Variations of Umbral Magnetic Field Strength with Umbral Area, Brightness, and Sunspot Number

Sunspots are regions on the Sun where the magnetic field is highly concentrated. The magnetic field drives the physical conditions within and around sunspots. The study of the relationship between the magnetic field strength in the sunspot umbra and the umbral area, umbral brightness and sunspot number (SSN) provides important information about the physical properties of sunspots and the overall structure of the Sun. In this study, we analyzed high-resolution sunspot images obtained from the Big Bear Solar Observatory (BBSO)/Goode Solar Telescope (GST) for 2015 - 2022 time intervals. The corresponding daily sunspot number (SSN) data were taken from the Solar Influences Data Analysis Center (SIDC) website, and the magnetic field measurements were obtained from the GST/Near InfraRed Imaging Spectropolarimeter (NIRIS). The variations of the mean umbral magnetic field intensity with respect to the umbral area, umbral brightness, and SSN were investigated, and Pearson correlation analysis was performed to explore the relationships between them. Our analysis revealed the following results: i) There is a power-law relationship between the mean umbral area and the magnetic field strength and the magnetic field strength increases with increasing umbral area. ii) The magnetic field strength decreases with increasing mean umbral brightness. iii) A weak relationship was found between the umbral magnetic field strength and the SSN.