Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model

Abstract

In the Sun and Sun-like stars, it is believed that cycles of the large-scale magnetic field are produced due to the existence of differential rotation and helicity in the plasma flows in their convection zones (CZs). Hence, it is expected that for each star, there is a critical dynamo number for the operation of a large-scale dynamo. As a star slows down, it is expected that the large-scale dynamo ceases to operate above a critical rotation period. In our study, we explore the possibility of the operation of the dynamo in the subcritical region using the Babcock–Leighton type kinematic dynamo model. In some parameter regimes, we find that the dynamo shows hysteresis behavior, i.e., two dynamo solutions are possible depending on the initial parameters—decaying solution if starting with weak field and strong oscillatory solution (subcritical dynamo) when starting with a strong field. However, under large fluctuations in the dynamo parameter, the subcritical dynamo mode is unstable in some parameter regimes. Therefore, our study supports the possible existence of subcritical dynamo in some stars which was previously demonstrated in a mean-field dynamo model with distributed α and MHD turbulent dynamo simulations.

Toroidal Flux Loss due to Flux Emergence Explains why Solar Cycles Rise Differently but Decay in a Similar Way

“…The underlying reason behind the sustained cyclic variation of strength of the solar magnetic fields is believed to be the dynamo mechanism working in the solar convection zone. In recent times, the Babcock-Leighton (Babcock 1961;Leighton 1969) type solar dynamo models have made significant progress in explaining various observed features of magnetic activity of the Sun and Sun like stars (Charbonneau 2020;Karak 2010;Karak and Miesch 2018;Vashishth et al 2021Vashishth et al , 2023 and have been extensively used for forecasting solar cycle strength (Choudhuri et al 2007;Bhowmik and Nandy 2018;Kumar et al 2021Kumar et al , 2022Biswas et al 2023a).…”

“…The magnetic activity of the Sun, as generally measured by the presence of sunspots (or more generally bipolar magnetic regions) on the solar surface evolves in a cyclic fashion with a period of about 11 years, commonly known as the 'Solar Cycle' (Hathaway 2015). The long term study of the solar magnetic activity reveals that the 11 year solar cycles possess significant variations in their characteristics which makes the otherwise similar looking cycles unique and widely different from each other (Karak 2023;Usoskin 2013;Biswas et al 2023b).…”

Temperature Dependence of Stellar Activity Cycles

“…Exception from this rule is the rare case of metastability, which is hardly possible to realise with the BL-type dynamo models(Vashishth et al 2021). …”

Investigations of the solar dynamo within the framework of the Babcock-Leighton mechanism

“…The SOCA turbulence coefficients given in § §6.2 and 6.3 are valid only for either arbitrary rotation rate and negligible magnetic field strength, or vice versa. In the literature, almost all dynamo models based on SOCA use expressions either valid for arbitrary rotation rate (Rüdiger and Brandenburg 1995, Pipin and Seehafer 2009, Kitchatinov and Nepomnyashchikh 2017b, Kitchatinov and Khlystova 2021 or magnetic field strengths (Rüdiger et al 1994, Kitchatinov and Olemskoy 2010, Vashishth et al 2021, or even pick different turbulent effects valid in different regimes (Rüdiger and Brandenburg 1995, Pipin and Kosovichev 2011, Pipin 2022. But in the real Sun, we expect both rotation and magnetic fields to have a large effect at depth.…”