Transport of Internetwork Magnetic Flux Elements in the Solar Photosphere

Tuesday, October 23, 2018

The motions of small-scale magnetic flux elements in the solar photosphere can provide some measure of the Lagrangian properties of the convective flow. Measurements of these motions have been critical in estimating the turbulent diffusion coefficient in flux-transport dynamo models and in determining the Alfvén wave excitation spectrum for coronal heating models.

Graph of displacement probability distributions
Displacement probability distributions for Hinode/NFI data (left column) and for a random walk model (right column) at different temporal increments, are shown here. The red stars are the distribution values, the blue (dashed) and the green (solid) curves refer to the best-fit Rayleigh and Gaussian curves, respectively. Note that only 2% of the flux elements survive to contribute to the Hinode/NFI data distribution at 120 minutes, and since the bin size is held constant at about 0.13 Mm, the histogram is noisy. The distribution function is Rayleigh (corresponding to a random walk) for intermediate increments of about 6 minutes, but deviates for both shorter and longer time scales.

We examine the motions of internetwork flux elements in Hinode/Narrowband Filter Imager magnetograms and study the scaling of their mean squared displacement and the shape of their displacement probability distribution as a function of time. We find that the mean squared displacement scales super-diffusively with a slope of about 1.48. Super-diffusive scaling has been observed in other studies for temporal increments as small as 5 s, increments over which ballistic scaling would be expected. Using high-cadence MURaM simulations, we show that the observed super-diffusive scaling at short increments is a consequence of random changes in barycenter positions due to flux evolution. We also find that for long temporal increments, beyond granular lifetimes, the observed displacement distribution deviates from that expected for a diffusive process, evolving from Rayleigh to Gaussian. This change in distribution can be modeled analytically by accounting for supergranular advection along with granular motions. These results complicate the interpretation of magnetic element motions as strictly advective or diffusive on short and long timescales and suggest that measurements of magnetic element motions must be used with caution in turbulent diffusion or wave excitation models. We propose that passive tracer motions in measured photospheric flows may yield more robust transport statistics.

Publication Name: Astrophysical Journal

First HAO Author's Name: Matthias Rempel