Subresolution Activity in Solar and Stellar Coronae from Magnetic Field Line Tangling

The heating of coronal loops is investigated to understand the observational consequences in terms of the thermodynamics and radiative losses from the Sun as well as the magnetized coronae of stars with an outer convective envelope. The dynamics of the Parker coronal heating model are studied for different ratios of the photospheric forcing velocity timescale $t_p$ to the Alfv\'en crossing time along a loop $t_A$. It is shown that for $t_p/t_A \gtrsim$ 10--24 the heating rate and maximum temperature are largest and approximately independent of $t_p/t_A$, leading to a strong emission in X-rays and EUV. On the opposite decreasing $t_p/t_A$ to smaller values leads to lower heating rates and plasma temperatures, and consequently fading high-energy radiative emission once $t_p/t_A \lesssim$ 1--3. The average volumetric loop heating rate is shown to scale as $\ell_p u_p B_0^2/4\pi L^2$, where $\ell_p$ and $u_p$ are respectively the convective granule length-scale and velocity, $B_0$ is the intensity of the strong magnetic field threading the loop, and $L$ the loop length. These findings support a recent hypothesis explaining ultracool dwarf observations of stars with similar magnetic field strength but radically different topologies displaying different radiative emission.