The Tachocline

Theme Leads: Nic Brummell & Gustavo Guerrero

The rotation profile of the solar interior was perhaps the most startling revelation of early helioseismology and sparked major challenges to our understanding of interior dynamics and magnetic field generation. The tachocline is mysterious both for its origin and its dynamical influence, and understanding these will be breakthrough science. Helioseismic inferences locate the tachocline at ∼0.7 Rsun with a width of ∼0.04 Rsun, although there is variation with latitude (e.g. Corbard et al., 2001; Howe, 2009). The width probably reflects the limited resolution of the inversion at this depth rather than its true width, and therefore may be considered an upper bound (Elliott et al., 1999). The position and width are not strong functions of the solar cycle, although this may be a result of the modeling used to provide these numbers. Understanding the dynamical origin of the tachocline is an area of research previously addressed by members of the CV and DY Teams individually, but is now being addressed collaboratively as an essential component of SQ1. The tachocline is not simply a passive connective interface between two regions; some other dynamics must be present to account for its thinness. Current theories are either purely hydrodynamic (e.g., enhanced horizontal mixing due to anisotropic hydrodynamic turbulence in the strong stratification) or can rely on the presence of magnetic fields. The latter seem most likely with our present understanding, where magnetic stresses supply the forces that balance the radiative spreading of the differential rotation. These stresses can be supplied by fossil fields, as in the magnetohydrodynamic laminar boundary layer solution proposed by Gough et al. (1998), or by the penetration of the oscillating dynamo field, as championed by e.g., Forgács-Dajka et al. (2002). The former is a “slow” tachocline theory, since the dynamical balances operate on the long Eddington-Sweet timescale, whereas the latter proposes a “fast” tachocline, with timescales related to the much quicker dynamo oscillation time or perhaps even a convective turnover time. Our Teams have been involved in testing and validating elements of these theories via simulations that are more dynamically complete than the original proposed theories e.g., Korre et al., 2021; Wood et al., 2018. The central question is to discern which theory is most likely. Phase II provides an opportunity not only to continue these cross-Team collaborative investigations, but also to plan and ultimately use optimized observations generated by the HS Team. In particular, when helioseismic systematic errors are reduced, then time-varying information about circulation and thermal structure may enable us to distinguish between theories of the origin of the tachocline by their timescale of variation and thermodynamics. This would allow us to (1) distill the question of the dynamical origin of the tachocline to a likely prevailing theory from amongst the many.

Beyond its origin, the role of the tachocline in the overall global interior dynamics is not well understood. The layer is often cited as being central to the operation of the global solar dynamo, since it is a region of strong shear and therefore very capable of converting weak poloidal field into strong toroidal field (commonly referred to under the umbrella term “the Ω effect”). This issue is therefore central to our SQ2, sitting firmly in the purview of the CV and DY Teams. A primary cross-Team effort of COFFIES involves incorporating the more realistic tachocline dynamics (as produced from the separate models of the CV and DY Teams as mentioned above) into the global dynamo models of the DY Team (which would also utilize the expertise of the MI Team, and involve further coordination with the HS Team regarding the observational consequences). (2) Incorporating more representative tachocline dynamics into dynamo models would be another major breakthrough. However, this is not an easy task, since, even assuming that we had established the correct dynamics that maintain the tachocline, some of the elements that may be necessary are not accurately modeled in the global dynamo models. For example, a slow tachocline requires weak rotational effects to dominate over viscous effects in order to confine the radiation zone fossil field, and it is not clear how to obtain this state in global dynamo models, where the viscous effects are usually controlled by the numerics. The confinement of the fossil magnetic field may also prevail because of faster turbulent mechanisms, but again the small-scale turbulence is not explicitly represented in most current global dynamo models. Ultimately, we may have to distill the essence of the tachocline dynamics into sub-grid scale models instead of direct incorporation, utilizing the expertise of the MI. As a Center, we do have the tools to achieve this goal with cross-Team effort.

This goal offers the potential of understanding the operation of the global solar dynamo (SQ2). Adding the realistic dynamics of the tachocline allows us to examine whether this layer is a dynamically essential element or simply a more passive boundary. This has recently become a crucial question. For example, work before and during Phase I that included members of the CV and DY Teams regarding global convective systems with no tachoclines has shown that dynamos are plausible where the lower boundary condition is a passive entity and all the dynamo action occurs within the convection zone (Nelson et al., 2013; Warnecke, 2018). Similarly, some team members have also been involved in examining the effects of the tachocline shear layers on global dynamo models (Guerrero et al. 2016, 2019). These latter models find that deep-seated dynamos can operate beneath the convection zone and yet still produce magnetic fields that are sufficiently strong to become buoyantly unstable, have magnetic cycles compatible to the solar dynamo period, and have variations of angular velocity with patterns similar to (though stronger than) the torsional oscillations. Both kinds of model still face the challenge of reproducing recent observations of magnetism in Sun-like stars (SQ4). Ultimately, only the inclusion of improved tachocline dynamics, coupled with the predicted helioseismic output of such models to connect with actual observations from the HS Team, can distinguish between these different scenarios.

Eventually we must (3) connect large-scale dynamo fields and the much smaller scale magnetic structures that subsequently emerge at the photosphere as ARs, since their dynamics supply some of our strongest observational constraints. The tachocline region may or may not hold the key to this issue, as outlined above, but has the advantage (over other possible locations for origination of active-region scale flux) that fields are not immediately buoyant, and must be amplified before they begin to rise, leading to some ideas of what might control emergence timescales and strengths. Our CV and DY Teams have been heavily involved in understanding the release of stored flux via MHD instabilities in the tachocline (e.g., Gilman, 2018; Manek et al., 2021). These issues potentially dictate the answers to our whole SQ3. This latter issue bridges this Theme and the FT&E Theme, confirming that a full Center-level effort is definitely required to succeed.