Multi-height probing of horizontal flows in the solar photosphere

TL;DR

This paper tackles how to constrain depth-dependent horizontal flows in the solar photosphere by combining multi-height FLCT tracking with spectropolarimetric information from two lines, Fe I $525.0\,\mathrm{nm}$ and Mg I $b2$, across $\log\tau_{500}=0$ to $-4$. Using a realistic MURaM simulation and synthetic spectra, the authors show that velocities inferred from the LOS magnetic field component ($B_z$) tracked across depths reproduce the true horizontal velocities up to the temperature minimum ($\log\tau_{500}=-3$) with high fidelity after temporal and spatial averaging, while tracking temperature fails beyond the lower photosphere. Inference of $B_z$ from the Fe I and Mg I lines yields velocities that correlate well with the simulation for $\log\tau_{500}\approx-1$ to $-2$ (Fe I) and $-3$ to $-4$ (Mg I), respectively, indicating that the two lines complement each other to cover a broad height range; however, velocity amplitudes are systematically underestimated. Divergence estimates from FLCT are notably less reliable, though smoothing improves correlations. The results suggest that high-resolution spectropolarimetric imaging, potentially augmented by AI-based tracking methods, can provide meaningful, height-resolved velocity information with practical implications for solar magnetism, energy transport, and dynamo studies.

Abstract

We tested whether simultaneous spectropolarimetric imaging in two magnetically sensitive optical spectral lines, which probe two different layers of the solar atmosphere (the photosphere and the temperature minimum), can help constrain the depth variation of horizontal flows. We first tested the feasibility of our method using Fourier local correlation tracking (FLCT) to track physical quantities at different optical depths ($\logτ_{500}={-1,-2,-3,-4}$) in an atmosphere simulated with the MURaM code. We then inferred the horizontal distribution of the LOS magnetic field component from synthetic spectropolarimetric observations of Fe I 525.0 nm and Mg I b2 spectral lines, applied FLCT to the time sequence of these synthetic magnetograms, and compared our findings with the original height-dependent horizontal velocities. Tracking the LOS magnetic field component (which coincides with the vertical component at the disk center) yields horizontal velocities that, after appropriate temporal and spatial averaging, agree excellently with the horizontal component of the simulated velocities, both calculated at constant $τ_{500}$ surfaces, up to the temperature minimum ($\logτ_{500}=-3$). When tracking the temperature at constant $τ_{500}$ surfaces, this agreement already breaks down completely at the mid photosphere ($\logτ_{500}=-2$). Tracking the vertical component of the magnetic field inferred from synthetic observations of the Fe I 525.0 nm and the Mg I b2 spectral lines yields a satisfactory inference of the horizontal velocities in the mid-photosphere ($\logτ_{500}\approx-1$) and the temperature minimum ($\logτ_{500}\approx-3$), respectively. Our results indicate that high-spatial-resolution spectropolarimetric imaging in solar spectral lines can provide meaningful information about the horizontal plasma velocities over a range of heights.

Figures (11)

• Figure 1: Temperature, vertical magnetic field, and the three components of the velocity at $\log \tau_{500} = 0$ for the first considered timestep of the simulation. The black square in the upper-right panel marks the region shown in the lower-right panel. Arrows in the lower-right panel indicate horizontal velocities.
• Figure 2: Synthetic observables calculated for the first snapshot in the series. Top left: Continuum image at 517.2 nm. Top middle: Nominal line core of the Mg I b2 line. Top right: Nominal line core of Fe I 525.0 nm line. Bottom left: Spatially averaged spectra of the considered spectral lines, Fe I lines are shifted for clarity. Bottom middle: Circular polarization in the wing of the Mg I line. Bottom right: Circular polarization in the wing of the Fe I line. The upper-row panels are shown in units of the mean quiet-Sun continuum.
• Figure 3: Comparison between the $x$ component of the horizontal velocity retrieved by FLCT applied to intensity maps and the simulated velocity at $\log\tau_{500}=0$. Color maps indicate the magnitude of velocity. Bottom row: Scatter plot showing the least-squares fit between $\vec{v}_o$ and $\vec{v}_f$. Results are shown for two different sizes of apodizing windows: left, $600km$; right, $300km$.
• Figure 4: Same as Fig. \ref{['fig:track_I']}, but for FLCT applied to $B_z$ at $\log\tau_{500}=0$.
• Figure 5: Comparison between the $x$ component of the horizontal velocity retrieved by FLCT using FWHM = 600 km, applied to temperature (top panel), and $B_z$ (middle panel), and the simulated velocity (bottom panel) at $\log\tau_{500}=\{-1, -3\}$.