The Maximum Magnetic Flux in an Active Region

George Livadiotis, Xenophon Moussas

Department of Astrophysics, Astronomy and Mechanics, Faculty of Physics, National University of Athens, Panepistimiopolis, GR15784, Zografos, Athens, Greece

The Photometric-Magnetic dynamical model (G. Livadiotis and X. Moussas, Physica A 379 (2007) 436) handles the evolution of an individual sunspot as an autonomous nonlinear, though integrable, dynamical system. One of its consequences is the prediction of an upper limit of the sunspot areas. This upper limit is analytically expressed by the model parameters, while its calculated value is verified by the observational data. In addition, by considering an upper limit for the magnetic strength inside the sunspot, we conclude in the following significant result: The upper limit of the total magnetic flux in an active region is found to be of about 7.23 1023 Mx, namely equal to the magnetic flux concentrated in the totality of the granules of the quite Sun, having a typical maximum magnetic strength of about 12G. Therefore, the magnetic flux concentrated in an active region cannot exceed the magnetic flux concentrated in the photosphere as a whole.