Rossby numbers and stiffness values inferred from gravity-mode asteroseismology of rotating F- and B-type dwarfs

Abstract

Context. Multi-dimensional (magneto-)hydrodynamical simulations of physical processes in stellar interiors depend on a multitude of uncalibrated free parameters, which set the spatial and time scales of their computations. Aims. We aim to provide an asteroseismic calibration of the wave and convective Rossby numbers, and of the stiffness at the interface between the convective core and radiative envelope of intermediate-mass stars. We deduce these quantities for rotating dwarfs from the observed properties of their identified gravity and gravito-inertial modes. Methods. We relied on near-core rotation rates and asteroseismic models of 26 B- and 37 F-type dwarf pulsators derived from 4-year Kepler space photometry, high-resolution spectroscopy, and Gaia astrometry in the literature to deduce their convective and wave Rossby numbers. We computed the stiffness at the interface of the convective core and the radiative envelope from the inferred maximum buoyancy frequency at the interface and the convective turnover frequency in the core. We use those asteroseismically inferred quantities to make predictions of convective penetration levels, local flux levels of gravito-inertial waves triggered by the convective core, and of the cores’ potential rotational and magnetic states. Results. Our sample of 63 gravito-inertial mode pulsators covers near-core rotation rates from almost zero up to the critical rate. The frequencies of their identified modes lead to models with stiffness values between 102.69 and 103.60 for the B-type pulsators, while those of F-type stars cover the range from 103.47 to 104.52. The convective Rossby numbers derived from the maximum convective diffusion coefficient in the convective core, based on mixing length theory and a value of the mixing length coefficient relevant for these pulsators, vary between 10−2.3 and 10−0.8 for B-type stars and 10−3 and 10−1.5 for F-type stars. The 17 B-type dwarfs with an asteroseismic estimate of the penetration depth reveal it to be in good agreement with recent theory of convective penetration that takes rotation into account. Theoretical estimates based on the observationally inferred convective Rossby numbers and stiffness values lead to local stochastically-excited gravito-inertial wave fluxes which may exceed those predicted for non-rotating cores, in agreement with observations. Finally, the convective core of rapid rotators is expected to have cylindrical differential rotation causing a magnetic field of 20–400 kG for B-type stars and of 0.1–3 MG for F-type stars. Conclusions. Our results provide asteroseismic calibrations to guide realistic (magneto-)hydrodynamical simultations of rotating (magnetised) core convection in stellar interiors of dwarfs and future modelling of transport and mixing processes in their interiors.