J. Ballot1, T. Roudier1, J. M. Malherbe2, and Z. Frank3
1 IRAP, Université de Toulouse, CNRS, UPS, CNES, 31400 Toulouse, France
2 LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 92195 Meudon, France
3 Lockheed Martin Solar and Astrophysics Laboratory, 3251 Hanover Street, Palo Alto, CA 94303, USA
Different from other stars, the Sun offers unique possibilities to observe surface convection with high spatial resolutions and high temporal cadences. Although the main characteristics of the granulation are widely described in literature for decades, studying its variations over activity cycles is difficult because that requires the acquisition of homogeneous sets of images over a whole 11-year solar cycle.
From physics theory, we expect that changes in magnetic fields induce changes in convective scales. Indeed, it has already been shown that magnetic fields affect the granulation: especially, granules in magnetic plages are smaller than those in the quiet Sun. However, variations in granule sizes in the quiet Sun over a cycle has long been unsuccessfully searched until a study we just published. To reach this goal, we took advantage of very stable and homogeneous datasets acquired by the SDO/HMI to measure temporal evolution of the granule density and mean area.
Since data reduction was very time consuming, we selected one day per month over nine years, starting on 1 July 2010, with a time step as regular as possible, and for each selected day, we picked hourly images, rejecting a few ones with low quality. We thus ended up with a set of 2711 white-light images, which were re-binned by a factor of two and deconvolved from the HMI transfer function. To limit projection effects, the field of view was restricted around the disk center. We then segmented the images to extract all the granules. To do so, we identified granules as convex elements of images. Figure 1 shows the progression of the central part of a processed image.
Figure 1| Progression of the central part of a processed image. Left: original image of solar granulation observed with HMI around the disc center with a pixel size of 0.5″ for a field of view of 100″×100″. Middle: same image after deconvolution, with a pixel size of 0.25″ Right: same image, segmented at the granulation level (each white element corresponds to a granule).
Once images are segmented, it is straightforward to compute the granule density and mean area for each frame and to follow their temporal evolution. These measurements show a clear annual variation of around 5%. We proceeded to an exhaustive inspection of the whole data reduction chain to understand the origin of this phenomenon. We concluded that the changes in pixel size with the distance of SDO to the Sun generate an artificial oscillation and we corrected our measurements from this spurious variation.
Figure 2| Evolution of the mean granule area (corrected for the pixel size). Dots correspond to individual measurements, and crosses show daily averages with estimated error bars. Dates where spots (pores) are present in the field of view are indicated with red (blue) symbols. Variations of the 13-month smoothed monthly mean total sunspot number are overplotted (solid line).
Figure 2 displays the corrected mean granule area during the cycle. We performed daily averages and compared their evolution to the sunspot number, which is used as a proxy for the solar magnetic activity. When the activity is higher, there is a higher possibility of finding spots, or simply pores, in our field of view. The points that are potentially affected by spots and pores are identified with colored symbols in the figure. A very clear trend appears in this plot. The mean granule area decreases as activity increases and reaches a minimum; the mean granule area then increases again when the activity weakens. The variation amplitude is around 2% and the minimum is delayed by 300-400 days compared to the activity maximum. Granule density has a similar behavior and is perfectly anti-correlated with the mean granule area. We confirmed our results by analyzing Hinode observations that have shown consistent and significant, if noisier, variations.
Figure 3| Evolution of the mean granule area (corrected for the pixel size) in the inter-network. This figure is similar to Figure 2, but masks have been applied to remove regions with a magnetic field stronger than 30 G.
Going a step further, we wanted to see whether the observed variations are related to plage regions or to active network structures or whether granulation variations are still present in the inter-network. To achieve this objective, we took advantage of magnetograms that are simultaneously provided by HMI with each white-light image. We thus built masks to remove any region with a magnetic field greater than 30 G. Results are shown in Figure 3. The variations observed along the solar cycle are weaker but still present. We conclude that although small magnetic structures of the network explain a part of the variations reported, there are also variations in the inter-network regions.
 Title, A. M., Topka, K. P., Tarbell, T. D., et al. 1992, ApJ, 393, 782
 Muller, R., Hanslmeier, A., Utz, D., Ichimoto, K. 2018, A&A, 616, A87
 Ballot, J., Roudier, T., Malherbe, J. M., Frank, Z. 2021, A&A, 652, A103
 SILSO World Data Center 2008-2019: International Sunspot Number Monthly Bulletin and online catalogue, https://wwwbis.sidc.be/silso/)