On the Lorentz Force and Torque of Solar Photospheric Emerging Magnetic Fields

Magnetic flux generated and intensified by the solar dynamo emerges into the solar atmosphere, forming active regions (ARs) including sunspots. Existing theories of flux emergence suggest that the magnetic flux can rise buoyantly through the convection zone but is trapped at the photosphere, while its further rising into the atmosphere resorts to the Parker buoyancy instability. To trigger such an instability, the Lorentz force in the photosphere needs to be as large as the gas pressure gradient to hold up an extra amount of mass against gravity. This naturally results in a strongly non-force-free photosphere, which is indeed shown in typical idealized numerical simulations of flux tube buoyancy from below the photosphere into the corona. Here we conduct a statistical study of the extents of normalized Lorentz forces and torques in the emerging photospheric magnetic field with a substantially large sample of Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We found that the photospheric field has a rather small Lorentz force and torque on average, and thus is very close to a force-free state, which is not consistent with theories as well as idealized simulations of flux emergence. Furthermore, the small extents of forces and torques seem not to be influenced by the emerging AR's size, the emergence rate, or the nonpotentiality of the field. This result puts an important constraint on future development of theories and simulations of flux emergence.