M. García-Rivas^1,2, J. Jurčák¹ and N. Bello González³

1. Astronomical Institute of the Czech Academy of Sciences, Fričova 298, 25165 Ondřejov, Czech Republic
2. Astronomical Institute, Charles University, V Holešovickách 2, 18000 Praha, Czech Republic
3. Leibniz-Institut für Sonnenphysik (KIS), Schöneckstrasse 6, 79104 Freiburg, Germany

A number of observational studies found an invariant value of the vertical magnetic field B_ver on umbra-penumbra boundaries of stable sunspots ^[1,2]. These analyses have led to the so-called Jurčák criterion, an empirical law that states that umbra-penumbra boundaries in stable sunspots are equally defined by a constant value of the vertical magnetic field, , and by a 50% continuum intensity of the quiet Sun, I_QS. Umbrae with B_ver > are stable, whereas umbrae with B_ver < are unstable and prone to vanishing. The stabilizing factor of B_ver against more vigorous modes of magneto-convection has also been studied in other evolutionary stages of sunspots. For instance, during the development of a penumbra^[3], B_ver on the umbra-penumbra boundary increases until it reaches an invariant value when the sunspot is completely formed. However, during the development of a penumbra around a pore with weak B_ver, the penumbra colonizes the pore^[4]. In this case study, we aim to analyze the stabilizing role of B_ver on a pore-quiet Sun boundary.

To investigate the existence of a critical value of B_ver on a pore, we analyze 113 SDO/HMI vector field maps, after being corrected for scattered light, from 09:24 UT on 18 March 2011 to 12:00 UT on 19 March 2011. The pore boundary is defined using a continuum intensity threshold (I_c = 0.55 I_QS), along which we average magnetic properties (total magnetic field strength B, vertical magnetic field B_ver, and inclination) and examine their temporal evolutions (e.g. Figure 1). We find that B_ver on the boundary behaves similarly to the case of sunspots.

Figure 1| Temporal evolution of the averaged B_ver on the boundary of the pore (I_c = 0.55 I_QS ). The uncertainties are given by the standard deviation. The plot is divided into evolutionary stages: first period of formation (For-I), stability (Sta), second period of formation (For-I), and decay (Dec).

During the first formation phase (For-I), B and B_ver increase to their maximum values of ~1920 G and ~1730 G, respectively. Thus the pore reaches its stable phase (Sta). During this period, continuum images of the pore do not significantly change while B and B_ver fluctuate around their maximum values. The mean maximum vertical value is comparable to the found on umbra-penumbra boundaries. Consequently, the mean values weighted by their standard deviations during this stage are used as magnetic thresholds (B = 1921 G and B_ver = 1731 G). In Figure 2, we compare the evolution of the areas encircled by the intensity and magnetic thresholds.

Figure 2| Temporal evolution of the areas of the pore encircled by intensity and magnetic thresholds. Top: comparison of the areas encircled by the isocontours I_c = 0.55 I_QS (red), B = 1921 G (orange), and B_ver = 1731 G (blue). Vertical lines divide the evolutionary stages of the pore as in Fig. 1. Bottom: detail of the decaying stage. The straight lines are linear fits of the decay for each of the sub-periods (1, 2) with continuous data available.

The stability phase is followed by a second formation phase (For-II). The pore undergoes a rapid growth caused by an accumulation of new flux in the northern part of the pore. The newly gathered magnetic field is weaker and more horizontal than the original and leads to a decrease of B and B_ver averaged along the intensity boundary (Figure 1).

Immediately after the accumulation of additional magnetic flux is finished, the pore starts to decay (Dec). We divide this period in two sub-periods with continuous data, for each of which the decaying rates of the areas encircled by the intensity and magnetic thresholds are studied (bottom plot in Figure 2). During the first sub-period, regions with strong magnetic fields disappear faster than regions with weak magnetic fields. Areas with B_ver > 1731 G on average do not decay, while regions with B < 1921G on average decay 3.4 times faster than regions with B > 1921 G. Therefore, the B_ver and B averaged along the intensity boundary increase during this period (Figure 1). During the second sub-period, the pore is fragmented into multiple small patches that have nearly identical intensity and B_ver isocontours. These small patches decay at a rate of 1.78 Mm² h^-1. Since regions with B > 1921 G are located only in some of the cores of the pore’s segments, the decay rate is slower.

In conclusion, we find that the most stable regions of the pore, similarly to the case of umbral boundaries, are defined by a that is comparable to the one found in stable sunspots. In addition, in this case study the B threshold behaves similarly to B_ver and could have a stabilizing factor as well. For more details of this work, please refer to our full publication Ref [5].

References

[1] Schmassmann, M., R. Schlichenmaier, & N. Bello González 2018, A&A, 620, A104
[2] Lindner, P., R. Schlichenmaier, & N. Bello González 2020, A&A, 638, A25
[3] Jurčák, J., N. Bello González, R. Schlichenmaier, & R. Rezaei 2015, A&A, 580, L1
[4] Jurčák, J., N. Bello González, R. Schlichenmaier, & R. Rezaei 2017, A&A, 597, A60
[5] García-Rivas, M., Jurčák, J., & N. Bello González 2021, A&A, 649, A129