Brandon Rajkumar
White light images and magnetograms of 16 active regions observed between June-November 2015 were obtained from the University College of the Cayman Islands Observatory and the Joint Science Operations Centre (JSOC) and used to determine the scale free fractal dimensions of their umbrae, penumbrae and underlying magnetic fields. The fractal dimensions for the umbral and penumbral regions were found to be 2.09 ± 0.42 and 1.72 ± 0.4 respectively using the area-perimeter method. Using the same method, the fractal dimensions for strong and weak magnetic fields groups were found to be 1.79 ± 0.49 and 1.96 ± 0.29 respectively. Using the fractal dimensions as an indicator for complexity, it was observed that less complex, strong magnetic fields produced more complex umbral structures while the more complex, weak magnetic fields produced less complex penumbral regions. These observations support a recent model of sunspot formation where strong magnetic fields are trapped within the umbra. These trapped magnetic fields have a reduced freedom of motion and therefore form less complex structures indicated by the lower fractal dimensions. However, the trapped, strong magnetic fields reduce the temperature in the umbral regions leading to more complex umbral structures. In the penumbral regions, unbound, weak magnetic fields are free to form complex structures indicated by the higher fractal dimension while the higher temperatures form more complex penumbral structures. It was also determined, through an initial temporal analysis, that the changes in complexity between the umbral and penumbral regions may be linked.
Introduction:
The Sun is complex and dynamic with many features being driven by the underlying solar magnetic fields, the most prominent of which are sunspots. Sunspots are observed on the photosphere (visible surface) of the sun.
These sunspots are also considered natural fractal phenomena as they exhibit many fractal properties. Fractals refer to a type of geometry which describes the complexity of shapes or objects in terms of a non-integer number.
Flattened Intensity images show the sunspot structures on the photosphere, such as the umbra and penumbra, while colour magnetogram images show the underlying magnetic fields that drive them. Colour magnetograms divide the magnetic fields into four main magnetic field groups: strong positive, weak positive, strong negative and weak negative magnetic fields.
Method and Results:
The fractal dimension of each structure (umbra, penumbra, strong magnetic fields and weak magnetic fields) is determined by using the Area-Perimeter method which relates the area (S) of each structure to its respective perimeter (L) by S~L^q.
Therefore, q= Log S⁄Log L
where q is related to the fractal dimension (d) by d= 2⁄q.
The fractal dimensions for umbral and penumbra regions as well as strong and weak magnetic fields were found to be 2.09 ± 0.42, 1.72 ± 0.40, 1.79 ± 0.49 and 1.96 ± 0.29 respectively.
A preliminary temporal analysis was performed on AR 12403 over a period of 8 days with a temporal resolution of 1 day. A correlation of r = 0.623, it suggests that changes in complexity between the umbra and penumbra may be linked.
Discussion and Conclusion:
It was observed that strong magnetic fields dominate the umbral regions while weak magnetic fields dominate the penumbral regions.
Using the fractal dimensions determined as an indicator for complexity of these regions, it was determined that more complex weak magnetic fields result in less complex penumbral structures while less complex strong magnetic fields result in more complex umbral structures. These results support a recent model of sunspot formation proposed by (Jaeggli, Lin, and Uitenbroek 2012).
Cooler temperatures within the umbra allow for the formation of molecular hydrogen. As they move toward the umbra/penumbra boundary, temperatures increase leading to an increase in ionised hydrogen. This results in an increased outer pressure which traps strong magnetic fields within the umbra region. Trapped magnetic fields suggest a reduced freedom of motion and thus the formation of less complex (strong) magnetic structures. Unbound weak magnetic fields within the penumbral regions are free to move, twist and form more complex structures.
Using an unrelated gold colloid analysis (Weitz et al. 1985) as an analogy for umbral and penumbral structure formation, it is suggested that an increased abundance of molecular hydrogen in the umbra leads to more complex umbral structures while the greater abundance of ionised hydrogen in penumbral regions result in less complex penumbral regions.
Further fractal analysis of active regions may present a quick and simple method for predicting their behaviour and thus the behaviour of solar magnetic activity.