S IZE OF PARTICLES AND C LUMPS
IN S ATURNIAN R INGS I NFERRED
FROM C ASSINI UVIS O CCULTATIONS
DPS meeting, Cambridge, UK, September 9, 2005
Miodrag Sremčević
Larry W. Esposito
Josh E. Colwell
LASP, University of Colorado at Boulder
M. Sremčević et al.: UVIS S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
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Excess variance
hk2i − hki2
hki
D ring
hk2i − hki2
hki
Inner A ring
DPS meeting, Cambridge, UK, September 9, 2005
M. Sremčević et al.: UVIS S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
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Showalter & Nicholson (1990)
• Particle size comparable with Fresnel zone → excess variance
• Problems:
? Not well defined boxes (diffraction pattern?)
? Ring microstructure (clumps, wakes, ...)?
DPS meeting, Cambridge, UK, September 9, 2005
M. Sremčević et al.: UVIS S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
4/8
New analytic solution
k — number of detected photons at UVIS (PPS),
k
f (k) = exp [−I?∆tP] (I?∆tP) /k!
RR
P — ring transparency, P = area p(x, y)dxdy,
p(x, y) is 0 or 1 giving hPi = e−τ
Excess variance is: ∆σk2 = hk2i − hki2 − hki
RR
2 −τ
2
−τ 1
∆σk = (I?∆t) e (1 − e ) area area dwxdwyCpp(wx, wy)
Cpp(wx, wy) is autocorrelation function of the ring
transparency.
DPS meeting, Cambridge, UK, September 9, 2005
M. Sremčević et al.: UVIS S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
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UVIS & PPS autocorrelation length λ — A ring
DPS meeting, Cambridge, UK, September 9, 2005
M. Sremčević et al.: UVIS S TELLAR O CCULTATIONS
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R ING S TATISTICS
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N-body simulations – autocorrelation function
(Simulation by G. Stewart & J. Weiss, LASP, University of Colorado)
Autocorrelation function ≈ tilted ellipsoid with axes (λ 1, λ2)
√
→ observed autocorrelation length λeff = λ1λ2
DPS meeting, Cambridge, UK, September 9, 2005
M. Sremčević et al.: UVIS S TELLAR O CCULTATIONS
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R ING S TATISTICS
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Spica occultation – deeper analysis
Spica Ingress Hphi=20 degreesL
1
lambda1lambda2=1
0.8
0.6
0.4
lambda1lambda2=5
0.2
20
40
60
phi @degreesD
80
lambdaHsimple_modelLSQRTHlambda1*lambda2L
lambdaHsimple_modelLSQRTHlambda1*lambda2L
Very small Fresnel zone: sample box comparable in size with λ eff !
Spica Egress Hphi=80 degreesL
1
lambda1lambda2=1
0.8
0.6
lambda1lambda2=5
0.4
0.2
20
40
60
phi @degreesD
80
Autocorrelation ellipsoid (λ1, λ2) with λ1/λ2 > 1 easily explains λeff
profiles for Spica.
DPS meeting, Cambridge, UK, September 9, 2005
M. Sremčević et al.: UVIS S TELLAR O CCULTATIONS
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R ING S TATISTICS
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Conclusions
• New analytic solution based on
the autocorrelation functions.
• Observed autocorrelation length λeff is size of
the largest particles or size of the microstructures.
• A ring: highest autocorrelation length in the middle
(λeff ≈ 10 − 12 m).
• Different UVIS occultations point to microstructures,
√
rather than uniformly distributed particles (λeff = λ1λ2).
• For a better fit of (λ1, λ2) we need more
stellar occultations closer to rings.
DPS meeting, Cambridge, UK, September 9, 2005