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

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.

[1]  Z. Musielak,et al.  Vertical propagation of acoustic waves in the solar internetworkas observed by IRIS , 2018, Monthly Notices of the Royal Astronomical Society.

[2]  Mark Peter Rast,et al.  The Scales of Granulation, Mesogranulation, and Supergranulation , 2003 .

[3]  A. Hanslmeier,et al.  Dynamics of solar mesogranulation , 2005 .

[4]  S. Tsuneta,et al.  Emergence of Small-Scale Magnetic Loops in the Quiet-Sun Internetwork , 2007, 0708.0844.

[5]  J. C. del Toro Iniesta,et al.  The Polarimetric and Helioseismic Imager on Solar Orbiter , 2019, Astronomy & Astrophysics.

[6]  S. Solanki,et al.  Where the Granular Flows Bend , 2010, 1008.0517.

[7]  P. Charbonneau Dynamo Models of the Solar Cycle , 2005 .

[8]  J.-M. Malherbe,et al.  Dynamics of the solar granulation. , 1987 .

[9]  On the Formation of a Stable Penumbra in a Region of Flux Emergence in the Sun , 2016, 1611.04749.

[10]  L. B. Rubio,et al.  Magnetic field emergence in quiet Sun granules , 2007, 0712.2663.

[11]  D. Del Moro,et al.  DIFFUSION OF SOLAR MAGNETIC ELEMENTS UP TO SUPERGRANULAR SPATIAL AND TEMPORAL SCALES , 2013, 1305.4006.

[12]  P. Holmes Chaotic Dynamics , 1985, IEEE Power Engineering Review.

[13]  A. Hanslmeier,et al.  Dynamics of small-scale convective motions , 2016, 1611.06786.

[14]  P. Young,et al.  IRIS Observations of Magnetic Interactions in the Solar Atmosphere between Preexisting and Emerging Magnetic Fields. I. Overall Evolution , 2018, 1802.05657.

[15]  W. Herschel XIII. Observations tending to investigate the nature of the sun, in order to find the causes or symptoms of its variable emission of light and heat; with remarks on the use that may possibly be drawn from solar observations , 1801, Philosophical Transactions of the Royal Society of London.

[16]  J. T. Hoeksema,et al.  The Helioseismic and Magnetic Imager (HMI) Investigation for the Solar Dynamics Observatory (SDO) , 2012 .

[17]  L. Gizon,et al.  Interpreting the Helioseismic and Magnetic Imager (HMI) Multi-Height Velocity Measurements , 2014, 1404.3569.

[18]  T. Shimizu,et al.  Height-dependent Velocity Structure of Photospheric Convection in Granules and Intergranular Lanes with Hinode/SOT , 2016, 1612.06175.

[19]  T. Duvall,et al.  Long-lived giant cells detected at the surface of the Sun , 1998, Nature.

[20]  E. Hijano,et al.  DEAD CALM AREAS IN THE VERY QUIET SUN , 2012, 1206.4545.

[21]  F. Moreno-insertis,et al.  Magnetic flux emergence into the solar photosphere and chromosphere , 2009 .

[22]  G. Scharmer Comments on the optimization of high resolution Fabry-Pérot filtergraphs , 2006 .

[23]  T. Riethmüller,et al.  Linear Polarization Features in the Quiet-Sun Photosphere: Structure and Dynamics , 2018, Solar Physics.

[24]  M. Rieutord,et al.  Acoustic Events in the Solar Atmosphere from Hinode/SOT NFI Observations , 2012, 1207.1170.

[25]  D. F. Gray,et al.  Solar Surface Magneto-Convection , 2022 .

[26]  Magnetic upflow events in the quiet-Sun photosphere. I. Observations , 2015, 1507.07355.

[27]  F. Berrilli,et al.  Dynamics and Structure of Supergranulation , 2004 .

[28]  S. Solanki,et al.  The Small-scale Structure of Photospheric Convection Retrieved by a Deconvolution Technique Applied to Hinode/SP Data , 2017, 1709.06933.

[29]  Mats G. Lofdahl Multi-frame blind deconvolution with linear equality constraints , 2002, SPIE Optics + Photonics.

[30]  Dirk Soltau,et al.  European Solar Telescope: Progress status , 2010 .

[31]  S. Solanki,et al.  The Frontier between Small-scale Bipoles and Ephemeral Regions in the Solar Photosphere: Emergence and Decay of an Intermediate-scale Bipole Observed with SUNRISE/IMaX , 2011, 1110.1405.

[32]  L. B. Rubio,et al.  MULTIWAVELENGTH OBSERVATIONS OF SMALL-SCALE RECONNECTION EVENTS TRIGGERED BY MAGNETIC FLUX EMERGENCE IN THE SOLAR ATMOSPHERE , 2010, 1007.4657.

[33]  P. Young,et al.  IRIS Observations of Magnetic Interactions in the Solar Atmosphere between Preexisting and Emerging Magnetic Fields. II. UV Emission Properties , 2018, The Astrophysical Journal.

[34]  L. B. Rubio,et al.  EMERGENCE OF SMALL-SCALE MAGNETIC LOOPS THROUGH THE QUIET SOLAR ATMOSPHERE , 2009, 0905.2691.

[35]  Pawan Kumar,et al.  Wave generation by turbulent convection , 1990 .

[36]  B. Jurcevich,et al.  The Solar Optical Telescope for the Hinode Mission: An Overview , 2007, 0711.1715.

[37]  B. Pontieu,et al.  New View of the Solar Chromosphere , 2019, Annual Review of Astronomy and Astrophysics.

[38]  J. C. del Toro Iniesta,et al.  On the Magnetic Nature of an Exploding Granule as Revealed by Sunrise/IMaX , 2020, The Astrophysical Journal.

[39]  Francesco Berrilli,et al.  Testing the Steady-State Fluctuation Relation in the Solar Photospheric Convection , 2020, Entropy.

[40]  Kinematics of Magnetic Bright Features in the Solar Photosphere , 2016, 1610.07634.

[41]  J. Toomre,et al.  The detection of mesogranulation on the sun. , 1981 .

[42]  A. Tritschler,et al.  Plasma flows and magnetic field interplay during the formation of a pore , 2017, 1701.06440.

[43]  D. Del Moro,et al.  DIFFUSION OF MAGNETIC ELEMENTS IN A SUPERGRANULAR CELL , 2014, 1405.0677.

[44]  Viggo Hansteen,et al.  The stellar atmosphere simulation codeBifrost: Code description and validation , 2011 .

[45]  B. Freytag,et al.  Lyapunov exponents for solar surface convection. , 1995 .

[46]  K. R. Sreenivasan,et al.  Turbulent convection at very high Rayleigh numbers , 1999, Nature.

[47]  M. Rieutord,et al.  Families of Granules, Flows, and Acoustic Events in the Solar Atmosphere from Hinode Observations , 2015 .

[48]  G. Consolini,et al.  Polarized Kink Waves in Magnetic Elements: Evidence for Chromospheric Helical Waves , 2017, 1704.02155.

[49]  L. B. Bellot Rubio,et al.  Quiet Sun magnetic fields: an observational view , 2019, Living Reviews in Solar Physics.

[50]  F. Giorgi,et al.  A Comparative Analysis of Photospheric Bright Points in an Active Region and in the Quiet Sun , 2012 .

[51]  Arnold Hanslmeier,et al.  Time Series of Solar Granulation Images. I. Differences between Small and Large Granules in Quiet Regions , 1997 .

[52]  M. Rieutord,et al.  The Sun’s Supergranulation , 2010, 1005.5376.

[53]  On the polarimetric signature of emerging magnetic loops in the quiet-Sun , 2012, 1201.6501.

[54]  F. Cavallini IBIS: A New Post-Focus Instrument for Solar Imaging Spectroscopy , 2006 .

[55]  Characterization and formation of on-disk spicules in the Ca II K and Mg II k spectral lines , 2019, Astronomy & Astrophysics.

[56]  F. Berrilli,et al.  Structure Properties of Supergranulation and Granulation , 2004 .

[57]  Robert F. Stein,et al.  Solar Surface Convection , 2009, Living reviews in solar physics.

[58]  T. Berger,et al.  The Horizontal Magnetic Flux of the Quiet-Sun Internetwork as Observed with the Hinode Spectro-Polarimeter , 2008 .

[59]  D. Hathaway,et al.  Giant Convection Cells Found on the Sun , 2013, Science.

[60]  F. Berrilli,et al.  Observational evidence for buffeting-induced kink waves in solar magnetic elements , 2014, 1408.3987.

[61]  A. Hanslmeier,et al.  Time Series of Solar Granulation Images. II. Evolution of Individual Granules , 1999 .

[62]  M. Asplund,et al.  Simulations of the solar near-surface layers with the CO5BOLD, MURaM, and Stagger codes , 2012, 1201.1103.

[63]  Mats G. Löfdahl,et al.  Solar Image Restoration By Use Of Multi-frame Blind De-convolution With Multiple Objects And Phase Diversity , 2005 .

[64]  M. Stangalini,et al.  Height Dependence of the Penumbral Fine-scale Structure in the Inner Solar Atmosphere , 2018, The Astrophysical Journal.

[65]  G. Puglisi,et al.  Comparison of different populations of granular features in the solar photosphere , 2017 .

[66]  M. Löfdahl,et al.  CRISPRED: A data pipeline for the CRISP imaging spectropolarimeter , 2014, 1406.0202.

[67]  Thuy Mai,et al.  Solar Dynamics Observatory (SDO) , 2015 .

[68]  J. C. del Toro Iniesta,et al.  TRANSVERSE COMPONENT OF THE MAGNETIC FIELD IN THE SOLAR PHOTOSPHERE OBSERVED BY Sunrise , 2010, 1008.1535.

[69]  V. Pillet,et al.  Small scale horizontal magnetic fields in the solar photosphere , 1996 .

[70]  M. Roth,et al.  Dynamics of the solar granulation. VII. A nonlinear approach , 2001 .

[71]  J. C. del Toro Iniesta,et al.  The Solar Orbiter mission , 2020, Optics & Photonics - Optical Engineering + Applications.

[72]  R. Shine,et al.  Evolution and advection of solar mesogranulation , 1992, Nature.

[73]  R. Erdélyi,et al.  THE GENERATION AND DAMPING OF PROPAGATING MHD KINK WAVES IN THE SOLAR ATMOSPHERE , 2013, 1310.4650.

[74]  M. Rieutord,et al.  On mesogranulation, network formation and supergranulation , 2000 .

[75]  Bernhard Fleck,et al.  The solar orbiter mission , 2003 .

[76]  W. Schaffenberger,et al.  Simulations of stellar convection with CO5BOLD , 2011, J. Comput. Phys..