Stefan J. Hofmeister1, Dominik Utz1, Stephan G. Heinemann1, Astrid Veronig1,2, Manuela Temmer1
1 Institute of Physics, University of Graz, Graz, Austria
2 Kanzelhöhe Observatory for Solar and Environmental Research, University of Graz, Graz, Austria
It is well known that coronal holes exhibit a magnetic field topology open toward interplanetary space, however, their sources have not been studied in detail. We use HMI’s low-noise line-of-sight magnetograms to analyze the distribution and properties of photospheric magnetic elements below 98 coronal holes, which are the footpoints of both closed loops and open magnetic funnels within coronal holes. The magnetic elements were identified by applying a threshold of ±25 G on the magnetograms and requiring that they contain at least a core of 2×2 pixels above the threshold to remove spurious artefacts originating from noises (Fig. 1).
We find that all magnetic elements follow a power law between their area and magnetic fluxes (cc=0.984), given by
Therefore, their magnetic flux is statistically well determined by their size. Further, by tracking them for ±2days, we find that their lifetimes group them into four categories. The first three categories are given by their half-lives of 14 min, 2.1 h, and 11.7 h, which relate them to the convective motions of granulation, mesogranulation, and supergranulation. By comparing the number of magnetic elements with lifetimes > 4 days in our dataset with the number we expect from supergranulation, we find elements two orders of magnitude more than we should have. Therefore, we define a fourth class of magnetic elements, i.e., long-lived magnetic elements with lifetimes > 40 h.
Figure 2| Number densities of magnetic elements vs. their magnetic field strength. Top left: magnetic elements belonging to the class of granulation. Top right: to mesogranulation. Bottom left: to supergranulation. Bottom right: long-lived magnetic elements.
In Figure 2, for each of the four classes, we show a superposed epoch analysis for their number densities within coronal holes. Thereby, the magnetic field strength of the magnetic elements has been transformed so that positive values represent the dominant coronal-hole polarity. For the short- to medium-lived classes of magnetic elements, i.e., magnetic elements related to granulation, mesogranulation, and supergranulation, there are almost as many magnetic elements with dominant coronal-hole polarity as with non-dominant coronal-hole polarity. Since their polarities are well balanced, their contribution to the open magnetic flux of coronal holes is almost negligible; they are mostly likely the foot points of closed loops. In contrast, the long-lived magnetic elements have almost exclusively the dominant coronal-hole polarity, with an average contribution to the open magnetic flux of 69 %. Thus, they are the main source of open magnetic flux. The remaining percentage of open magnetic flux can be modelled as a weak background magnetic field of 0.2 G to 1.2 G, which is strongly correlated to the magnetic flux arising from the long-lived magnetic elements (cc=0.88). Here, we cannot distinguish whether this background magnetic field is real or an artefact created by the point-spread function of HMI.
Figure 3| Mean magnetic field strength (left) and mean unsigned magnetic field strength (mid) of the overall coronal holes vs. the percentage area the long-lived magnetic elements cover. Percentage unbalanced magnetic versus the mean magnetic field strength of coronal holes (right).
Finally, we compare the properties of the magnetic elements with the mag- netic properties of the overall coronal holes (Fig. 3). We find that the magnetic field strength of coronal holes is fully determined by the percentage area the long-lived magnetic elements cover (cc=0.988):
This relationship follows from the area-flux relationship of individual magnetic elements (Eq. 1), and from them being the main contributor to the open magnetic flux of the overall coronal hole. Further, the mean unsigned magnetic field strength is given by
The first term is set by the noise level in the magnetograms, and the second term describes the increase of unsigned magnetic flux with increasing number of long-lived magnetic elements; the contribution of the short- to medium-lived magnetic elements is negligible. The percentage of unbalanced magnetic flux of coronal holes is defined and given by
It is usually interpreted as the percentage of magnetic flux which is open to the flux which belongs to closed loops. This equation, however, shows that it is only a measure on the magnetic flux arising from the long-lived magnetic elements as compared to the magnetogram noise level, and thus has no reasonable physical meaning.
To conclude, long-lived magnetic elements with lifetimes > 40 h set the magnetic properties of the coronal holes. More details can be found in Ref .
 Hofmeister, S. J., Utz, D., Heinemann, S. G., Veronig, A., & Temmer, M. 2019, A&A, 629, A22