2017A&A...601A..14M

Context. Some Ap stars that have a strong enough magnetic field and a sufficiently low vsini show spectral lines resolved into their magnetically split components.
Aims. We present the results of a systematic study of the magnetic fields and other properties of those stars.
Methods. This study is based on 271 new measurements of the mean magnetic field modulus <B> of 43 stars, 231 determinations of the mean longitudinal magnetic field <B_z> and of the crossover <X_z> of 34 stars, and 229 determinations of the mean quadratic magnetic field <B_q> of 33 stars. Those data were used to derive new values or meaningful lower limits of the rotation periods P_rot of 21 stars. Variation curves of the mean field modulus were characterised for 25 stars, the variations of the longitudinal field were characterised for 16 stars, and the variations of the crossover and of the quadratic field were characterised for 8 stars. Our data are complemented by magnetic measurements from the literature for 41 additional stars with magnetically resolved lines. Phase coverage is sufficient to define the curve of variation of <B> for 2 of these stars. Published data were also used to characterise the <B_z> curves of variation for 10 more stars. Furthermore, we present 1297 radial velocity measurements of the 43 Ap stars in our sample that have magnetically resolved lines. Nine of these stars are spectroscopic binaries for which new orbital elements were derived.
Results. The existence of a cut-off at the low end of the distribution of the phase-averaged mean magnetic field moduli <B>_av of the Ap stars with resolved magnetically split lines, at about 2.8kG, is confirmed. This reflects the probable existence of a gap in the distribution of the magnetic field strengths in slowly rotating Ap stars, below which there is a separate population of stars with fields weaker than ∼2kG. In more than half of the stars with magnetically resolved lines that have a rotation period shorter than 150 days, <B>_av>7.5kG, while those stars with a longer period all have <B>_av<7.5kG. The difference between the two groups is significant at the 100.0% confidence level. The relative amplitudes of variation of the mean field modulus may tend to be greater in stars with P_rot>100d than in shorter period stars. The root-mean-square longitudinal fields of all the studied stars but one is less than one-third of their phased-average mean field moduli, which is consistent with the expected behaviour for fields whose geometrical structure resembles a centred dipole. However, moderate but significant departures from the latter are frequent. Crossover resulting from the correlation between the Zeeman effect and the rotation-induced Doppler effect across the stellar surface is definitely detected in stars with rotation periods of up to 130 days and possibly even up to 500 days. Weak, but formally significant crossover of constant sign, has also been observed in a number of longer period stars, which could potentially be caused by pulsation velocity gradients across the depth of the photosphere. The quadratic field is in average ∼1.3 times greater than the mean field modulus and both of those moments vary with similar relative amplitudes and almost in phase in most stars. Rare exceptions almost certainly have unusual field structures. The distribution of the known values and lower limits of the rotation periods of the Ap stars with magnetically resolved lines indicates that for some of them, P_rot must almost certainly reach 300 yr or possibly even much higher values. Of the 43 Ap stars that we studied in detail, 22 are in binary systems. The shortest orbital period P_orb of those systems is 27 days. For those non-synchronised Ap binaries for which both the rotation period and the orbital period, or meaningful lower limits thereof, are reliably determined, the distribution of the orbital periods of the systems in which the Ap star has a rotation period that is shorter than 50 days is different from its distribution for those systems in which the rotation period of the Ap star is longer, at a confidence level of 99.6%. The shortest rotation and orbital periods are mutually exclusive: all but one of the non-synchronised systems that contain an Ap component with P_rot<50d, have P_orb>1000 d.
Conclusions. 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 these stars are genuine slow rotators, whose consideration provides new insight into the long-period tail of the distribution of the periods of 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. Confirmation that pulsational crossover is indeed occurring at a detectable level would open the door to the study of non-radial pulsation modes of degree l, which is 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 to their (extremely) slow rotation remains to be fully understood, but the very existence of a correlation between the two periods lends support to the merger scenario for the origin of Ap stars.