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.     

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.     

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.     

Clues for the origin of the fundamental metallicity relations – I. The hierarchical building up of the structure

We analyse the evolutionary history of galaxies formed in a hierarchical scenario consistent with the concordance Lambda cold dark matter (ΛCDM) model focusing on the study of the relation between their chemical and dynamical properties. Our simulations consistently describe the formation of the structure and its chemical enrichment within a cosmological context. Our results indicate that the luminosity–metallicity and the stellar mass–metallicity (LZR and MZR) relations are naturally generated in a hierarchical scenario. Both relations are found to evolve with redshift. In the case of the MZR, the estimated evolution is weaker than that deduced from observational works by approximately 0.10 dex. We also determine a characteristic stellar mass, M _c≈ 3 × 10¹⁰ M_⊙, which segregates the simulated galaxy population into two distinctive groups and which remains unchanged since z ∼ 3, with a very weak evolution of its metallicity content. The value and role played by M _c is consistent with the characteristic mass estimated from the SDSS galaxy survey by Kauffmann et al. Our findings suggest that systems with stellar masses smaller than M _c are responsible for the evolution of this relation at least from z ≈ 3. Larger systems are stellar dominated and have formed more than 50 per cent of their stars at   z ≥ 2  , showing very weak evolution since this epoch. We also found bimodal metallicity and age distributions from z ∼ 3, which reflects the existence of two different galaxy populations. Although SN feedback may affect the properties of galaxies and help to shape the MZR, it is unlikely that it will significantly modify M _c since, from   z = 3  this stellar mass is found in systems with circular velocities larger than 100 km s⁻¹.     

Evolutionary Processes in Low-Mass Binary Systems

We consider the evolution of certain low-mass binaries, incorporating models of (a) internal evolution, (b) tidal friction, (c) dynamo activity driven by an elementary α,Ω dynamo, (d) stellar wind driven by the activity, and (e) magnetic braking as a consequence of wind and poloidal dynamo-generated magnetic field. In some circumstances the stellar wind is found to remove mass on a nuclear timescale, as is necessary to explain some observed systems. We can hope that various uncertainties in the model may be clarified by a careful comparison of the models with such observed quantities as rotation periods. These are modified by processes (a), (b) and (e). Assuming that stellar evolution is slow, rotation rate should in some circumstances represent a balance between magnetic braking trying to slow the star down and tidal friction trying to spin it up. Preliminary attempts are promising, but indicate that some fine tuning is necessary. When there is a third body present, in an orbit which is inclined but not necessarily of short period, the eccentricity of a close binary can be strongly modified by ‘Kozai cycles’. We show that this may complicate attempts to account for spin rates of stars in close binaries.     

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.     

Rotational evolution of the Sun

The evolutionary behaviour of rotating solar models with different initial angular-momentum distributions has been investigated through the pre-Main-Sequence and Main-Sequence phases. The angular momentum was removed from the convective evelope of the solar models according to the Kawaler's model of magnetic stellar wind (Kawaler, 1988). The models show that (i) the surface rotational velocities of the solar mass stars are independent of initial angular momentum for ages greater than 10⁸ years and (ii) it is not possible to explain the neutrino problem and the sufficient depletion of lithium in the Sun.     

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.     

Structure and evolution of low-mass W Ursae Majoris type systems – III. The effects of the spins of the stars

In a previous paper, using Eggleton's stellar evolution code, we have discussed the structure and evolution of low-mass W Ursae Majoris (W UMa) type contact binaries with angular momentum loss owing to gravitational radiation or magnetic braking. We find that gravitational radiation is almost insignificant for cyclic evolution of low-mass W UMa type systems, and it is possible for angular momentum to be lost from W UMa systems in a magnetic stellar wind. The weaker magnetic activity shown by observations in W UMa systems is likely caused by the lower mass of the convective envelopes in these systems than in similar but non-contact binaries. The spin angular momentum cannot be neglected at any time for W UMa type systems, especially for those with extreme mass ratios. The spin angular momenta of both components are included in this paper and they are found to have a significant influence on the cyclic evolution of W UMa systems. We investigate the influence of the energy transfer on the common convective envelopes of both components in detail. We find that the mass of the convective envelope of the primary in contact evolution is slightly more than that in poor thermal contact evolution, and that the mass of the convective envelope of the secondary in contact evolution is much less than that in poor thermal contact evolution. Meanwhile, the rate of angular momentum loss of W UMa type systems is much lower than that of poor thermal contact systems. This is indeed caused by the lower masses of the convective envelopes of the components in W UMa type systems. Although the models with angular momentum loss for W UMa systems exhibit cyclic evolution, they seem to show that a W UMa system cannot continue this type of cyclic evolution indefinitely, and it might coalesce into a fast-rotating star after about 1200 cycles of evolution (about  7.0 × 10⁹ yr  ).     

Magnetic activity and evolution of Algol-type stars – II

We examine the possibility of probing dynamo action in mass-losing stars, components of Algol-type binaries. Our analysis is based on the calculation of non-conservative evolution of these systems. We model the systems U Sge and β Per where the more massive companion fills its Roche lobe at the main sequence (case AB) and where it has a small helium core (early case B) respectively. We show that to maintain evolution of these systems at the late stages which are presumably driven by stellar 'magnetic braking', an efficient mechanism for producing large-scale surface magnetic fields in the donor star is needed. We discuss the relevance of dynamo operation in the donor star to the accelerated mass transfer during the late stages of evolution of Algol-type binaries. We suggest that the observed X-ray activity in Algol-type systems may be a good indicator of their evolutionary status and internal structure of the mass-losing stellar components.     

Possible relations between the rotational axis of the Earth's inner core and the magnetic dipole axis

The geomagnetic field is maintained by amagnetohydrodynamic dynamo process within the liquid outer core. The distribution of the associated electric currents is modified if the outer core is bounded by electrically conducting material. Then, eddy currents and the related magnetic fields are generated within these regions. In particular, the relative rigid rotation of the inner core produces a secondary magnetic field, which is superimposed on the dynamo field. The angle between the dipole axis of the total field and the rotational axis of the inner core is an important quantity needed for the theory of polar motion of the Earth. This angle is investigated for a broad spectrum of angular velocities of the inner core. To simplify the mathematical procedure, we model the dynamo field using an axisymmetric field generated by a system of electric currents within the outer core. The conductivity of the mantle is neglected. We find that the position of the dipole axis depends on the angular velocity of the inner core as well as on the distribution of the current system within the outer core. Coincidence of both axes can be reached if the angular velocity is high enough and if the current system is concentrated within a thin sheet near the outer core-inner core boundary.     

Invisible dynamo in mean-field models

The inverse problem in a spherical shell to find the two-dimensional spatial distributions of the α-effect and differential rotation in a mean-field dynamo model has been solved. The derived distributions lead to the generation of a magnetic field concentrated inside the convection zone. The magnetic field is shown to have no time to rise from the region of maximum generation located in the lower layers to the surface in the polarity reversal time due to magnetic diffusion. The ratio of the maximum magnetic energy in the convection zone to its value at the outer boundary reaches two orders of magnitude or more. This result is important in interpreting the observed stellar and planetary magnetic fields. The proposed method of solving the inverse nonlinear dynamo problem is easily adapted for a wide class of mathematical-physics problems.     

Magnetohydrodynamic instabilities and turbulence in accretion disks

In this paper we review the possibilities for magnetohydrodynamic processes to handle the angular momentum transport in accretion disks. Traditionally the angular momentum transport has been considered to be the result of turbulent viscosity in the disk, although the Keplerian flow in accretion disks is linearly stable towards hydrodynamic perturbations. It is on the other hand linearly unstable to some magnetohydrodynamic (MHD) instabilities. The most important instabilities are the Parker and Balbus-Hawley instabilities that are related to the magnetic buoyancy and the shear flow, respectively. We discuss these instabilities not only in the traditional MHD framework, but also in the context of slender flux tubes, that reduce the complexity of the problem while keeping most of the stability properties of the complete problem. In the non-linear regime the instabilities produce turbulence. Recent numerical simulations describe the generation of magnetic fields by a dynamo in the resulting turbulent flow. Eventually such a dynamo may generate a global magnetic field in the disk. The relation of the MHD-turbulence to observations of accretion disks is still obscure. It is commonly believed that magnetic fields can be highly efficient in transporting the angular momentum, but emission lines, short-time scale variability and non-thermal radiation, which a stellar astronomer would take as signs of magnetic variability, are more commonly observed during periods of low accretion rates. Received October 12, 1995 / Accepted November 16, 1995     

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.     

The evolution of the magnetic fields of neutron stars

Observational evidence, and theoretical models of the magnetic field evolution of neutron stars is discussed. Observational data indicates that the magnetic field of a neutron star decays significantly only if it has been a member of a close interacting binary. Theoretically, the magnetic field evolution has been related to the processing of a neutron star in a binary system through the spin evolution of the neutron star, and also through the accretion of matter on the neutron star surface. I describe two specific models, one in which magnetic flux is expelled from the superconducting core during spin-down, via a copuling between Abrikosov fluxoids and Onsager-Feynman vortices; and another in which the compression and heating of the stellar crust by the accreted mass drastically reduces the ohmic decay time scale of a magnetic field configuration confined entirely to the crust. General remarks about the behaviour of the crustal field under ohmic diffusion are also made.     

Mass loss from the inner regions of accretion discs due to centrifugally driven magnetic wind flows

Wind flows and collimated jets are believed to be a feature of a range of disc accreting systems. These include active galactic nuclei, T Tauri stars, X-ray binaries and cataclysmic variables. The observed collimation implies large-scale magnetic fields and it is known that dipole-symmetry fields of sufficient strength can channel wind flows emanating from the surfaces of a disc. The disc inflow leads to the bending of the poloidal magnetic field lines, and centrifugally driven magnetic winds can be launched when the bending exceeds a critical value. Such winds can result in angular momentum transport at least as effective as turbulent viscosity, and hence they can play a major part in driving the disc inflow.
It is shown here that if the standard boundary condition of vanishing viscous stress close to the stellar surface is applied, together with the standard connection between viscosity and magnetic diffusivity, then poloidal magnetic field bending increases as the star is approached with a corresponding increase in the wind mass loss rate. A significant amount of material can be lost from the system via the enhanced wind from a narrow region close to the stellar surface. This occurs for a Keplerian angular velocity distribution and for a modified form of angular velocity, which allows for matching of the disc and stellar rotation rates through a boundary layer above the stellar surface. The enhanced mass loss is significantly affected by the behaviour of the disc angular velocity as the stellar surface is approached, and hence by the stellar rotation rate. Such a mechanism may be related to the production of jets from the inner regions of disc accreting systems.     

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.     

Optimal dynamos in the cores of terrestrial exoplanets: Magnetic field generation and detectability

A potentially promising way to gain knowledge about the internal dynamics of extrasolar planets is by remote measurement of an intrinsic magnetic field. Strong planetary magnetic fields, maintained by internal dynamo action in an electrically conducting fluid layer, are helpful for shielding the upper atmosphere from stellar wind induced mass loss and retaining water over long (Gyr) time scales. Here we present a whole planet dynamo model that consists of three main components: an internal structure model with composition and layers similar to the Earth, an optimal mantle convection model that is designed to maximize the heat flow available to drive convective dynamo action in the core, and a scaling law to estimate the magnetic field intensity at the surface of a terrestrial exoplanet. We find that the magnetic field intensity at the core surface can be up to twice the present-day geomagnetic field intensity, while the magnetic moment varies by a factor of 20 over the models considered. Assuming electron cyclotron emission is produced from the interaction between the stellar wind and the exoplanet magnetic field we estimate the cyclotron frequencies around the ionospheric cutoff at 10 MHz with emission fluxes in the range 10⁻⁴-10⁻⁷ Jy, below the current detection threshold of radio telescopes. However, we propose that anomalous boosts and modulations to the magnetic field intensity and cyclotron emission may allow for their detection in the future.     

Reconnection X-winds: spin-down of low-mass protostars

We investigate the interaction of a protostellar magnetosphere with a large-scale magnetic field threading the surrounding accretion disc. It is assumed that a stellar dynamo generates a dipolar-type field with its magnetic moment aligned with the disc magnetic field. This leads to a magnetic neutral line at the disc mid-plane and gives rise to magnetic reconnection, converting closed protostellar magnetic flux into open field lines. These are simultaneously loaded with disc material, which is then ejected in a powerful wind. This process efficiently brakes down the protostar to 10–20 per cent of the break-up velocity during the embedded phase.     

An accretion disc model with a magnetic wind and turbulent viscosity

A model is presented for an accretion disc with turbulent viscosity and a magnetically influenced wind. The magnetic field is generated by a dynamo in the disc, involving the turbulence and radial shear. Disc-wind solutions are found for which the wind mass flux is sufficient to play a major part in driving an imposed steady inflow, but small enough for most material to be accreted on to the central object. Constraints arise for the magnetic Reynolds and Prandtl numbers in terms of the turbulent Mach number and vertical length-scale of the disc's horizontal magnetic field. It is shown that the imposition of a stellar boundary condition enhances the wind mass flux in the very inner region of the disc and may result in jet formation.