Magnetic field dependence of bipolar magnetic region tilts on the Sun: Indication of tilt quenching

TL;DR

The paper tests whether the tilt of bipolar magnetic regions (BMRs) is quenched by strong magnetic fields, a key aspect of saturating Babcock–Leighton dynamos. It analyzes 6-hour LOS magnetograms from MDI and HMI across 1996–2018 to measure BMR tilts as a function of the maximum field $B_{\rm max}$ and to test nonlinear tilt quenching. The main findings are a bimodal distribution of $B_{\rm max}$ with WS at high fields and NS at lower fields, the presence of Joy's law for both classes, and a clear tilt quenching above $B_{\rm max} \approx 2$ kG, with a nonlinear quenching form $f_q \propto 1/[1+(B_{\rm max}/B_0)^n]$ where $n \approx 5.8$ and $B_0 \approx 2.9$ kG. These results support nonlinear saturation in the Babcock–Leighton mechanism and are broadly compatible with thin-flux-tube models that include convection, strengthening the case that strong-field BMRs limit poloidal-field generation.

Abstract

The tilt of bipolar magnetic region (BMR) is crucial in the Babcock--Leighton process for the generation of the poloidal magnetic field in Sun. Based on the thin flux tube model of the BMR formation, the tilt is believed to be caused by the Coriolis force acting on the rising flux tube of the strong toroidal magnetic field from the base of the convection zone (BCZ). We analyze the magnetic field dependence of BMR tilts using the magnetograms of Michelson Doppler Imager (MDI) (1996-2011) and Helioseismic and Magnetic Imager (HMI) (2010-2018). We observe that the distribution of the maximum magnetic field ($B_{\rm max}$) of BMRs is bimodal. Its first peak at the low field corresponds to BMRs which do not have sunspots as counterparts in the white light images, whereas the second peak corresponds to sunspots as recorded in both types of images. We find that the slope of Joy's law ($γ_0$) initially increases slowly with the increase of $B_{\rm max}$. However, when $B_{\rm max} \gtrsim 2$ kG, $γ_0$ decreases. Scatter of BMR tilt around Joy's law systematically decreases with the increase of $B_{\rm max}$. The decrease of observed $γ_0$ with $B_{\rm max}$ provides a hint to a nonlinear tilt quenching in the Babcock--Leighton process. We finally discuss how our results may be used to make a connection with the thin flux tube model.

Figures (4)

• Figure 1: Representatives magnetograms of (c) MDI and (d) HMI (saturated to $\pm$1.5 kG) with BMR$_{\rm{WS}}$ (red box) and BMR$_{\rm{NS}}$ (blue). (a, b, e, and f): show IC counterparts.
• Figure 2: (a-b): Distributions of $B_{\rm max}$ in the BMRs from MDI (left panel) and HMI (right). Red and blue respectively show $B_{\rm max}$ distributions of BMR$_{\rm WS}$ (having counterpart in IC) and BMR$_{\rm NS}$ (no counterpart in IC). The vertical axes of two panes are divided by 315 and 388, respectively to bring the maxima of distributions to unity. Bottom: Time-latitude distribution of BMR$_{\rm WS}$ (red) and BMR$_{\rm NS}$ (blue).
• Figure 3: (a-b): Red and blue show tilt distributions of BMR$_{\rm WS}$ and BMR$_{\rm NS}$, respectively. Points represent the data and lines show the fitted Gaussians with parameters printed on the panels. (c-d): Mean tilt in each latitude bin as a function of the latitude. Solid and dashed lines are Joy's law ($\gamma = \gamma_0 \sin\lambda$) fits for BMR$_{\rm WS}$ and BMR$_{\rm NS}$.
• Figure 4: Magnetic field ($B_{\rm max}$) dependences of: (a) Joy's law slope $\gamma_0$ and (c) the tilt scatter $\sigma$. (b) and (d) are the same as left panels but as functions of flux.