The force-freeness of the solar photosphere: Revisit with new approach and large data sets

Although it is generally believed that the solar photosphere is not magnetically force-free owing to its high plasma beta, the estimations of force-freeness using observed magnetograms have produced disputable results. Some studies confirmed that the photosphere is largely not force-free whereas some authors argued that the photosphere is not far away from being force-free. In a previous paper of ours we demonstrated that, due to the fact that the noise levels of the transverse field in the magnetograms are much larger than those of the vertical field, wrong judgments on the force-freeness could be made: a truly force-free field could be judged as being not-force-free and a truly not-force-free field could be judged as being force-free. Here in this Letter, we propose an approach to overcome this serious problem. By reducing the spatial resolution to lower the noise level, the heavy influence of the measurement noise on the force-freeness judgment can be significantly suppressed. We first use two analytical solutions to show the success and effectiveness of this approach. Then, we apply this new approach to two large data sets of active region magnetograms, obtained with the Helioseismic and Magnetic Imager/Solar Dynamics Observatory and Spectro-Polarimeter (SP)/Hinode, respectively. Our analysis shows that the photospheric magnetic fields are actually far away from being force-free. Particularly, and most notably, the mean value of F-z/F-p (where F-z is the net Lorentz force in the vertical direction and F-p the total Lorentz force) is as low as -0.47, with more than 98% of the active regions having divided by F-z/F-p divided by > 0.1 when using the SP/Hinode magnetograms of true field strength.