Impact of spatially correlated fluctuations in sunspots on metrics related to magnetic twist

Abstract

The twist of the magnetic field above a sunspot is an important quantity in solar physics. For example, magnetic twist plays a role in the initiation of flares and coronal mass ejections (CMEs). Various proxies for the twist above the photosphere have been found using models of uniformly twisted flux tubes, and are routinely computed from single photospheric vector magnetograms. One class of proxies is based on $α_z$, the ratio of the vertical current to the vertical magnetic field. Another class of proxies is based on the so-called twist density, $q$, which depends on the ratio of the azimuthal field to the vertical field. However, the sensitivity of these proxies to temporal fluctuations of the magnetic field has not yet been well characterized. We aim to determine the sensitivity of twist proxies to temporal fluctuations in the magnetic field as estimated from time-series of SDO/HMI vector magnetic field maps. To this end, we introduce a model of a sunspot with a peak vertical field of 2370 Gauss at the photosphere and a uniform twist density $q= -0.024$ Mm$^{-1}$. We add realizations of the temporal fluctuations of the magnetic field that are consistent with SDO/HMI observations, including the spatial correlations. Using a Monte-Carlo approach, we determine the robustness of the different proxies to the temporal fluctuations. The temporal fluctuations of the three components of the magnetic field are correlated for spatial separations up to 1.4 Mm (more than expected from the point spread function alone). The Monte-Carlo approach enables us to demonstrate that several proxies for the twist of the magnetic field are not biased in each of the individual magnetograms. The associated random errors on the proxies have standard deviations in the range between $0.002$ and $0.006$ Mm$^{-1}$, which is smaller by approximately one order of magnitude than the mean value of $q$.