Variation of the magnetic field of the Ap star HD 50169 over its 29-year rotation period

Abstract

Context. The Ap stars that rotate extremely slowly, with periods of decades to centuries, represent one of the keys to the understanding of the processes leading to the differentiation of stellar rotation. Aims. We characterise the variations of the magnetic field of the Ap star HD 50169 and derive constraints about its structure. Methods. We combine published measurements of the mean longitudinal field B z of HD 50169 with new determinations of this field moment from circular spectropolarimetry obtained at the 6-m telescope BTA of the Special Astrophysical Observatory of the Russian Academy of Sciences. For the mean magnetic field modulus B , literature data are complemented by the analysis of ESO spectra, both newly acquired and from the archive. Radial velocities are also obtained from these spectra. Results. We present the first determination of the rotation period of HD 50169, P rot = 29.04 ± 0.82 y. HD 50169 is currently the longest-period Ap star for which magnetic field measurements have been obtained over more than a full cycle. The variation curves of both B z and B have a significant degree of anharmonicity, and there is a definite phase shift between their respective extrema. We confirm that HD 50169 is a wide spectroscopic binary, refine its orbital elements, and suggest that the secondary is probably a dwarf star of spectral type M. Conclusions. The shapes and mutual phase shifts of the derived magnetic variation curves unquestionably indicate that the magnetic field of HD 50169 is not symmetric about an axis passing through its centre. Overall, HD 50169 appears similar to the bulk of the long-period Ap stars.

Modeling of magneto-rotational stellar evolution

“…The peak rotation velocity of ∼40 km s −1 (Netopil et al 2017) is considerably slower than the major peak at ∼200 km s −1 of the wide distribution of rotation velocities of normal AB-type stars. Some of the Ap/Bp stars even show superlong rotational periods of P rot > 1000 d (Kochukhov & Bagnulo 2006;Netopil et al 2017;Mathys et al 2019Mathys et al , 2020. Interestingly, a similar tendency is also observed for pre-MS stars known as Herbig Ae/Be stars: magnetic Herbig Ae/Be stars are concentrated to have slow rotation velocities of 50 km s −1 , while normal Herbig Ae/Be stars obey a wide distribution with a typical velocity of 50−250 km s −1 (Alecian et al 2013).…”

“…The angular momentum loss rate linearly correlates with the wind mass-loss rate of a nonmagnetic star and the magnetic braking efficiency, which also linearly correlates with the surface field strength in a strong field limit (see Appendix C). Under this simplified case, ∼97% reduction of the currently applied value of ∼10 −12 M yr −1 , which is estimated according to de Jager et al (1988), will be required to stay within the rotation period of HD 50169 of 10 600 d, the slowest rotating Ap star with accurate magnetic field determinations so far discovered, for a magnetic stellar model with P rot,ini = 100 d and the field strength of HD 50169 of B p ∼ 4300 G (Mathys et al 2019(Mathys et al , 2020. Where a magnetic star of B p ∼ 100 G is assumed to acquire 40 times slower rotation period at TAMS phase (Table 1) with the mass loss rate from de Jager et al (1988).…”

Long-period Ap stars discovered with TESS data

“…This complementarity was already recognised by Preston (1969), who showed how it could be exploited to derive a simple model of the geometrical structure of an Ap star magnetic field (Preston 1970a). Fifty years on, a similar approach, albeit refined, is still used to build simple models of the magnetic fields of the Ap stars with the longest accurately determined periods, which simultaneously match the variation curves of their mean longitudinal fields and their mean magnetic field moduli (Mathys et al 2016;Mathys et al 2019a;Mathys et al 2019b;Mathys et al 2020).…”

“…Otherwise, one may at most derive a lower limit of the period value, which may represent a more or less meaningful constraint according to the case. This limitation has been discussed in detail by Mathys et al (2019a).…”

“…It is important to note here that the first determination of the rotation period of an Ap star was achieved just over 100 years ago (Belopolsky 1913); that hardly more than 70 years have elapsed since the first detection of a magnetic field in such a star (Babcock 1947); that for the star that has been observed in a sustained manner over the longest time base without covering yet a full rotation period, γ Equ (= HD 201601), the available magnetic measurements span ∼70 years (Bychkov et al 2016); and that the longest rotation period that has been accurately determined up to now for an Ap star (HD 50169 = BD −1 1414) is 29 yr (Mathys et al 2019a). These time scales are all considerably shorter than the longest periods of 300-1000 yr that are expected for some Ap stars.…”