Exploring the $P_{cyc}$ vs $P_{rot}$ relation with flux transport dynamo models of solar-like stars

TL;DR

This study uses 2-D flux transport dynamo models incorporating 3-D simulation scaling laws to analyze the relationship between stellar magnetic cycle periods and rotation rates, revealing limitations of single-cell meridional flow assumptions.

Contribution

It introduces a novel approach by integrating 3-D simulation scaling laws into 2-D dynamo models to test their effectiveness against stellar activity observations.

Findings

Models reproduce magnetic field topology changes with rotation rate.

Single-cell meridional flow models struggle to match observed cycle period relations.

Complex meridional flow profiles may better explain the $P_{cyc}$ vs $P_{rot}$ relation.

Abstract

Aims: To understand stellar magnetism and to test the validity of the Babcock-Leighton flux transport mean field dynamo models with stellar activity observations Methods: 2-D mean field dynamo models at various rotation rates are computed with the STELEM code to study the sensitivity of the activity cycle period and butterfly diagram to parameter changes and are compared to observational data. The novelty is that these 2-D mean field dynamo models incorporate scaling laws deduced from 3-D hydrodynamical simulations for the influence of rotation rate on the amplitude and profile of the meridional circulation. These models make also use of observational scaling laws for the variation of differential rotation with rotation rate. Results: We find that Babcock-Leighton flux transport dynamo models are able to reproduce the change in topology of the magnetic field (i.e. toward being more toroidal with increasing rotation rate) but seem to have difficulty reproducing the cycle period vs activity period correlation observed in solar-like stars if a monolithic single cell meridional flow is assumed. It may however be possible to recover the $P_{cyc}$ vs $P_{rot}$ relation with more complex meridional flows, if the profile changes in a particular assumed manner with rotation rate. Conclusions: The Babcock-Leighton flux transport dynamo model based on single cell meridional circulation does not reproduce the $P_{cyc}$ vs $P_{rot}$ relation unless the amplitude of the meridional circulation is assumed to increase with rotation rate which seems to be in contradiction with recent results obtained with 3-D global simulations.