Neural network supplies the sideways flows needed to measure the quiet Sun's magnetic energy

The work

Technical · from the record

The study estimates the vertical flux of magnetic energy (Poynting flux) in the quiet-Sun photosphere from SUNRISE/IMaX spectropolarimetry, which requires plane-of-sky velocities that cannot be measured directly. A convolutional neural network, DeepVel, was trained on STAGGER radiative MHD simulations to infer transverse flows from pairs of continuum images, and on a STAGGER map outside the training set its instantaneous velocities correlated with the simulated velocities at r=0.91, compared with a Pearson coefficient below 0.45 for Fourier local correlation tracking. Using DeepVel velocities, the authors computed Poynting flux with an ideal-MHD expression and with the PDFI_SS inductive electric field inversion, under several azimuth disambiguation choices, and compared the values with a published threshold for chromospheric and coronal energy losses. Ideal-MHD estimates restricted to pixels with field strength above 50 G reached that threshold while the all-pixel average did not, PDFI_SS values oscillated around zero, and MURaM simulations showed the flux varying strongly with optical depth with the shear term dominating, unlike in the observations.

How AI was used

A convolutional neural network, DeepVel, was trained by supervised learning on frames from the STAGGER radiative MHD simulation, where the full flow field is known, to map a pair of continuum intensity images at two timesteps to the transverse velocity field at a given optical depth or geometrical height. The trained network was then run on a STAGGER intensity map held outside the training set, alongside Fourier local correlation tracking applied to the same simulated intensities, and the two methods were compared with the simulation's reference velocities using Pearson correlation, a spatially averaged relative error, a vector correlation coefficient and a cosine similarity index, as well as divergence and vorticity. DeepVel was then applied to the phase-diversity-reconstructed IMaX continuum intensitygrams to retrieve transverse velocities for the observed time series. These velocities were combined with Doppler line-of-sight velocities and with Milne-Eddington vector magnetograms, disambiguated in azimuth by randomisation, Poynting-flux optimisation, potential-field acute angle matching and divergence minimisation, to form the electric field under a strict ideal-MHD Ohm's law and, separately, through the PDFI_SS inductive inversion, from which vertical and horizontal Poynting fluxes were computed. No learned model was used in the magnetic field inversion, the azimuth disambiguation, the electric field inversion or the MURaM simulation analysis.