Filling factors and magnetic field strengths of nanoflare-heated coronal active regions: Yohkoh and MDI observations

The scaling laws describing the relationship between thermal and magnetic properties of active regions are derived using the concept that solar coronal active regions are heated by numerous small flare-like events (nanoflares). Thus, a coronal active region is viewed as an ensemble of hot elementary filaments created within the coronal magnetic field by random impulsive heating events. The scaling laws obtained are governed by the global energy balance of the active regions and are independent of the details of any heating process (such as the energy of individual heating event or energy spectral index of nanoflares). We examined 61 coronal active regions observed with the soft X-ray telescope aboard Yohkoh and found that such a model yields filling factors (defined as the ratio of the volume of hot plasma to the total volume) in the range 0.002 to 0.015 and magnetic field strengths of 20 G to 40 G. The analysis determining the mean magnetic field strength and filling factors of a large number of coronal active regions, observed by Yohkoh, based on nanoflare-heating concept is the first such analysis. We also examine 24 active regions observed with the Michelson Doppler Imager aboard Solar and Heliospheric Observatory and find that the total thermal energy content E-th is related to the total magnetic flux phi by a power-law index of 1.24 i.e. E-th proportional to phi(1.24). The thermal pressure p(th) of the active regions is related to the magnetic flux density B-p obtained from MDI measurement as: p(th) proportional to B-p(0.5).