# Analysis of Pseudo-Lyapunov Exponents of Solar Convection Using State-of-the-Art Observations

^{1}

INAF—Osservatorio Astronomico di Roma, Via Frascati 33, I-00078 Monte Porzio Catone, Italy

^{2}

INAF—Osservatorio Astrofisico di Catania, Via S. Sofia 78, I-95123 Catania, Italy

^{3}

INAF—Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Rome, Italy

^{4}

Rosseland Centre for Solar Physics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo, Norway

^{5}

Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo, Norway

^{*}

Author to whom correspondence should be addressed.

Academic Editor: José A. Tenreiro Machado

Received: 24 February 2021 / Revised: 24 March 2021 / Accepted: 28 March 2021 / Published: 31 March 2021

(This article belongs to the Special Issue New Achievements on Chaos, Turbulence and Complexity in Heliospheric Space Plasma Dynamics)

The solar photosphere and the outer layer of the Sun’s interior are characterized by convective motions, which display a chaotic and turbulent character. In this work, we evaluated the pseudo-Lyapunov exponents of the overshooting convective motions observed on the Sun’s surface by using a method employed in the literature to estimate those exponents, as well as another technique deduced from their definition. We analyzed observations taken with state-of-the-art instruments at ground- and space-based telescopes, and we particularly benefited from the spectro-polarimetric data acquired with the Interferometric Bidimensional Spectrometer, the Crisp Imaging SpectroPolarimeter, and the Helioseismic and Magnetic Imager. Following previous studies in the literature, we computed maps of four quantities which were representative of the physical properties of solar plasma in each observation, and estimated the pseudo-Lyapunov exponents from the residuals between the values of the quantities computed at any point in the map and the mean of values over the whole map. In contrast to previous results reported in the literature, we found that the computed exponents hold negative values, which are typical of a dissipative regime, for all the quantities derived from our observations. The values of the estimated exponents increase with the spatial resolution of the data and are almost unaffected by small concentrations of magnetic field. Finally, we showed that similar results were also achieved by estimating the exponents from residuals between the values at each point in maps derived from observations taken at different times. The latter estimation technique better accounts for the definition of these exponents than the method employed in previous studies.