Dipolar Magnetic Moment of the Bodies of the Solar System and the Hot Jupiters

TL;DR

This paper develops an empirical formula to estimate the magnetic moments of planets, including Hot Jupiters, based on their mass, rotation, and internal conductivity, providing insights into planetary magnetic fields and atmospheric erosion.

Contribution

It introduces a new empirical relationship for planetary magnetic moments derived from solar system data and applies it to predict magnetic fields of exoplanets like Hot Jupiters.

Findings

Empirical relation fits solar system data well.

Predicted magnetic moment for Hot Jupiters like Osiris.

Explains absence of magnetic fields on Venus and Mars.

Abstract

The planets magnetic field has been explained based on the dynamo theory, which presents as many difficulties in mathematical terms as well as in predictions. It proves to be extremely difficult to calculate the dipolar magnetic moment of the extrasolar planets using the dynamo theory. The aim is to find an empirical relationship (justifying using first principles) between the planetary magnetic moment, the mass of the planet, its rotation period and the electrical conductivity of its most conductive layer. Then this is applied to Hot Jupiters. Using all the magnetic planetary bodies of the solar system and tracing a graph of the dipolar magnetic moment versus body mass parameter, the rotation period and electrical conductivity of the internal conductive layer is obtained. An empirical, functional relation was constructed, which was adjusted to a power law curve in order to fit the data. Once this empirical relation has been defined, it is theoretically justified and applied to the calculation of the dipolar magnetic moment of the extra solar planets known as Hot Jupiters. Almost all data calculated is interpolated, bestowing confidence in terms of their validity. The value for the dipolar magnetic moment, obtained for the exoplanet Osiris (HD209458b), helps understand the way in which the atmosphere of a planet with an intense magnetic field can be eroded by stellar wind. The relationship observed also helps understand why Venus and Mars do not present any magnetic field.