Poster presented at the Division of Planetary Science Meeting 2018

1. Photometry of Giant Propellers in Saturn’s Rings
Jakayla M. Robinson1, and Matthew S. Tiscareno2
1U of Alabama at Birmingham, Dept of Physics and 2SETI Institute Mountain View, Ca
matt@seti.org jrobin12@uab.edu
11707
a
Close flyby images of giant propellers were obtained by
Cassini during the Ring Grazing Orbit /Grand Finale [1].
The photometry of propellers has previously been
found difficult to interpret [4,5]. We use the lit/unlit
pair of Santos-Dumont images as a “Rosetta Stone” to
determine how the propeller’s photometry follows or
deviates from classic Chandrasekhar theory.
References
[1] Spahn et al. 2018, in Tiscareno and Murray, eds., Planetary Ring Systems (Cambridge
Univ. Press), 157. [2] Tiscareno et al. 2010, ApJL 718, L92. [3] Tiscareno et al. 2018,
Science, submitted. [4] Tiscareno et al. 2008, AJ 135, 1. [5] Tiscareno et al. 2010. AJ 139,
492. [6] Chandrasekhar 1960. Radiative Transfer (Dover). [7] Cuzzi et al. 1984, in
Greenberg and Brahic, eds., Planetary Rings (Univ. Arizona Press), 73.
What is the Cassini Ring Grazing
Orbit/Grand Finale?
During its RGO and GF, the Cassini spacecraft passed very
close to the outer and inner edges (respectively) of Saturn’s
main rings. During these maneuvers, the Cassini ISS camera
executed a series of very high-resolution images of the main
rings [3].
The reflected brightness of Saturn’s rings varies with
wavelength , solar incidence, phase, and ring opening
angles, and radial location due to the scattering properties
of individual ring particles as well as their collective spatial
and size distributions.
Particle clustering in elongated and preferentially oriented
formations fundamentally impacts the observed optical
depth and its dependence on the ring viewing geometry. It
also impacts the strength and shape of the collective near-
forward scattering (diffraction) pattern as well as the
higher order moments of random fluctuations in the
observed signal intensity[7].
What are propellers?
“Propellers” are eponymously-shaped disturbances in Saturn’s
rings centered on embedded moons (see [1] and references
therein). In particular, a handful of “giant propellers,” created
by km-size embedded moons [2], have predominantly
keplerian orbits that have been shown to contain clear but
enigmatic patterns of change as they have been tracked for
over 10 years by frequent Cassini images [1].
Figure 1. The propellers “Blériot” (left)
and “Earhart” (right) as imaged by
Cassini on (respectively) the unlit and lit sides of the rings.
Figure 2. Snapshot of “Stochastic orbital migration of a small
body (propellers) in Saturn's rings” simulation with particles
representing dust and ice.
Investigating propeller photometry
1. Create reprojected versions of both the lit-side and unlit-
side images of Santos-Dumont that are truly comparable at a
pixel-by-pixel level.
For each pixel:
2. Use the lit-side I/F to calculate τ, by inverting Eq. 1.
3. Using the τ from the previous step, along Eq. 2, predict the
I/F of the corresponding pixel in the unlit-side image.
4. Find the ratio between the prediction from the previous
step and the actual I/F in that pixel of the unlit-side image,
and create an array storing the values of this ratio for every
pixel.
Figure 3. By manipulating the sampling rates in the radius and
longitude, the lit- and unlit-side images of Santos-Dumont
were reprojected on identical pixel scales
Figure 4. Propeller “Santos-Dumont” as imaged by Cassini on
the lit (top) and unlit (middle) sides of the rings. (bottom) The
ratio between the unlit brightness as predicted from the lit
side, and as actually measured. All three panels are
reprojected to exactly the same scale.
N
R = Reflection (lit)
T = transmission (unlit)
τ = optical depth ( ring plane
thickness able to block light)
P(α) = phase function for phase
angle α
ϖ0 ≈1 = single-scattering albedo of
a ring particle(unitless, Mie
scattering)
μ = cosine of the emission angle
while
μ′ = cosine of the solar incidence
angle
Observations
In Figure 4c, parts of the propeller that are in the translucent
regime, and all of the continuum ring, have a consistent ratio
between prediction and observation (≈0.3) The parts of the
propeller that are in the opaque regime have a different ratio
(mostly 0.4–0.6, with some points as high as 1.1).
Concluding Remarks
By observing the lit and unlit sides of Santos-Dumont, we can
investigate how brightness correlates to optical depth and
evaluate exactly how empty and opaque regions are different
from each other.
Accretion is a ubiquitous process in galaxies, planets, and
stars. With knowledge of what propellers are and how they
form, we can gain insight into other disk-embedded orbiting
objects similar to protoplanetary disks.
Future work would include gaining further understanding the
differences in ratios in the opaque regions
A Ring
μ
ϖ0
μ′
P(α)
Chandrasekhar[6]
presents the
subject of radiative
transfer in plane-
parallel
atmosphere as a
branch of
mathematical
physics, with its
own characteristic
methods and
techniques
Radiative Transfer Model
Solve for 𝝉
𝑰
𝑭 𝑹
=
𝑷(∝)𝝕 𝟎
𝟒𝝁
𝝁𝝁′
𝝁′ + 𝝁
(𝟏 − 𝒆
−
𝝉 𝝁+𝝁′
𝝁𝝁′
)
𝑰
𝑭
𝟒𝝁
𝑷 𝜶
𝝁′
+ 𝝁
𝝁𝝁′
= ( 𝟏 − 𝒆
−
𝝉 𝝁+𝝁′
𝝁𝝁′
)
𝒆
−
𝝉 𝝁+𝝁′
𝝁𝝁′
= 𝟏 −
𝑰
𝑭 𝑹
𝟒𝝁
𝑷 𝜶
Apply logarithm on both sides
𝒍𝒏 𝒆
−
𝟎 𝝁+𝝁′
𝝁𝝁′
= 𝒍𝒏 𝟏 −
𝑰
𝑭 𝑹
𝟒𝝁
𝑷 𝜶
Multiply
𝝁′+𝝁
𝝁𝝁′ on both sides
𝝉 =
𝝁′
+ 𝝁
𝝁𝝁′
𝒍𝒏 𝟏 −
𝑰
𝑭 𝑹
𝟒𝝁
𝑷 𝜶
Value of 𝝉 represents a data file of values
calculated by the pixel values
And is now applied to solve for (I/F)T
𝑰
𝑭 𝑻
=
𝑷(∝)𝝕 𝟎
𝟒𝝁
𝝁𝝁′
𝝁′ − 𝝁
(𝒆
−
𝝉
𝝁′
− 𝒆
−
𝝉
𝝁)