The Statistical Relationship between White-light Emission and Photospheric Magnetic Field Changes in Flares

Continuum emission, also called white-light emission (WLE), and permanent changes of the magnetic field ($\Delta{B}_{{\rm{LOS}}}$) are often observed during solar flares. But their relation and their precise mechanisms are still unknown. We study statistically the relationship between $\Delta{B}_{{\rm{LOS}}}$ and WLE during 75 solar flares of different strengths and locations on the solar disk. We analyze SDO/HMI data and determine for each pixel in each flare if it exhibited WLE and/or $\Delta{B}_{{\rm{LOS}}}$. We then investigate the occurrence, strength, and spatial size of the WLE, its dependence on flare energy, and its correlation to the occurrence of $\Delta{B}_{{\rm{LOS}}}$. We detected WLE in 44/75 flares and $\Delta{B}_{{\rm{LOS}}}$ in 59/75 flares. We find that WLE and $\Delta{B}_{{\rm{LOS}}}$ are related, and their locations often overlap between 0-60\%. Not all locations coincide, thus potentially indicating differences in their origin. We find that the WL area is related to the flare class by a power law and extend the findings of previous studies, that the WLE is related to the flare class by a power law, to also be valid for C-class flares. To compare unresolved (Sun-as-a-star) WL measurements to our data, we derive a method to calculate temperatures and areas of such data under the black-body assumption. The calculated unresolved WLE areas improve, but still differ to the resolved flaring area by about a factor of 5-10 (previously 10-20), which could be explained by various physical or instrumental causes. This method could also be applied to stellar flares to determine their temperatures and areas independently.