Connecting the large- and the small-scale magnetic fields of solar-like stars

Abstract

A key question in understanding the observed magnetic field topologies of cool stars is the link between the small-and the large-scale magnetic field and the influence of the stellar parameters on the magnetic field topology. We examine various simulated stars to connect the small-scale with the observable large-scale field. The highly resolved 3D simulations we used couple a flux transport model with a nonpotential coronal model using a magnetofrictional technique. The surface magnetic field of these simulations is decomposed into spherical harmonics which enables us to analyse the magnetic field topologies on a wide range of length scales and to filter the large-scale magnetic field for a direct comparison with the observations. We show that the large-scale field of the self-consistent simulations fits the observed solar-like stars and is mainly set up by the global dipolar field and the large-scale properties of the flux pattern, e.g. the averaged latitudinal position of the emerging small-scale field and its global polarity pattern. The stellar parameters flux emergence rate, differential rotation and meridional flow affect the large-scale magnetic field topology. An increased flux emergence rate increases the magnetic flux in all field components and an increased differential rotation increases the toroidal field fraction by decreasing the poloidal field. The meridional flow affects the distribution of the magnetic energy across the spherical harmonic modes.

Observing the simulations: applying ZDI to 3D non-potential magnetic field simulations

“…The higher the flux emergence rate the more active regions are present at the same time and the stronger the axisymmetric toroidal = 2-mode (see Figs.7-8b). An increase in differential rotation decreases the poloidal field of the active regions, which further increases the toroidal fraction, see Lehmann et al (2018). The increase of the axisymmetry and toroidal fraction with stellar activity results therefore from the strengthening of the axisymmetric toroidal = 2 mode, mainly due to the increase of active regions on the stellar surface following the solar flux emergence pattern.…”

“…To summarise: ZDI recovers the visible structure of the large-scale field morphology of solar-like stars but loses the magnetic field strength. Limiting the original input maps to the large-scale field via the spherical harmonic decomposition (see Lehmann et al 2017;Lehmann et al 2018) provides a very good approximation of the magnetic field morphology structure that will be recovered by ZDI. Although ZDI is allowed to use -modes up = 7 it recovers structures up to ≤ 5 most of the time.…”

The magnetic field vector of the Sun-as-a-star – II. Evolution of the large-scale vector field through activity cycle 24

“…For example, while the toroidal energy of the quadrupole ( = 2) is larger than that of the dipole ( = 1) or octupole ( = 3), for the poloidal energy, the inverse is true (see Figure 4, right panels). This happens because the sun's magnetic polarity switches across the equator, which enhances even toroidal degrees and odd poloidal degrees (Lehmann et al 2017(Lehmann et al , 2018. This creates a 'zig-zag' distribution of toroidal or poloidal energies per degree as a function of .…”

“…This definition is similar to that used in See et al (2015) and Lehmann et al (2017Lehmann et al ( , 2018. In some other ZDI works, alternative definitions of the axisymmetric condition have been used (e.g., m < /2, Fares et al 2009).…”

The Solar Wind in Time II: 3D stellar wind structure and radio emission

“…Maps for the minima and maxima are taken at Carrington rotations 1983 and 2078 respectively, which were observed with SOHO/MDI in the years 2001 and 2008. We have removed the higher degree harmonics ( ≥ 5) for both maps, so as to replicate the Sun as if observed similarly to the other slowly rotating stars in the sample (Vidotto 2016;Vidotto et al 2018;Lehmann et al 2018). We note that the Sun at maximum possesses a much more complex magnetic geometry than the solar minimum, including a stronger magnetic field (e.g.…”