Covariation of solar granulation size and sunspot indices in activity cycle 24

New theoretical arguments and empirical evidence for correlated changes in sun granulation size and sunspot indices were obtained during this two-year study using blue continuum image data acquired by the Hinode solar optical telescope in 2006-2016 and simultaneous time series of daily sunspot numbers (SSN) and areas (SSA). An original set of simple scaling equations linking the relative variation in the average size of granular cells to the sum change in the total number of granular cells, SSA and surface gravity was written under the assumption that at the height of the blue continuum formation, the entire surface of the Sun is the sum of the areas of granular cells, pores and sunspots. The magnitudes of relative changes in the horizontal size of granular cells due to variations in global solar parameters were estimated and it was shown that variations in the SSA have the dominant influence on variations in the mean granular size. Periodic spurious changes in the mean granular size due to the sun's variable tilt with respect to the telescope and apparent changes in rotational speed and surface gravity were also mentioned.

Our empirical research focussed on the automatic identification and precise morphometric measurements of granular cells in high-resolution Hinode images using an efficient marker-controlled watershed segmentation algorithm. A total of seven image sequences with a 30-, 27- and 1-day cadence, all of which contained 840 images, were compiled, processed and corrected with regard to the variable sun-earth distance and heliographic coordinates. The resultant granulation parameters, including mean area, equivalent diameter, extent and contrast were compared to SSN and SSA data using temporal cross-correlation. An essential anti-correlation was measured between the mean size of granular cells and the daily SSN for the medium time intervals of four months, which were characterized with the optimal orbital conditions for the imaging of solar granulation. The decrease in the cellular scale by 3% with the increase in the average SSN index of 20%, was revealed for both ascending and descending phases of the 24^th activity cycle, while the average contrast characterizing image quality remained almost unchanged. The approximately 14-day delay in the cause-effect relationship between the SSN and the granulation scale was revealed and a plausible explanation for this delay was given.

In the quiet sun at the disk centre, the mean equivalent diameter of granules was measured at 1.37 arcseconds, while the same parameter for granular cells was given as 2.06 arc seconds, which was in good agreement with the results of other researchers. In the close vicinity of sunspots, the mean size of granular cells decreased by a few percent, while the width of intergranular lanes decreased by 60%, indicating the existence of bright rings with higher temperatures around these sunspots. The significance of all these observations is that they confirm the results of the predecessors, positively support the 70-year-old hypothesis about the dependence of granulation properties on the sunspot cycle, and stimulate the use of the granulation scale as a cyclical proxy for solar activity over medium-term periods.