ISSN 1990-3413, Astrophysical Bulletin, 2018, Vol. 73, No. 2, pp. 201–210.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
Yu.V. Glagolevskij, A.F. Nazarenko, 2018, published in Astroﬁzicheskii Byulleten’, 2018, Vol. 73, No. 2, pp. 207–216.
Probable Inner Magnetic Structures of Magnetic Stars. I
Yu. V. Glagolevskij
and A. F. Nazarenko
Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnii Arkhyz, 369167 Russia
Received November 3, 2017; in ﬁnal form, March 5, 2018
Abstract—In this paper we consider two-dipole inner structures of magnetic ﬁelds of magnetic stars
obtained by modelling. A series of our papers on modelling the structures including this paper shows that
there is an extraordinary variety of structures and parameters of stellar magnetic ﬁelds. Actually, there are no
two stars with exactly the same properties. This indicates a large variety of magnetized parent protostellar
clouds, from which magnetic stars are formed.
Key words: stars: magnetic ﬁeld—stars: chemically peculiar
A possible scenario of formation of magnetic
structures at the gravitational-collapse stage in mag-
netic stars is considered in details in papers [1–3].
Apparently, the largest magnetic structures are pre-
served during the unstable Hayashi phase and du-
ring the evolution of a young radiant star. In Main
Sequence stars, the small-scale component of the
magnetic ﬁeld  can still be observed which was
preserved from previous periods of evolution, but it al-
ready has little eﬀect on the observed large structures.
Toroidal ﬁelds do not cause the observed Zeeman
eﬀect. This implies that the ﬁeld of magnetic stars is of
a poloidal character. High-order multipoles also give
a small integral eﬀect, but the predominant compo-
nent is dipole. This fundamental conclusion made by
Preston  is the basis for modelling a magnetic ﬁeld
of magnetic stars. Even earlier Babcock  suggested
that from the form of spectral line proﬁles, the mag-
netic ﬁeld does not belong to a single spot, as it is on
the Sun. A star is entirely magnetized, the structure
of the magnetic ﬁeld is dipole, but the presence
of a small-scale fraction is possible. Large-scale
structures of protostellar magnetic clouds contract
when collapsing into poloidal structures. In the stellar
phase, they are described (at a ﬁrst approximation) by
a “non-point” virtual dipole, in which the distance
between monopoles sometimes reaches the fractions
of the radius. In such a dipole, the ﬁeld lines converge
at the location points of virtual monopoles. It is
diﬃcult to imagine a situation in which a magnetized
cloud compressed during a collapse will contract into
a volume at which the structure of a magnetic ﬁeld in
its center is described by a theoretical “point” dipole.
In order to describe inner and surface structures, such
a dipole is selected when modelling, whose ﬁeld lines
near the surface of the star coincide with the observed
ﬁeld lines. Obviously, the structure of the ﬁeld near
thedipoleisdiﬀerent, the ﬁeld is poloidal there. This
should be kept in mind when considering the ﬁgures
presented below. Modelling results  show that the
dipole representation of magnetic ﬁeld structures is
close to the current reality. This method provides
good results even when measurements are conducted
with a precise accuracy of several Gausses. Almost
in all cases, the model phase curves of magnetic ﬁeld
variations coincide with the observed within the range
of 3σ. If both phase dependencies of the longitudinal
and mean surface B
magnetic ﬁelds are known,
then the model and observed phase dependencies
coincide within the limits of errors with similar given
parameters. Thus, we obtain a self-consistent result.
This conﬁrms not only the correctness of the model
but also the correctness of the measurements.
In the papers [8, 9], magnetic ﬁeld structures of
three unique stars were studied. They contain three
magnetized regions that create a complex distribution
of the inner and surface magnetic ﬁelds. In the present
paper, we will consider simpler structures formed by
two magnetized volumes. In such structures, dipoles
can be located in the equatorial plane or at an angle to
it. Therefore, we will consider both variants.
2. MODELS WITH DIPOLES IN THE PLANE
OF THE ROTATION EQUATOR
Paper  gives the main parameters of the mag-
netic ﬁeld of magnetic stars, including those in which
the dipoles are in the equatorial plane. Table 1 shows