tokens: a coronal loop in our model) is significantly lower. While our whole computational domain covers more grid points () than the Rappazzo et al. (2008) models (up to ), in their model they describe only a single loop structure (straightened out), and consequently can reach significantly higher Reynolds numbers. Table 1 Exponents for different coronal heating scaling laws as used in Eqs. ( 10 ) and ( 11 ) together with the fitting results from Sect. 5.3 . The coronal heating scaling law we fit to our model data indicates a dependency on the magnetic field that lies between the exponents given by Rappazzo et al. (2008) and van Ballegooijen et al. (2011) . We also find that the homogeneous atmospheric background in the MHD-turbulence setup of Rappazzo et al. (2008) may be problematic when estimating the coronal magnetic energy input or braiding of field lines because the Alfvén crossing time , which determines their scaling law exponents, varies strongly within our stratified atmosphere. In a recent study van Ballegooijen et al. (2014) speculate that the quasi-static behavior of the coronal magnetic field found in models like ours is due to the limited spatial resolution of the photospheric magnetic driving. They suggest that in the case of increased resolution, the heating might be wave-dominated. Certainly, with increasing resolution AC heating will also be present, but this does not automatically imply that the DC heating becomes less efficient. To the contrary, models that employ reduced MHD (allowing for a higher spatial resolution) show that MHD turbulence will lead to a DC-type heating by the build-up of current sheets also for high spatial resolution (e.g., Rappazzo et al. 2008 ). This is backed by the argument that in the coronal part of the atmosphere a field line will adapt quickly to any wave excitation from below because coronal Alfvén speeds are at least one order of magnitude faster than within the lower atmosphere (cf. Fig. A.1 and Table A.1 ). More realistic full MHD simulations with increased resolution will have to show the relative merits of AC and DC heating based on the photospheric driving. The temperature scaling laws we tested against our model field lines ( Rosner et al. 1978 ; Serio et al. 1981 ) indicate only general trends for the most heated field lines and EUV-emissive loops. This puts all attempts to set up scaling laws of the coronal heating into their context, namely that these laws are deduced from and are only applicable to a small subset of coronal field lines, namely the ones that are bright in EUV or X-rays. Non-emissive and weakly heated field lines are often not consistent with scaling laws intended for 1D loop structures. Some of their plasma parameters need to be determined differently, for example, through self-consistent 3D MHD simulations. It is an interesting question whether such observationally motivated scaling laws would benefit from new and much more precise observations of hot coronal loops. We
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