From stellar coronae to gyrochronology: A theoretical and observational exploration

Context. Stellar spin down is the result of a complex process involving rotation, dynamo, wind, and magnetism. Multiwavelength surveys of solar-like stars have revealed the likely existence of relationships between their rotation, X-ray luminosity, mass losses, and magnetism. They impose strong constraints on the corona and wind of cool stars.Aims. We aim to provide power-law prescriptions of the mass loss of stars, of their magnetic field, and of their base coronal density and temperature that are compatible with their observationally-constrained spin down.Methods. We link the magnetic field and the mass-loss rate from a wind torque formulation, which is in agreement with the distribution of stellar rotation periods in open clusters and the Skumanich law. Given a wind model and an expression of the X-ray luminosity from radiative losses, we constrained the coronal properties by assuming different physical scenarios linking closed loops to coronal holes.Results. We find that the magnetic field and the mass loss are involved in a one-to-one correspondence that is constrained from spin down considerations. We show that a magnetic field, depending on both the Rossby number and the stellar mass, is required to keep a consistent spin down model. The estimates of the magnetic field and the mass-loss rate obtained from our formalism are consistent with statistical studies as well as individual observations and they give new leads to constrain the magnetic field-rotation relation. The set of scaling-laws we derived can be broadly applied to cool stars from the pre-main sequence to the end of the main sequence (MS), and they allow for stellar wind modeling that is consistent with all of the observational constraints available to date.