Constraints on sunspot group lifetimes from far-side Sun-as-a-star helioseismology with BiSON

ABSTRACT Frequencies of low-degree solar p modes are sensitive to activity over the entire Sun, including the unobservable far-side hemisphere. When frequency shifts extracted from week-long Birmingham Solar-Oscillations Network (BiSON) data sets are fitted to a linear combination of observed near-side activity and a far-side proxy made from the near-side measures shifted by half the solar rotation period, the solution favours a slightly higher weighting from the far-side contribution. Here, we demonstrate that this unphysical mismatch is due to the inherent inaccuracy of the far-side proxy, which fails to capture active regions that evolve fully on the solar far side, or that evolve (or have evolved) significantly as they rotate off (or on to) the visible disc. By simulating the evolution of sunspot group areas over time, which act as a suitable measure of solar activity, we show that the solution is sensitive to the lifetime of the activity. Assuming an underlying mapping from maximum group areas $A_{\rm max}$ (measured in millionths of the solar hemispheric area), to group lifetimes $\tau$ (measured in days) of the form $\tau = \alpha A_{\rm max}$, we find that $\alpha \simeq 0.025^{+0.055}_{-0.016}\, \rm d\, MSH^{-1}$ gives results consistent with the BiSON finding. This is to be compared with the value of $\alpha = 0.1\, \rm d\, MSH^{-1}$ implied by the well-known Gnevyshev–Waldmeier rule. While our best-fitting $\alpha$ maps to an average group lifetime of $\tau \simeq 5^{+10}_{-3}\, \rm d$, the best-fitting distribution includes a reasonable fraction of groups with lifetimes longer than the solar rotation period, which is essential to reproducing the mismatch.