A new model for the (geo)magnetic power spectrum, with application to planetary dynamo radii

Research areas:
Earth Planet. Sci. Lett.
We propose two new analytical
expressions to fit the Mauersberger~Lowes
geomagnetic field spectrum at the core~mantle
boundary. These can be used to estimate the radius
of the outer liquid core where the geodynamo
operates, or more generally the radius of the
planetary dynamo regions. We show that two
sub-families of the geomagnetic field are
independent of spherical harmonics degree nat the
core~mantle boundary and exhibit flat spectra. The
first is the non-zonal field, i.e., for spherical
harmonics order mdifferent from zero. The second is
the quadrupole family, i.e., n +meven. The flatness
of their spectra is motivated by the nearly
axisymmetric time-average paleomagnetic field (for
the non-zonal field) and the dominance of rotational
effects in core dynamics (for the quadrupole
family). We test our two expressions with two
approaches using the reference case of the
Earth. First we estimate at the seismic core radius
the agreement between the actual spectrum and the
theoretical one. Second we estimate the magnetic
core radius, where the spectrum flattens. We show
that both sub-families offer a better agreement with
the actual spectrum compared with previously
proposed analytical expressions, and predict a
magnetic core radius within less than 10 km of the
Earth~s seismic core radius. These new expressions
supersede previous ones to infer the core radius
from geomagnetic field information because the low
degree terms are not ignored. Our formalism is then
applied to infer the radius of the dynamo regions on
Jupiter, Saturn, Uranus and Neptune. The
axisymmetric nature of the magnetic field of Saturn
prevents the use of the non-zonal expression. For the
three other planets both expressions converge and
offer independent constraints on the internal
structure of these planets. These non-zonal and
quadrupole family expressions may be implemented to
extrapolate the geomagnetic field spectrum beyond
observable degrees, or to further regularize
magnetic field models constructed from modern or
historical observations.