A number of recent works have highlighted that it is possible to express the properties of general-relativistic stellar equilibrium configurations in terms of functions that do not depend on the specific equation of state employed to describe matter at nuclear densities. These functions are normally referred to as "universal relations" and have been found to apply, within limits, both to static or stationary isolated stars, as well as to fully dynamical and merging binary systems. Further extending the idea that universal relations can be valid also away from stability, we show that a universal relation is exhibited also by equilibrium solutions that are not stable. In particular, the mass of rotating configurations on the turning-point line shows a universal behaviour when expressed in terms of the normalized Keplerian angular momentum. In turn, this allows us to compute the maximum mass allowed by uniform rotation, M max , simply in terms of the maximum mass of the nonrotating configuration, M TOV , finding that M max (1.203 ± 0.022) M TOV for all the equations of state we have considered. We further introduce an improvement to previouly published universal relations by Lattimer & Schutz between the dimensionless moment of inertia and the stellar compactness, which could provide an accurate tool to constrain the equation of state of nuclear matter when measurements of the moment of inertia become available.

Context. Coronal loops are the basic building block of the upper solar atmosphere as seen in the extreme UV and X-rays. Comprehending how these are energized, structured, and evolve is key to understanding stellar coronae. Aims. Here we investigate how the energy to heat the loop is generated by photospheric magneto-convection, transported into the upper atmosphere, and how the internal structure of a coronal magnetic loop forms. Methods. In a 3D magnetohydrodynamics model, we study an isolated coronal loop rooted with both footpoints in a shallow layer within the convection zone using the MURaM code. To resolve its internal structure, we limited the computational domain to a rectangular box containing a single coronal loop as a straightened magnetic flux tube. Field-aligned heat conduction, gray radiative transfer in the photosphere and chromosphere, and optically thin radiative losses in the corona were taken into account. The footpoints were allowed to interact self-consistently with the granulation surrounding them. Results. The loop is heated by a Poynting flux that is self-consistently generated through small-scale motions within individual magnetic concentrations in the photosphere. Turbulence develops in the upper layers of the atmosphere as a response to the footpoint motions. We see little sign of heating by large-scale braiding of magnetic flux tubes from different photospheric concentrations at a given footpoint. The synthesized emission, as it would be observed by the Atmospheric Imaging Assembly or the X-Ray Telescope, reveals transient bright strands that form in response to the heating events. Overall, our model roughly reproduces the properties and evolution of the plasma as observed within (the substructures of) coronal loops. Conclusions. With this model we can build a coherent picture of how the energy flux to heat the upper atmosphere is generated near the solar surface and how this process drives and governs the heating and dynamics of a coronal loop.

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Context. Vortex flows have been found in the photosphere, chromosphere, and low corona in observations and simulations. It has been suggested that vortices play an important role in channeling energy and plasma into the corona. However, the impact of vortex flows on the corona has not been studied directly in a realistic setup. Aims. We investigate the role vortices play for coronal heating using high-resolution simulations of coronal loops. The vortices are not artificially driven and they arise, instead, self-consistently from magnetoconvection. Methods. We performed 3D resistive (magnetohydrodynamic) MHD simulations with the MURaM code. Studying an isolated coronal loop in a Cartesian geometry allows us to resolve the structure of the loop interior. We conducted a statistical analysis to determine vortex properties as a function of height from the chromosphere into the corona. Results. We find that the energy injected into the loop is generated by internal coherent motions within strong magnetic elements. A significant part of the resulting Poynting flux is channeled through the chromosphere in vortex tubes forming a magnetic connection between the photosphere and corona. Vortices can form contiguous structures that reach up to coronal heights, but in the corona itself, the vortex tubes get deformed and eventually lose their identity with increasing height. Vortices show increased upward directed Poynting flux and heating rate in both the chromosphere and corona, but their effect becomes less pronounced with increasing height. Conclusions. While vortices play an important role for the energy transport and structuring in the chromosphere and low corona, their importance higher up in the atmosphere is less clear since the swirls are less distinguishable from their environment. Vortex tubes reaching the corona reveal a complex relationship with the coronal emission.