Seismic inference of differential rotation in Procyon A

The differential rotation of the F5V-IV star Procyon A is computed for a class of models which are consistent with recent astrometric and asteroseismic data. The rotation pattern is determined by solving the Reynolds equation for motion, including the convective energy transport, where the latter is anisotropic owing to the Coriolis force action which produces a horizontal temperature gradient between the poles and the equator. All the models show a decrease of the rotation rate with increasing radius and solar-type isorotation surfaces with the equator rotating faster than the poles, the horizontal rotational shear being much smaller for models with a less extended convective envelope. The meridional flow circulation can be either clockwise or counter-clockwise, and in some cases a double latitudinal cell appears. The rotational splittings are calculated for low degree $p$-modes with $l=1, m=1$ and $l=2, m=1,2$, and it is shown that, for modes with $m=1$, the stronger is the horizontal differential rotation shear the weaker the effect on the average rotational splitting expected, whilst the opposite happens for the mode with $m=2$. On the basis of the present study, a resolution of $10 \rm nHz$ in individual oscillation frequencies seems to be necessary to test the different dynamical behaviour of the proposed models, that appears barely achievable even in the forthcoming space missions. However, the average over several observed splittings could produce the required accuracy.