Reconciling solar and stellar
magnetic cycles with nonlinear
A. Strugarek,1,2 P. Beaudoin,1 P. Charbonneau,1 A. S. Brun,2 J.-D. do Nascimento Jr.3,4
The magnetic fields of solar-type stars are observed to cycle over decadal periods—11 years
in the case of the Sun. The fields originate in the turbulent convective layers of stars and
have a complex dependency upon stellar rotation rate. We have performed a set of turbulent
global simulations that exhibit magnetic cycles varying systematically with stellar rotation
and luminosity. We find that the magnetic cycle period is inversely proportional to the
Rossby number, which quantifies the influence of rotation on turbulent convection. The trend
relies on a fundamentally nonlinear dynamo process and is compatible with the Sun’s cycle
and those of other solar-type stars.
The characterization of stellar activity and its dynamo origin has broad applications, from exoplanet searches to space weather forecasting. Observational data now allow the determination of absolute luminosities
via accurate parallax measurements, rotation
through Doppler line broadening and precision
photometry, stellar differential rotation through
photometry and asteroseismic sounding, and the
large-scale spatial structure of stellar photospheric
magnetic fields through Zeeman-Doppler imag-
ing. These data complement stellar activity mea-
surements, available from long-term monitoring
programs (1, 2), that showed complex varia-
tions of stellar cycle amplitudes and periods as a
function of fundamental stellar parameters such
as mass, luminosity, rotation, and age. The phys-
ical understanding of stellar activity is henceforth
more complex than suggested by earlier inter-
pretation of stellar cycle data through mean-
field dynamo theory (3–5).
Modern global magnetohydrodynamic (MHD)
simulations of solar convection and large-scale
flows have succeeded in producing, in a self-consistent manner, large-scale magnetic fields
(6, 7), in some cases generating regular, solar-like
cyclic magnetic polarity reversals (8–11). Thus, these
simulations are used today to help our physical interpretation of stellar magnetic cycle observations.
We have performed a set of global MHD simulations with the EULAG-MHD code (12), using
a fixed-background stellar structure but covering
rotation periods (Prot) between 14 and 29 days
and a convective luminosity between 0.2 and 0.6
solar luminosity (table S1). The simulated domain consists of a global (i.e., spherical) stellar
convection zone with a solar-like aspect ratio
(the radius at the bottom of the spherical shell is
70% of the radius at the top, Rtop), covering 3.22
density scale-heights with no underlying stable
radiation zone. All simulations in the set generate some solar-like features, including (i) an
accumulation of a kilo-Gauss, large-scale axisym-metric magnetic field at the bottom of the convection zone; (ii) regular polarity reversals on a
decadal time scale, reasonably synchronized
across hemispheres; (iii) an equatorial propagation of the large-scale magnetic field (Fig. 1);
and (iv) solar-like differential rotation (fast at
the equator, slow at the poles). Some nonsolar
features were also produced, including the concentration of toroidal magnetic field at mid-rather than low latitudes, and an irregularly
alternating pattern of symmetric and antisymmetric equatorial parity. This is apparent in Fig.
1D, where periods of symmetrical and antisymmetrical states follow one another. Such parity
drifts are understood to reflect the interactions
between the two families of dynamo symmetry
(13–16), which couple in nonlinear regimes such
as the one achieved in our experiment.
The magnetic cycle trends in our set of simulations are displayed in Fig. 2 (blue circles with
error bars), where two main trends are identified.
First, the magnetic cycle period (Pcyc) is found
to decrease in proportion to the rotation rate
when the convective luminosity is held constant
(Fig. 2A). Second, the cycle period also decreases
Fig. 1. A nonlinear, global magnetic
cycle. (A to C) Snapshots of a representative three-dimensional nonlinear
simulation of a regular magnetic cycle.
White (positive) and purple (negative)
volumes represent the radial velocity
(in meters per second) of the convective flow. A half sector of the spherical
shell has been cut out to display the
large-scale magnetic field lines (
averaged over 50 rotation periods) buried in
the convection zone (the red or blue
coloring of the magnetic tubes labels
positive or negative azimuthal magnetic
field, respectively). The magnetic field
lines extending beyond the simulation
domain are derived from a standard
potential field extrapolation (28).
(D) Longitudinal average of the azimuthal
component of the magnetic field (Bϕ) as
a function of latitude and time at
depth r = 0.72Rtop (where Rtop is the
radius at the top of the spherical shell).
1Département de Physique, Université de Montréal, C.P. 6128
Succursale Centre-Ville, Montréal, Quebec H3C-3J7, Canada.
2Laboratoire Astrophysique, Instrumentation, Modélisation
Paris-Saclay, Commissariat à l'Energie Atomique et aux
Energies Alternatives/Irfu Université Paris-Diderot CNRS/
Institut National des Sciences de l’Univers, F-91191 Gif-sur-Yvette, Paris, France. 3Departamento de Física Teórica e
Experimental, Universidade Federal do Rio Grande do Norte,
CP 1641, 59072-970 Natal, Rio Grande do Norte, Brazil.
4Harvard–Smithsonian Center for Astrophysics, Cambridge,
MA 02138, USA.
*Corresponding author. Email: email@example.com