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The aerosol single scattering albedo (SSA) is the dominant intensive particle parameter determining aerosols direct radiative forcing. For homogeneous spherical particles and a complex refractive index in- dependent of wavelength, the SSA is solely dependent on size parameter (ratio of particle circumference and wavelength) and complex refractive index of the particle. Here, we explore this dependency for the small and large particle limits with size parameters much smaller and much larger than one. We show that in the small particle limit of Rayleigh scattering, a novel, generalized size parameter can be introduced that unifies the SSA dependence on particle size parameter independent of complex refractive index. In the large particle limit, SSA decreases with increasing product of imaginary part of the refractive index and size parameter, another generalized parameter, until this product becomes about one, then stays fairly constant until the imaginary part of the refractive index becomes comparable with the real part minus one. Beyond this point, particles start to acquire metallic character and SSA quickly increases with the imaginary part of the refractive index and approaches one.
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This content will become publicly available on November 27, 2026
Implications of Shallow‐Shell Models for Topographic Relaxation on Icy Satellites
Abstract Icy satellites host topography at many length scales, from rifts and craters on the small end to equatorial‐pole shell thickness differences that are comparable to these bodies' circumference. The current paradigm is that icy satellites should not host stable small‐scale topography. This idea comes from previous work using a “shallow”‐shell model (i.e., ice shell circumference much larger than shell thickness) with a rigid outer crust. In this limit, large‐scale topography relaxes over a longer time scale than small‐scale features. Here we revisit this paradigm and analyze relaxation of topography starting from the Stokes equations for viscous fluid flow. For a shell with a viscosity that decreases exponentially with depth, we show numerically that there is a regime where the larger viscosity outer crust acts as a nearly rigid boundary. In this case, the relaxation time scale depends on the wavelength. For the largest spatial scales, however, the time scale becomes independent of wavelength and the value is set by the average shell viscosity. However, the spatial scale that this transition occurs at becomes larger as the viscosity contrast increases, limiting the applicability of the scale‐independent relaxation rate. These results for the relaxation of topography have implications for interpreting relaxed crater profiles, inferences of ice shell thickness from topography, and upcoming observations from missions to the outer solar system.
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- Award ID(s):
- 2012958
- PAR ID:
- 10655860
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Planets
- Volume:
- 130
- Issue:
- 12
- ISSN:
- 2169-9097
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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