From stellar coronae to gyrochronology: A theoretical and observational exploration

Abstract

Context. Stellar spin-down is the result of a complex process involving rotation, dynamo, wind and magnetism. Multi-wavelength surveys of solar-like stars have revealed the likely existence of relationships between their rotation, X-ray luminosity, mass-losses and magnetism. Those 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 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 constrain the coronal properties by assuming different physical scenarii 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 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 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 PMS to the end of the MS, and allow for a stellar wind modelling consistent with all the observational constraints available to date.

Magnetic and tidal migration of close-in planets

“…Such a modeling requires knowledge of the temperature T c and density n c at the base of the wind. For consistency with the observational constraints on stellar rotation, wind, and magnetism, we rely on the Ahuir et al (2020) prescriptions for those quantities. More precisely, as the stellar magnetic field measured from Zeeman broadening and Zeeman-Doppler imaging (see Montesinos & Jordan 1993;Vidotto et al 2014;See et al 2017) have only exhibited linear or super-linear dependencies between the large-scale magnetic field and the Rossby number, we consider for the sake of simplicity the following scaling law to assess the magnetic field at the stellar surface B (Ahuir et al 2020):…”

“…( 19)) can affect the relative importance of the magnetic torque in our model. To illustrate this we consider the alternative prescription proposed by Ahuir et al (2020), which shows the steepest Rossby number dependency:…”

“…To keep a consistent wind model, the T c and n c prescriptions need to be updated as (Ahuir et al 2020):…”

“…As this intricacy may significantly affect the evolution of a given star-planet system, it is necessary to take such processes into account as much as possible. This requires models calibrated on gyrochronology and rotational distributions in open clusters (Gallet & Bouvier 2015;Matt et al 2015), leading up to general frameworks combining stellar rotation, wind, and magnetism (Johnstone et al 2015;Ahuir et al 2020). Past studies have taken these constraints into account to some extent.…”

Models of Star-Planet Magnetic Interaction

“…The largest uncertainty lies here in the lack of knowledge of the key stellar properties (rotation period, magnetic field) in the sample. For this review I revisited the updated ensemble of Kepler-observed exosystems while using the wind-modelling strategy developed by Ahuir et al (2020). This strategy can be applied for the stars with a detected rotational period (McQuillan et al 2014): a stellar Rossby number can then be estimated based on the scaling law derived from 3D numerical simulation by Brun et al (2017).…”