Ap stars with resolved magnetically split lines: Magnetic field determinations from Stokes $I$ and $V$ spectra

We present the results of a systematic study of the magnetic fields and other properties of the Ap stars with resolved magnetically split lines. This study is based on new measurements of the mean magnetic field modulus, the mean longitudinal magnetic field, the crossover, the mean quadratic magnetic field, and the radial velocity of 43 stars, complemented by magnetic data from the literature for 41 additional stars. Stars with resolved magnetically split lines represent a significant fraction, of the order of several percent, of the whole population of Ap stars. Most of them are genuine slow rotators, whose consideration provides new insight into the long-period tail of the distribution of the periods of the Ap stars. Emerging correlations between rotation periods and magnetic properties provide important clues for the understanding of the braking mechanisms that have been at play in the early stages of stellar evolution. The geometrical structures of the magnetic fields of Ap stars with magnetically resolved lines appear in general to depart slightly, but not extremely, from centred dipoles. However, there are a few remarkable exceptions, which deserve further consideration. We suggest that pulsational crossover can be observed in some stars; if confirmed, this would open the door to the study of non-radial pulsation modes of degree $\ell$ too high for photometric or spectroscopic observations. How the lack of short orbital periods among binaries containing an Ap component with magnetically resolved lines is related with their (extremely) slow rotation remains to be fully understood, but the very existence of acorrelation between the two periods lends support to the merger scenario for the origin of Ap stars.