Magnetic confinement of the solar tachocline: II. Coupling to a convection zone A. Strugarek, A.S. Brun, J.-P. Zahn To cite this version: A. Strugarek, A.S. Brun, J.-P. Zahn. Magnetic confinement of the solar tachocline: II. Coupling to a convection zone. Astronomy and Astrophysics - A&A, EDP Sciences, 2011, 532, pp.A34. 10.1051/0004-6361/201116518. cea-00828296 HAL Id: cea-00828296 https://hal-cea.archives-ouvertes.fr/cea-00828296 Submitted on 22 Jul 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Astronomy & Astrophysics manuscript no. Magnetic˙Confinement_TachoclineII_arxiv c ESO 2018 October 12, 2018 Magnetic confinement of the solar tachocline: II. Coupling to a convection zone A. Strugarek1, A. S. Brun1 and J.-P. Zahn2;1 1 Laboratoire AIM Paris-Saclay, CEA/Irfu Universit´eParis-Diderot CNRS/INSU, F-91191 Gif-sur-Yvette, France 2 LUTH, Observatoire de Paris, CNRS-Universit´eParis Diderot, Place Jules Janssen, 92195 Meudon, France Received 14 january 2011 / Accepted 12 June 2011 ABSTRACT Context. The reason for the observed thinness of the solar tachocline is still not well understood. One of the explanations that have been proposed is that a primordial magnetic field renders the rotation uniform in the radiation zone. Aims. We test here the validity of this magnetic scenario through 3D numerical MHD simulations that encompass both the radiation zone and the convection zone. Methods. The numerical simulations are performed with the anelastic spherical harmonics (ASH) code. The computa- tional domain extends from 0:07 R to 0:97 R . Results. In the parameter regime we explored, a dipolar fossil field aligned with the rotation axis cannot remain confined in the radiation zone. When the field lines are allowed to interact with turbulent unstationary convective motions at the base of the convection zone, 3D effects prevent the field confinement. Conclusions. In agreement with previous work, we find that a dipolar fossil field, even when it is initially buried deep in- side the radiation zone, will spread into the convective zone. According to Ferraro's law of iso-rotation, it then imprints on the radiation zone the latitudinal differential rotation of the convection zone, which is not observed. Key words. Sun: interior { Sun: rotation { Magnetohydrodynamics { Convection { Magnetic Fields 1. Introduction because Miesch (2003) found in his numerical simulations that this turbulence is indeed anti-diffusive in the verti- The discovery of the solar tachocline can be considered as cal direction, but the shear is reduced in latitude. Similar one of the great achievements of helioseismology (see Brown conclusions were reached through theoretical (analytical) et al. 1989). In this layer the rotation switches from differ- studies by Kim (2005), Leprovost & Kim (2006), and Kim ential (i.e., varying with latitude) in the convection zone & Leprovost (2007). to nearly uniform in the radiation zone below. Its extreme thinness (less than 5 % of the solar radius) came as a sur- Gough & McIntyre proposed an alternate model, in prise (see Charbonneau et al. 1999) and has still not been which a primordial magnetic field is buried in the radia- explained properly. tive zone and inhibits the spread of the tachocline. This is Spiegel & Zahn (1992) made the first attempt to model achieved through a balance between the confined magnetic the tachocline, and they showed that it should spread deep field and a meridional flow pervading the base of the convec- into the radiation zone owing to thermal diffusion. As a re- tion zone. Such a fossil field was also invoked by Rudiger & Kitchatinov (1997) to explain the thinness of the tachocline sult, the differential rotation should extend down to 0:3 R after 4:5 Gyr, contrary to what is inferred from helioseis- and by Barnes et al. (1999) to interpret the lithium-7 de- mology (Schou et al. 1998; Thompson et al. 2003). The au- pletion at the solar surface. Moreover, it would easily ac- thors suggested one way to confine the tachocline, namely count for the quasi uniform rotation of the radiative inte- to counter-balance thermal diffusion by an anisotropic tur- rior, which the hydrodynamic model of Spiegel & Zahn does bulence, which would smooth the differential rotation in not (at least in its original formulation). However, one may latitude. This model was successfully simulated in 2D by expect that such a field would spread by ohmic diffusion, arXiv:1107.3665v1 [astro-ph.SR] 19 Jul 2011 Elliott (1997). and that it would eventually connect with the convection Gough & McIntyre (1998) (GM98 hereafter) argued zone, thus imposing the differential rotation of that zone that such an anisotropic turbulent momentum transport is on the radiation zone below. not able to erode a large-scale latitudinal shear, citing ex- In order to test the magnetic confinement scenario and amples from geophysical studies (see Starr 1968 and more to put constraints on the existence of such a primordial recently Dritschel & McIntyre 2008 for a comprehensive field, several numerical simulations of the solar radiation review). For instance, the quasi-biennal oscillation in the zone were performed by Garaud (2002) in 2D, and by Brun Earth's stratosphere arises from the anti-diffusive behavior & Zahn (2006) (i.e. paper I, hereafter BZ06) in 3D. These of anisotropic turbulence. But the question is hardly settled simulations exhibit a propagation of the differential rota- tion into the radiation zone (primarily in the polar region). Send offprint requests to: A. Strugarek The primordial magnetic field successfully connects to the e-mail: [email protected] base of the convection zone where the shear is imposed 2 Strugarek, Brun, & Zahn: Magnetic confinement of the tachocline : II. Coupling to a convection zone and, according to Ferraro's law of iso-rotation (Ferraro In the present work, we start our simulation from a ma- 1937), the angular velocity is transmitted along the mag- ture model with a convection and a radiation zone. We then netic field lines from the convection zone into the radiative introduce an axisymmetric dipole-like magnetic field deep interior, much faster than it would through thermal diffu- in the inner radiation zone. This work is meant to explore sion. However, in the aforementioned calculations the base further the mechanisms considered in BZ06. The system is of the convection zone was treated as an impenetrable wall, then evolved self-consistently through the interplay of fluid i.e. radial motions could not penetrate in either direction and magnetic field dynamics. As in Brun et al. (2011), the (from top down or from bottom up). No provision was made computational domain extends from rbottom = 0:07R to for a meridional circulation originating in the convection rtop = 0:97R , and the boundary between radiation and zone that would penetrate into the radiation zone and could convection zone is defined at rbcz ∼ 0:715 R , based on prevent the upward spread of the magnetic field. This pene- the initial entropy profile (see Figs. 1(a) and 1(c)) that tration was taken into account in numerical simulations by is assumed to setup the background equilibrium state. We Sule et al. (2005), Rudiger & Kitchatinov (2007), Garaud also define in Fig. 1(c) the convective overshooting depth & Garaud (2008), in a model of the polar region by Wood rov ∼ 0:675 R (see Sect. 2.2), the penetration depth of the & McIntyre (2007), and in simulations coupling the radia- meridional circulation rMC ∼ 0:68 R (see Sect. 3.2), and tive zone to a convective zone by Rogers (2011) to prop- the shear depth rshear ∼ 0:58 R (see Sect. 2.2). erly represent the GM98 scenario. In most of these models, an axisymmetric and stationary meridional circulation was The diffusivities (Fig. 2) were chosen to achieve a realis- imposed at the top of the radiation zone, strong enough tic rotation profile in the convective envelope (see Sect. 2.2) to bend the magnetic field lines of the primordial field. As by means of an efficient angular momentum redistribution could be expected, various profiles of meridional circulation by Reynolds stresses (Brun & Toomre 2002; Miesch et al. resulted in different confinement properties, thus emphasiz- 2006). In the radiation zone, they have the same values as in ing the need for a more self-consistent approach. We thus BZ06 for consistency with previous studies. We define the propose here to treat the problem by letting a genuine con- following step function to construct our diffusivity profiles: vective envelope dynamically generate its meridional cir- culation and differential rotation and to study how these nonlinearly generated flows interact with a fossil field. 1 r − r step(r) = 1 + tanh 10−10 ν ; Our 3D simulations treat the nonlinear coupling of the 2 νs convection and radiation zones, and the model includes all ν = ν ν + ν (1 − ν ) step; (1) physical ingredients that play a role in the tachocline con- e t t e finement (thermal and viscous diffusion, meridional circula- tion, convective penetration, solar-like stratification, mag- 10 netic fields, pumping, ...). The paper is organized as follows. where rν = 4:7 10 cm and νs = 0:1 control the radial In Sect. 2 we describe the model we use to address the ques- localization and the thickness of the diffusivity jump. The 12 2 −1 tion of the magnetic confinement of the tachocline.