Comparison Between Coronal Loop Solutions and Coronal Scaling Laws

During the past several years we have developed an accurate and efficient numerical technique for solving the steady-state energy and momentum balance equations in the solar corona, given an assumed variation of the coronal heating rate with the magnetic field strength and coronal loop length. By solving the energy equation for thousands of magnetic field lines in a given active region, one can build up a global solution for the thermodynamic structure of an active region, given its magnetic configuration. In contrast with other published results, our solutions explicitly allow for the arbitrary variation of field strength along a loop, and self-consistently determine the steady flows that will result from asymmetries in the field variation. While the steady-state energy balance assumption is probably not correct for most of the loops in an active region, our hope is that we will still gain insights as to how global properties of the corona are related to one another from the large number of loop solutions we can obtain. In this poster, we use the large number of field-line solutions to empirically test and correct the well-known scaling laws relating loop pressure, temperature, loop length, and magnetic field strength. We also present new results relating the variation of steady-state loop flow speeds with asymmetries in the loop geometry.