An Upper Limit on Turbulent Viscosity in the Circumjovian Nebula
Abstract
Circumplanetary disks are open, dynamic systems sustained by a meridional circulation that draws gas and dust from the parent nebula along nearly polar streamlines, and ultimately returns some of this material through a viscously driven, in-plane outflow. In such a disk, the water ice line acts as a site of solid-mass accumulation: inward-drifting icy solids sublimate interior to the ice line, the resulting vapor is advected outward by the gas, and recondensation beyond the ice line resets the material to a small Stokes number. The operation of this drift-mediated loop requires the fragmentation-limited Stokes number of the mass-dominant icy aggregates to exceed the equilibrium Stokes number at which the radial drift of solids reverses. Because the former scales inversely with the Shakura-Sunyaev viscosity parameter α while the latter is directly proportional to it, this requirement yields a compact upper bound on the vigor of turbulence in the satellite-forming region. Adopting an actively heated, steady-state circumjovian disk truncated at the tidal radius, we find a marginal bound of α≲ 10−3 for an icy-particle fragmentation threshold of vf≃1 m s−1 - appropriate for cold ice with sticking properties similar to silicate dust. This bound scales linearly with vf, reaching α≲5×10−3 for more adhesive, warm ice (vf≃5 m s−1). The bound carries no explicit dependence on the disk's mass flux, and is set entirely by the local thermal state, pressure gradient, and geometry of the circumjovian nebula.
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BibTeX
@misc{batygin2026upper,
title = {{An Upper Limit on Turbulent Viscosity in the Circumjovian Nebula}},
author = {Konstantin Batygin and Fred C. Adams},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00458},
eprint = {2609.00458},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00458},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Upper Limit on Turbulent Viscosity in the Circumjovian Nebula
AU - Konstantin Batygin
AU - Fred C. Adams
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00458
UR - https://arxiv.org/abs/2609.00458
AB - Circumplanetary disks are open, dynamic systems sustained by a meridional circulation that draws gas and dust from the parent nebula along nearly polar streamlines, and ultimately returns some of this material through a viscously driven, in-plane outflow. In such a disk, the water ice line acts as a site of solid-mass accumulation: inward-drifting icy solids sublimate interior to the ice line, the resulting vapor is advected outward by the gas, and recondensation beyond the ice line resets the material to a small Stokes number. The operation of this drift-mediated loop requires the fragmentation-limited Stokes number of the mass-dominant icy aggregates to exceed the equilibrium Stokes number at which the radial drift of solids reverses. Because the former scales inversely with the Shakura-Sunyaev viscosity parameter α while the latter is directly proportional to it, this requirement yields a compact upper bound on the vigor of turbulence in the satellite-forming region. Adopting an actively heated, steady-state circumjovian disk truncated at the tidal radius, we find a marginal bound of α≲ 10^−3 for an icy-particle fragmentation threshold of v_f≃1 m s^−1 - appropriate for cold ice with sticking properties similar to silicate dust. This bound scales linearly with v_f, reaching α≲5×10^−3 for more adhesive, warm ice (v_f≃5 m s^−1). The bound carries no explicit dependence on the disk's mass flux, and is set entirely by the local thermal state, pressure gradient, and geometry of the circumjovian nebula.
ER -