Properties of sunspot umbrae observed in cycle 24

Aims. There is an ongoing debate whether the solar activity cycle is overlaid with a long-term decline that may lead to another grand minimum in the near future. We used the size, intensity, and magnetic field strength of sunspot umbrae to compare the present cycle 24 with the previous one. Methods. We used data of the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and selected all sunspots between May 2010 and October 2012, using one image per day. We created two subsets of this dataset with a manual tracking algorithm, both without duplication. One contains each sunspot (910 umbrae within 488 spots) and was used to analyze the distribution of umbral areas, selected with an automated thresholding method. The other subset contains 205 fully evolved sunspots. We estimated their magnetic field and the total magnetic flux and discuss the relations between umbral size, minimum continuum intensity, maximum field strength, and total magnetic flux. Results. We find non-linear relations between umbral minimum intensity and size and between maximum magnetic field strength and size. The field strength scales linearly with the intensity and the umbral size scales roughly linearly with the total magnetic flux, while the size and field strength level off with stronger flux. When separated into hemispheres and averaged temporally, the southern umbrae show a temporal increase in size and the northern umbrae remain constant. We detected no temporal variation in the umbral mean intensity. The probability density function of the umbral area in the ascending phase of the current solar cycle is similar to that of the last solar cycle. Conclusions. From our investigation of umbral area, magnetic field, magnetic flux, and umbral intensity of the sunspots of the rising phase of cycle 24, we do not find a significant difference to the previous cycle, and hence no indication for a long-term decline of solar activity