The Influence of Spatial Resolution on Estimating the Force-freeness of Magnetic Fieldtwo

It is a common practice in the solar physics community to judge whether the measured photospheric vector magnetograms are force-free or not. In the previous work, it was studied how the measurement limitations such as the limited field of view, instrument sensitivity, and measurement error could affect the judgement of force-freeness based on the observed magnetograms. A further research on the influence of the spatial resolution on the force-freeness judgement is carried out in this article. The result shows that changing (mainly reducing) the spatial resolution has little influence on the force-freeness judgement in the ideal noiseless case. In the case when there are white noises in the magnetograms as those in the really observed magnetograms, it is opposite to the common intuition that properly reducing the spatial resolution can actually suppress the error, and significantly reduce the heavy influence of the measurement error on the force-freeness judgement, thus to enhance effectively the accuracy of the force-freeness judgement of magnetic field. This result sets up a theoretical foundation and an instructive guidance for judging the force-freeness of solar magnetic field correctly by using the observed magnetograms.