Relative variation of granulation size as a function of global solar parameters

Reliable data on the range and distribution of solar granulation size are essential for modeling plasma convection, studying the magnetic activity cycle, and measuring the Sun's global parameters. Most known morphometric studies of solar granulation measure and document mean area or equivalent diameter of granules from high-resolution optical image time series. One of the main shortcomings of these studies is that the mean area or equivalent diameter cannot represent the characteristic scale of granular cells due to the skewed size distribution. The measured mean granular size is particularly susceptible to the influence of outliers due to occasional irregularities in image time series, unsuitable image quality, e.g. local blurring, and errors in automatic image processing. The lack of consolidated analytical formulations linking changes in granulation size to global solar variability complicates verification of empirical results. It is significant that over the last 70 years the observed value of the relative changes in the average size of granular cells associated with the solar magnetic cycle has declined by an order of magnitude from 20% to 2%.

In this study, we introduce the normalized version of the mean granular area, called the mean extent, which is defined as the area of a granular cell divided by the area of the smallest bounding box enclosing the cell, with averaging over all cells in the observation frame. In contrast to other known granulation properties, the proposed dimensionless parameter has a normal distribution, is less scattered and invariant to scaling effects, e.g. because of defocus. We write some basic expressions for the relative variation in granulation extent and determine the magnitudes of the relative changes in the horizontal size of granular cells due to variations in global solar parameters. We define that the total number of granular cells and their mean size decrease while the solar radius, effective temperature, luminosity and granulation time scale increase with increasing sunspot area.

The specific behavior of mean extent versus mean area and contrast of granular cells was tested using Hinode image sequences obtained in the blue continuum channel with a 27- and 1-day cadence over descending and ascending phases of the 24th activity cycle, and compared to corresponding sunspot indices. The consistent 14- and 378-day delays in the cause-and-effect relationship between sunspot number and granulation scale were revealed in the daily and synoptic time series, respectively, and explained by rotational effects. Remarkably, the mean granular extent varies in phase with the sunspot indices; its long-term average was measured at 0.65, which corresponds to the predominantly hexagonal shape of the granular cells. Higher values of granular extent indicate regularization and compaction of the granulation pattern in both quiescent and active regions. We conclude that the mean size and extent of granular cells measured at the center of the disk could become a reliable index of solar convection and a reactive indicator of global magnetic activity, although the mean granulation size in polar regions remains somewhat uncertain, worthy of further study with high-resolution optical data from extra-ecliptic missions.