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Nature | Vol 610 | 6 October 2022 | 43
Article
Magnetic fields of 30 to 100 kG in the cores
of red giant stars
Gang Li1, Sébastien Deheuvels1 ✉, Jérôme Ballot1 & François Lignières1
A red giant star is an evolved low- or intermediate-mass star that has exhausted its
central hydrogen content, leaving a helium core and a hydrogen-burning shell.
Oscillations of stars can be observed as periodic dimmings and brightenings in the
optical light curves. In red giant stars, non-radial acoustic waves couple to gravity
waves and give rise to mixed modes, which behave as pressure modes in the envelope
and gravity modes in the core. These modes have previously been used to measure the
internal rotation of red giants1,2, leading to the conclusion that purely hydrodynamical
processes of angular momentum transport from the core are too inecient3.
Magnetic elds could produce the additional required transport4–6. However, owing
to the lack of direct measurements of magnetic elds in stellar interiors, little is
currently known about their properties. Asteroseismology can provide direct
detection of magnetic elds because, like rotation, the elds induce shifts in the
oscillation mode frequencies7–12. Here we report the measurement of magnetic elds
in the cores of three red giant stars observed with the Kepler13 satellite. The elds
induce shifts that break the symmetry of dipole mode multiplets. We thus measure
eld strengths ranging from about 30 kilogauss to about 100 kilogauss in the vicinity
of the hydrogen-burning shell and place constraints on the eld topology.
Rotation lifts the degeneracy between the angular frequencies ω of
oscillation modes with same degree l and radial order n but different
azimuthal order m. This produces multiplets with (2l + 1) components,
which can be used to probe the internal rotation of stars. At first order,
rotational multiplets are symmetric with respect to the central (m = 0)
component, as is the case for all red giants studied so far
2
. Magnetic
fields are known to break this symmetry9–12,14.
We detected clear asymmetries in the multiplets of three hydrogen-
shell burning giants observed with Kepler, namely KIC 8684542,
KIC 7518143 and KIC 11515377 (Fig.1). We notice several common charac-
teristics for the three stars. First, the asymmetries of dipole multiplets,
defined as δ
asym
= ω
m=−1
+ ω
m=+1
− 2ω
m=0
(ref.
15
), consistently have the same
sign for each star: they are all positive (or consistent with zero) for KIC
8684542 (Fig.2) and KIC 7518143, but negative for KIC 11515377. Second,
the absolute values of the asymmetries are systematically lower for
pressure (p)-dominated modes (dark shaded regions in Fig.2) than
for gravity (g)-dominated modes (light shaded regions). This indicates
that the cause of the asymmetries is located in the core. Finally, the
detected asymmetries sharply decrease with frequency.
In the presence of magnetic fields, we showed that, under very gen-
eral assumptions, the average frequency shift of the components in a
dipole multiplet is given by
I∫
δω
ζ
μω Kr Br=()d,(1
)
r
r
rB
0
32
i
o
where B
r
2
is a horizontal average of the squared radial field Br, ri and ro
are the turning points of the g-mode cavity,
I
is a term depending on
the core structure (Supplementary Information), and
μ0
is the perme-
ability of the vacuum. The weight function K(r) sharply peaks near the
hydrogen-burning shell, so that δωB essentially measures B
r
2
near this
shell (Extended Data Fig.1). The dependence of δω
B
in ω
−3
shows that
magnetic perturbations are expected to sharply decrease with fre-
quency. The factor ζ corresponds to the fraction of the mode kinetic
energy that is trapped in the g-mode cavity (ζ = 1 for pure gravity
modes). Equation(1) shows that magnetic shifts are expected to be
larger for g-dominated modes than for p-dominated modes. The char-
acteristics of magnetic shifts are thus very similar to those of the
detected asymmetries.
Asymmetries originate from the dependence of magnetic shifts on
|m|. The asymmetry of dipole multiplets can be directly related to the
average magnetic shift by the expression
δaδω=3 .
(2
)
asym B
The coefficient a involves an average of
Br
2
weighted by the second
degree Legendre polynomial
Pθ θ(cos )=(3cos−1)
/2
22
, where θ is the
colatitude, and we have shown that −1/2 ⩽ a ⩽ 1 (Supplementary Infor-
mation). For instance, a dipole magnetic field (Br ~ cosθ) yields a posi-
tive asymmetry (a = 2/5). A field that is entirely concentrated on the
poles produces maximal asymmetry (a = 1). Conversely, a field con-
centrated near the equator gives minimal asymmetry (a = −1/2).
We then compared the measured asymmetries with those that
would be produced by internal magnetic fields. We fit an expression
of δasym based on equations(1) and (2) to the observed asymmetries.
The results are shown in Fig.2. The agreement with the observed
https://doi.org/10.1038/s41586-022-05176-0
Received: 15 April 2022
Accepted: 2 August 2022
Published online: 5 October 2022
Check for updates
1IRAP, Université de Toulouse, CNRS, CNES, UPS, Toulouse, France. ✉e-mail: sebastien.deheuvels@irap.omp.eu
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