42.17 Size of Particles and Clumps in Saturnian Rings Inferred from Cassini UVIS Occultations
M. Sremčević, L. W. Esposito, J. E. Colwell
Excess noise in Cassini UVIS occultation data
Fig. 1a: Leo (rev 9)

Fig. 1b: Vir (rev 8)

Correlation length and size of microstructures
Cassini UVIS occultation data of Saturnian rings show excess of noise above the expected Poisson level. The effect was first observed in the Voyager 2 PPS occultation and was attributed to the finite size of ring particles [1]. If the size of the ring particles is comparable to the observed portion of the ring during one integration period (roughly area defined by the sampling interval and Fresnel zone), the fractional area blocked by particles behaves as a stochastic variable. This additional variability increases the noise in the transmitted stellar flux.
Fig. 1 displays measured optical depth (lines ­ arbitrary units: blue UVIS and black Voyager PPS) and excess variance (red diamonds) in two UVIS occultations (both with ingress and egress). The difference in optical depths is real and is due to the different orientation of the self­gravity wakes [2]. The  =
excess variance is defined here as 
/ P
(variance­mean)/mean. For a Poissonian variate the defined excess variance is 0 (e.g. unattenuated stellar flux, or occultation of a ring of fine dust particles). However the occultation data of A ring in Fig. 1 show that the measured variance can be orders of magnitude larger than the mean value. Fig. 
1b displays occultation data for Vir (rev 8). Despite similar measured optical depths and geometrical parameters in ingress and egress, the level of the excess noise is significantly different (see also Fig. 3).

Small scale structure in Leo (rev 9) turnaround
Fig. 3
Fig. 2
Fig. 2: Local ring simulations with self gravity wakes (by Heikki Salo).
The main criticism of the original work by Showalter and Nicholson [1] is that they interpreted the excess variance solely in terms of ring particles' sizes. Clumps of particles or ring microstructure, such as self­gravity wakes (Fig. 2), can as well give rise to additional noise, provided that they are comparable in size with the sampled area during one integration interval. We lifted this shortcoming by developing a new model based on the autocorrelation functions of the ring transparency. The autocorrelation functions can describe both ring particle size distribution and possible microstructures.
In our model the excess variance is given by
2
2
 2=I star
e − 1−e − eff
/area
where is the effective correlation length. In the simplest eff
case of a featureless ring the correlation length would be roughly equal to the size of largest particles.
The results are displayed in Fig 3, where the black line stands for Voyager PPS, while colored lines denote the correlation length from different UVIS occultations.
Small radial structure (100 ­ 300m) in A and B rings Fig. 5a: Sgr (rev 11)

Fig. 5c: Sgr (rev 11)

Fig. 5b: Sco (rev 29)

Fig. 5d: Vir (rev 8) egress

Fig. 4b
Fig. 4a

Leo (rev 9) turnaround point at Rmin=114150km (B ring) has a very fine radial resolution (1600 points within 600m in R around Rmin). Fig. 4 displays Weighted Wavelet Z­transform (WWZ) [3] of the data. The WWZ method can handle unevenly spaced measurements, and it is used here to show period analysis of the UVIS photon counts as a function of radial coordinate (panel 4a; ingress: Rmin­R, egress: R­Rmin), and the azimuthal distance (panel 4b; azimuth=0 corresponds to Rmin). Radial WWZ (Fig. 4a) shows clear signature of a 150m structure, while azimuthal WWZ displays a strong signal of a wavelength increasing towards Rmin.
In order to explain the observed wavelet spectra we have to consider local Keplerian motion of the ring material, which together with the occultation point velocity leads to an effect similar to the Doppler shift. Depending on a cant angle of the ring material wave structure, the observed wavelengths can be shortened or enlarged. Starting from a density peak, the next peak might appear sooner if the ring material moves toward the occultation track, or later if moving away. The only solution which is possible to fit to both radial and azimuthal WWZ in Fig. 4 is a perfectly radial wave structure with a wavelength of 150m (red dotted lines in Fig. 4). Cant angles of the structure as small as 0.1 degree (measured from local azimuthal direction) significantly shift wavelengths and are rejected by the data (green and blue dotted lines). Small scale radial wave structure with wavelengths between 100m and 300m is observed in Cassini UVIS occultations in the inner A ring and throughout the whole B ring (Fig. 5: radial WWZ of the occultation data). Since the wave structure appears at exactly same locations in the rings, and with the same wavelengths (cf. Fig. 5), we conclude that the structures are perfectly radial. Namely the similar “Doppler effect”, as discussed for 
Leo occultation, would imply a changing wavelength of the observed structures for different occultations (e.g. 10 degrees canted structures would have wavelengths shift between 0.2 and 5 of the true value). Summary
Excess variance New analytic solution based on the autocorrelation functions ● Observed autocorrelation length is either size of the largest particles or microstructures or both ● Largest autocorrelation length in the mid A ring
● Different UVIS occultations point to microstructures in A ring ●
A
References
Small scale radial structure Wavelength 100m ­ 300m
● “Doppler shift” effect: structures are perfectly radial ● Inner A ring (9 occultations; optical depth 0.5 – 0.7)
● B ring (lower optical depth 0.5 – 1.5)
● Most likely explanation: viscous oscillatory instability (overstability) in dense rings [4]
●
In the A ring we observe small scale structure at two places in the inner ring: 123150 – 123350km (Figs 5c and 5d, and background image) and 123850 ­ 124800km (with small interruptions). This region of A ring has highest optical depth, however, the structures appear at optical depths of about 0.5 to 0.7, and are observed in all 9 occultations which have sufficiently small scale (radial sampling interval + projected Fresnel zone < 50m).
The structures are observed throughout the B ring, at places of lower optical depths (between 0.5 and 1.5). However, due to the small number of occultations that penetrated B ring and worse signal to noise, we cannot rule out higher optical depths. [1] M. R. Showalter and P. D. Nicholson, Icarus, 87, 285­306, 1990.
[2] J. E. Colwell, L. W. Esposito and M. Sremčević, GRL, 33, L07201, 2006.
[3] G. Foster, AJ, 112, 1709, 1996.
[4] J. Schmidt, H. Salo, F. Spahn and O. Petzschmann, Icarus, 153, 316­331, 2001.
Authors acknowledge Jürgen Schmidt for the idea of a "Doppler effect" in observations of canted self­gravity wakes and many helpful comments.