Standing torsional Alfvén waves as the source of the rotational period variation in magnetic early-type stars

Context. The influence of magnetic fields on stellar evolution remains unresolved. It has been proposed that if there is a large-scale magnetic field in the stellar interior, torsional Alfvén waves could arise, efficiently transporting angular momentum. In fact, the observed variations in the rotation periods of some magnetic stars can be attributed to these torsional Alfvén waves’ standing waves. Aims. We aim to demonstrate the existence of torsional Alfvén waves through modeling of the rotational period variations. Methods. We conducted an eigenmode analysis of standing Alfvén waves based on one-dimensional magnetohydrodynamic equations. We parametrically represented internal magnetic field structures to treat poloidal fields with different degrees of central or surface concentration. We compared the obtained frequencies with the observed frequencies of the rotational period variations, thereby constraining the internal magnetic field structures. Results. The cycle length of CU Vir’s rotational period variation of 67.6 years is reproduced for surface-concentrated magnetic field structures. The rotational period variations of all ten magnetic stars analyzed in this study are inconsistent with a centrally concentrated magnetic field. Conclusions. Torsional Alfvén waves can reproduce the observations of rotational period variations. The large-scale magnetic fields within magnetic stars are likely concentrated on the surface.