标题： 太阳活动周期的长期调制 显示英文标题

标题： Long-term modulation of solar cycles

摘要： 太阳活动具有周期性，其中约11年的施瓦贝周期主导了其在多年时间尺度上的变化。然而，太阳周期在长度、形状和幅度上表现出显著的调制，从接近无黑子的大极小期到非常活跃的大极大期。长达约400年的直接黑子数序列质量不均且太短，无法研究长期太阳变化的稳健参数。宇宙成因同位素替代指标将时间尺度延长至一万两千多年，并提供了长期太阳发电机调制的关键观测约束。 在这里，我们简要概述了太阳活动在百年到千年时间尺度上的长期变化。讨论了大极小期和极大期的发生以及现有的准周期性现象，如百年格利斯伯格周期、210年苏斯/德弗里斯周期和2400年哈尔施塔特周期。研究表明，太阳周期包含重要的随机成分且没有时钟式的相位锁定，这表明缺乏长期记忆。 我们还简明扼要地回顾了用以解释发电机模型框架下观测特征的理论前景，包括发电机中的非线性和随机波动。随着新数据的获取和新模型的发展，我们不断增进对驱动太阳变化过程的认识。 显示英文摘要

摘要： Solar activity has a cyclic nature with the ~11-year Schwabe cycle dominating its variability on the interannual timescale. However, solar cycles are significantly modulated in length, shape and magnitude, from near-spotless grand minima to very active grand maxima. The ~400-year-long direct sunspot-number series is inhomogeneous in quality and too short to study robust parameters of long-term solar variability. The cosmogenic-isotope proxy extends the timescale to twelve millennia and provides crucial observational constraints of the long-term solar dynamo modulation. Here, we present a brief up-to-date overview of the long-term variability of solar activity at centennial--millennial timescales. The occurrence of grand minima and maxima is discussed as well as the existing quasi-periodicities such as centennial Gleissberg, 210-year Suess/de Vries and 2400-year Hallstatt cycles. It is shown that the solar cycles contain an important random component and have no clock-like phase locking implying a lack of long-term memory. A brief yet comprehensive review of the theoretical perspectives to explain the observed features in the framework of the dynamo models is presented, including the nonlinearity and stochastic fluctuations in the dynamo. We keep gaining knowledge of the processes driving solar variability with the new data acquainted and new models developed.