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).     

Exploring Magnetic Activity from The Sun to the Stars

Sun-like stars are known to display a wide variety of magnetic activity which is likely to be the signature of a hydromagnetic dynamo mechanism working in stellar interiors. This dynamo mechanism has been studied extensively in the context of the Sun. Here we take ideas and experiences gained from solar dynamo modeling and build upon it to study the inferred scaling laws, involving stellar parameters, from observations of stellar magnetic activity. We also discuss how such a synthesis of theoretical dynamo modeling of Sun-like stars and stellar cycle observations may help us reconstruct the long-term variability of the Sun – an important ingredient for understanding the effects of solar forcing on space and global climate.     

Activity cycle periods in late-type stars

Period of magnetic activity versus the stellar angular velocity for stars of given spectral type having extended convective shells is estimated within the framework of mean field dynamo theory. The dependence appears to be not monotonous, and can be checked by observations.     

Photospheric Magnetic Activity in a Proxy for the Young Sun: HD 134319

We present the results of a long-term photometric monitoring of the young single main-sequence star HD134319. It shows short-term variability of the optical-band continuum flux with a period of 4.448 days. The variability is attributed to dark spots or spots groups unevenly distributed in longitude on the star's photosphere, whose visibility is modulated by the star's rotation. Maps of the photospheric spot pattern have been obtained with light curve inversion techniques based on the Maximum Entropy and the Tikhonov regularization criteria. The overall spot pattern shows evidence for two long-lasting active longitudes located about 180° apart, with a total area of at least 16% of the stellar surface (assuming an inclination of the stellar rotation axis of 90° on the line of sight). The longitude distribution of the spot pattern and its total area do not show any clear evidence for a long-term variation along the five years of observations. A comparison with recent mean field dynamo models is also addressed, suggesting a possible interpretation of such a behaviour. Singularity, spectral type, youth and a high level of photospheric and chromospheric activity make HD134319 a suitable proxy for studying the magnetic activity of the young Sun not far after its arrival on the zero age main sequence.     

Butterfly diagrams of strongly spotted late type stars

At present, long-term (over 30 years) multicolor photometric observations give the possibility to determine general properties of spotted areas on late-type stars. Star-spot modeling from broadband photometric data has been carried out by Alekseev and Gershberg since 1996 under the assumption that spots are situated in two latitudinal zones. Here we propose a new analysis of their results for several G and K dwarf stars with high irregular activity. On these stars, EK Dra, VY Ari, V775 Her, and V833 Tau, two spot belts exist separately and do not merge into a single equatorial active region, as occurs on cooler red-dwarf stars. The zonal spottedness models allow us to fit simultaneously both rotational modulation and long-term variability of stellar brightness. These models give evidence for an equatorward drift of the lower latitude boundary of the spotted region, φ₀, during the rising phase of activity, beyond any possible errors concerned with our methodology. In order to evaluate the drift rate we introduce the concept of `effective' spot belt, whose width is independent of longitude. This permits us to construct butterfly diagrams for stellar spots. The equatorward drift rates of the lower boundary of the spotted region D=dφ_low/dt are (− 1)–(− 2) deg year⁻¹ in the years of increasing spottedness. These values are less than the analogous solar one D≈−4 deg year⁻¹ for the rising phase of the cycle. Thus, cyclic activity can be revealed from butterfly diagrams and derived drifts of starspots prior to a possible detection from the spectral analysis of photometric variability. Finally, we briefly discuss a possible explanation of high-latitude activity and surface drifts of starspots in the framework of the current state of dynamo theory.     

Pre-main-sequence variability across the radiative–convective gap

We use I -band imaging to perform a variability survey of the 13-Myr-old cluster h Per. We find a significant fraction of the cluster members to be variable. Most importantly, we find that variable members lie almost entirely on the convective side of the gap in the cluster sequence between fully convective stars and those which have a radiative core. This result is consistent with a scenario in which the magnetic field changes topology when the star changes from being fully convective to one containing a radiative core. When the star is convective, the magnetic field appears dominated by large-scale structures, resulting in global-size spots that drive the observed variability. For those stars with radiative cores, we observe a marked absence of variability due to spots, which suggests a switch to a magnetic field dominated by smaller-scale structures, resulting in many smaller spots and thus less apparent variability. This implies that wide field variability surveys may only be sensitive to fully convective stars. On the one hand, this reduces the chances of picking out young groups (since the convective stars are the lower mass and therefore fainter objects), but conversely the absolute magnitude of the head of the convective sequence provides a straightforward measure of age for those groups which are discovered.     

Origin of stellar magnetic fields

It is pointed out that the magnetic field of a star is originated from dynamo action associated with the stellar evolution. The magnetic field of a star is related with how much nuclear energy is generated in its phase of evolution. From this we can explain why some stars possess a magnetic field high than that of the Sun. In our case the magnetic field of the star is a by-product of the stars evolution and it has no influence on the internal structure of the star but it does have influence on the flare, chromosphere and coronal activities of the star. Again it is stressed that to confirm the activities of the star, the details of evolution of stars should be calculated according to the photon-neutrino coupling theory.     

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.     

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.     

Surface magnetic fields on two accreting T Tauri stars: CV Cha and CR Cha

We have produced brightness and magnetic field maps of the surfaces of CV Cha and CR Cha: two actively accreting G- and K-type T Tauri stars in the Chamaeleon I star-forming cloud with ages of 3–5 Myr. Our magnetic field maps show evidence for strong, complex multipolar fields similar to those obtained for young rapidly rotating main-sequence stars. Brightness maps indicate the presence of dark polar caps and low-latitude spots – these brightness maps are very similar to those obtained for other pre-main-sequence and rapidly rotating main-sequence stars.
Only two other classical T Tauri stars have been studied using similar techniques so far: V2129 Oph and BP Tau. CV Cha and CR Cha show magnetic field patterns that are significantly more complex than those recovered for BP Tau, a fully convective T Tauri star.
We discuss possible reasons for this difference and suggest that the complexity of the stellar magnetic field is related to the convection zone; with more complex fields being found in T Tauri stars with radiative cores (V2129 Oph, CV Cha and CR Cha). However, it is clearly necessary to conduct magnetic field studies of T Tauri star systems, exploring a wide range of stellar parameters in order to establish how they affect magnetic field generation, and thus how these magnetic fields are likely to affect the evolution of T Tauri star systems as they approach the main sequence.     

On the rotation–activity correlation for active binary stars

We present an investigation of rotation–activity correlations using International Ultraviolet Explorer ( IUE ) SWP measurements of the C  iv emission line at 1550Å for 72 active binary systems. We use a standard stellar evolution code to derive non-empirical Rossby numbers, R ₀, for each star in our sample and compare the resulting C  iv rotation–activity correlation to that found for empirically derived values of the Rossby number and that based on rotation alone. For dwarf stars our values of R ₀ do not differ greatly from empirical ones and we find a corresponding lack of improvement in correlation. Only a marginal improvement in correlation is found for evolved components in our sample. We discuss possible additional factors, other than rotation or convection, that may influence the activity levels in active binaries. Our observational data imply, in contrast to the theoretical predictions of convective motions, that activity is only weakly related to mass in evolved stars. We conclude that current dynamo theory is limited in its application to the study of active stars because of the uncertainty in the angular velocity-depth profile in stellar interiors and the unknown effects of binarity and surface gravity.     

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.     

Relating stellar cycle periods to dynamo calculations

Stellar magnetic activity in slowly rotating stars is often cyclic, with the period of the magnetic cycle depending critically on the rotation rate and the convective turnover time of the star. Here we show that the interpretation of this law from dynamo models is not a simple task. It is demonstrated that the period is (unsurprisingly) sensitive to the precise type of non-linearity employed. Moreover the calculation of the wave-speed of plane-wave solutions does not (as was previously supposed) give an indication of the magnetic period in a more realistic dynamo model, as the changes in length-scale of solutions are not easily captured by this approach. Progress can be made, however, by considering a realistic two-dimensional model, in which the radial length-scale of waves is included. We show that it is possible in this case to derive a more robust relation between cycle period and dynamo number. For all the non-linearities considered in the most realistic model, the magnetic cycle period is a decreasing function of | D | (the amplitude of the dynamo number). However, discriminating between different non-linearities is difficult in this case and care must therefore be taken before advancing explanations for the magnetic periods of stars.     

Dynamo-generated magnetic fields at the surface of a massive star

Spruit has shown that an astrophysical dynamo can operate in the non-convective material of a differentially rotating star as a result of a particular instability in the magnetic field (the Tayler instability). By assuming that the dynamo operates in a state of marginal instability, Spruit has obtained formulae which predict the equilibrium strengths of azimuthal and radial field components in terms of local physical quantities. Here, we apply Spruit's formulae to our previously published models of rotating massive stars in order to estimate Tayler dynamo field strengths. There are no free parameters in Spruit's formulae. In our models of 10- and  50-M_⊙  stars on the zero-age main sequence, we find internal azimuthal fields of up to 1 MG, and internal radial components of a few kG. Evolved models contain weaker fields. In order to obtain estimates of the field strength at the stellar surface, we examine the conditions under which the Tayler dynamo fields are subject to magnetic buoyancy. We find that conditions for Tayler instability overlap with those for buoyancy at intermediate to high magnetic latitudes. This suggests that fields emerge at the surface of a massive star between magnetic latitudes of about 45° and the poles. We attempt to estimate the strength of the field which emerges at the surface of a massive star. Although these estimates are very rough, we find that the surface field strengths overlap with values which have been reported recently for line-of-sight fields in several O and B stars.     

Magnetic accretion onto young stars

Young T Tauri stars exhibit strong solar-type magnetic activity, with extremely high temperature coronae and energetic flares. In a few systems discovered with Chandra and XMM-Newton there is also evidence for X-ray emission produced by shocks associated with magnetically channeled accretion. A recent 489 ksec Chandra HETG/ACIS-S observation of the classical T Tauri star TW Hydrae has provided a wealth of spectroscopic diagnostics not available in lower signal-to-noise ratio observations. Using line ratios for electron temperature, electron density, and column density we have found that the shock produced by the accelerating material in the accretion stream behaves as predicted by standard theory. However, the properties of the post-shock plasma differ substantially from the predictions of standard 1D shock models (Brickhouse et al. in Astrophys. J. 710:1835, 2010). The accretion process apparently heats the stellar atmosphere up to soft X-ray emitting temperatures, providing hot ions to populate the magnetic corona, in loops, stellar wind, and/or jets. This gas is highly turbulent, as evidenced by non-thermal line broadening. The observed properties of the accretion-fed corona should constrain theoretical models of an accretion-driven dynamo.     

Dust formation above cool magnetic spots in evolved stars

We examine the structure of cool magnetic spots in the photospheres of evolved stars, specifically asymptotic giant branch (AGB) stars and R Coronae Borealis (RCB) stars. We find that the photosphere of a cool magnetic spot will be above the surrounding photosphere of AGB stars, which is the opposite of the situation in the Sun . This results from the behaviour of the opacity, which increases with decreasing temperature, which again is the opposite of the behaviour of the opacity near the effective temperature of the Sun . We analyse the formation of dust above the cool magnetic spots, and suggest that the dust formation is facilitated by strong shocks, driven by stellar pulsations, which run through and around the spots. The presence of both the magnetic field and cooler temperatures makes dust formation easier as the shock passes above the spot. We review some observations supporting the proposed mechanism, and suggest further observations to check the model.     

Flip-Flops as Observational Signatures of Different Dynamo Modes in Cool Stars

Cool, rapidly rotating stars exhibit enhanced magnetic activity with cyclic behavior on various time scales. In particular, the longitude of the dominant activity region switches quasi-periodically by 180^∘, which is known as the “flip-flop” phenomenon. In the present paper we introduce a new approach for the interpretation of stellar cycles based on light curve modeling with dipole and quadrupole dynamo modes. We discuss the observational signatures of different combinations of the dynamo modes. The proposed simple model is able to reproduce the basic properties of long-term photometric behavior of active stars and allows us to study different mechanisms resulting in flip-flops.     

Magnetic cycles of the planet-hosting star τ Bootis – II. A second magnetic polarity reversal

In this paper, we present new spectropolarimetric observations of the planet-hosting star τ Bootis, using ESPaDOnS and Narval spectropolarimeters at Canada–France–Hawaii Telescope and Telescope Bernard Lyot, respectively.
We detected the magnetic field of the star at three epochs in 2008. It has a weak magnetic field of only a few gauss, oscillating between a predominant toroidal component in January and a dominant poloidal component in June and July. A magnetic polarity reversal was observed relative to the magnetic topology in 2007 June. This is the second such reversal observed in 2 years on this star, suggesting that τ Boo has a magnetic cycle of about 2 years. This is the first detection of a magnetic cycle for a star other than the Sun. The role of the close-in massive planet in the short activity cycle of the star is questioned.
τ Boo has a strong differential rotation, a common trend for stars with shallow convective envelope. At latitude 40°, the surface layer of the star rotates in 3.31 d, equal to the orbital period. Synchronization suggests that the tidal effects induced by the planet may be strong enough to force at least the thin convective envelope into corotation.
τ Boo shows variability in the Ca  ii H & K and Hα throughout the night and on a night-to-night time-scale. We do not detect enhancement in the activity of the star that may be related to the conjunction of the planet. Further data are needed to conclude about the activity enhancement due to the planet.     

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.     

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.