Context. The relation between the intensity of chromospheric emissions and the photospheric magnetic field strength has been examined in several studies, but the effect of the magnetic field inclination on chromospheric emissions remains almost unexplored. Aims. We study how the inclination of the photospheric magnetic field, as measured by the full 3D magnetic vector from the Helioseismic and Magnetic Imager (HMI), affects the relationship between the magnetic field strength and the far-ultraviolet emission at around 1600 Å observed by the Atmospheric Imaging Assembly (AIA). We also study how these parameters change spatially close to the active region perimeter. Methods. We analyzed the mutual dependence of 1168 co-temporal AIA and HMI observations from 2014 to 2017. We focused on magnetically active regions outside sunspots (e.g., plages and network) close to the solar disk center. We studied how the AIA and HMI parameters change with distance from the active region perimeter. Results. The AIA 1600 emission typically decreases with increasing (more horizontal) inclination. For all inclinations, AIA 1600 emission increases with increasing magnetic field strength until saturating at some peak intensity, which depends on the cosine of the inclination, with horizontal regions saturating at lower intensities. In addition, we find that activity clusters have a narrow boundary (< 2 arcsec) in which the AIA 1600 intensity, magnetic field strength, and inclination distributions and relations differ significantly from those in the inner layers. Conclusions. This study demonstrates the significant effect that magnetic field inclination and activity cluster border regions have on chromospheric emissions. Although the observed effects are likely reduced in low-resolution observations where different regions are averaged together, a detailed study is needed to examine the emission–magnetic field relation at different resolutions.
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