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Astron. Astrophys. 329, 315-318 (1998)

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1. Introduction

It is now a well known result of helioseismology that the radiative part of the Sun rotates almost as a solid body, at least down to [FORMULA] (cf. e.g. Brown et al. 1989). Until recently, the only way to achieve that result was to advocate a magnetic field. Indeed, both rotation-induced turbulent diffusion (Endal & Sofia 1978; Pinsonneault et al. 1989) and wind-driven meridian circulation (Zahn 1992) fail to extract sufficient angular momentum from the radiative interior (Chaboyer et al. 1995; Matias & Zahn 1997). However, there is a problem with the magnetic solution: if the field lines are anchored in the convection zone, they should enforce differential rotation in the radiative interior, unless the link occurs in narrow region at mid latitude.

A step forward was taken recently by Zahn et al. (1997) (which will be referred to as ZTM) and by Kumar & Quataert (1997) when they examined the role of the gravity waves generated at the base of the convective zone. They found that such waves transport momentum "non-locally" on a rather short timescale, and that they tend to flatten the rotation profile.

Let us recall briefly the somewhat different approaches used by the two groups. Gravity waves conserve their momentum as long as they are not damped. Thus when assuming that both prograde ( [FORMULA] ) and retrograde ( [FORMULA] ) waves are excited with the same intensity at the base of the convective region, differential damping is required in order to get a net deposit of momentum. This differential damping will be provided by the Doppler shift due to differential rotation, since radiative damping varies as [FORMULA] (where [FORMULA] is the local frequency). Zahn et al. consider only the damping in the critical layer where this local frequency goes to zero. There the waves are completely damped, and they deposit the totality of their momentum. At the same time, the frequency of their [FORMULA] counterparts increases, diminishing their damping. Thus they will be able to travel all the way to the core and back, to be re-absorbed by the convective zone 1. On the other hand, Kumar & Quataert retained those waves for which the differential damping between the [FORMULA] and [FORMULA] waves remains small, and they use a linearized form of that difference to study the deposition of momentum. The two approaches are thus complementary, and it is planned to combine both effects.

However in this first numerical study, we keep only the transport of angular momentum by the waves which are completely damped in their critical layer. This contribution will be added to that due to meridional circulation and shear turbulence.

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© European Southern Observatory (ESO) 1998

Online publication: November 24, 1997