Rossby waves play an important role in mediating the angular momentum of rotating spherical fluids, creating weather on Earth and tuning exoplanet orbits in distant stellar systems (Ogilvie 2014). Their recent discovery in the solar convection zone provides an exciting opportunity to appreciate the detailed astrophysics of Rossby waves. Large-scale Rossby waves create subtle drifts in acoustic oscillations in the convection zone, which we measure using helioseismology to image properties of Rossby waves in the interior. We analyze 20 years of space-based observations, from 1999 to 2018, to measure Rossby-mode frequencies, line-widths, and amplitudes. Spatial leakage affects the measurements of normal model coupling and complicates the analysis of separating out specific harmonic degree and the azimuthal number of features on the Sun. Here we demonstrate a novel approach to overcome this difficulty and test it by performing synthetic tests. We find that the root-mean-square velocity of the modes is of the order of 0.5 m/s at the surface.
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…
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…
Magnetic activity is a global property of the Sun; the complex processes of solar activity are connected with the solar magnetic fields. For solar-type stars and the Sun magnetic activity depends on the physical parameters of the star. In this article we study the relationships between the duration of activity cycle and effective temperature for solar-type stars and the Sun. We've tried to explain these relationships due to the existence of layer of laminar convection near the bottom of the convective zone of the star. In this layer the Rossby waves are formed. They generate the primary poloid…
Magnetic fields of late-type stars are presumably generated by a dynamo mechanism at the interface layer between the radiative interior and the outer convective zone. The Rossby number, which is related to the dynamo process, shows an observational correlation with activity. It represents the ratio between the rotation period of the star and the local convective turnover time. The former is well determined from observations but the latter is estimated by an empirical iterated function depending on the color index (B-V) and the mixing-length parameter. We computed the theoretical Rossby number …
Quasi-biennial oscillations (QBO) are frequently observed in the solar activity indices. However, no clear physical mechanism for the observed variations has been suggested so far. Here we study the stability of magnetic Rossby waves in the solar tachocline using the shallow water magnetohydrodynamic approximation. Our analysis shows that the combination of typical differential rotation and a toroidal magnetic field with a strength > 10^5 G triggers the instability of the m=1 magnetic Rossby wave harmonic with a period of 2 years. This harmonic is antisymmetric with respect to the equator and …
Context: Solar sectoral Rossby waves have only recently been unambiguously identified in Helioseimsic and Magnetic Imager (HMI) and Michelson Doppler Imager (MDI) maps of flows near the solar surface. So far this has not been done with the Global Oscillation Network Group (GONG) ground-based observations, which have different noise properties. Aims: We utilize 17 years of GONG++ data, to identify and characterize solar Rossby waves using ring-diagram helioseismology. We compare directly with HMI ring-diagram analysis. Methods: Maps of the radial vorticity are obtained for flows within the top …
The Sun's complex dynamics is controlled by buoyancy and rotation in the convection zone and by magnetic forces in the atmosphere and corona. While small-scale solar convection is well understood, the dynamics of large-scale flows in the solar convection zone is not explained by theory or simulations. Waves of vorticity due to the Coriolis force, known as Rossby waves, are expected to remove energy out of convection at the largest scales. Here we unambiguously detect and characterize retrograde-propagating vorticity waves in the shallow subsurface layers of the Sun at angular wavenumbers below…
The generation of Rossby rogue waves (Rossby rogons), as well as the excitation of bright and dark Rossby envelpe solitons are demonstrated on the basis of the modulational instability (MI) of a coherent Rossby wave packet. The evolution of an amplitude modulated Rossby wave packet is governed by one-dimensional (1D) nonlinear Schrödinger equation (NLSE). The latter is used to study the amplitude modulation of Rossby wave packets for fluids in Earth's atmosphere and in the solar photosphere. It is found that an ampitude modulated Rossby wave packet becomes stable (unstable) against quasi-stati…
Anti-solar differential rotation profiles have been found for decades in numerical simulations of convective envelopes of solar-type stars. These profiles are characterized by a slow equator and fast poles (i.e., reversed with respect to the Sun) and have been found in simulations for high Rossby numbers (slow rotators). Rotation profiles like this have been reported observationally in evolved stars, but have never been unambiguously observed for cool solar-type stars on the main sequence. In this context, detecting this regime in main-sequence solar-type stars would improve our understanding …
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…
Effects of density stratification on Rossby waves in deep atmospheres
JILA；Department of Astrophysical and Planetary Sciences, University of Colorado Boulder（科罗拉多大学博尔德分校天体物理与行星科学系）；Department of Applied Mathematics, University of Colorado Boulder（科罗拉多大学博尔德分校应用数学系）
In a previous paper we studied the effect of latitudinal rotation on solar equatorial Rossby modes in the beta-plane approximation. Since then, a rich spectrum of inertial modes has been observed on the Sun, which is not limited to the equatorial Rossby modes and includes high-latitude modes. Here we extend the computation of toroidal modes in 2D to spherical geometry, using realistic solar differential rotation and including viscous damping. The aim is to compare the computed mode spectra with the observations and to study mode stability. At fixed radius, we solve the eigenvalue problem numer…
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…
Retrograde-propagating waves of vertical vorticity with longitudinal wavenumbers between 3 and 15 have been observed on the Sun with a dispersion relation close to that of classical sectoral Rossby waves. The observed vorticity eigenfunctions are symmetric in latitude, peak at the equator, switch sign near $20^\circ$-$30^\circ$, and decrease at higher latitudes. We search for an explanation that takes into account solar latitudinal differential rotation. In the equatorial $β$ plane, we study the propagation of linear Rossby waves (phase speed $c <0$) in a parabolic zonal shear flow, $U = - \ov…
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））
Apart from the 11-year solar cycle, another periodicity around 155-160 days was discovered during solar cycle 21 in high energy solar flares, and its presence in sunspot areas and strong magnetic flux has been also reported. This periodicity has an elusive and enigmatic character, since it usually appears only near the maxima of solar cycles, and seems to be related with a periodic emergence of strong magnetic flux at the solar surface. Therefore, it is probably connected with the tachocline, a thin layer located near the base of the solar convection zone, where strong dynamo magnetic field is…
Global-scale Rossby waves have recently been unambiguously identified on the Sun. Here we study the latitude and depth dependence of the Rossby wave eigenfunctions. By applying helioseismic ring-diagram analysis and granulation tracking to SDO/HMI observations, we compute maps of the radial vorticity of flows in the upper solar convection zone (down to depths of more than $16$ Mm). We use a Fourier transform in longitude to separate the different azimuthal orders m in the range $3 \le m \le 15$. At each $m$ we obtain the phase and amplitude of the Rossby waves as a function of depth using the …
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…
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 w…
Rossby waves play a fundamental role in angular momentum processes in rotating fluids. In addition to the potential to shed light on physical mechanisms operating in the solar convection zone, the recent detection of Rossby waves in the Sun (Löptien et al. 2018; Liang et al. 2018) also serves as a means of comparison between different helioseismic methods. Time-distance helioseismology, ring-diagram analysis and other techniques have all proven successful in recovering the Rossby-wave dispersion relation from analyses of Helioseismic and Magnetic Imager data (HMI; Schou et al. 2012). In this a…
Magnetic fields are at the heart of the observed stellar activity in late-type stars, and they are presumably generated by a dynamo mechanism at the interface layer between the radiative and the convective stellar regions. Since dynamo models are based on the interaction between differential rotation and convective motions, the introduction of rotation in the ATON 2.3 stellar code allows for explorations regarding a physically consistent treatment of magnetic effects in stellar structure and evolution, even though there are formidable mathematical and numerical challenges involved. As examples…
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…
Long-term records of sunspot number and concentrations of cosmogenic radionuclides (10Be and 14C) on the Earth reveal the variation of the Sun's magnetic activity over hundreds and thousands of years. We identify several clear periods in sunspot, 10Be, and 14C data as 1000, 500, 350, 200 and 100 years. We found that the periods of the first five spherical harmonics of the slow magnetic Rossby mode in the presence of a steady toroidal magnetic field of 1200-1300 G in the lower tachocline are in perfect agreement with the time scales of observed variations. The steady toroidal magnetic field can…
On the one hand, several types of global-scale inertial modes of oscillation have been observed on the Sun. They include the equatorial Rossby modes, critical-latitude modes, and high-latitude modes. On the other hand, the columnar convective modes (predicted by simulations; also known as banana cells or thermal Rossby waves) remain elusive. We aim to investigate the influence of turbulent diffusivities, non-adiabatic stratification, differential rotation, and a latitudinal entropy gradient on the linear global modes of the rotating solar convection zone. We solve numerically for the eigenmode…
Retrograde Rossby waves, measured to have significant amplitudes in the Sun, likely have notable implications for various solar phenomena. Rossby waves create small-amplitude, very-low frequency motions (on the order of the rotation rate and lower), which in turn shift the resonant frequencies and eigenfunctions of the acoustic modes of the Sun. The detection of even azimuthal orders Rossby modes using mode coupling presents additional challenges and prior work therefore only focused on odd orders. Here, we successfully extend the methodology to measure even azimuthal orders as well. We analyz…
Several types of inertial modes have been detected on the Sun. Properties of these inertial modes have been studied in the linear regime but have not been studied in nonlinear simulations of solar rotating convection. Comparing the nonlinear simulations, the linear theory, and the solar observations is important to better understand the differences between the models and the real Sun. We wish to detect and characterize the modes present in a nonlinear numerical simulation of solar convection, in particular to understand the amplitudes and lifetimes of the modes. We developed a code with a Yin-…
The observation of global acoustic waves (p modes) in the Sun has been key to unveiling its internal structure and dynamics. A different kind of wave, known as sectoral Rossby modes, have been observed and identified, which potentially opens the door to probing internal processes that are inaccessible through p mode helioseismology. Yet another set of waves, appearing as retrograde-propagating, equatorially antisymmetric vorticity waves, have also been observed but their identification remained elusive. Here, through a numerical model implemented as an eigenvalue problem, we provide evidence s…
Simulations of the onset and dynamical evolution of inertial waves in solar/stellar interior
Universidade Federal de Minas Gerais（米纳斯吉拉斯联邦大学）；Observatório Nacional（国家天文台）；Royal Observatory of Belgium（比利时皇家天文台）；High Altitude Observatory, NSF National Center for Atmospheric Research（美国国家大气研究中心高空观测站）；National Center for Atmospheric Research（美国国家大气研究中心）
Effects of Magnetic Fields on Solar Inertial Modes in Global Nonlinear Simulations
Universidade Federal de Minas Gerais（米纳斯吉拉斯联邦大学）；Royal Observatory of Belgium（比利时皇家天文台）；High Altitude Observatory, NSF National Center for Atmospheric Research（美国国家科学基金会国家大气研究中心高海拔天文台）；National Center for Atmospheric Research（国家大气研究中心）
In this dissertation, several components of large-scale solar flows are studied observationally: solar equatorial Rossby waves (waves of radial vorticity), large-scale convection, and surface flows around active regions. Maps of horizontal flows are derived from photospheric observations by the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO) using two different techniques: granulation tracking and local helioseismology. First, the eigenfunctions of solar Rossby waves are measured from helioseismic ring-diagram flow maps with a correlation method and a spectra…
We investigate how rotationally-constrained, deep convection might give rise to supergranulation, the largest distinct spatial scale of convection observed in the solar photosphere. While supergranulation is only weakly influenced by rotation, larger spatial scales of convection sample the deep convection zone and are presumably rotationally influenced. We present numerical results from a series of nonlinear, 3-D simulations of rotating convection and examine the velocity power distribution realized under a range of Rossby numbers. When rotation is present, the convective power distribution po…
Can atmospheric waves in planet-hosting solar-like stars substantially resonate to tidal forcing? Substantially at a level of impacting the space weather or even of being dynamo-relevant? In particular, low-frequency Rossby waves, which have been detected in the solar near-surface layers, are predestined at responding to sunspot cycle-scale perturbations. In this paper, we seek to address these questions as we formulate a forced wave model for the tachocline layer, which is widely considered as the birthplace of several magnetohydrodynamic planetary waves, i.e., Rossby, inertia-gravity (Poinca…
Large-scale Rossby waves have recently been discovered from measurements of horizontal surface and near-surface solar flows (Löptien at al. 2018). We are interested in understanding why only the sectoral modes are seen in the observations and also in modelling the radial structure of the observed modes. To do so, we characterise here the radial eigenfunctions of r modes for slowly-rotating polytropes in uniform rotation. We find that for free-surface boundary conditions on a spheroid of non-vanishing surface density, r modes can only exist for $\ell=m$ spherical harmonics in the inviscid case,…
In this paper, we have studied the convectively coupled equatorially trapped waves in rotating stars, with and without magnetic field. The equatorial trapped HD and MHD Poincaré, Rossby, mixed Rossby-Poincaré, and Kelvin waves were identified. The effects of stratification and non-traditional Coriolis force terms have been investigated. When the flow is strongly stratified, the wave frequencies of the convectively coupled model are almost the same as those of shallow water model. However, when the flow is weakly stratified, the wave frequencies are constrained by the buoyancy frequency. The no…
A major outstanding problem in solar physics is the confinement of the solar tachocline, the thin shear layer that separates nearly solid-body rotation in the radiative interior from strong differential rotation in the convection zone. Here, we present the first 3-D, global solar simulation in which a tachocline is confined by a self-excited dynamo. The non-axisymmetric magnetism is initially built in the convection zone and then diffusively imprints downward. Additionally, the field is locally amplified throughout the radiative interior by vigorous horizontal motions that arise from equatoria…
Inertial waves, which are dominantly driven by the Coriolis force, likely play an important role in solar dynamics, and additionally, provide a window into the solar subsurface. The latter allows us to infer properties that are inaccessible to the traditional technique of acoustic-wave helioseismology. Thus, a full characterization of these normal modes holds promise in enabling the investigation of solar subsurface dynamics. In this work, we develop a spectral eigenvalue solver to model the spectrum of inertial waves in the Sun. We model the solar convection zone as an anelastic medium, and s…
The aim of this article is to study how the differential rotation of solar-like stars is influenced by rotation rate and mass in presence of magnetic fields generated by a convective dynamo. We use the ASH code to model the convective dynamo of solar-like stars at various rotation rates and masses, hence different effective Rossby numbers. We obtained models with either prograde (solar-like) or retrograde (anti-solar-like) differential rotation. The trends of differential rotation versus stellar rotation rate obtained for simulations including the effect of the magnetic field are weaker compar…
Effects of the radiative interior on solar inertial modes
Max-Planck-Institut für Sonnensystemforschung（马克斯·普朗克太阳系统研究所）；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）
The solar convection zone rotates differentially, with its equatorial region rotating more rapidly than the polar regions. This form of differential rotation, also observed in many other low-mass stars, is understood to arise when Coriolis effects are stronger than those associated with buoyant driving of the convection. When buoyancy dominates, a so-called antisolar state of differential rotation results, characterized by rapidly-rotating poles and a slow equator. The transition between these two states has been shown to occur when the intensity of these two forces is roughly equal or, equiva…
Magnetic bright points in the solar photosphere, visible in both continuum and G-band images, indicate footpoints of kilogauss magnetic flux tubes extending to the corona. The power spectrum of bright-point motion is thus also the power spectrum of Alfven wave excitation, transporting energy up flux tubes into the corona. This spectrum is a key input in coronal and heliospheric models. We produce a power spectrum of bright-point motion using radiative magnetohydrodynamic simulations, exploiting spatial resolution higher than can be obtained in present-day observations, while using automated tr…
The oscillations of a slowly rotating star have long been classified into spheroidal and toroidal modes. The spheroidal modes include the well-known 5-min acoustic modes used in helioseismology. Here we report observations of the Sun's toroidal modes, for which the restoring force is the Coriolis force and whose periods are on the order of the solar rotation period. By comparing the observations with the normal modes of a differentially rotating spherical shell, we are able to identify many of the observed modes. These are the high-latitude inertial modes, the critical-latitude inertial modes,…
This paper considers the dominant dynamical, thermal and rotational balances within the solar convection zone. The reasoning is such that: Coriolis forces balance pressure gradients. Background vortex stretching, baroclinic torques and nonlinear advection balance jointly. Turbulent fluxes convey what part of the solar luminosity that radiative diffusion cannot. These four relations determine estimates for the dominant length scales and dynamical amplitudes strictly in terms of known physical quantities. We predict that the dynamical Rossby number for convection is less than unity below the nea…
Convection in the solar interior is thought to comprise structures on a spectrum of scales. This conclusion emerges from phenomenological studies and numerical simulations, though neither covers the proper range of dynamical parameters of solar convection. Here, we analyze observations of the wavefield in the solar photosphere using techniques of time-distance helioseismology to image flows in the solar interior. We downsample and synthesize 900 billion wavefield observations to produce 3 billion cross-correlations, which we average and fit, measuring 5 million wave travel times. Using these t…
The revolution of helio- and asteroseismology provides access to the detailed properties of stellar interiors by studying the star's oscillation modes. Among them, gravity (g) modes are formed by constructive interferences between progressive internal gravity waves (IGWs), propagating in stellar radiative zones. Our new 3D nonlinear simulations of the interior of a solar-like star allows us to study the excitation, propagation, and dissipation of these waves. The aim of this article is to clarify our understanding of the behavior of IGWs in a 3D radiative zone and to provide a clear overview o…
The Sun is the major source of heat and light in our solar system. The solar cycle is the 11-year cycle of solar activity that can be determined by the rise and fall in the numbers and surface area of sunspots. Solar activity is associated with several factors including radio flux, solar irradiance, magnetic field, solar flares, coronal mass ejections, and solar cycles. This study attempts to determine the Sun's activity specifically for the coronal mass ejection, its trend during solar cycle 23, and its apparent difference. A time series analysis was used to measure the CME data for larger ca…
