The dynamo mechanism, responsible for the solar magnetic activity, is still an open problem in astrophysics. Different theories proposed to explain such phenomena have failed in reproducing the observational properties of the solar magnetism. Thus, ab-initio computational modeling of the convective dynamo in a spherical shell turns out as the best alternative to tackle this problem. In this work we review the efforts performed in global simulations over the past decades. Regarding the development and sustain of mean-flows, as well as mean magnetic field, we discuss the points of agreement and divergence between the different modeling strategies. Special attention is given to the implicit large-eddy simulations performed with the EULAG-MHD code.
We study the relation between stellar dynamo-wave propagation and the structure of the stellar magnetic field. Modeling dynamo waves by the well-known Parker migratory dynamo, we vary the intensity of dynamo drivers in order to obtain activity-wave propagation toward the Equator (as in the solar-activity cycle) or towards the Poles. We match the magnetic field in the dynamo active shell with that in the surrounding stellar material, using a simple dissipativ magnetohydrodynamic system for the transition region. Introducing a weak asymmetry between the stellar hemispheres, we study phase shifts…
Our understanding of stellar dynamos has largely been driven by the phenomena we have observed of our own Sun. Yet, as we amass longer-term datasets for an increasing number of stars, it is clear that there is a wide variety of stellar behavior. Here we briefly review observed trends that place key constraints on the fundamental dynamo operation of solar-type stars to fully convective M dwarfs, including: starspot and sunspot patterns, various magnetism-rotation correlations, and mean field flows such as differential rotation and meridional circulation. We also comment on the current insight t…
In this review, we discuss whether the present solar dynamo models can be extrapolated to explain various aspects of stellar activity. We begin with a summary of the following kinds of data for solar-like stars: (i) data pertaining to stellar cycles from Ca H/K emission over many years; (ii) X-ray data indicating hot coronal activity; (iii) starspot data (especially about giant polar spots); and (iv) data pertaining to stellar superflares. Then we describe the current status of solar dynamo modelling---giving an introduction to the flux transport dynamo model, the currently favoured model for …
[Abridged abstract:] Stellar activity data provide evidence of activity wave branches propagating polewards rather than equatorwards (the solar case). Stellar dynamo theory allows polewards propagating dynamo waves for certain governing parameters. We try to unite observations and theory, restricting our investigation to the simplest mean-field dynamo models. We suggest a crude preliminary systematization of the reported cases of polar activity branches. Then we present results of dynamo model simulations which contain magnetic structures with polar dynamo waves, and identify the models which …
Asteroseismological determinations of stellar ages have shown that old main-sequence dwarfs do not obey gyrochronology. Their rotation is slow compared to young stars but faster than gyrochronology predicts. This can be explained by the presence of a maximum rotation period beyond which the large-scale dynamo switches off and stops providing global magnetic fields necessary for stellar spindown. Assuming this explanation, the excess of stellar dynamo parameters over their marginal values can be estimated for given spectral type and rotation rate. The estimation gives the dynamo number for the …
In this paper we first discuss observational evidence of longitudinal concentrations of magnetic activity in the Sun and rapidly rotating late-type stars with outer convective envelopes. Scenarios arising from the idea of rotationally influenced anisotropic convective turbulence being the key physical process generating these structures are then presented and discussed - such effects include the turbulent dynamo mechanism, negative effective magnetic pressure instability (NEMPI) and hydrodynamical vortex instability. Finally, we discuss non-axisymmetric stellar mean-field dynamo models, the re…
Stellar cycle variability in Mount Wilson stars and dynamo models: Rotation rate and dynamo number dependency
The University of Tokyo（东京大学）；Research Center for Early Universe, The University of Tokyo（东京大学早期宇宙研究中心）；Indian Institute of Technology (Banaras Hindu University)（印度理工学院（贝拿勒斯印度教大学））
We study turbulent generation of large-scale magnetic fields using nonlinear dynamo models for solar-type stars in the range of rotational periods from 14 to 30 days. Our models take into account non-linear effects of dynamical quenching of magnetic helicity, and escape of magnetic field from the dynamo region due to magnetic buoyancy. The results show that the observed correlation between the period of rotation and the duration of activity cycles can be explained in the framework of a distributed dynamo model with a dynamical magnetic feedback acting on the turbulent generation either from ma…
Young solar-type stars rotate rapidly and are very magnetically active. The magnetic fields at their surfaces likely originate in their convective envelopes where convection and rotation can drive strong dynamo action. Here we explore simulations of global-scale stellar convection in rapidly rotating suns using the 3-D MHD anelastic spherical harmonic (ASH) code. The magnetic fields built in these dynamos are organized on global-scales into wreath-like structures that span the convection zone. We explore one case rotates five times faster than the Sun in detail. This dynamo simulation, called …
The evolution of a star is influenced by its internal rotation dynamics through transport and mixing mechanisms, which are poorly understood. Magnetic fields can play a role in transporting angular momentum and chemical elements, but the origin of magnetism in radiative stellar layers is unclear. Using global numerical simulations, we identify a subcritical transition to turbulence due to the generation of a magnetic dynamo. Our results have many of the properties of the theoretically-proposed Tayler-Spruit dynamo mechanism, which strongly enhances transport of angular momentum in radiative zo…
When stars like our Sun are young they rotate rapidly and are very magnetically active. We explore dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code. The magnetic fields built in these dynamos are organized on global-scales into wreath-like structures that span the convection zone. Wreath-building dynamos can undergo quasi-cyclic reversals of polarity and such behavior is common in the parameter space we have been able to explore. These dynamos do not appear to require tachoclines to achieve their spatial or temporal organization. Wreath-building d…
We live near a magnetic star whose cycles of activity are driven by dynamo action beneath the surface. In the solar convection zone, rotation couples with plasma motions to build highly organized magnetic fields that erupt at the surface and undergo relatively regular cycles of polarity reversal. Despite our proximity to the Sun, the nature of its dynamo remains elusive, but observations of other solar-type stars show that surface magnetism is a nearly ubiquitous feature. In recent time, numerical simulations of convection and dynamo action have taken tremendous strides forward. Global-scale o…
We focus on the connection between the internal dynamo magnetic field and the stellar wind. If the star has a cyclic dynamo, the modulations of the magnetic field can affect the wind, which in turn can back-react on the boundary conditions of the star, creating a feedback loop. We have developed a 2.5-dimensional numerical set-up to model this essential coupling. We have implemented an alpha-Omega mean-field dynamo in the PLUTO code, and then coupled it to a spherical polytropic wind model via an interface composed of four grid layers with dedicated boundary conditions. We present here a dynam…
We investigate the relations between tachocline-based dynamos and the surface flux transport mechanisms in stars with outer convection zones. Using our combined models of flux generation and transport, we demonstrate the importance of the buoyant rise of magnetic flux, which physically determines the emergence latitudes and tilt angles of bipolar magnetic regions. The combined effects of the dynamo strength, flux rise, and surface transport lead to various cyclic and non-cyclic time series of total unsigned surface magnetic flux.
Recent spectro-polarimetric observations of solar-type stars have shown the presence of photospheric magnetic fields with a predominant toroidal component. If the external field is assumed to be current-free it is impossible to explain these observations within the framework of standard mean-field dynamo theory. In this work it will be shown that if the coronal field of these stars is assumed to be harmonic, the underlying stellar dynamo mechanism can support photospheric magnetic fields with a prominent toroidal component even in the presence of axisymmetric magnetic topologies. In particular…
Convectively driven dynamos with rotation generating magnetic fields on scales large compared with the scale of the turbulent eddies are being reviewed. It is argued that such fields can be understood as the result of an alpha effect. Simulations in Cartesian domains show that such large-scale magnetic fields saturate on a time scale compatible with the resistive one, suggesting that the magnitude of the alpha effect is here still constrained by approximate magnetic helicity conservation. It is argued that, in the absence of shear and/or any other known large-scale dynamo effects, these simula…
Global and semi-global convective dynamo simulations of solar-like stars are known to show a transition from an anti-solar (fast poles, slow equator) to solar-like (fast equator, slow poles) differential rotation (DR) for increasing rotation rate. The dynamo solutions in the latter regime can exhibit regular cyclic modes, whereas in the former one, only stationary or temporally irregular solutions have been obtained so far. In this paper we present a semi-global dynamo simulation in the transition region, exhibiting two coexisting dynamo modes, a cyclic and a stationary one, both being dynamic…
This paper provides a brief overview of dynamo scaling relationships for the degree of equipartition between magnetic and kinetic energies. Three basic approaches are adopted to explore these scaling relationships, with a first look at two simple models: one assuming magnetostrophy and another that includes the effects of inertia. Next, a third scaling relationship is derived that utilizes the assumptions that the dynamo possesses two integral spatial scales and that it is driven by the balance of buoyancy work and ohmic dissipation as studied in Davidson 2013. The results of which are then co…
Models of rotationally-driven dynamos in stellar radiative zones have suggested that magnetohydrodynamic transport of angular momentum and chemical composition can dominate over the otherwise purely hydrodynamic processes. A proper consideration of the interaction between rotation and magnetic fields is therefore essential. Previous studies have focused on a magnetic model where the magnetic field strength is derived as a function of the stellar structure and angular momentum distribution. We have adapted our one-dimensional stellar rotation code, RoSE, to model the poloidal and toroidal magne…
Recent observations reveal the surprising breakdown of stellar gyrochronology relations at about the Sun's age hinting that middle-aged, solar-like stars transition to a magnetically inactive future. We provide a theoretical basis for these intriguing observations inspired by simulations with a mathematical dynamo model that can explore long-term solar cycle fluctuations. We reproduce the observed bimodal distribution of sunspot numbers, but only for subcritical dynamos. Based on a bifurcation analysis, we argue that ageing of solar-like stars makes the magnetically-weak dynamo regime readily …
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…
In this work the latitude dependent stellar spot rotation is investigated based on dynamo models. The maps of the magnetic pressure at the surface from the dynamo calculations are treated similarly to the temperature maps obtained using Doppler imaging techniques. A series of snapshots from the dynamo models are cross-correlated to obtain the shift of the magnetic patterns at each latitude and time point. The surface differential rotation patterns obtained from the snapshots of the dynamo calculations show in all studied cases variability over the activity cycle. In the models using only the l…
The magnetic activity of solar-type stars generally increases with stellar rotation rate. The increase, however, saturates for fast rotation. The Babcock-Leighton mechanism of stellar dynamos saturates as well when the mean tilt-angle of active regions approaches ninety degrees. Saturation of magnetic activity may be a consequence of this property of the Babcock-Leighton mechanism. Stellar dynamo models with a tilt-angle proportional to the rotation rate are constructed to probe this idea. Two versions of the model - treating the tilt-angles globally and using Joy's law for its latitude depend…
Using a new uniform sample of 824 solar and late-type stars with measured X-ray luminosities and rotation periods we have studied the relationship between rotation and stellar activity that is believed to be a probe of the underlying stellar dynamo. Using an unbiased subset of the sample we calculate the power law slope of the unsaturated regime of the activity -- rotation relationship as $L_X/L_{bol}\propto Ro^β$, where $β=-2.70\pm0.13$. This is inconsistent with the canonical $β= -2$ slope to a confidence of 5$σ$ and argues for an interface-type dynamo. We map out three regimes of coronal em…
An update is given on the current status of solar and stellar dynamos. At present, it is still unclear why stellar cycle frequencies increase with rotation frequency in such a way that their ratio increases with stellar activity. The small-scale dynamo is expected to operate in spite of a small value of the magnetic Prandtl number in stars. Whether or not the global magnetic activity in stars is a shallow or deeply rooted phenomenon is another open question. Progress in demonstrating the presence and importance of magnetic helicity fluxes in dynamos is briefly reviewed, and finally the role of…
Early-type stars show a bimodal distribution of magnetic field strengths, with some showing very strong fields ($\gtrsim 1\,\mathrm{kG}$) and others very weak fields ($\lesssim 10\,\mathrm{G}$). Recently, we proposed that this reflects the processing or lackthereof of fossil fields by subsurface convection zones. Stars with weak fossil fields process these at the surface into even weaker dynamo-generated fields, while in stars with stronger fossil fields magnetism inhibits convection, allowing the fossil field to remain as-is. We now expand on this theory and explore the time-scales involved i…
Existing stellar X-ray surveys suggest major problems in our understanding of the evolution of stellar magnetic activity in solar and late-type stars, reaching conflicting conclusions over the rate of decay of X-ray activity and the spectral types responsible. We are confronting these discrepancies with a new model of the expected stellar X-ray luminosity distribution, combining a Galactic population synthesis model with current theories for rotational spin- down and the rotation - activity relation for the stellar magnetic dynamo. Here we test our model using new observations of the stellar c…
The 3-D magnetohydrodynamic (MHD) Anelastic Spherical Harmonic (ASH) code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo generated magnetic fields possesses many time scales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the…
Rotational shear layers at the boundary between radiative and convective zones, tachoclines, play a key role in the process of magnetic field generation in solar-like stars. We present two sets of global simulations of rotating turbulent convection and dynamo. The first set considers a stellar convective envelope only; the second one, aiming at the formation of a tachocline, considers also the upper part of the radiative zone. Our results indicate that the resulting mean-flows and dynamo properties like the growth rate, saturation energy and mode depend on the Rossby (Ro) number. For the first…
Observations of the solar butterfly diagram from sunspot records suggest persistent fluctuation in parity, away from the overall, approximately dipolar structure. We use a simple mean-field dynamo model with a solar-like rotation law, and perturb the $α$-effect. We find that the parity of the magnetic field with respect to the rotational equator can demonstrate what we describe as resonant behaviour, while the magnetic energy behaves in a more or less expected way. We discuss possible applications of the phenomena in the context of various deviations of the solar magnetic field from dipolar sy…
Retarded Stellar Dynamo in Tidally Deformed M Dwarfs
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；Beijing Normal University（北京师范大学）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；University of Chinese Academy of Sciences（中国科学院大学）；Chongqing University（重庆大学）
In this Chapter we examine the role of the ngVLA to further our understanding of the different manifestations of convective or turbulence-driven stellar activity on red giant and supergiant stars. The combination of high spatial resolution and high sensitivity will enable the ngVLA to significantly improve our understanding of the processes that dissipate energy in the extended atmospheres of cool evolved stars, and drive ubiquitous stellar outflows. The high spatial resolution will enable us to image the surfaces of nearby red supergiants, and to measure the atmospheric extent of red giants. …
This paper introduces a new empirical model for the rotational evolution of Sun-like stars -- those with surface convection zones and non-convective interior regions. Previous models do not match the morphology of observed (rotation period)-color diagrams, notably the existence of a relatively long-lived "C-sequence" of fast rotators first identified by Barnes(2003). This failure motivates the Metastable Dynamo Model (MDM) described here. The MDM posits that stars are born with their magnetic dynamos operating in a mode that couples very weakly to the stellar wind, so their (initially very sho…
In a rigidly-rotating magnetohydrodynamic (MHD) system with convective turbulence, a large-scale dynamo, categorized as the $α^2$-type, can be excited when the spin rate is large enough. In this paper, the rotational dependence of the $α^2$-type dynamo and the cause of it are explored by mean-field (MF) dynamo models coupled with direct numerical simulations (DNSs) of MHD convections. Bearing the application to the solar/stellar dynamo in mind, we adopt a strongly-stratified polytrope as a model of the convective atmosphere. Our DNS models show that the $α^2$-type dynamo is excited when ${\rm …
We demonstrate that for weak flares the dependence on spottedness can be rather weak. The fact is that such flares can occur both in small and large active regions. At the same time, powerful large flares of classes M and X occur much more often in large active regions. In energy estimates, the mean magnetic field in starspots can also be assumed equal to the mean field in the sunspot umbra. So the effective mean magnetic field is 900 Mx/cm$^2$ in sunspots and 2000 Mx/cm$^2$ in starspots. Moreover, the height of the energy storage cannot be strictly proportional to A$^{1/2}$. For stars, the fi…
Global dynamo simulations solving the equations of magnetohydrodynamics (MHD) have been a tool of astrophysicists who try to understand the magnetism of the Sun for several decades now. During recent years many fundamental issues in dynamo theory have been studied in detail by means of local numerical simulations that simplify the problem and allow the study of physical effects in isolation. Global simulations, however, continue to suffer from the age-old problem of too low spatial resolution, leading to much lower Reynolds numbers and scale separation than in the Sun. Reproducing the internal…
Helioseismology shows that the regions occupied by convection and differential rotation inside the sun almost coincide. This supports the leading theoretical concept for the origin of differential rotation as a result of interaction between convection and rotation. This talk outlines the current state of the differential rotation theory. Numerical models based on the theory reproduce the observed solar rotation quite closely. The models also compute meridional flow and predict that the flow at the bottom of the convection zone is not small compared to the surface. Theoretical predictions for s…
We review some of the recent progress on modeling planetary and stellar dynamos. Particular attention is given to the dynamo mechanisms and the resulting properties of the field. We present direct numerical simulations using a simple Boussinesq model. These simulations are interpreted using the classical mean-field formalism. We investigate the transition from steady dipolar to multipolar dynamo waves solutions varying different control parameters, and discuss the relevance to stellar magnetic fields. We show that owing to the role of the strong zonal flow, this transition is hysteretic. In th…
Cool main-sequence stars, such as the Sun, have magnetic fields which are generated by an internal dynamo mechanism. In the Sun, the dynamo mechanism produces a balance between the amounts of magnetic flux generated and lost over the Sun's 11-year activity cycle and it is visible in the Sun's different atmospheric layers using multi-wavelength observations. We used the same observational diagnostics, spanning several decades, to probe the emergence of magnetic flux on the two close by, active- and low-mass K dwarfs: 61 Cygni A and Epsilon Eridani. Our results show that 61 Cygni A follows the S…
Our understanding of large-scale magnetic fields in stellar radiative zones remains fragmented and incomplete. Such magnetic fields, which must be produced by some form of dynamo mechanism, are thought to dominate angular-momentum transport, making them crucial to stellar evolution. A major difficulty is the effect of stable stratification, which generally suppresses dynamo action. We explore the effects of stable stratification on mean-field dynamo theory with a particular focus on a non-helical large-scale dynamo (LSD) mechanism known as the magnetic shear-current effect. We find that the me…
One interpretation of the activity and magnetism of late-type stars is that these both intensify with decreasing Rossby number up to a saturation level, suggesting that stellar dynamos depend on both rotation and convective turbulence. Some studies have claimed, however, that rotation alone suffices to parametrise this scaling adequately. Here, we tackle the question of the relevance of turbulence to stellar dynamos by including evolved, post main sequence stars in the analysis of the rotation-activity relation. These stars rotate very slowly compared with main sequence stars, but exhibit simi…
We present a sample of 824 solar and late-type stars with X-ray luminosities and rotation periods. This is used to study the relationship between rotation and stellar activity and derive a new estimate of the convective turnover time. From an unbiased subset of this sample the power law slope of the unsaturated regime, L_X / L_bol = Ro^β, is fit as β= -2.70 +/- 0.13. This is inconsistent with the canonical β=-2 slope to a confidence of 5 sigma, and argues for an additional term in the dynamo number equation. From a simple scaling analysis this implies ΔΩ/ Ω= Ω^0.7, i.e. the differential rotati…
Precise photometry from the Kepler space telescope allows not only the measurement of rotation in solar-type field stars, but also the determination of reliable masses and ages from asteroseismology. These critical data have recently provided the first opportunity to calibrate rotation-age relations for stars older than the Sun. The evolutionary picture that emerges is surprising: beyond middle-age the efficiency of magnetic braking is dramatically reduced, implying a fundamental change in angular momentum loss beyond a critical Rossby number (Ro~2). We compile published chromospheric activity…
Context. The recently developed test-field method permits to compute dynamo coefficients from global, direct numerical simulations. The subsequent use of these parameters in mean-field models enables us to compare self-consistent dynamo models with their mean-field counterparts. So far, this has been done for a simulation of rotating magnetoconvection and a simple benchmark dynamo, which are both (quasi-)stationary. Aims. It is shown that chaotically time-dependent dynamos in a low Rossby number regime may be appropriately described by corresponding mean-field results. Also, it is pointed out …
Recent data from the Kepler mission has revealed the occurrence of superflares in sun-like stars which exceed by far any observed solar flares in release of energy. A natural idea is that the dynamo mechanism in superflaring stars differs in some respect from that in the Sun. We search for a difference in the dynamo-related parameters between superflaring stars and the Sun to suggest a dynamo-mechanism as close as possible to the conventional solar/stellar dynamo but capable of providing much higher magnetic energy. Dynamo based on joint action of differential rotation and mirror asymmetric mo…
Magnetic field observations of low-mass stars reveal an increase of magnetic activity with increasing rotation rate. The so-called activity-rotation relation is usually attributed to changes in the underlying dynamo processes generating the magnetic field. We examine the dependence of the field strength on rotation in global numerical dynamo models and interpret our results on the basis of energy considerations. In agreement with the scaling law proposed by Christensen & Aubert (2006), the field strength in our simulations is set by the fraction of the available power used for the magnetic fie…
A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly reviewed. The main open questions that remain are concerned with the subsurface dynamics, including why sunspots emerge at preferred latitudes as seen in the familiar butterfly wings, why the cycle is about 11 years long, and why the sunspot groups emerge tilted with respect to the equator (Joy's law). Next, we turn to magnetic helicity, whose conservation property …
We present results from four convectively-driven stellar dynamo simulations in spherical wedge geometry. All of these simulations produce cyclic and migrating mean magnetic fields. Through detailed comparisons we show that the migration direction can be explained by an $αΩ$ dynamo wave following the Parker--Yoshimura rule. We conclude that the equatorward migration in this and previous work is due to a positive (negative) $α$ effect in the northern (southern) hemisphere and a negative radial gradient of $Ω$ outside the inner tangent cylinder of these models. This idea is supported by a strong …
Several solar-like stars exhibit cyclic magnetic activity similar to the Sun as found in photospheric and chromospheric emission. We want to understand the physical mechanism involved in rotational dependence of these activity cycle periods. We use three-dimensional magnetohydrodynamical simulations of global convective dynamos models of solar-like stars to investigate the rotational dependency of dynamos. We further apply the test-field method to determine the $α$ effect in these simulations. We find dynamo with clear oscillating mean magnetic fields for moderately and rapidly rotating runs. …
The main aim of this paper is to introduce the most important observables that help us to investigate stellar dynamos and compare those to the modeling results. We give an overview of the available observational methods and data processing techniques that are suitable for such purposes, with touching upon examples of inadequate interpretations as well. Stellar observations are compared to the solar data in such a way, which ensures that the measurements are comparable in dimension, wavelength, and timescale. A brief outlook is given to the future plans and possibilities. A thorough review of t…
Stellar winds are an integral part of the underlying dynamo, the motor of stellar activity. The wind controls the star's angular momentum loss, which depends on the magnetic field geometry which varies significantly in time and latitude. Here we study basic properties of a self-consistent model that includes simple representations of both the global stellar dynamo in a spherical shell and the exterior in which the wind accelerates and becomes supersonic. We numerically solve an axisymmetric mean-field model for the induction, momentum, and continuity equations using an isothermal equation of s…
