Electromagnetic waves in a homogeneous medium

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Icy satellite microwave observations

Both active and passive microwave observations have been conducted throughout the Solar System, as described in Sections. 2.3.1 and 2.4.1. This section focuses on studies of Jupiter’s and Saturn’s icy satellites from ground-based and spacecraft radars and radiometers. Although this thesis concentrates on the satellites of Saturn, it is important to review the microwave properties of the Jovian icy satellites (Europa, Ganymede, and Callisto), which have been observed from ground-based radars and radiotelescopes on more occasions than the Saturnian satellites. These observations have led to new models of radar backscatter.

Icy Galilean satellites: radiometry observations

Passive radiometry measurements of the brightness temperatures of the icy Galilean satellites (by increasing distance from Jupiter: Europa, Ganymede, and Callisto) have been conducted at multiple μm–cm wavelengths, and are plotted in Fig. 2.13 (Ulich et al., 1984; de Pater et al., 1989; Muhleman and Berge, 1991, and references therein). The brightness temperature visibly decreases as the observation wavelength increases. Although the longest wavelengths are expected to probe deeper than the diurnal thermal skin depth and therefore to exhibit lower temperatures (for daytime observations), this effect alone is insufficient to explain the low mm–cm values of TB, especially on Europa and Ganymede (de Pater et al., 1984). Estimating the effective physical temperature with a simplified (temperature equilibrium) model yields low emissivities, around 0.5–0.8, for Europa and Ganymede at mm–cm wavelengths (Muhleman and Berge, 1991; Trumbo et al., 2018), to be compared with the emissivity of 0.8–0.95 of most terrestrial surfaces.
Similarly low microwave emissivities have been reported on other icy bodies, more specifically Trans-Neptunian Objects TNO) (Fornasier et al., 2013; Lellouch et al., 2017b; Brown and Butler, 2017) including Pluto and Charon (Lellouch et al., 2000, 2016), comets (Boissier, J. et al., 2011), and thick snow and lake ice on Earth (Wiesmann et al., 1998; Hewison and English, 1999). Low asteroid sub-millimeter to millimeter emissivities have also been detected (e.g., Redman et al., 1998; Gulkis et al., 2010), but for most asteroids (except perhaps Vesta; Redman et al., 1992; Leyrat et al., 2012) this likely results from large dielectric constants, surface roughness, and subsurface sounding of colder night-time temperatures (Keihm et al., 2013). This explanation remains insufficient for Earth snow and TNOs, as for the Galilean satellites (Lellouch et al., 2016, 2017b). Instead, the preferred explanation is subsurface scattering, by subsurface voids or inhomogeneities on scales comparable to the wavelength (see Section 2.2.5).
For the Galilean satellites, the low microwave emissivities are most likely caused by buried mm–cm-sized scattering inhomogeneities; because of their size, these scatterers affect more centimetric than millimetric wavelengths. It is also possible that the top few mm of the surface probed at shorter (submillimeter) wavelengths are smoother and more uniform than greater depths probed at centimeter wavelengths, where the scattering inhomogeneities would be buried (Muhleman and Berge, 1991; Wiesmann et al., 1998). It is likely that these subsurface inhomogeneities also cause the Galilean satellites’ unusual radar properties (discussed below), as high radar reflectivities are generally associated with low emissivities (Eq. 2.32; de Pater et al., 1984; Muhleman and Berge, 1991).

Galilean satellites: radar observations

The Arecibo (13 cm and 70 cm) and Goldstone (3.5 cm) radar systems are the only two radar systems powerful and sensitive enough to observe outer Solar System satellites. The resulting radar properties of the three outer Galilean satellites (Europa, Ganymede, and Callisto) have been assembled by Ostro et al. (1992) and Ostro et al. (2006) and are summarized in Table 2.2.
Table 2.2 – Radar properties of icy satellites, summarized from Ostro et al. (2006, and references therein) for the Galilean satellites, Lorenz and Lunine (1997) and Black et al. (2011) for Titan, Black
et al. (2004) for Iapetus, and Black et al. (2007) for Saturn’s other icy satellites. LH and TH indicate The radar properties of the icy Galilean moons were quickly recognized as anomalous (e.g., Campbell et al., 1978). Their circular polarization ratios μC are indeed considerably higher (> 1) than those of rocky regoliths (μC ∼ 0.1 − 0.4). Furthermore, compared to the commonly encountered reflectivity of 0.1 in the inner Solar System, their surfaces show very high total power albedo. The radar albedo increases from Callisto, to Ganymede, and to Europa (see Table 2.2), with the highest radar return correlated to the youngest and most ice-rich surfaces (Ostro et al., 1992; Black et al., 2001a). Although the circular polarization ratios are high both at 3.5 to 70 cm wavelengths, this is not true for the reflectivity, which decreases at 70 cm, indicating that the mechanism that causes it is less active at this wavelength. The returned radar echoes also follow a diffuse scattering law, exhibiting no quasi-specular reflections.
Similar radar properties (high reflectivities and circular polarization ratios) have been observed within the icy permanently shadowed craters at Mercury’s poles (Harmon et al., 2001; Harcke, 2005), the polar ice caps of Mars (Muhleman et al., 1991; Butler, 1993), the Greenland ice sheet (Rignot et al., 1993; Rignot, 1995), and high-altitude ices (Haldemann and Muhleman, 1999). Although these four environments differ in their temperatures, atmospheric properties, and erosion processes, they have in common a water ice composition. It is therefore likely that different ice modification processes (e.g., melting/refreezing, thermal stresses, seasonal layering…) lead to common radar properties.
A variety of subsurface properties and structures have been suggested as the cause for the Galilean moons’ unusual radar properties, but none is fully satisfactory. Surface scatterers such as hemispherical craters (Ostro and Pettengill, 1978) or randomly oriented facets (Goldstein and Green, 1980) are an unlikely explanation for a high-transparency medium like water ice. Instead, buried craters have been theorized by Eshleman, 1986, but would not lead to the observed radar properties (Baron et al., 2003). Hagfors et al. (1985, 1997) proposed that the incoming signal was being refracted (rather than reflected) by subsurface meter-sized lenses of higher refractive index (due to higher density and/or presence of powdered silicates); however, it remains unclear how such structures would form in sufficient numbers (Baron et al., 2003). Multiple reflections on solid ice pipes and ice layers within a snowy medium, forming from seasonal melt, are a good explanation for the radar properties within the Greenland ice sheet and high-altitude ices, but would not form at icy satellite surface temperatures (Rignot et al., 1993; Rignot, 1995; Haldemann and Muhleman, 1999).
The mechanism which best reproduces the Galilean satellites’ radar behavior (high radar brightness, diffuse scattering, and high circular polarization ratio) is the Coherent Backscattering Effect (CBE), described in Section 2.2.5 (Hapke, 1990; Peters, 1992; Black et al., 2001b). Ganymede and Callisto’s radar properties are consistent with 2% and 5% volume fractions of such scattering inhomogeneities in their subsurface. Europa’s high radar albedo, however, requires a scatterer volume density as high as 80% (Black et al., 2001b). The drop in radar reflectivity from 13-cm to 70-cm observations indicates that the scattering inhomogeneities are more numerous at cm scales than at decimeter or meter scales, supporting the power-law size distribution proposed by Black et al. (2001b). However, the CBE does not predict the specific shape and formation mechanism of these subsurface inhomogeneities.

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Table of contents :

Introduction
1 Saturn’s icy satellites: discovery and exploration 
1.1 First discoveries
1.2 Spacecraft exploration
1.2.1 Before Cassini
1.2.2 The Cassini-Huygens mission
1.2.3 After Cassini
1.3 A variety of worlds
1.4 Outer system satellites: Phoebe, Iapetus, and Hyperion
1.4.1 Phoebe
1.4.2 Iapetus
1.4.3 Hyperion
1.5 Inner mid-sized icy satellites
1.5.1 Rhea
1.5.2 Dione
1.5.3 Tethys
1.5.4 Enceladus
1.5.5 Mimas
1.6 Inner icy satellite formation and age
1.7 Icy satellite surface processes
1.8 Conclusion
2 Microwave remote sensing: from theory to icy satellite observations 
2.1 Principles of microwave remote sensing
2.1.1 Advantages of microwave remote sensing
2.1.2 Radar/radiometer antennas
2.2 Interactions of microwaves with matter
2.2.1 Medium electromagnetic properties
2.2.2 Electromagnetic waves in a homogeneous medium
2.2.3 Wave reflection and transmission
2.2.4 Wave scattering
2.2.5 Subsurface scattering
2.3 Radars for planetary exploration
2.3.1 Types of radars used in planetary exploration
2.3.2 Fundamental radar equation
2.3.3 Radar albedo
2.4 Microwave radiometry
2.4.1 Planetary exploration with microwave radiometry
2.4.2 Thermal emission from a surface and near subsurface
2.4.3 Microwave radiometers
2.5 Icy satellite microwave observations
2.5.1 Icy Galilean satellites: radiometry observations
2.5.2 Galilean satellites: radar observations
2.5.3 Galilean satellites: future microwave exploration
2.5.4 Titan radar/radiometry observations
2.5.5 Saturn’s icy satellite radar/radiometry observations
3 Saturn’s icy satellites seen by the Cassini radar 
3.1 The radar/radiometer on the Cassini spacecraft
3.1.1 Characteristics
3.1.2 Observation strategy
3.1.3 Observation geometry recalculation
3.2 Distant radar observations: Disk-integrated radar albedos
3.2.1 Observations and derivation of the disk-integrated radar albedo
3.2.2 Results
3.3 Resolved radar observations: scatterometry
3.3.1 Observations
3.3.2 Data reduction
3.3.3 Results
3.4 Interpretations
3.4.1 Radar albedo and water ice purity
3.4.2 Interactions with Saturn’s E ring
3.4.3 Structure of the regoliths
4 Saturn’s icy satellites seen by the Cassini radiometer 
4.1 Observations
4.2 Calibration
4.2.1 Radiometry calibration
4.2.2 Removal of the far sidelobe contribution
4.2.3 Determination of the baseline offset
4.2.4 Pointing and time offset correction
4.2.5 Measurement uncertainties
4.3 Preliminary analysis: disk-integrated temperatures
4.3.1 Extraction of disk-integrated temperatures
4.3.2 Results
4.4 Towards a resolved analysis: deconvolution
4.4.1 Deconvolution method
4.4.2 Deconvolution results
4.5 Conclusion
5 Simulation of microwave radiometry observations 
5.1 Thermal model
5.1.1 Incident flux
5.1.2 Derivation of the temperature profile below the surface
5.1.3 Model parameters
5.1.4 Model outputs
5.2 Radiative transfer model
5.2.1 Model hypotheses
5.2.2 Calculating the effective temperature Te f f
5.2.3 Model parameters
5.2.4 Numerical application
5.2.5 Model outputs
5.3 Emissivity model
5.3.1 Combined emissivity-backscatter model
5.3.2 Model parameters
5.3.3 Application to Rhea, Dione, and Iapetus
5.4 Simulating the antenna temperature
5.4.1 Obtaining the brightness temperature
5.4.2 Convolution with the beam pattern
5.4.3 Data fitting method
5.4.4 Deriving subsurface thermal, physical, and compositional properties
5.4.5 Application to Rhea, Dione, and Iapetus
5.4.6 Model limitations
5.5 Conclusion
6 Derivation of thermal, physical, and compositional subsurface properties from Cassini radiometry 
6.1 Disk-integrated emissivities
6.1.1 Method
6.1.2 Application to Iapetus
6.1.3 Application to Enceladus
6.1.4 Application to Dione
6.1.5 Application to Rhea
6.2 Thermal, structural, and compositional properties of Rhea’s subsurface
6.2.1 Method
6.2.2 Results
6.2.3 Interpretations and discussion
6.2.4 Summary and conclusion
6.3 Preliminary results for Dione
6.3.1 Method
6.3.2 Results
6.3.3 Preliminary interpretations
6.4 Preliminary results for Iapetus
6.4.1 Method
6.4.2 Results
6.4.3 Preliminary interpretations
6.5 Conclusion
7 Radiotelescope observations of Iapetus and Phoebe 
7.1 The hemispherical dichotomy of Iapetus in the microwaves
7.1.1 Radar observations
7.1.2 Ground-based microwave radiometry
7.1.3 Iapetus ground-based radiometry: pre-existing observations and interpretations
7.1.4 Outstanding questions and motivations for the present study
7.2 Disk-integrated observations of Iapetus from the IRAM 30 meter telescope
7.2.1 The NIKA2 camera on the IRAM 30-meter telescope
7.2.2 Observation strategy
7.2.3 Calibration and flux derivation
7.2.4 Results
7.3 Observations of Iapetus and Phoebe from the VLA
7.3.1 The Karl G. Jansky Very Large Array (VLA) interferometer
7.3.2 Observations and calibration
7.3.3 Results
7.4 Discussion and interpretations
7.4.1 The LH and TH microwave spectra of Iapetus
7.4.2 Comparison with a thermal model
7.4.3 Emissivity variations with wavelength
7.5 Conclusion and perspectives
7.5.1 Future observations
7.5.2 Towards a resolved analysis of VLA observations
7.5.3 Need for a multi-layer thermal model
7.5.4 Emissivity modeling
Conclusion and perspectives
Bibliography 

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