An astrophysical Dynamo is a mechanism by which a body transforms thermal and Kinetic Energy into electrical energy and through it, generates and maintains Magnetic Fields. It is analogous to an artificial mechanical dynamo, a type of electric generator, but rather than a mechanical commutator, electricity is carried by fluids that are moving and conduct electricity. The body must be spinning and carry a conducting fluid. The mechanism follows the rules of Magnetohydrodynamics.
There exists a "chicken-and-egg" issue: electrical current is generated by a conductor moving through a magnetic field, which, in turn, is formed by the electrical current. Starting the process only requires that a weak magnetic field be present, e.g., a weak magnetic field surrounding it.
The Earth's magnetic field is maintained by such a dynamo (the Geodynamo), with molten Iron in the core being the conducting fluid. The Sun also has such a dynamo (Solar Dynamo), its gaseous interior being a conductor. Other stars, planets, as well as galaxies are thought to maintain magnetic fields through the dynamo mechanism. I assume the sun's magnetic field could "seed" the Earth's dynamo, but I'm not sure how magnetism was first triggered in the solar dynamo: perhaps by convection including ions.
The presence of a Magnetic Field around a Rocky Planet or Moon implies the presence of a dynamo, implying a Molten Core, Convective Mantle and Plate Tectonics. Such convection, in turn, is a sign of World Cooling, e.g., from residual heat or from an active energy source such as radioactivity or Tidal Forces.
Interplanetary Medium (IPM)
Rossby Number (Ro)