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The solar-stellar connection after CoRoT and Kepler

The solar-stellar experiment started with the HK Project at Mount Wilson Observatory initiated by Olin Wilson in 1966, continued with the hunt for solar analogs up through the eighties and nighties and have culminated so-far with the remarkable results from CoRoT and Kepler.

With the term *the solar-stellar connection* we understand primary the field where studies of Sun-like stars are used to increase our understanding of the Sun. In this review we will focus on how Sun-like stars can be used to increased our understanding of the solar dynamo. The solar dynamo can theoretical be described by the magnetohydrodynamical (MHD) induction equation(Charbonneau 2005):

\[\frac{\partial {\rm \bf B}}{\partial t} = \nabla \times \left({\rm \bf u} \times {\rm \bf B} - \eta \nabla \times {\rm \bf B} \right)\]

where \({\bf B}\) is the magnetic field, \(\eta\) is the magnetic diffusivity and \({\bf u}\) is the large-scale flow field. This flow filed can be expressed as a sum of an axisymmetric azimuthal component originating from the differential rotation ans a axisymmetric poloidal component originating from the meridional circulation:

\[{\rm \bf u} = {\rm \bf u_p}\left( r,\theta \right) + r ~{\rm sin}~\theta ~ \Omega \left( r, \theta \right) \hat {\rm e}_{\phi}\]

where \(r\) is the distance from the center of the Sun and \(\Omega\) is the angular velocity.

It is thus clear that in order for the Sun or other Sun-like stars to host a dynamo they need to have magnetic fields, differential rotation and meridional circulation or convection. These ingredience have thus been chosen as the subject to be covered by this review:

Magnetic fields

Rotation

Convection

One chapter will thus be dedicated to each of these subjects in this review. We have also dedicated a chapter to the discussion of the ’Solar Analogs’ and ’The Sun in Time’ projects (Strobel, 1996; Güdel, 2007).

This review will be based on

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