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Multi-dimensional (magneto-)hydrodynamical simulations of physical processesin stellar interiors depend on a multitude of uncalibrated free parameters,which set the spatial and time scales of their computations. We aim to providean asteroseismic calibration of the wave and convective Rossby numbers, and ofthe stiffness at the interface between the convective core and radiativeenvelope of intermediate-mass stars. We deduce these quantities for rotatingdwarfs from the observed properties of their identified gravity andgravito-inertial modes. We rely on near-core rotation rates and asteroseismicmodels of 26 B- and 37 F-type dwarf pulsators derived from 4-year Kepler spacephotometry, high-resolution spectroscopy and Gaia astrometry in the literatureto deduce their convective and wave Rossby numbers. We compute the stiffness atthe convection/radiation interface from the inferred maximum buoyancy frequencyat the interface and the convective turnover frequency in the core. We usethose asteroseismically inferred quantities to make predictions of convectivepenetration levels, local flux levels of gravito-inertial waves triggered bythe convective core, and of the cores' potential rotational and magneticstates. Our sample of 63 gravito-inertial mode pulsators covers near-corerotation rates from almost zero up to the critical rate. The frequencies oftheir identified modes lead to models with stiffness values between $10^{2.69}$and $10^{3.60}$ for the B-type pulsators, while those of F-type stars cover therange from $10^{3.47}$ to $10^{4.52}$. The convective Rossby numbers derivedfrom the maximum convective diffusion coefficient in the convective core, basedon mixing length theory and a value of the mixing length coefficient relevantfor these pulsators, vary between $10^{-2.3}$ and $10^{-0.8}$ for B-type starsand $10^{-3}$ and $10^{-1.5}$ for F-type stars. (abridged)

astronomy and astrophysics

Rossby numbers and stiffness values inferred from gravity-mode  asteroseismology of rotating F- and B-type dwarfs: consequences for mixing,  transport, magnetism, and convective penetration