Observed Joys law of Bipolar Magnetic Region tilts at the emergence supports the thin flux tube model

TL;DR

The paper investigates the origin of Joy's law tilts in Bipolar Magnetic Regions (BMRs) by backtracking two solar cycles of high-resolution LOS magnetogram data with AutoTAB to identify the earliest emergence times ($T_e$) and measure tilts at emergence. It finds that BMRs exhibit a Joy's law tilt at emergence with amplitude $γ_0 ≈ 25.98°$ (consistent with $γ = γ_0 \sin λ + b$), and that the scatter around the mean tilt decreases as flux increases, aligning with a Coriolis-force-driven tilt in the deep convection zone predicted by the thin flux tube model. This provides robust observational support for the idea that tilts are imprinting beneath the photosphere, with surface turbulence dampening their early-time variability. The results strengthen the connection between solar dynamo theory and observable BMR tilts and motivate more sophisticated 3D MHD simulations of flux-tube rise in convective envelopes to capture the interplay with near-surface flows.

Abstract

Bipolar sunspots, or more generally, Bipolar Magnetic Regions, BMRs, are the dynamic magnetic regions that appear on the solar surface and are central to solar activity. One striking feature of these regions is that they are often tilted with respect to the equator, and this tilt increases with the latitude of appearance, popularly known as Joys law. Although this law has been examined for over a century through various observations, its physical origin is still not established. An attractive theory that has been put forward behind Joys law is the Coriolis force acting on the rising flux tube in the convection zone, which has been studied using the thin flux tube model. However, observational support for this theory is limited. If the Coriolis force is the cause of the tilt, then we expect BMRs to hold Joys law at their initial emergence on the surface. By automatically identifying the BMRs over the last two solar cycles from high resolution magnetic observations, we robustly capture their initial emergence signatures on the surface. We find that from their appearance, BMRs exhibit tilts consistent with Joys law. This early tilt signature of BMRs suggests that the tilt is developed underneath the photosphere, driven by the Coriolis force and helical convection, as predicted by the thin flux tube model. Considerable scatter around Joys law observed during the emergence phase, which reduces in the post emergence phase, reflects the interaction of the vigorous turbulent convection with the rising flux tubes in the near surface layer.

Figures (9)

• Figure 1: Timeline of the BMR evolution, illustrating two tracking phases: the backtracking and forward tracking. The backtracking phase traces BMRs from $T_0$ (AutoTAB's first detection) to the very initial emergence $T_e$. Forward tracking follows a BMR's growth from $T_0$ through $T_m$ when the unsigned flux reaches its peak to the end of tracking $T_f$ ($T_e < T_0 < T_m < T_f$).
• Figure 2: Evolution of two typical BMRs. (a) and (c), Respectively represent the BMR at the times of initial detection ($T_{e}$) and the starting of our backtracking phase ($T_0$); see Figure \ref{['fig:timeline']} for the timeline. (b), The BMR at the middle of the backtracking phase. (d), The same BMR but for comparison at its maximum flux. (e--h) The same as the top row but for a different BMR. The corresponding (near simultaneous) intensity continuum for these two BMRs are shown in Figure \ref{['fig:IC']}. Numbers in brackets on each panel denote the mean latitude and longitude of the region. The magnetic field is saturated at 1.5 kG in all panels. The line in each panel connects the flux-weighted centroids of BMR's poles. Each box is of size 145 Mm $\times$ 145 Mm. The Movie S1 shows a detailed evolution of (a--d).
• Figure 3: Joy's law (latitude variation of the tilt angle) at different stages of BMR's evolution. (a), At the initial emergence $T_e$. (b--e) Respectively represent tilt and Joy's law fit at approximately 25%, 50%, 75%, and 100% (i.e., at $T_0$) of the backtracked phase. (Hence, the panel (c) presents the middle of the backtracking phase.) (f), At the matured phase ($T_{m}$). We note that (a), (e), and (f) include the whole usable BMRs (1876), while the temporal bins in (b), (c), and (d) are chosen in such a way that they accommodate an equal number of BMRs ($\sim 1500$). The error bars are computed from the Gaussian fitting of the tilt data in each latitude bin.
• Figure 4: Tilt distribution at different times. (a), (b) and (c) Respectively represent the distributions of the BMR tilt angles at $T_e$, $T_0$, and $T_m$. The parameters of the Gaussian fit, $\mu$ and $\sigma$ are printed on each panel.
• Figure 5: Evolution of Joy's law with the flux emergence during BMR's early phase. Joy's law computed when the BMR flux falls between (a) 0--5%, (b) 0--10%, (c) 5--15%, and (d) 20--30% of the maximum flux. No of BMRs belonging to (a) to (d) are 436, 729, 809, and 862. It is essential to remember that due to the unequal growth rates of the BMRs, we capture the different phases of BMRs at the fixed flux range.