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 poloidal magnetic field, which is the source of energy of the complex phenomena of magnetic activity.
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…
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…
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 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…
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…
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 mea…
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…
We analyze the X-ray emission and chromospheric activity of Sun-like stars of F, G and K spectral classes (late-type stars) studied in the framework of the HK project. More powerful coronas are possessed by stars displaying irregular variations of their chromospheric emission, while stars with regular cyclic activity are characterized by comparatively modest X-ray luminosities and ratios of the X-ray to bolometric luminosity. This indicates that the nature of processes associated with magnetic-field amplification on the convective envelope changes appreciably in the transition from small to la…
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）
Rapidly rotating stars show short-period oscillations in magnetic activity and polar appearance of starspots. The aim of this paper is to study large-scale shallow water waves in the tachoclines of rapidly rotating stars and their connection to the periodicity and the formation of starspots at high latitudes. Shallow-water magnetohydrodynamic equations were used to study the dynamics of large-scale waves at the rapidly rotating stellar tachoclines in the presence of toroidal magnetic field. Dispersion relations and latitudinal distribution of wave modes were derived. We found that low-frequenc…
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…
In young sun-like stars and field M dwarf stars, chromospheric and coronal magnetic activity indicators such as H$α$, X-ray and radio emission are known to saturate with low Rossby number ($Ro \lesssim 0.1$), defined as the ratio of rotation period to convective turnover time. The mechanism for the saturation is unclear. In this paper, we use photospheric Ti I and Ca I absorption lines in $Y$ band to investigate magnetic field strength in M dwarfs for Rossby numbers between 0.01 and 1.0. The equivalent widths of the lines are magnetically enhanced by photospheric spots, a global field or a com…
Magnetic activity in Sun-like and low-mass stars causes X-ray coronal emission, which is stronger for more rapidly rotating stars. This relation is often interpreted in terms of the Rossby number, i.e., the ratio of rotation period to convective overturn time. We reconsider this interpretation on the basis of the observed X-ray emission and rotation periods of 821 stars with masses below 1.4 Msun. A generalized analysis of the relation between X-ray luminosity normalized by bolometric luminosity, L_X/L_bol, and combinations of rotational period, P, and stellar radius, R, shows that the Rossby …
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））
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…
The cyclicity of 33 solar-type stars that are similar to 11-year and to the quasi-biennial variations of solar radiation have studied. Our calculation were based on new simultaneous observations of the flux variations of the photospheric and chromospheric emissions of 33 solar-type stars and the Sun during the HK project that were conducted over the last 20 years. The method of Fast Fourier Transform was applied to these observed data. In addition to the known cyclic chromospheric emission variations of stars at the 11-year time scale, which were discovered at the Mount Wilson Observatory, we …
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…
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-…
High precision photometry of solar-like members of the open cluster M67 with Kepler/K2 data has recently revealed enhanced activity for stars with a large Rossby number, which is the ratio of rotation period to the convective turnover time. Contrary to the well established behavior for shorter rotation periods and smaller Rossby numbers, the chromospheric activity of the more slowly rotating stars of M67 was found to increase with increasing Rossby number. Such behavior has never been reported before, although it was theoretically predicted to emerge as a consequence of antisolar differential …
We applied the method of continuous wavelet-transform to high-quality time-frequency analysis to the sets of observations of relative sunspot numbers. Wavelet analysis of these data reveals the following pattern: at the same time there are several activity cycles whose periods vary widely from the quasi biennial up to the centennial period. These relatively low-frequency periodic variations of the solar activity gradually change the values of periods of different cycles in time. This phenomenon can be observed in every cycle of activity.
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…
The activity of the Sun as a result of cyclic changes of the global magnetic field is studied. As a consequence of the analysis of magnetic activity of solar-type stars the following power dependencies were found: the dependence between the rotation periods and the effective temperatures, the dependence between the duration of the "11-year" cycles of activity and the effective temperatures, and the dependence between the duration of quasi-biennial cycles and the effective temperatures. It is shown that the physical nature of these dependencies associated with the observed properties of solar-t…
Turbulent magnetic fields fill most of the volume of the solar atmosphere. However, their spatial and temporal variations are still unknown. Since 2007, during the current solar minimum, we are periodically monitoring several wavelength regions in the solar spectrum to search for variations of the turbulent magnetic field in the quiet Sun. These fields, which are below the resolution limit, can be detected via the Hanle effect which influences the scattering polarization signatures (Q/I) in the presence of magnetic fields. We present a description of our program and first results showing that …
The analysis of the effect of the hysteresis, which manifests itself in an ambiguous relationship of radiation from the photosphere, chromosphere and corona on the rise and decline phases of the solar and stellar activity cycles have done. Some indices of solar activity: the flux of the hydrogen Lyman-alpha emission, the 10.7 cm flux, the sunspot number SSN, the flux in the coronal green line 530.3 nm, the solar constant TSI and the 280 nm Mg II flux were studied. The stars with the well-determined cycles were examined to detect the effect of hysteresis between the chromosphere's S-index CaII …
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 …
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 …
We combine stellar surface rotation periods determined from NASA's Kepler mission with spectroscopic temperatures to demonstrate the existence of pileups at the long-period and short-period edges of the temperature-period distribution for main-sequence stars with temperatures exceeding $\sim 5500$K. The long-period pileup is well-described by a curve of constant Rossby number, with a critical value of $\mathrm{Ro_{crit}} \lesssim 2$. The long-period pileup was predicted by van Saders et al. (2019) as a consequence of weakened magnetic braking, in which wind-driven angular momentum losses cease…
The questions whether the Sun shrinks with the solar activity and what causes this have been a subject of debate. Helioseismology provides means to measure with high precision the radial displacement of subsurface layers, co-called "seismic radius", through analysis of oscillation frequencies of surface gravity (f) modes. Here, we present results of a new analysis of twenty one years of helioseismology data from two space missions, Solar and Heliospheric Observatory (SoHO) and Solar Dynamics Observatory (SDO), which allow us to resolve previous uncertainties and compare variations of the seism…
alpha_theta waves in the tachoclines of Sun-like stars
Institute of Physics, University of Graz（格拉茨大学物理研究所）；Department of Astronomy and Astrophysics at Space Research Center, Ilia State University（伊利亚州立大学空间研究中心天文与天体物理系）；Evgeni Kharadze Georgian National Astrophysical Observatory（叶夫根尼·哈拉泽格鲁吉亚国家天文台）；High Altitude Observatory, NCAR（NCAR高空观测站）
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…
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）
The heliophysics catalogues published by the Ebro Observatory during 1910--1937 have been converted into a digital format in order to provide the data for computational processing. This has allowed us to study in detail the North-South (N-S) asymmetry of solar activity in that period, focusing on two different structures located at two different layers of the solar atmosphere: sunspots (Photosphere) and solar plages (Chromosphere). The examination of the absolute and normalised N-S asymmetry indices in terms of their monthly sum of occurrences and areas has made possible to find out a cyclic b…
The Maunder minimum (MM) of greatly reduced solar activity took place in 1645-1715, but the exact level of sunspot activity is uncertain as based, to a large extent, on historical generic statements of the absence of spots on the Sun. Here we aim, using a conservative approach, to assess the level and length of solar cycle during the Maunder minimum, on the basis of direct historical records by astronomers of that time. A database of the active and inactive days (days with and without recorded sunspots on the solar disc respectively) is constructed for three models of different levels of conse…
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…
Measurements from the Mount Wilson Observatory (MWO) are used to study the long-term variations of sunspot field strengths from 1920 to 1958. Following a modified approach similar to that in Pevtsov et al. (2011), for each observing week we select a single sunspot with the strongest field strength measured that week and then compute monthly averages of these weekly maximum field strengths. The data show the solar cycle variation of the peak field strengths with an amplitude of about 500-700 gauss (G), but no statistically significant long-term trends. Next, we use the sunspot observations from…
The X-ray and extreme-ultraviolet (EUV) emissions from the low-mass stars significantly affect the evolution of the planetary atmosphere. However, it is, observationally difficult to constrain the stellar high-energy emission because of the strong interstellar extinction of EUV photons. In this study, we simulate the XUV (X-ray+EUV) emission from the Sun-like stars by extending the solar coronal heating model that self-consistently solves, with sufficiently high resolution, the surface-to-coronal energy transport, turbulent coronal heating, and coronal thermal response by conduction and radiat…
The distribution of magnetic fields of positive and negative polarities over the surface of the Sun was studied. Synoptic maps of the photospheric magnetic field (NSO Kitt Peak, 1978--2016) were used for the analysis. In the time-latitude diagram for weak magnetic fields ($B \leq 5 G$), inclined bands are clearly visible, indicating the alternating dominance of magnetic fields with positive or negative polarity drifting towards the poles of the Sun. Analysis of the time-latitude diagram using the method of empirical orthogonal functions (EOF) made it possible to establish a cyclic change in th…
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…
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…
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…
To better understand the observed distributions of rotation rate and magnetic activity of sun-like and low-mass stars, we derive a physically motivated scaling for the dependence of the stellar-wind torque on Rossby number. The torque also contains an empirically-derived scaling with stellar mass (and radius), which provides new insight into the mass-dependence of stellar magnetic and wind properties. We demonstrate that this new formulation explains why the lowest mass stars are observed to maintain rapid rotation for much longer than solar-mass stars, and simultaneously, why older population…
The 11-year solar cycle is the dominant pattern of solar activity reflecting the oscillatory dynamo mechanism in the Sun. Solar cycles were directly observed since 1700, while indirect proxies suggest their existence over a much longer period of time but generally without resolving individual cycles and their continuity. Here we reconstruct individual cycles for the last millennium using recent 14C data and state-of-the-art models. Starting with the 14C production rate determined from the so far most precise measurements of radiocarbon content in tree rings, solar activity is reconstructed in …
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…
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…
