Scaling laws of coronal loops compared to a 3D MHD model of an active region

Context. The structure and heating of coronal loops have been investigated for decades. Established scaling laws relate fundamental quantities like the loop apex temperature, pressure, length, and coronal heating. Aims. We test these scaling laws against a large-scale 3D magneto-hydrodynamics (MHD) model of the solar corona, which became feasible with current high-performance computing. Methods. We drove an active region simulation with photospheric observations and find strong similarities to the observed coronal loops in X-rays and extreme-ultraviolet (EUV) wavelength. A 3D reconstruction of stereoscopic observations shows that our model loops have a realistic spatial structure. We compared scaling laws to our model data extracted along an ensemble of field lines. Finally, we fit a new scaling law that represents hot loops and also cooler structures, which was not possible before based only on observations. Results. Our model data gives some support for scaling laws that were established for hot and EUV-emissive coronal loops. For the Rosner-Tucker-Vaiana (RTV) scaling law we find an off set to our model data, which can be explained by 1D considerations of a static loop with a constant heat input and conduction. With a fit to our model data we set up a new scaling law for the coronal heat input along magnetic field lines. Conclusions. RTV-like scaling laws were fitted to hot loops and therefore do not predict well the coronal heat input for cooler structures that are barely observable. The basic differences between 1D and self-consistent 3D modeling account for deviations between earlier scaling laws and ours. We also conclude that a heating mechanism by MHD-turbulent dissipation within a braided flux tube would heat the corona stronger than is consistent with our model corona.