von Karman - Howarth Similarity of Spatial Correlations and the Distribution of Correlation Lengths in Solar Photospheric Turbulence

Abstract

Fluctuations in the Sun's photospheric magnetic field are the primary source of the turbulence that can heat and accelerate the solar atmosphere, and thus play an important role in the production and evolution of the solar wind that permeates the heliosphere. A key parameter that characterizes this turbulence is the correlation scale of fluctuations, which determines the injection of turbulent energy into the plasma and the diffusive transport of solar energetic particles. This study employs magnetogram data from the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory to characterize an ensemble of spatial autocorrelation functions (ACFs) of turbulence in the photosphere. It is shown that the two-point ACFs satisfy the similarity-decay hypothesis of von Kármán and Howarth, a fundamental property of turbulent systems: rescaling the ACFs by their respective energies and correlation lengths yields a quasi-universal exponential form. The probability distribution function of transverse correlation lengths (\(λ\)) is shown to be approximately log-normal, which is consistent with observations of turbulence in the solar wind. A ``mosaic'' of the spatial distribution of \(λ\) over the photosphere is presented; the ``quiet Sun'' tends to have \(λ\sim 1500\) km (albeit with a wide distribution), which is close to the scale of solar granulation; systematically longer lengths are associated with active regions. A positive correlation is observed between mean magnetic field magnitude and \(λ\), and empirical fits quantify this relationship. These results improve our understanding of solar turbulence while providing observational constraints for models that describe turbulence transport from solar and stellar photospheres into their atmospheres.

arXiv commentAccepted for publication in the Monthly Notices of the Royal Astronomical Society

References in corpus (23)

• Self-consistent Coronal Heating and Solar Wind Acceleration from Anisotropic Magnetohydrodynamic Turbulence
• The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: Overview and Performance
• Alfven Wave Solar Model (AWSoM): Coronal Heating
• Alfven Waves in the Lower Solar Atmosphere
• Alfven Waves and Turbulence in the Solar Atmosphere and Solar Wind
• A turbulence-driven model for heating and acceleration of the fast wind in coronal holes
• 25 Years of Self-Organized Criticality: Concepts and Controversies
• Magnetic Flux Transport at the Solar Surface
• Validating a Time-Dependent Wave-Turbulence-Driven Model of the Solar Wind
• Fading Coronal Structure and the Onset of Turbulence in the Young Solar Wind
• In situ observations of large amplitude Alfvén waves heating and accelerating the solar wind
• Turbulence, Complexity, and Solar Flares
• Closed-Field Coronal Heating Driven by Wave Turbulence
• Cosmic Ray Diffusion Coefficients Throughout The Inner Heliosphere From Global Solar Wind Simulation
• Turbulence in the Solar Atmosphere: Manifestations and Diagnostics via Solar Image Processing
• Characterization of the Turbulent Magnetic Integral Length in the Solar Wind: From 0.3 to 5 Astronomical Units
• Strategies for determining the cascade rate in MHD turbulence: isotropy, anisotropy, and spacecraft sampling
• Direct Measurement of the Solar-Wind Taylor Microscale using MMS Turbulence Campaign Data
• Turbulence in the Solar Photosphere
• Characteristic Length of Energy-Containing Structures at the Base of a Coronal Hole
• Random Walk and Trapping of Interplanetary Magnetic Field Lines: Global Simulation, Magnetic Connectivity, and Implications for Solar Energetic Particles
• Statistics of Photospheric Supergranular Cells Observed by SDO/HMI
• Correlation Functions of Photospheric Magnetic Fields in Solar Active Regions