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 …
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 …
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…
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…
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…
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…
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…
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…
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…
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. …
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…
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…
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…
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…
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 …
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. …
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…
