HSP S TELLAR O CCULTATIONS
AND R ING S TATISTICS
July 27, 2005
Miodrag Sremčević
Larry W. Esposito
Josh E. Colwell
LASP, University of Colorado at Boulder
M. Sremčević et al.: HSP S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
2/10
Excess variance
D ring
Inner A ring
UVIS team meeting, July 27, 2005, Berlin
M. Sremčević et al.: HSP S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
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Physics of stellar occultations
√
• Fresnel zone dFZ = Dλ
directly transmitted photons
2d S
2dFZ
• Forward scattered photons from
zone dS ≈ Dλ/R, dS > dFZ
• Smear
dsm = V ∆t
• HSP (PPS) signal
hki = I?∆t exp[−τ/µ] + IB∆t
I? – star signal, IB – background, µ = cos α
ring
plane
D
HSP
• Variance σk 2 = hki?
UVIS team meeting, July 27, 2005, Berlin
M. Sremčević et al.: HSP 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:
? Ill defined boxes.
? Ring microstructure (clumps, wakes, ...)?
UVIS team meeting, July 27, 2005, Berlin
M. Sremčević et al.: HSP S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
5/10
New analytic solution
k — number of detected photons at HSP (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 autocovariance function of the ring
transparency.
UVIS team meeting, July 27, 2005, Berlin
M. Sremčević et al.: HSP S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
6/10
Uniformly distributed particles
2D power-law size d., tau=80.05, 0.25, 0.5, 1., 1.5, 2.<
1
autocorrelation
CpHwL
0.8
0.6
0.4
0.2
0.2
∆σ ≈ (I?∆t) e
2
2 −τ/µ
0.4
1−e
0.6
w  H2 RL
0.8
1
−τ/µ πR
2
eff
Lx Ly
UVIS team meeting, July 27, 2005, Berlin
M. Sremčević et al.: HSP S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
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HSP & PPS autocorrelation length — A ring
UVIS team meeting, July 27, 2005, Berlin
M. Sremčević et al.: HSP S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
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Gravitational wakes — toy model
0.25
0.2
0.15
20
40
60
80
100
120
0.05
UVIS team meeting, July 27, 2005, Berlin
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AND
R ING S TATISTICS
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Conclusions
• New analytic solution based on the autocovariance
functions.
• A ring: highest autocorrelation length in the middle.
• Different HSP occultations point to microstructures, rather
than uniformly distributed particles.
• To be done:
? Incorporate diffraction pattern.
? Fit non-isotropic autocorrelation lengths (λ1, λ2) from
all HSP occultations
? Explore wakes/clumps toy models
UVIS team meeting, July 27, 2005, Berlin
M. Sremčević et al.: HSP S TELLAR O CCULTATIONS
AND
R ING S TATISTICS
10/10
UVIS team meeting, July 27, 2005, Berlin