Overview: Magnetic Field for Jupiter and Neptune Class exoplanets

Dynamo is the process by which a planetary magnetic field is generated through the movement of electrically conductive materials within the planet's interior. The dynamo region is identified based on the magnetic Reynolds number.

At the top of this region, the maximum magnetic field is 

 where 𝑞0 is the reference convective flux, ⟨𝜌⟩ is the average density,

𝐹 is an efficiency factor that accounts for all radially varying features of the dynamo region, and is calculated as 

where 𝐻T(𝑟) is the temperature length scale given by

 𝑃(𝑟) is the pressure, 𝑔(𝑟) the gravitational acceleration, and ∇adv the adiabatic, logarithmic gradient of temperature over pressure.

The convective flux 𝑞c is

𝑣conv the velocity of convective motions, and 𝛿 is the derivative of ln 𝜌 with respect to lnT.

Re mag is a non-dimensional quantity that measures the effects of convection against magnetic diffusion. 

As per study, for Jupiter and Neptune class planets, Magnetic field decay occurs because as planets age, they cool down and their luminosities and their convective flux become gradually weaker. Higher atmospheric envelope fractions cause more material available for convection, which yields stronger magnetic fields and extends the dynamo region.

 The field strength reduces for extremely irradiated planets because they have lower average density. The surface magnetic field decreases past the threshold value as orbital separation (distance between the exoplanet and its host star) further increases.

The magnetic fields could be observable in the radio wavelengths via auroral emission using ground based observations.

Jupiter-class planets have magnetic fields large enough to generate radiation whose peak frequency exceeds the Earth’s ionospheric cutoff. The same occurs for the Neptune-class planets  if they have  𝑀 > 15 𝑀⊕ and 𝑓env> 4%.

For hot jupiter class planets, atmospheric evaporation does not affect magnetic field generation. For hot Neptunes, atmospheric evaporation leads to greater mass loss and causes less material for convection, so they produce weaker magnetic fields. 

Source: https://arxiv.org/html/2411.00674v1