Relationship of the Magnetic-Field Strength and the Brightness of the Sunspot Umbra and the Center of a Facular Knot

Two main features define a sunspot as an object: a strong magnetic field and a low umbra temperature. The same can be said about a facular knot, in the center of which there is a dark micropore, and the magnetic field is several hundred Gauss (which noticeably exceeds the level of equipartition of about 200–250 G), sometimes reaching 1000 or 1200 G. The temperature decrease in these activity elements is explained by the suppression of circulation (overturning) convection by a strong vertical magnetic field. The first to express this idea was Biermann (1941). Within the framework of this conception, a saturation effect should be expected: when the magnetic field completely suppresses convection, its further growth should not lead to a decrease in temperature. There is still no clear answer to the question of the saturation effect. We will try to answer it in the first part of the work according to the Solar Dynamics Observatory. We show that saturation occurs at B = 2300–2400 G. A further increase in the magnetic field of the spot no longer leads to a decrease in the brightness of its umbra. The relationship of the magnetic field and intensity is also manifested in long-period oscillations of the magnetic field of spots. In this case, the brightness of the spot umbra changes in antiphase with its magnetic field (Efremov et al., 2020) in accordance with the theoretical model of a shallow sun spot (Solov’ev and Kirichek, 2014, 2016). A similar effect was established by us in the second part of this work for facular knots: during slow facular oscillations with periods of more than 1 h, its brightness changes in antiphase with a magnetic field. The obtained results convincingly confirm the Birman hypothesis.