📝 SummarXiv

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 influences the diffusive transport of solar energetic particles. This study employs magnetogram data acquired by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory to characterize an ensemble of spatial autocorrelation functions (ACFs) of magnetic fluctuations in the photosphere. It is shown that the two-point ACFs satisfy the similarity-decay hypothesis of von K\'arm\'an and Howarth, a fundamental property of turbulent systems: following a rescaling of the ACFs by energy and correlation lengths, a quasi-universal functional form is obtained demonstrating exponential decay of correlations. The probability distribution function of transverse correlation lengths (\(\lambda\)) is shown to be approximately log-normal. A mosaic of the spatial distribution of \(\lambda\) over the photosphere is presented; the ``quiet Sun'' tends to have \(\lambda\sim 1500\) 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 \(\lambda\), and empirical fits are derived to quantify this relationship. These results improve our understanding of the nature of turbulence in the solar photosphere and the origin of coronal and solar-wind turbulence, while providing observational constraints for models that describe the transport of turbulence from solar and stellar photospheres into their atmospheres.