Ice Giants Study
2014/07/28-30
Maryland, USA
Dynamics of Uranus’ Dusty Rings
H.-W. Hsu, M. Horányi, and S. Kempf
LASP, Uni. of Colorado Boulder, USA
The dynamics of small (µm and sub-µm sized) dust particles in planetary rings are of particular interest because, in addition to gravity, they are also sensitive to various other forces, and
thus are able to illustrate subtle processes that cannot be probed otherwise. Studying the processes that shape planetary rings comprised of small particles provides important constraints
on their sources / sinks, transport processes, as well as clues on the history and evolution of these rings. Here we present preliminary results about the dynamical simulations of Uranus’
dusty rings. Our simulations suggest that micron-sized particles in the recently discovered µ ring need to be either positively charged or highly negatively charged, in order to
remain confined in the observed region (planet-centric distance of 86,000 to 103,000 km). The ultimate goal of this study is to provide a comprehensive theoretical understanding of
the dust environment around Uranus in preparation for in situ dust measurements and dust hazard assessments for future missions.
✜ Equation of motion of a ring particle
md · ad = FG,Sun + FG,U ranus + FEM + FRP + FP R + FGD
𝜙dust = -1O Volt
𝜙dust = +3 Volt
𝜙dust = +10 Volt
3.6
3.4
986-024)
Poynting-Robertson Drag"
Radiation Pressure"
decrease of particle’s semi-major axis
(0.23 km/yr for a µ ring particle [Sfair & Giuliatti Winter, 2009])
adopted β = 0.57
❖ Properties of µ and ʋ rings
Ring
ʋ
µ
Peak Radius
Width
2.62 R
2.59 - 2.73 R
(67,300 km)
(3,800 km)
3.82 R
3.36 - 4.03 R
(97,700 km) (17,000 km)
Peak
5.6
8.5
Showalter & Lissauer, 2006
𝜙dust = -3 Volt
0.4
[Broadfoot et al., 1986]
assuming constant dust charge
Eccentricity
0.5
from Uranus’ exosphere
Electromagnetic Force"
𝜙dust
= -3 Volt
0.6
Gas Drag"
from the Sun & Uranus (J2 included)
Semi-major axis (R U)
3.8
⌦
ng Voyage
r 2 flyby
(1
Gravitational Forces
𝜙dust = +3 Volt
(stable)
µ
0.1
❖ Moons near µ and ʋ rings.
Moon
Orbital distance
ʋ
Size
Portia
2.59 R
135±8km
Rosalind
2.74 R
72±12km
Puck
3.36 R
~162 km
Mab
3.82 R
~25 km
Miranda
5.06 R
472 km
◘1 RU ≃ 25,560 km, is one Uranus radius.
𝜙dust = -3 Volt
(unstable)
Mab’s orbit
0.3
0.2
The equation of motion of test particles starting from Mab’s orbit are
integrated with 4th-order Runge-Kutta method for 100 years. Particles‘
electric charge remains constant through out the simulations. The gravitational
J2 term [Elliot 1982] and the Q3 magnetic field model [Connerney et al., 1987]
of Uranus are adopted. The orbital elements (a, e, i) and the trajectories of
particles with surface potential 𝜙dust of -3, -10, +3, and +10 Volt are shown in
Fig. 1 and 2.
ction duri
4.0
Not considered
Sun’s dire
The color of the recently discovered diffuse rings of
Uranus, the ʋ and the µ rings [Showalter and Lissauer,
2006, de Pater et al., 2007], indicates peculiar dusty
ring dynamics that may be similar to Saturn’s G and E
rings. Red/blue colors indicate board/narrow ring
particle size distributions. While red rings can be
produced and replenished by the ejecta produced
from exogenous material impacts on the embedded
moon(s), the blue ring color most likely indicates
other ring-shaping mechanism(s) that are sizedependent. Investigation of these mechanisms
provides information on the environment as well as
the source of the ring. Here we present preliminary
dynamical analysis of µ ring particles.
✜ Simulation
ʋ
N
✜ Motivation
µ
S
12
Inclination ( )
o
10
8
6
𝜙dust = -3 Volt
4
Fig. 2. Edge-on (85°) profiles of 1 µm dust particles from Mab with
yellow
remains in the vicinity of Mab’s orbits even after 100 years in the simulation. The -3
Volt potential particle, on the contrary, drifts from the initial 3.8 R
eccentric orbit covering 2-6 R
▲
2
0
0
▲
10
20
30
Year
history of
40
50 Year
Fig. 1. Orbital element evolution
1 µm dust particles from Mab’s orbit with various dust surface
potentials (
its eccentricity reaches ~0.5 within 20 years. In other cases, i.e., with positive or much more negative
particles stay close to the Mab’s orbit, which coincides with the location of the recently discovered µ ring.
This shows that the charge-to-mass ratio of ring particles play an important role in
their dynamical evolution. If Mab is in fact the source of the µ ring, considering its tiny
size (25 km) and thus the low probability of current geo-activities, the blue ring color
most likely reflects local electromagnetic/plasma conditions, which may bear significant
diurnal and seasonal variations due to Uranus’ large obliquity and dipole tilt.