The further from Saturn, the bigger Radius: Mimas (198 km), Enceladus (252 km), Tethys (531 km), Dione (561 km) and Rhea (764 km) Enceladus is the source of the E-ring, presence of a plume The further from Enceladus, the darker Albedo geometric at 0.55 m: Mimas (0.96), Enceladus (1.37, 0.99 for Bond), Tethys (1.23, 0.80 for Bond), Dione (0.99), Rhea(0.95) Mainly composed of water ice + an UV absorber: density close to 1
Affecting the scattering properties and/or the chemistry, the structure of the surface, we have: Charged particle (ion and electrons) bombardment: affect the surface chemistry by radiolysis, leading to products that absorb efficiently in the UV but not in the visible (e.g. SO2, O3, H2O2); Bombardment by plasma and energetic electrons have a darkening effect on the surface. Plasma impact the trailing and energetic electrons impact the leading (retrograde motion). Ion bombardment, produce defects in ices (voids and bubbles) and trap gases which can produce spectral absorption features. E ring grain coating/bombardment: have been suggested to have a brightening effect (coating and/or sandblasting) BUT the surface of satellites are UV dark, implying that if E- ring grains dominate the optical properties, then in FUV we are seeing a non-ice component of the E-ring (H2O is bright in UV). Photolysis, breaks up water ice and produces species as H2O2 and O3, O2 Bombardment by incoming dark material (micrometeorites), garden the surface and produce finer particles Exogenic processes
Direction of motion Leading Trailing Mimas Tethys & Dione Leading Trailing Energetic electrons Plasma E-ring grains
The phase angle is the angle between the Sun, the moon and the observer A phase angle of 0˚ represents the full moon. It means that shadows disappear, which increase the brightness of the moon Phase Angle ~ 0˚ 180˚ ~ 90˚
Data sets/Calibration We analyze data in term of reflectance : r = I/F The measured signal depends not only of the albedo but also of the photometric properties of the surface I use solar data measured by SOLSTICE on the SORCE spacecraft on the days of the observations. The background (RTG and other) have been subtracted from the data and then they have been calibrated Usually I sum data on two pixels and average it on several samples (integration time is usually 120 sec)
Spectrum This is a good representation of the spectra of all the icy satellites of the E-ring. We note an absorption band of H2O around 165 nm. The spectrum is very dark at wavelengths shorter than 165 nm. 180 nm is a good wavelength, bright enough to create a phase curve. Disk-average reflectance spectrum of Enceladus at solar phase = 2˚ Hendrix et al., 2010
Tethys disk-integrated phase curve
Dione disk-integrated phase curve
Mimas disk-integrated phase curve
Modeling Hapke model: radiative transfer-based photometric model for light scattering in a semi-transparent porous medium. It is the analytical model that has the widest application to icy surfaces. Buratti model is a combination of the generalized Lommel-Seeliger law and the Lambert’s law. Shkuratov model: semi-empirical description of the photometric function of a surface. It is a useful way to describe the reflectance empirically, but the physical interpretation of the parameters is unclear. It uses fractals to describe roughness, cratering characteristics Lummel-Bowell model takes into account multiple and single scattering but does not include CBOE.
Opposition effect It is the fact that an object appears brighter at very low phase angle. It is a backscattering peak near 0˚ phase angle. The first historical record of it is from an Italian sixteenth- century artist, Benvenuto Cellini. He noted that he often saw a glow around shadow of his head on the grass. Since he did not see it around the shadow of anyone else, he took this as an evidence that he was especially favored by God! 2 mechanisms to explain it: - coherent backscatter and - shadow hiding
Coherent backscatter Backscatter is the reflection of waves back to the direction from which they came. Particles can be smaller or larger than the wavelength. The light is scattered two or more times before exiting the medium at small phase angle (less than 2˚). For every such path another portion of the same wave will traverse the same path within the medium but in the opposite direction. At large phase angle there is not coherence between the two wavelets.
Shadow hiding Shadow hiding consists in particles near the surface that cast shadows on the deeper grains, so the shadows become invisible. The grains must be larger than the wavelength to have shadows. We only take this mechanism into account in our Hapke model. It involves only singly scattered light.
Only Shadow-Hiding Opposition Effect (SHOE) / No coherent backscatter The single scattering function P( ) is the double Henyey-Greenstein function P( ) = [(1 - c) * (1 – b 2 )] / [1 + 2 * b * cos( ) + b 2 ] + [c * (1 – b 2 )] / [(1 – 2 * b * cos( ) + b 2 ) 3/2 ] Hapke model’s parameters: , single scattering albedo b, asymmetry parameter (width of the forward and backward scattering lobes) c, asymmetry parameter (relatives amplitudes of the scattering lobes) , surface roughness fix to 20 deg needs phase angles greater than 90 deg B0, amplitude of the SHOE fix to 0.55 (Verbiscer and Veverka, 1992) h, angular width of the SHOE fix to 0.066 (Verbiscer and Veverka, 1992) B0 and h need phase angles lower than 30 deg Ap, geometric albedo Hapke model
Tethys Hapke model (1800 Å) 2 minima
Hapke model (1800 Å) Leading
Hapke model (1800 Å) The leading hemisphere of Tethys is brighter than the one of Dione. This is logical, Dione being further from Enceladus ad thus receiving a lower E-ring grain flux Tethys and Dione have a leading hemisphere brighter than the trailing. Mimas seems to have a trailing hemisphere brighter than the leading. This is what is expected from the theory showing that E-ring grains have a retrograde motion at the orbit of Mimas. The trailing hemisphere of Mimas has the lowest single scattering albedo and the fewest data points at phase angles less than 50˚ Dione has a asymmetry on the amplitude of its scattering lobes on the trailing hemisphere different from 1, suggesting a forward scattering component We observe a forward scattering peak on each satellite: instrumental effect or physical property? We cannot affirm anything for the opposition parameters due to a lack of data. B0 is a measure of the regolith grain transparency; h is strictly a function of porosity.
Tethys trailing phase functions (1800 Å) These variations of h do not significantly modify the fit of the phase curve A variation of B0 from 0.4 to 0.7 induces the same variations in the phase function h = 0.1 h = 0.04
Derived phase functions (1800 Å) Forward scatterBack scatter P( ) = [(1 - c) * (1 – b 2 )] / [1 + 2 * b * cos( ) + b 2 ] + [c * (1 – b 2 )] / [(1 – 2 * b * cos( ) + b 2 ) 3/2 ]
Geometric albedo Dione is 2.4 times further from Enceladus, than Tethys and Mimas, that are approximately equidistant to the source of the E-ring, the density of the E-ring diminishing with the distance to Enceladus (Verbiscer, 2007).
The forward scatter peak All observations included in these forward peaks was taken during a short period of time, between January, 18 th 2006 and September, 13 th 2006 It is difficult to identify the source of this forward- scattering peak. We have few hypothesis: 1- it could come from the surface 2- from an possible plume (especially on Dione) 3- it could be due to scattering from the E-ring grains 4- it could be a stray light from the Sun close to the FOV. On the ISS data, a stray light influence the data. The signal increase as the camera points closer to the Sun. We need to check UVIS data, looking at spectra when the phase angle is near 160˚ and when there is not objects in the field of view.
A linear superposition of a lunar-like scattering law and a Lambert component that provide an adequate simple representation of the scattering properties For disk-resolved observations: A is a parameter such that for a lunar-like purely single scattering, A = 1 and for a diffuse (Lambert) scatterer A = 0. f( ) is the surface phase function, which express changes in intensity due to factors such as the single particle phase function and mutual shadowing among regolith particles. For disk-integrated observations: ( ) represents the flux normalized to a common distance and scaling for = 0˚ Buratti model (1983)
Summary: UVIS phase curves The first published phase curves in FUV of Mimas, Tethys and Dione Brightening effect of the E-ring: the trailing hemisphere of Mimas is brighter than his leading, and the contrary for Tethys and Dione. In addition, Dione has a geometric albedo lower than the Tethys compatible with its distance from Enceladus Surprising behavior of the trailing hemisphere of Dione We see a FUV forward scattering peak (small but significant) at high phase angle that requires more investigations.
Perspectives/Future work Produce results with the Buratti model Investigate about the forward scattering peak that appear on the phase curves How the bright structures on Dione impact the results ? Rotational correction ? Is the contribution of the coherent backscattering important? Use different versions of the Hapke model. We need more low phase angle data. The data could be available among the disk-resolved data The photometric parameters are inputs for a spectral model in order to investigate the composition and grain size of the icy surfaces.