Observations of magnetic A, B and O stars show that the poloidal magnetic flux per unit mass has an upper bound of 10^-6.5 G cm^2/g. A similar upper bound is found for magnetic white dwarfs even though the highest magnetic field strengths at their surfaces are much larger. For magnetic A and B stars there also appears to be a well defined lower bound below which the incidence of magnetism declines rapidly. According to recent hypotheses, both groups of stars may result from merging stars and owe their strong magnetism to fields generated by a dynamo mechanism as they merge. We postulate a simple dynamo that generates magnetic field from differential rotation. The growth of magnetic fields is limited by the requirement that the poloidal field stabilizes the toroidal and vice versa. While magnetic torques dissipate the differential rotation, toroidal field is generated from poloidal by an Omega dynamo. We further suppose that mechanisms that lead to the decay of toroidal field lead to the generation of poloidal. Both poloidal and toroidal fields reach a stable configuration which is independent of the size of small initial seed fields but proportional to the initial differential rotation. We pose the hypothesis that strongly magnetic stars form from the merging of two stellar objects. The highest fields are generated when the merge introduces differential rotation that amounts to critical break up velocity within the condensed object. Calibration of a simplistic dynamo model with the observed maximum flux per unit mass for main-sequence stars and white dwarfs indicates that about 1.5×10^-4 of the decaying toroidal flux must appear as poloidal. The highest fields in single white dwarfs are generated when two degenerate cores merge inside a common envelope or when two white dwarfs merge by gravitational-radiation angular momentum loss.
Date added: Fri, 11 Oct 13