Various laboratory experiments were conducted to try and simulate the haze particles of Titan, and these suggested that the particles could be aggregates of small spheres [Bar-Nun et al., 1988].

West & Smith [1991] carried out further models to calculate the optical properties of these types of particles, with a code utilising a method known as the discrete dipole approximation [see Draine, 1988]. A model fit of the Pioneer 11 and Voyager 2 disk-integrated polarisation data was found, with two models of di↵ering aggregate structures. Data were fitted reasonably well with a model atmosphere containing aggregate particles of monomer radius 0.06µm, with smaller particles located near the top of the haze layer. This model fitted the polarisation from the small monomer size and the open structure of the particles, with the strong forward scattering produced by coherent scattering in the forward direction, which was found to be sensitive to the overall size of the aggregate particle [West et al., 2015].

Further models of the aggregated haze considering the microphysical processes in- volved and the particle structure and optical properties were carried out [Cabane et al., 1992, 1993; Rannou et al., 2003; Bar-Nun et al., 2008; Lavvas et al., 2009], with the models evolving in sophistication over the years. Data acquired with the Huygens lander helped to further advance this modelling e↵ort.

biter to study the Saturn system (Cassini) and a probe designed to descend into the atmosphere of Titan (Huygens). As the Huygens probe travelled through the atmo- sphere, polarisation (Stokes F and Q) data were acquired between 160 and 30 km from the surface. The photometric, spectroscopic, and polarimetric measurements that were conducted by the Huygens probe provided a major advancement for the study of the haze on Titan [West et al., 2015]. It was found by Tomasko et al. [2009] that the average haze particle over the probe landing site was made of around 4000 individual monomers with mean radius 0.04±0.01µm at a range of altitudes from 150 km all the way down to the surface.