ner_tags: B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O
tokens: Hazra et al. 2014 ; Passos et al. 2014 ). Indeed, LC17 observed that when their model enters into an extended grand minimum of the weaker magnetic field, the generation of poloidal field stops due to a lack of BMRs, and the model never recovers from that quiescent phase. Their model recovers only when the magnetic field does not fall below a certain level. 2. Model In this Letter, we explore the Babcock–Leighton dynamo mechanism during grand minima, focusing in particular on how the dynamo might recover from such episodes through the Babcock–Leighton process alone. To do so, we first produce grand minima. In our study, we build on our recent work, KM17 , which is an updated version of the original model (Miesch Dikpati 2014 ; Miesch Teweldebirhan 2016 ). In this model, BMRs are produced near the surface based on the toroidal flux at the BCZ and most of the statistical properties of BMRs are based on solar observations. We refer readers to Section 2 of KM17 for the details of this model. From KM17 , we consider Runs B10–11, in which the diffusivity in the bulk of the CZ is in the order of 10 12 cm 2 s −1 . The BMR flux distribution is fixed at the observed value and the time delay between two successive BMR emergences is obtained from the observed log-normal distribution, which changes in response to the toroidal field at the base of the CZ to allow more frequent BMRs when the toroidal field is strong and vice versa. The BMR tilt has a Gaussian scatter around Joy’s law with standard deviation ( σ δ ) of 30° (15°) for Run B11 (B10). Another key ingredient of the model is the downward magnetic pumping which has the same form as in KM17 and it is given bywhere γ CZ = 2 m s −1 and γ S = 20 m s −1 . Thus, the pumping has a value of γ S only near the surface, while in the rest of the CZ it is γ CZ . Pumping is a process in which the magnetic flux can be transported in a stratified convective medium due to the topological asymmetry in the convective flow. A variety of theoretical and numerical models suggest that it is operating in the solar CZ, particularly near the surface where both the velocity amplitude and the density stratification are largest (e.g., Drobyshevski Yuferev 1974 ; Krause Rädler 1980 ; Petrovay Szakaly 1993 ; Tobias et al. 1998 ). Although at present, we do not have a stringent constraint on the strength of the pumping, previous studies (Käpylä et al. 2006 ; Karak et al. 2014b ) suggest its value to be at least a few tenths of the convective velocity. Keeping in mind that the upper layer of the Sun is highly convective with the observed surface convection speed of a few km s −1 , a value of 20 m s −1 pumping speed is realistic (Spruit 1997 ; Nordlund et al. 2009 ). This value is also large enough to make the magnetic field near the surface approximately vertical, which improves the agreement between Babcock–Leighton dynamo models and Surface Flux Transport (SFT) models. 4 4 Cameron et al. ( 2012 ) showed that the inclusion of