Reexamining the Power-law Relationship between Global Solar X-Ray Luminosity and Total Unsigned Magnetic Flux

Abstract The mechanism heating the solar corona remains unclear but is generally hypothesized to involve magnetic fields. One probe of this hypothesis is a statistical study relating coronal emission to magnetic flux. A. A. Pevtsov et al. conducted such a survey relating X-ray luminosity ( L X ) to unsigned photospheric magnetic flux (Φ m ) for a variety of heated plasmas, ranging from solar quiet regions to T Tauri stars. They reported that a power-law relationship, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">X</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">Φ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1.15</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , described the entire collection but found that the subset from solar disk–integrated flux was better fit by a broken power law. Several parameters entering the calculations of L X and Φ m have the potential to impact this analysis. The present study uses more recent data to reanalyze the flux–luminosity relationship for the full solar disk and examines its dependence on parameters. We find the most significant effects from two parameters: the cutoff field strength used in computation of Φ m and the range of wavelengths defining L X . We find further that lower choices of cutoff yield a broken power law, while an optimal choice yields a single power law and minimizes the fitting residual. The critical cutoff is well above the magnetogram noise level, suggesting that weaker fields may not contribute significantly to the X-ray corona. We also find that L X defined by decreasing wavelength ranges requires an increasing critical cutoff. The resulting power-law indices vary, but all fall around 1.2.