  We applied automatic identification of sunspot umbrae and penumbrae to daily
observations from the Helioseismic Magnetic Imager (HMI) on board the Solar
Dynamics Observatory (SDO) to study their magnetic flux (B) and area (A). The
results confirm a previously known logarithmic relationship between the area of
sunspots and their maximum flux density. In addition, we find that the relation
between average magnetic flux (Bavg) and sunspot area shows a bimodal
distribution: for small sunspots and pores (A < 20 millionth of solar
hemisphere, MSH), Bavg = 800 G (gauss), and for large sunspots (A > 100 MSH),
Bavg is about 600 G. For intermediate sunspots, average flux density linearly
decreases from about 800 G to 600 G. A similar bimodal distribution was found
in several other integral parameters of sunspots. We show that this bimodality
can be related to different stages of sunspot penumbra formation and can be
explained by the difference in average inclination of magnetic fields at the
periphery of small and large sunspots.

Solar and Stellar Astrophysics