Analysis of BMR tilt from AutoTAB catalog: Hinting towards the thin flux tube model?

TL;DR

This study tests the thin flux tube model for BMR tilts by analyzing 12,610 unique BMRs tracked with AutoTAB from 1996 to 2023. It examines tilt distributions, Joy’s law behavior, and the tilt–flux relationship, including tilt fluctuations across lifetimes, to assess whether the Coriolis force acting on rising flux tubes can explain observed tilts. The results show a Gaussian tilt distribution with mean $\mu \approx 7.78^\ extdegree$ and $\sigma \approx 16.46^\ extdegree$, and reveal Joy’s law–like latitudinal dependence as well as a positive tilt–flux trend, with higher-flux BMRs tilting more; tilt fluctuations are larger in low-flux BMRs, suggesting stronger convective buffeting for weaker structures. Joy’s law is observed from first detection, indicating an early Coriolis contribution, though significant scatter remains and not all TBM predictions are unequivocally confirmed. Overall, the work provides partial but meaningful observational support for aspects of the thin flux tube picture while highlighting the need for further data/model refinement.

Abstract

One of the intriguing mechanisms of the Sun is the formation of the bipolar magnetic regions (BMRs) in the solar convection zone which are observed as regions of concentrated magnetic fields of opposite polarity on photosphere. These BMRs are tilted with respect to the equatorial line, which statistically increases with latitude. The thin flux tube model, employing the rise of magnetically buoyant flux loops and their twist by Coriolis force, is a popular paradigm for explaining the formation of tilted BMRs. In this study, we assess the validity of the thin flux tube model by analyzing the tracked BMR data obtained through the Automatic Tracking Algorithm for BMRs (AutoTAB). Our observations reveal that the tracked BMRs exhibit the expected collective behaviors. We find that the polarity separation of BMRs increases over their normalized lifetime, supporting the assumption of a rising flux tube from the CZ. Moreover, we observe an increasing trend of the tilt with the flux of the BMR, suggesting that rising flux tubes associated with lower flux regions are primarily influenced by drag force and Coriolis force, while in higher flux regions, magnetic buoyancy dominates. Furthermore, we observe Joy's law dependence for emerging BMRs from their first detection, indicating that at least a portion of the tilt observed in BMRs can be attributed to the Coriolis force. Notably, lower flux regions exhibit a higher amount of fluctuations associated with their tilt measurement compared to stronger flux regions, suggesting that lower flux regions are more susceptible to turbulent convection.

Figures (2)

• Figure 1: (a) Evolution of magnetic flux ($\Phi_m$) of a representative BMR tracked by AutoTAB. The shaded area indicates the duration during which the measured $\Phi_m$ is greater than 80% of the maximum $\Phi_m$ recorded for the BMR. (b) Mean of the standard deviation of BMR tilt, $\sigma_t(\gamma)$ in each 5 $\times$ 10$^{21}$ Mx flux bin plotted against $\Phi_m$ of the DP class BMRs.
• Figure 2: (a) Tilt Distribution: Number of BMRs in $5\degree$ tilt bins are shown as bars. The blue solid line represents the Gaussian fitted curve (with an offset) with fitting parameters mentioned in the panel. The vertical solid blue line represents the $0\degree$ tilt, and the dashed blue line represents the Gaussian fitted mean at $7.78\degree$. (b) (Gaussian) Mean tilt in each $5\degree$ latitude bin as a function of the latitude. Blue solid and red dashed lines represent Joy’s law ($\gamma = \gamma_{0}\sin\lambda + b$) and straight line fits ($\gamma = m_{\rm Joy}\lambda + b$) with fitting parameters mentioned in the panel along with $\chi^2$ value for the fit at the bottom right. The numbers appearing below the points display the total number of BMRs in the associated bins.