The Schwabe cycle of solar activity exhibits modulations and frequency fluctuations on slow time scales of centuries and millennia. Plausible physical explanations for the cause of these long-term variations of the solar cycle are still elusive, with possible theories including stochasticity of alpha effect and fluctuations of the differential rotation. It has been suggested recently in the literature that there exists a possible relation between the spatio-temporal structure of Solar cycle and the nonlinear dynamics of magnetohydrodynamic Rossby waves at the solar tachocline, including both wave-wave and wave-mean flow interactions. Here we extend the nonlinear theory of MHD Rossby waves presented in a previous article to take into account long term modulation effects due to a recently discovered mechanism that allows significant energy transfers throughout different wave triads: the precession resonance mechanism. We have found a large number of Rossby-Haurwitz wave triads whose frequency mismatches are compatible with the solar cycle frequency. Consequently, by analyzing the reduced dynamics of two triads coupled by a single mode (five-wave system), we have demonstrated that in the amplitude regime in which precession resonance occurs, the energy transfer throughout the system yields significant long-term modulations on the main $\sim 11$yr period associated with intra-triad energy exchanges. We further show that such modulations display an inverse relationship between the characteristic wave amplitude and the period of intra-triad energy exchanges, which is consistent with the Waldmeier's law for the solar cycle. In the presence of a constant forcing and dissipation, the five-wave system in the precession resonance regime exhibits irregular amplitude fluctuations with some periods resembling the Grand Minimum states.
Context. Large-scale equatorial Rossby modes have been observed on the Sun over the last two solar cycles. Aims. We investigate the impact of the time-varying zonal flows on the frequencies of Rossby modes. Methods. A first-order perturbation theory approach is used to obtain an expression for the expected shift in the mode frequencies due to perturbations in the internal rotation rate. Results. Using the time-varying rotation from helioseismic inversions we predict the changes in Rossby mode frequencies with azimuthal orders from m = 1 to m = 15 over the last two solar cycles. The peak-to-pea…
The influence of a toroidal magnetic field on the dynamics of shallow water waves in the solar tachocline is studied. A sub-adiabatic temperature gradient in the upper overshoot layer of the tachocline causes significant reduction of surface gravity speed, which leads to trapping of the waves near the equator and to an increase of the Rossby wave period up to the timescale of solar cycles. Dispersion relations of all equatorial magnetohydrodynamic (MHD) shallow water waves are obtained in the upper tachocline conditions and solved analytically and numerically. It is found that the toroidal mag…
We discuss selected aspects regarding the magnetic field evolution of solar-type stars. Most of the stars with activity cycles are in the range where the normalized chromospheric Calcium emission increases linearly with the inverse Rossby number. For Rossby numbers below about a quarter of the solar value, the activity saturates and no cycles have been found. For Rossby numbers above the solar value, again no activity cycles have been found, but now the activity goes up again for a major fraction of the stars. Rapidly rotating stars show nonaxisymmetric large-scale magnetic fields, but there i…
Using the Hilbert-Huang transform technique, we investigate the midrange periodicities in solar radio flux at 2800 MHz (F10.7) and sunspot areas (SAs) from February 1, 1947 to September 30, 2016. The following prominent results are found: (1) The quasi-periodic oscillations of both data sets are not identical, such as the rotational cycle, the midrange periodicities, and the Schwabe cycle. In particular, the midrange periodicities ranging from 37.9 days to 297.3 days are related to the magnetic Rossby-type waves; 2) The 1.3-year and 1.7-year fluctuations in solar activity indicators are surfac…
Annual oscillations have been detected in many indices of solar activity during many cycles. Recent multi spacecraft observations of coronal bright points revealed slow retrograde toroidal phase drift (with the speed of 3 m/s of 1 yr oscillations, which naturally suggested their connection with Rossby-type waves in the interior. We have studied from a theoretical point of view the dynamics of global magneto-Kelvin and magneto-Rossby waves in the solar tachocline with toroidal magnetic field. Using spherical coordinates, the dispersion relations of the waves and latitudinal structure of solutio…
The periods of magnetic activity cycles in the Sun and solar-type stars do not exhibit a simple or even single trend with respect to rotation rate or luminosity. Dynamo models can be used to interpret this diversity, and can ultimately help us understand why some solar-like stars do not exhibit a magnetic cycle, whereas some do, and for the latter what physical mechanisms set their magnetic cycle period. Three-dimensional non-linear magnetohydrodynamical simulations present the advantage of having only a small number of tunable parameters, and produce in a dynamically self-consistent manner th…
The paper considers the influence of the solar global magnetic field structure (GMFS) cycle evolution on the occurrence rate and parameters of coronal mass ejections (CMEs) in cycles 23-24. It has been shown that over solar cycles, CMEs are not distributed randomly, but they are regulated by evolutionary changes in the GMFS. It is proposed, that the generation of magnetic Rossby waves in the solar tachocline results in the GMFS cycle changes. Each Rossby wave period favors a particular GMFS. It is proposed that the changes in wave periods result in the GMFS reorganization and consequently in C…
Temporal variations of solar inertial mode parameters from GONG (2002-2024) and HMI (2010-2024): Rossby modes ($3 \leq m \leq 16 $) and $m=1$ high-latitude mode
Max-Planck-Institut für Sonnensystemforschung（马克斯·普朗克太阳系统研究所）；National Solar Observatory（美国国家太阳天文台）；Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen（哥廷根大学天体物理与地球物理研究所）；Center for Astrophysics and Space Science, NYUAD Institute, New York University Abu Dhabi（纽约大学阿布扎比分校天体物理学与空间科学中心）；LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台拉伊尔实验室（隶属于巴黎文理研究大学、索邦大学、巴黎西岱大学、塞吉-蓬图瓦兹大学及法国国家科学研究中心））
Gravity modes and potential evidence for Rossby Waves in late O-type supergiants
Instituto de Astrofísica de La Plata（拉普拉塔天体物理研究所）；Facultad de Ciencias Astronómicas y Geofísicas（天文与地球物理科学学院）；Instituto de Estadística, Universidad de Valparaíso（瓦尔帕莱索大学统计研究所）；Astronomical Institute, Czech Academy of Sciences（捷克科学院天文研究所）；Astronomical Institute, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院天文研究所）；Royal Observatory of Belgium（比利时皇家天文台）
Solar activity undergoes a variation over time scales of several months known as Rieger-type periodicity, which usually occurs near maxima of sunspot cycles. An early analysis showed that the periodicity appears only in some cycles, and is absent in other cycles. But the appearance/absence during different cycles has not been explained. We performed a wavelet analysis of sunspot data from the Greenwich Royal Observatory and the Royal Observatory of Belgium during cycles 14-24. We found that the Rieger-type periods occur in all cycles, but they are cycle-dependent: shorter periods occur during …
Rieger-type periodicity has been detected in different activity indices over many solar cycles. It was recently shown that the periodicity correlates with solar activity having a shorter period during stronger cycles. Solar activity level is generally asymmetric between northern and southern hemispheres, which could suggest the presence of a similar behavior in the Rieger-type periodicity. We analyse the sunspot area/number and the total magnetic flux data for northern and southern hemispheres during solar cycles 19-23 which had remarkable north-south asymmetry. Using wavelet analysis of sunsp…
Two fundamental properties of stellar magnetic fields have been determined by observations for solar-like stars with different Rossby numbers (Ro), namely, the magnetic field strength and the magnetic cycle period. The field strength exhibits two regimes: 1) for fast rotation it is independent of Ro, 2) for slow rotation it decays with Ro following a power law. For the magnetic cycle period two regimes of activity, the active and inactive branches, also have been identified. For both of them, the longer the rotation period, the longer the activity cycle. Using global dynamo simulations of sola…
The magnetic fields of solar-type stars are observed to cycle over decadal periods -11 years in the case of the Sun. The fields originate in the turbulent convective layers of stars and have a complex dependency upon stellar rotation rate. We have performed a set of turbulent global simulations that exhibit magnetic cycles varying systematically with stellar rotation and luminosity. We find that the magnetic cycle period is inversely proportional to the Rossby number, which quantifies the influence of rotation on turbulent convection. The trend relies on a fundamentally non-linear dynamo proce…
Context. Solar Rossby waves (r modes) have recently been discovered in the near-surface horizontal flow field using the techniques of granulation-tracking and ring-diagram analysis applied to six years of SDO/HMI data. Aims. Here we apply time-distance helioseismology to the combined SOHO/MDI and SDO/HMI data sets, which cover 21 years of observations from May 1996 to April 2017. The goal of this study is to provide an independent confirmation over two solar cycles and in deeper layers of the Sun. Methods. We have measured south-north helioseismic travel times along the equator, which are sens…
Over the course of their lifetimes, the rotation of solar-type stars goes through different phases. Once they reach the zero-age main sequence, their global rotation rate decreases during the main sequence until at least the solar age, approximately following the empirical Skumanich's law and enabling gyrochronology. Older solar-type stars might then reach a point of transition when they stop braking, according to recent results of asteroseismology. Additionally, recent 3D numerical simulations of solar-type stars show that different regimes of differential rotation can be characterized with t…
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…
Aims: We aim to investigate how converging flows towards active regions affect the surface transport of magnetic flux, as well as their impact on the generation of the Sun's poloidal field. The inflows constitute a potential non-linear mechanism for the saturation of the global dynamo and may contribute to the modulation of the solar cycle in the Babcock-Leighton framework. Methods: We build a surface flux transport code incorporating a parametrized model of the inflows and run simulations spanning several cycles. We carry out a parameter study to assess how the strength and extension of the i…
The magnetic activity of the Sun changes with the solar cycle. Similar cycles are found in other stars as well, but their details are not known to a similar degree. Characterising stellar magnetic cycles is important for the understanding of the stellar and solar dynamos that are driving the magnetic activity. We present spectropolarimetric observations of five young, solar-type stars, and compare them to previous observations, with the aim to identify and characterise stellar equivalents of the solar cycle. We use Zeeman-Doppler imaging (ZDI) to map the surface magnetic field and brightness o…
The 22-Year Hale Cycle in Cosmic Ray Flux - Evidence for Direct Heliospheric Modulation
预测银河宇宙射线（GCR）通量的能力对于减少这些粒子对卫星通信，航空或宇航员造成的危害非常重要。宇宙射线的11年太阳周期变化与日光层磁场的强度高度相关。在交替的太阳周期中，GCR通量的差异产生了一个22年的周期，称为黑尔周期，这被认为是由于当太阳北极主要是正极性（表示为qA>0周期）或负极性（qA<0）时，粒子漂移模式不同。这导致了在qA>0的周期中，地球上宇宙线通量峰值的出现比qA 0的周期更早<0 cycles and hence the peak being more domed for qA>，而在qA<0的周期中，峰值更尖锐。在这项研究中，我们证明了大尺度日球磁场的性质是不同的qA <0 and qA>0太阳活动周的下降阶段，当GCR通量的差异是最明显的。这表明，粒子漂移可能不是唯一的机制，负责在地球上的GCR通量海尔循环。然而，它也表明，这些极性依赖日光层的差异是明显的，在太空时代，但在早期的数据不太清楚：使用地磁重建，它表明，在1905年至1965年期间，交替极性不给作为显着的差异在太阳周期的下降阶段。因此，我们认为，宇宙射线通量的22年周期至少部分是日光层磁场直接调制的结果，这种影响可能主要限于太空时代的太阳活动极大期。
Context. Two candidate mechanisms have recently been considered for the nonlinear modulation of solar cycle amplitudes. Tilt quenching (TQ) is a negative feedback between cycle amplitude and the mean tilt angle of bipolar active regions relative to the azimuthal direction; latitude quenching (LQ) consists in a positive correlation between cycle amplitude and average emergence latitude of active regions. Aims. Here we explore the relative importance of and the determining factors behind the LQ and TQ effects. Methods. The degree of nonlinearity induced by TQ, LQ and their combination is systema…
Our basic theoretical understanding of the sources of cosmic rays and their propagation through the interstellar medium is hindered by the Sun, that through the solar wind affects the observed cosmic-ray spectra. This effect is known as solar modulation. Recently released cosmic-ray observations from the Alpha Magnetic Spectrometer (AMS-02) and publicly available measurements of the solar wind properties from the Advanced Composition Explorer and the Wilcox observatory allow us to test the analytical modeling of the time-, charge- and rigidity-dependence of solar modulation. We rely on associa…
Active-region Modulation of Subsurface Meridional Flows and Magnetic Flux Transport on the Sun
Indian Institute of Astrophysics（印度天体物理研究所）；Pondicherry University（本地治里大学）；W. W. Hansen Experimental Physics Laboratory, Stanford University（斯坦福大学W.W.汉森实验物理实验室）；National Solar Observatory（国家太阳天文台）
A dynamo model of magnetic activity in solar-like stars with different rotational velocities
我们试图对类太阳恒星的Ca II H/K发射和X射线发射随Rossby数的减小而增加的观测结果提供定量的理论解释（即，更快的旋转）。假设这些排放是由类似于太阳黑子周期的磁循环引起的，我们构建了不同旋转周期的$1M_{\odot}$恒星的通量输运发电机模型。我们首先计算的微分旋转和纬向环流这些恒星内部的平均场流体动力学模型。然后这些被替换到我们的发电机代码中以产生周期解。我们发现，无量纲振幅$f_m$的环形通量通过恒星的旋转周期的减少而增加。如果我们假设辐射是$f_m$的3-4次方，观测数据就可以匹配。假设Babcock-Leighton机制随着旋转的增加而饱和，我们可以为在低Rossby数下观察到的发射饱和提供一个解释。我们的模型的主要失败之处在于，它预测的磁循环周期随着旋转速率的增加而增加，这与观测发现的相反。我们的许多计算都是基于磁浮力使磁通量管从对流区底部径向上升的假设。考虑到科里奥利力使磁通量管转向平行于快速旋转的恒星的旋转轴上升，结果并没有发生质的变化。
Evidence for Solar-Cycle Modulation of the Alpha-to-Proton Temperature Ratio in Solar Wind
Physical Research Laboratory (PRL)（物理研究实验室）；Indian Institute of Technology (IIT), Gandhinagar（甘地纳加尔印度理工学院）；Department of Physics and Astronomy, University of Iowa（爱荷华大学物理与天文系）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；The Catholic University of America（美利坚天主教大学）；Department of Geosciences, Tel Aviv University（特拉维夫大学地球科学系）
We use the ASH code to model the convective dynamo of solar-type stars. Based on a series of 15 3-D MHD simulations spanning 4 bins in rotation and mass, we show what mechanisms are at work in these stellar dynamos with and without magnetic cycles and how global stellar parameters affect the outcome. We also derive scaling laws for the differential rotation and magnetic field based on these simulations. We find a weaker trend between differential rotation and stellar rotation rate, ($ΔΩ\sim (|Ω|/Ω_{\odot})^{0.46}$) in the MHD solutions than in their HD counterpart $(|Ω|/Ω_{\odot})^{0.66})$, yi…
Systematic Investigation of Solar Modulation of Galactic Protons for Solar Cycle 23 using a Monte Carlo Approach with Particle Drift Effects and Latitudinal Dependence
Both the recent 2009 and 2020 solar minima were classified as unusually quiet and characterized with unusually high galactic cosmic ray (GCR) levels. However, unlike the trends from previous decades in which anomalous cosmic ray (ACR) and GCR levels strongly agreed, the ACR intensities did not reach such high record-setting levels.This discrepancy between the behaviour of GCRs and ACRs is investigated in this work by simulating the acceleration and transport of GCR and ACR oxygen under different transport conditions. After using recent observations to constrain any remaining free parameters pr…
