Multi-height probing of horizontal flows in the solar photosphere

¹ Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia
² Institute for Solar Physics, Georges-Khöler-Alee 401a, 79110 Freiburg, Germany
³ Department of Astronomy, Faculty of Mathematics, University of Belgrade, Studentski Trg 16-20, 11000 Belgrade, Serbia
⁴ High Altitude Observatory, NSF National Center for Atmospheric Research, Boulder, CO 80307, USA
⁵ Natural and Applied Sciences, University of Wisconsin – Green Bay, 2420 Nicolet Drive, Green Bay, WI 54311, USA
⁶ Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA
⁷ Department of Astrophysical and Planetary Sciences, University of Colorado Boulder, 2000 Colorado Avenue, Boulder, CO 80305, USA
⁸ National Solar Observatory, 3665 Discovery Drive, Boulder, CO 80303, USA
⁹ Instituto de Astrofísica de Canarias (IAC), Avda Vía Láctea s/n, 38200 La Laguna, Tenerife, Spain
¹⁰ Departamento de Astrofísica, Universidad de La Laguna, 38205 La Laguna, Tenerife, Spain
¹¹ Environment and Climate Change Canada, Science and Technology Branch, Meteorological Research Division, 2121 Transcanada Hwy, Dorval, Québec H9P 1J3, Canada

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 25 June 2025
Accepted: 20 October 2025

Abstract

Context. Optical flow methods aim to infer horizontal (transverse, in the general case) velocities in the solar atmosphere from the temporal changes in maps of physical quantities, such as intensity or magnetic field. So far, these methods have mostly been tested and applied to the continuum intensity and line-of-sight (LOS) magnetic field in the low to mid-photosphere.

Aims. 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.

Methods. We first tested the feasibility of our method using Fourier local correlation tracking (FLCT) to track physical quantities at different optical depths (log τ₅₀₀ = −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.

Results. 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 τ₅₀₀ surfaces, up to the temperature minimum (log τ₅₀₀ = −3). When tracking the temperature at constant τ₅₀₀ surfaces, this agreement already breaks down completely at the mid photosphere (log τ₅₀₀ = −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 (log τ₅₀₀ ≈ −1) and the temperature minimum (log τ₅₀₀ ≈ −3), respectively.

Conclusions. 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.