Modélisation hybride du cycle d’activité solaire : évolution couplée du flux magnétique photosphérique et de la dynamo interne

The solar magnetohydrodynamical (MHD) dynamo requires a mechanism of cyclic regeneration for the global poloidal magnetic field, that can be provided by the Coriolis force, but for which spatial scale and location remain uncertain despite a century of theoretical analysis and decades of numerical simulations. While axisymmetric mean fields and global 3D models find this source in an excess of helicity at small convective scales, Babcock–Leighton (BL)-type models rather suggest that the dominant mechanism is due to the torsion of rising flux loops ultimately responsible for the emergence of bipolar magnetic regions (BMRs) (and formation of sunspots) at the surface of the Sun.  We opt here for this second class of models, in a phenomenological approach that seeks to optimally reproduce observations, while accurately and intelligibly accounting for the physical processes that occur at multiple spatial and temporal scales, while also maintaining a numerical efficiency that allows for detailed and extended analyses. On one hand, a two-dimension (2D) modeling of the solar surface (namely surface flux transport (SFT)) is required to account for the observed emergence, transport, and diffusion of photospheric magnetic flux. On the other hand, the globally structured, roughly axisymmetric, magnetic fields in the convection zone, as inferred by the shape of the emergence patterns (the “butterfly diagram”), minimally require a 2D dynamo modeling in the meridional plane. Combining these two minimal configurations allows us to build a new coupled 2 × 2D BL dynamo model, where the probabilistic emergence of BMRs from deep toroidal field provides a source for the SFT, and the output of the SFT in turn provides a source for the internal dynamo.  In order to make this model most closely solar-like, a double calibration is performed, through a genetic algorithm, to obtain optimal values (with error estimates) for 18 free parameters: (1) the SFT results are compared with magnetographic maps of the solar surface (Lemerle et al, 2015, ApJ, 810, 78), and (2) the internal dynamo results are compared with the observed “butterfly diagram” of BMRs (Lemerle & Charbonneau, 2017, ApJ, 834, 133). We thus obtain a coupled 2 x 2D BL dynamo model that consistently reproduces several solar features: low-latitude BMR emergences that follow observed statistics, mid-latitude unipolar flux strips, suitable polar cap flux at activity minima, strong hemispheric coupling, forecast-enabling correlations between amplitude of the axial dipole at cycle minima and amplitude of the subsequent cycle, long term amplitude fluctuations, occurence of grand minima (like the Maunder minimum), etc. Work still in progress at the Groupe de Recherche en Physique solaire (GRPS) shows that this dynamo is highly subjected to stochastic fluctuations due to the specific realization of random emergence series, that it is these fluctuations that sometimes bring the dynamo into a descending phase toward a grand minimum, that a second order dynamo mechanism must exist to subsequently restart the system, but that, despite this inherent stochasticity, the model provides a strong predictive capability, possibly of the order of a full activity cycle.

Keyphrases: dynamo, Sun: activity, Sun: general, Sun: interior, Sun: magnetic fields, Sun: photosphere, Sun: sunspots