Magnetic Evolution and the Disappearance of Sun-Like Activity Cycles

After decades of effort, the solar activity cycle is exceptionally well characterized, but it remains poorly understood. Pioneering work at the Mount Wilson Observatory demonstrated that other Sun-like stars also show regular activity cycles, and suggested two possible relationships between the rotation rate and the length of the cycle. Neither of these relationships correctly describes the properties of the Sun, a peculiarity that demands explanation. Recent discoveries have started to shed light on this issue, suggesting that the Sun’s rotation rate and magnetic field are currently in a transitional phase that occurs in all middle-aged stars. Motivated by these developments, we identify the manifestation of this magnetic transition in the best available data on stellar cycles. We propose a reinterpretation of previously published observations to suggest that the solar cycle may be growing longer on stellar evolutionary timescales, and that the cycle might disappear sometime in the next 0.8?–?2.4 Gyr. Future tests of this hypothesis will come from ground-based activity monitoring of Kepler targets that span the magnetic transition, and from asteroseismology with the Transiting Exoplanet Survey Satellite (TESS) mission to determine precise masses and ages for bright stars with known cycles.     

Multiple cycles of magnetic activity in the Sun and Sun-like stars and their evolution

The wavelet transform method for high-quality time-frequency analysis is applied to sets of observations of relative sunspot numbers and stellar chromosphere fluxes of 10 Sun-like stars.Wavelet analysis of solar data shows that in a certain interval of time there are several cycles of activity with periods of duration which vary considerably from each other:from quasi-biennial cycles to 100-yr cycles.Cyclic activity was detected in almost all Sun-like stars that we examined,even those that previously were not considered as stars with cyclic activity according to analysis using a Scargle periodogram.The durations of solar and stellar cycles significantly change during the observation period.     

Night‐time science with large solar telescopes: The magnetic Sun through time

Today the Sun has a regular magnetic cycle driven by a dynamo action. But how did this regular cycle develop? How do basic parameters such as rotation rate, age, and differential rotation affect the generation of magnetic fields? Zeeman Doppler imaging (ZDI) is a technique that uses high‐resolution observations in circularly polarised light to map the surface magnetic topology on stars. Utilising the spectropolarimetric capabilities of future large solar telescopes it will be possible to study the evolution and morphology of the magnetic fields on a range of Sun‐like stars from solar twins through to rapidly‐rotating active young Suns and thus study the solar magnetic dynamo through time. In this article I discuss recent results from ZDI of Sun‐like stars and how we can use night‐time observations from future solar telescopes to solve unanswered questions about the origin and evolution of the Sun's magnetic dynamo (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-Axisymmetric Magnetic Fields and Flip-Flops on the Sun and Cool Stars

The modulation of solar activity closely follows the solar rotation period suggesting the existence of long-lived active regions at preferred longitudes. For instance, two preferred active longitudes in both southern and northern hemispheres are found to be persistent at the century time scale. These regions migrate with differential rotation and periodically alternate their activity levels showing a flip-flop cycle. The pattern and behaviour of active longitudes on the Sun is similar to that on cool, rapidly rotating stars with outer convective envelopes. This suggests that the magnetic dynamo, including non-axisymmetric magnetic fields and flip-flop cycles, is also similar in these stars. This allows us to overview the phenomenon of stellar magnetic activity and to study it in detail on the Sun.     

A dynamo scenario for polar and whole-surface starspot generation

Rapidly rotating young (T Tauri, pre-Main-Sequence, and Main-Sequence) stars as well as subgiants seem to show starspots not only at low and middle latitudes, as the Sun, but also at high latitudes and even around the poles. We consider a simple nonlinear Parker migratory dynamo model working in a thin shell in order to investigate how high latitude and polar spots may be produced for different values of the dynamo layer radius and thickness and for various rotation rates. Simple assumptions on the angular velocity gradient and helicity distribution are made according to symmetry properties and recent solar and stellar observations. A recently proposed asymptotic WKB-type approach is used to solve the dynamo problem and its drawbacks and advantages in the solar and stellar contexts are discussed. As a general result, we find that a sizable toroidal field can be produced over a much more extended latitude range than in the Sun, thus explaining in a natural way the occurrence of activity from the poles to the equator in such stars. Our approach complements that proposed by Schüssler et al. (1996) which is focused on the instability and emergence of the azimuthal flux tubes, as well as the analyses based on a dynamo working over an extended part of the stellar convective envelope (Moss, Tuominen, and Brandenburg, 1991; Moss et al., 1995).     

Seismology of stellar envelopes: probing the outer layers of a star through the scattering of acoustic waves

The outer layers of Sun-like stars are regions of rapid spatial variation which modulate the p-mode frequencies by partially reflecting the constituent acoustic waves. With the accuracy that has been achieved by current solar observations, and that is expected from imminent stellar observations, this modulation can be observed from the spectra of the low-degree modes. We present a new and simple theoretical calculation to determine the leading terms in an asymptotic expansion of the outer phase of these modes, which is determined by the structure of the surface layers of the star. Our procedure is to compare the stellar envelope with a plane-parallel polytropic envelope, which we regard as a smooth reference background state. Then we can isolate a seismic signature of the acoustic phase and relate it to the stratification of the outer layers of the convection zone. One can thereby constrain theories of convection that are used to construct the convection zones of the Sun and Sun-like stars. The accuracy of the diagnostic is tested in the solar case by comparing the predicted outer phase with an exact numerical calculation.     

Magnetic cycles of Sun-like stars with different levels of coronal and chromospheric activity——comparison with the Sun

The atmospheric activity of the Sun and Sun-like stars is analyzed involving observations from the HK-project at the Mount Wilson Observatory, the California and Carnegie Planet Search Program at the Keck and Lick Observatories and the Magellan Planet Search Program at the Las Campanas Observatory.We show that for stars of F, G and K spectral classes, the cyclic activity, similar to the 11-yr solar cycle, is different: it becomes more prominent in K-stars. Comparative study of Sun-like stars with different levels of chromospheric and coronal activity confirms that the Sun belongs to stars with a low level of chromospheric activity and stands apart among these stars by its minimum level of coronal radiation and minimum level of variations in photospheric flux.     

Starspots

Starspots are created by local magnetic fields on the surfaces of stars, just as sunspots. Their fields are strong enough to suppress the overturning convective motion and thus block or redirect the flow of energy from the stellar interior outwards to the surface and consequently appear as locally cool and therefore dark regions against an otherwise bright photosphere (Biermann in Astronomische Nachrichten 264:361, 1938; Z Astrophysik 25:135, 1948). As such, starspots are observable tracers of the yet unknown internal dynamo activity and allow a glimpse into the complex internal stellar magnetic field structure. Starspots also enable the precise measurement of stellar rotation which is among the key ingredients for the expected internal magnetic topology. But whether starspots are just blown-up sunspot analogs, we do not know yet. This article is an attempt to review our current knowledge of starspots. A comparison of a white-light image of the Sun (G2V, 5 Gyr) with a Doppler image of a young solar-like star (EK Draconis; G1.5V, age 100 Myr, rotation 10 × Ω _Sun) and with a mean-field dynamo simulation suggests that starspots can be of significantly different appearance and cannot be explained with a scaling of the solar model, even for a star of same mass and effective temperature. Starspots, their surface location and migration pattern, and their link with the stellar dynamo and its internal energy transport, may have far reaching impact also for our understanding of low-mass stellar evolution and formation. Emphasis is given in this review to their importance as activity tracers in particular in the light of more and more precise exoplanet detections around solar-like, and therefore likely spotted, host stars.     

Solar and stellar activity: The theoretical approach

The unified sight of solar and stellar activity has revealed a worthwhile concept under several aspects, gaming in the last decade the increasing favour of observers and theorists, and the term solar-stellar connection has recently been introduced to point out the complementarity of solar and stellar observations in the background of the basic role played by the magnetic field.The great development of stellar activity observations suggests a much wider scenario than it were possible to imagine even a few years ago and stimulates theoretical work, most of which is in the framework of the - dynamo theory.Although dynamo theory seems to be plausible and successful in capturing the fundamental mechanism of solar and stellar activity, several uncertainties and intrinsic limits do still exist and are discussed together with alternative or complementary suggestions.Further, it is stressed the relevance of nonlinear problems in dynamo theory — as magnetoconvection, growth and stability of flux tubes against magnetic buoyancy, hydromagnetic global dynamos — to improve our understanding of both small and large scale interaction of rotation, turbulent convection and magnetic field, and of the transition from linear to nonlinear regime. Finally, recent dynamo models of stellar activity are critically reviewed, as to the dependence of activity indexes and cycles on rotation rate and spectral type.Open problems to be solved by future work are outlined, pointing out the role of ever increasing stellar data in widening out our comprehension of the dynamo operation modes, which seem to depend on stellar structure, rotation and age.     

Theory of stellar magnetic activity: A review

The unified sight of solar and stellar activity has revealed a worthwhile concept under several aspects, gaining in the last decade the increasing favour of observers and theorists, and the term solar-stellar connection has recently been introduced to point out the complementarity of solar and stellar observations in the background of the basic role of the magnetic field. The great development of ground and space stellar activity observations suggests a much wider scenario than it were possible to imagine even a few years ago, and stimulates theoretical work, most of which is in the framework of the α–ω dynamo theory. Dynamo models of stellar activity in the main sequence, although subjected to different assumptions, do converge in predicting that activity should increase with the increasing angular velocity of rotation ω and colour index (B–V), in agreement with almost all existing observational evidence. However, even if linear dynamo theory seems to have captured the essentials of the mechanism of stellar activity, the complexity of stellar activity phenomenology and operation modes suggests that the future is in the non-linear approach. Finally, observational and theoretical uncertainties and difficulties, which affect the present status of dynamo theory, are briefly discussed.     

A new look at the relationship between activity, dynamo number and Rossby number in late-type stars

The correlation between stellar activity, as measured by the indicator Δ R _HK, and the Rossby number Ro in late-type stars is revisited in light of recent developments in solar dynamo theory. Different stellar interior models, based on both mixing-length theory and the full spectrum of turbulence, are used in order to see to what extent the correlation of activity with Rossby number is model dependent, or otherwise can be considered universal. Although we find some modest model dependence, we find that the correlation of activity with Rossby number is significantly better than with rotation period alone for all the models we consider. Dynamo theory suggests that activity should scale with the dynamo number. A current model of the solar dynamo, the so-called interface dynamo, proposes that the amplification of the toroidal magnetic field by differential rotation (the ω -effect) and the production of the poloidal magnetic field from toroidal by helical turbulence (the α -effect) take place in different, adjacent layers near the base of the convection zone. A new scale analysis based on the interface dynamo shows that the appropriate dynamo number does not depend on the Rossby number alone, but also depends on an additional dimensionless factor related to the differential rotation. This leads to a new interpretation of the correlation between activity and Rossby number, which in turn leads to some conclusions about the magnitude of differential rotation in the dynamo layers of late-type main-sequence stars.     

What can we hope to know about the symmetry properties of stellar magnetic fields?

We summarize evidence that neither dynamo theory nor the observational data give strong support to the idea that stellar magnetic fields must have dipolar rather than quadrupolar symmetry with respect to the stellar equator. We demonstrate that even the most basic model for magnetic stellar activity, i.e. the Parker migratory dynamo, provides many possibilities for the excitation of large-scale stellar magnetic fields of non-dipolar symmetry. We demonstrate the spontaneous transition of the dynamo-excited magnetic field from one symmetry type to another. We explore observational tests to distinguish between the two types of magnetic field symmetry, and thus detect the presence of quadrupolar magnetic symmetry in stars. Complete absence of quadrupolar symmetry would present a distinct challenge for contemporary stellar dynamo theory. We revisit some observations which, depending on further clarification, may already be revealing some properties of the quadrupolar component of the magnetic fields generated by stellar dynamos.     

Key problems in cool-star astrophysics

Selected key problems in cool-star astrophysics are reviewed, with emphasis on the importance of new ultraviolet missions to tackle the unresolved issues.UV spectral signatures are an essential probe of critical physical processes related to the production and transport of magnetic energy in astrophysical plasmas ranging, for example, from stellar coronae, to the magnetospheres of magnetars, and the accretion disks of protostars and Active Galactic Nuclei. From an historical point of view, our comprehension of such processes has been closely tied to our understanding of solar/stellar magnetic activity, which has its origins in a poorly understood convection-powered internal magnetic dynamo. The evolution of the Sun's dynamo, and associated magnetic activity, affected the development of planetary atmospheres in the early solar system, and the conditions in which life arose on the primitive Earth. The gradual fading of magnetic activity as the Sun grows old likewise will have profound consequences for the future heliospheric environment. Beyond the Sun, the magnetic activity of stars can influence their close-in companions, and vice versa.Cool star outer atmospheres thus represent an important laboratory in which magnetic activity phenomena can be studied under a wide variety of conditions, allowing us to gain insight into the fundamental processes involved. The UV range is especially useful for such studies because it contains powerful diagnostics extending from warm (∼ 10⁴ K) chromospheres out to hot (1–10 MK) coronae, and very high-resolution spectroscopy in the UV has been demonstrated by the GHRS and STIS instruments on HST but has not yet been demonstrated in the higher energy EUV and X-ray bands. A recent example is the use of the hydrogen Lyα resonance line—at 110 000 resolution with HST STIS—study, for the first time, coronal winds from cool stars through their interaction with the interstellar gas. These winds cannot be detected from the ground, for lack of suitable diagnostics; or in the X-rays, because the outflowing gas is too thin.A 2m class UV space telescope with high resolution spectroscopy and monitoring capabilities would enable important new discoveries in cool-star astronomy among the stars of the solar neighborhood out to about 150 pc. A larger aperture facility (4–6 m) would reach beyond the 150 pc horizon to fainter objects including young brown dwarfs and pre-main sequence stars in star-forming regions like Orion, and magnetic active stars in distant clusters beyond the Pleiades and α Persei. This would be essential, as well, to characterize the outer atmospheres of stars with planets, that will be discovered by future space missions like COROT, Kepler, and Darwin.Deceased October 23, 2005     

On the origin and structure of stellar magnetic fields

Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ?10²²Mx) and smaller elements ranging down to flux fibres (? 10¹⁸Mx). Some implications of similar features in other stars are discussed.     

The Solar-Stellar Connection: Magneto-Acoustic Pulsations in 1.5M ⊙ – 2M ⊙ Peculiar A Stars

Stellar astronomers look on in envy at the wealth of data, the incredible spatial resolution, and the maturity of the theoretical understanding of the Sun. Yet the Sun is but one star, so stellar astronomy is of great interest to solar astronomers for its range of different conditions under which to test theoretical understanding gained from the study of the Sun. The rapidly oscillating peculiar A stars are of particular interest to solar astronomers. They have strong, global, dipolar magnetic fields with strengths in the range 1?–?25?kG, and they pulsate in high-overtone p modes similar to those in the Sun; thus they offer a unique opportunity to study the interaction of pulsation, convection, and strong magnetic fields, as is now done in the local helioseismology of sunspots. Some of them even pulsate in modes with frequencies above the acoustic cutoff frequency, in analogy with the highest frequency solar modes, but with mode lifetimes up to decades in the roAp stars, very unlike the short mode lifetimes of the Sun. They offer the most extreme cases of atomic diffusion, a small, but important ingredient of the standard solar model with wide application in stellar astrophysics. They are compositionally stratified and are observed and modelled as a function of atmospheric depth and thus can inform plans to expand helioseismic observations to have atmospheric depth resolution. Study of this unique class of pulsating stars follows the advanced state of studies of the Sun and offers more extreme conditions for the understanding of physics shared with the Sun.     

Orbital period modulation and magnetic cycles in close binaries

We discuss the observed orbital period modulations in close binaries, and focus on the mechanism proposed by Applegate relating the changes of the stellar internal rotation associated with a magnetic activity cycle with the variation of the gravitational quadrupole moment of the active component; the variation of this quadrupole moment in turn forces the orbital motion of the binary stars to follow the activity level of the active star. We generalize this approach by considering the details of this interaction, and develop some illustrative examples in which the problem can be easily solved in analytical form. Starting from such results, we consider the interplay between rotation and magnetic field generation in the framework of different types of dynamo models, which have been proposed to explain solar and stellar activity. We show how the observed orbital period modulation in active binaries may provide new constraints for discriminating between such models. In particular, we study the case of the prototype active binary RS Canum Venaticorum, and suggest that torsional oscillations — driven by a stellar magnetic dynamo — may account for the observed behaviour of this star. Further possible applications of the relationship between magnetic activity and orbital period modulation, related to the recent discovery of binary systems containing a radio pulsar and a convecting upper main-sequence or a late-type low-mass companion, are discussed.     

Dynamo model with a small number of modes and magnetic activity of T Tauri stars

We suggest a model based on the representation of the stellar magnetic field as a superposition of a finite number of poloidal and toroidal free decay modes to describe the dynamo action in fully convective stars. For the adopted law of stellar differential rotation, we determined the dynamo number in exceeding which the generation of a cyclically varying magnetic field is possible in stars without a radiative core and derived an expression for the period of the cycle. The dynamo cycles in fully convective stars and in stars with thin convective envelopes are shown to differ qualitatively: first, the distributions of spots in latitude during the cycle are different for these two types of stars and, second, the model predicts a great weakening of the spot formation in fully convective stars at certain phases of the cycle. To compare the theory with observations, we have analyzed the historical light curve for the weak-line T Tauri star V410 Tau and found that its long-term activity is not a well-defined cycle with a definite period—its activity is more likely quasi-cyclic with a characteristic time of ～4 yr and with a chaotic component superimposed. we have also concluded that a redistribution of spots in longitude is responsible for the secular brightness variations in the star. This does not allow the results of photometric observations to be directly compared with predictions of ourmodel, in which, for simplicity, we assumed a symmetry in longitude and investigated the temporal evolution of the spot distribution in latitude. Therefore, we discuss the questions of what and how observations can be compared with predictions of the dynamo theory.     

Bimodal mass and angular momentum losses by magnetically controlled winds during stellar evolution

In recent times evidence for bimodal distributions of stars in the H–R diagram has reached a striking evidence. These bimodal distributions seem to be correlated with a bimodal distribution of masses and angular velocities. The approach we propose to explain the observed bimodality suggests that this latter is due to a bimodal mass loss by magnetically controlled stellar winds during stellar evolution, owing to different magnetic field configurations. It is assumed a mechanism analogous to that which produces solar wind, with magnetic field generated by dynamo working in the convection zone. Different field geometries (dipole cr quadrupole), which depend on the mode the dynamo operates, can produce different but discrete mass losses during stellar evolution, thus producing bimodal distributions of masses and angular velocities.     

The dynamic magnetic quiet Sun: physical mechanisms and UV signature

The changes in the Sun occurring at human time-scales can be pinned down to the presence of magnetic fields. These fields determine the structure of the outer solar atmosphere and, therefore, they are responsible for all the energetic part of the solar spectrum, including the UV. Our understanding of the magnetic fields existing at the base of the atmosphere has changed during the last years. The new spectro-polarimeters reveal an ubiquitous magnetic field, present even in the quiet regions. They are widespread and of complex topology, containing far more (unsigned) magnetic flux and magnetic energy that all traditional manifestations of solar activity. These so-called quiet Sun magnetic fields are the subject of the contribution. I summarize their main observational properties, as well as the models put forward to explain them. According to the common wisdom, they may be generated by a turbulent dynamo driven by convective motions. Their true physical role is not understood yet, but it may be consequential both for the Sun (e.g., in determining the structure of the quiet corona), and for other astronomical objects (e.g., if a turbulent dynamo operates in the Sun, the same mechanism provides a very efficient mean of creating surface magnetic fields in all stars with convective envelopes). I discuss the impact of the quiet Sun fields on the transition region and corona, trying to point out the UV signatures of those fields.     

Dynamo saturation in rapidly rotating solar-type stars

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 dependence- are considered. Both models show a saturation of dynamogenerated magnetic flux at high rotation rates. The model with latitude-dependent tilt angles also shows a change in dynamo regime in the saturation region. The new regime combines a cyclic dynamo at low latitudes with an(almost) steady polar dynamo.