How could Saturn form rings involving the third force of diamagnetic expulsion and the mechanism of magnetic anisotropic accretion

Introduction

We show how Saturn could create rings with the additional action of its magnetic field. Our model of the Saturn's rings origin includes the appearance of additional third force of diamagnetic expulsion of ice particle after emergence of axisymmetric Saturn’s magnetic field and mechanism of magnetic anisotropic accretion. This force of diamagnetic expulsion is acting together with force of gravity and centrifugal one on the particles within protoplanetary cloud. Cassini found 93% of ice in the particles of rings. The rings could have originated from the ice particles moving under the influence of centrifugal force and force of gravity in chaotic orbits around Saturn within protoplanetary cloud after the planet's magnetic field was emerged. After appearing of the force of diamagnetic expulsion of ice particles, all their chaotic orbits start shifting to the magnetic equator plane, where the minimum of magnetic energy of the particles is observed. Every particle on the magnetic equator comes to a stable position, and it prevents its horizontal and vertical shift. The particles are trapped within three-dimensional magnetic well and they form rings structure.  Our model doesn't refute earlier theories, but rather improves them and explains many of the observed phenomena in rings.

 

The origin of Saturn's rings by taking into account the diamagnetism of ice particles and the mechanism of magnetic anisotropic accretion

We follow our paper V. V. Tchernyi, S.V. Kapranov, arxiv.org/abs/2104.03967, May 17, 2021. The problem of the origin of Saturn's rings has no definitive answer.  Existing theories are based upon gravitational defragmentation of massive body approached Saturn or comet tidal disruption (A.I. Tsygan, SovA, 1977; A.M. Fridman, N.N. Gorkavyi, UFN, 1990; S. Charnoz et al, Icarus, 2009; R. M. Canup, Nature, 2010). These scenarios do not explain well how it turns out that the disk of sombrero rings is well constructed with separated particles, their fine structure, etc. The role of Saturn’s magnetic field is unclear. Once compare the ratio of the thickness of the rings to their diameter with the ratio of the thickness of the paper sheet to its length, the relative thickness of the disc of the rings is a thousand times less. It is a challenge that a thin film of ice particles of a huge diameter hangs in outer space. This is an emphasis on the important role of all interactions in the origin of rings, especially those that have not yet been described. It was experimentally determine the ice of the Saturn rings is like ice on the Earth (R. Clark al, Icarus, 2019, 322). Then the ice XI has stable parameters at the temperature of the rings and it is diamagnetic (R.J. Hemley, ARPC, 51, 2000). Our model assumes that after the appearance of Saturn's magnetic field and the force of diamagnetic expulsion of ice particles, the chaotic orbits of all the particles inside the protoplanetary cloud began to shift to the magnetic equator plane and finally formed a system of rings. We call this process magnetic anisotropic accretion due to the axisymmetric magnetic field of Saturn. The gravitational force in the orbit of the particle is balanced by the centrifugal force and the force of diamagnetic expulsion.                                                                                                          

We need to demonstrate how protoplanetary cloud can collapse into a disk of rings (Fig. 1).  

                        

                  a                          b                          c

 Fig. 1. Transformation of Saturn's protoplanetary cloud into a disk of rings after appearance of Saturn’s magnetic field and interaction of it with the iced particles: from (a) >> (b) >> to (c)

We use concept of V. Safronov: Evolution of the protoplanetary cloud and formation of Earth and planets, NASA, 1972. The mathematical solution of our problem is based on the work of V. Cherny and S. Kapranov (ApJ, 2020, May 6, 894, 1). First, we solve the problem of a single diamagnetic spherical particle located in the external gravitational field and magnetic field of Saturn. The equation for the azimuthal angle of the particles is:

We see all orbits of ice particles at the end of their movement entering to magnetic equator plane. The solution ϴ = π/2 accounts for essentially planar structure of Saturn’s rings and their location in the magnetic equator plane. The equation for azimuthal velocity of particles is:

We see the gravity force in the particle’s orbit is counterbalanced by both the centrifugal force and the force of diamagnetic expulsion.

Conclusions

It follows from our solution, in the superposition of the spherically symmetric gravitational field and axially symmetric magnetic field, the orbits of particles finally fall on the magnetic equator plane and formatted rings structure of Saturn. It also explains the essentially planar structure of the rings. Density gradient flow of the magnetic field repels particles of each other and it also cleans the gaps within rings system and forms rigid thin structure of separated rings.

Each particle comes to the stable position at the magnetic equator of Saturn and preventing its own move up or down of it due to minimum magnetic energy at this position. The horizontal displacement of the particles is prevented by the inhomogenity of the magnetic field along the radius.

The force of diamagnetic expulsion from the disk-shaped structure is stronger, and the potential barrier at the magnetic equator is larger. This means high stability of the particles inside the sombrero rings.

The spokes in the B ring have clear explanation due to diamagnetism of the ice particles. The action of magnetic field on diamagnetic particles is stronger the smaller particles size. Small particles coming to the anomalous positions of the magnetic field of Saturn change their position, and we see it as spokes.