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

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.

💡 Research Summary

Bipolar magnetic regions (BMRs) are the fundamental magnetic building blocks of solar activity, and their systematic tilt with respect to the solar equator—known as Joy’s law—has been documented for more than a century. The thin‑flux‑tube model attributes this latitude‑dependent tilt to the Coriolis force acting on buoyant magnetic flux tubes as they rise through the convection zone. However, direct observational confirmation that BMRs already obey Joy’s law at the moment of emergence has been lacking, with earlier studies suggesting that the tilt develops only after the regions appear at the surface.

In this work the authors employ the Automatic Tracking Algorithm for Bipolar Magnetic Regions (AutoT AB) to identify and follow BMRs in line‑of‑sight magnetograms from SOHO/MDI and SDO/HMI spanning September 1996 to December 2023, covering solar cycles 23, 24 and the early phase of cycle 25. AutoT AB normally begins tracking when the magnetic fluxes of the two polarities are roughly balanced (time T0). To capture the true emergence moment, the authors back‑track each region from T0 to earlier magnetograms, applying strict growth criteria: the unsigned flux may not drop by more than 40 % and the pixel area (pixels > 100 G) may not drop by more than 50 % relative to T0. The back‑tracking stops after five consecutive failures or when the region reaches a longitude of –45°. This procedure yields reliable emergence times (Te) for 3 012 BMRs, of which 1 876 show clear growth and are retained for tilt analysis.

Tilt angles are measured using flux‑weighted centroids of the two polarities, with the definition tan γ = Δλ / (Δφ cos λ̄). Southern‑hemisphere tilts are sign‑reversed to enforce hemispheric symmetry. The authors bin the data in 5° latitude intervals, fit a Gaussian to the tilt distribution in each bin, and then fit the standard Joy’s‑law form γ = γ0 sin λ + b. The resulting amplitude is γ0 = 25.98° ± 7.32° (b ≈ 0.45°), demonstrating that even at the earliest detectable emergence (Te) the tilt follows the expected latitude dependence.

Temporal evolution shows a large scatter in tilt at Te, which progressively diminishes as the BMR matures. At roughly 75 % of the back‑tracking interval (average age ≈ 0.78 day) the scatter is markedly reduced, and by the time of first detection (T0) and at peak flux (Tm) the Joy’s‑law trend is stable and comparable to previous studies that used later‑stage measurements. This behavior is interpreted as the imprint of the Coriolis force during the deep rise of the flux tube, combined with stochastic perturbations from vigorous near‑surface convection that temporarily blur the tilt signal.

The authors also examine the predicted dependence of tilt on magnetic flux (Φ) and initial field strength (B0) from thin‑tube theory (γ ∝ sin λ · Φ¹⁄⁴ · B0⁻⁵⁄⁴). In the observational sample, no robust correlation between tilt and Φ is found, consistent with recent simulations that suggest the flux dependence is weakened by convective turbulence.

Overall, the study provides the first large‑scale, statistically robust confirmation that Joy’s law is already present at the moment BMRs first become visible in photospheric magnetograms. This directly supports the thin‑flux‑tube picture in which the Coriolis force generates the systematic tilt deep within the convection zone, and it clarifies that the additional scatter observed during emergence is a surface‑convection effect that fades as the region stabilizes. The results have important implications for solar dynamo modeling, offering observational constraints on the tilt‑generation mechanism that underpins the poloidal‑field source term in flux‑transport dynamo models and improving the physical basis for solar cycle predictions.