## 1. Introduction

[2] Determining the properties of a planet's deep interior is difficult because we cannot observe this region directly as we can the surface of a planet. On Earth, seismology has provided important information on the structure and composition of the deep interior including the core. For example the radii of the inner and outer cores were determined from seismic studies [*Gutenberg*, 1913; *Lehmann*, 1936]. In addition, properties of the Earth's outer core motions have been determined mostly from observations of the geomagnetic field secular variation (for a review see *Bloxham and Jackson* [1991]). Unfortunately we are not, at present, able to conduct detailed seismic studies and observations of magnetic field secular variation for other planets to provide us with the same quality of information on their cores. We are however, capable of studying a planet's magnetic field morphology quite extensively with an orbiting spacecraft at relatively low altitude. This was demonstrated in convincing fashion by Mars Global Surveyor which mapped Mars' remanent crustal magnetic field to very high spherical harmonic degree and order [*Acuna et al.*, 1999; *Arkani-Hamed*, 2004].

[3] In rapidly rotating fluids, a two-dimensionality is imposed on the fluid flow as a result of the Taylor-Proudman theorem [*Proudman*, 1916; *Taylor*, 1917]. In the spherical shell geometry of planetary cores (see Figure 1), this two-dimensionality results in the division of the fluid outer core into two dynamical regimes by the inner core tangent cylinder (an imaginary cylinder tangent to the inner core boundary and coaxial with the rotation axis). Numerical and experimental models have demonstrated that the region outside this cylinder has convective motions governed by columnar structures (motions with little variation in the direction of the rotation axis). Depending on the parameter regime, convection can occur in the form of steady cylindrical rolls [*Busse*, 1970] or highly variable (in existence, shape and time) columnar structures (examples of convection patterns in numerical dynamo models are given by *Zhang and Schubert* [2000] and *Kono and Roberts* [2002]). The two regions inside the tangent cylinder (one north and one south of the equatorial plane) are more constrained by the rapid rotation and therefore require more complex helical motions to transport heat or a compositionally buoyant element from the inner core boundary to the core-mantle boundary. These regions have also been studied experimentally, numerically and by observational analysis [e.g., *Gubbins and Bloxham*, 1987; *Aurnou et al.*, 1998, 2003; *Olson and Aurnou*, 1999; *Sreenivasan and Jones*, 2005].

[4] Because magnetic fields in planetary cores are generated by interactions of fluid motions with existing magnetic fields, it seems likely that different motions and force balances inside and outside the tangent cylinder could lead to different magnetic field structures in these regions. This suggests that we may be able to use observed magnetic field structures to determine the division between these regions and hence, determine the size of the inner core in planets with active dynamos. Here we use numerical dynamo models to investigate whether any distinct magnetic field structures that are observable outside the core correlate with inner core size in an effort to guide future magnetic observations by planetary spacecraft missions.