The axisymmetric antidynamo theorem revisited

The axisymmetric kinematic dynamo problem is reconsidered and a number of open questions are answered. Apart from axisymmetry and smoothness of data and solution we deal with this problem under quite general conditions, i.e. we assume a compressible fluid of variable (in space and time) conductivity moving in an arbitrary (axisymmetric) domain. We prove unconditional, pointwise and exponential decay of magnetic field and electric current to zero. The decay rate of the external (meridional) magnetic field can become very small (compared to free decay) for special flow fields and large magnetic Reynolds numbers. We give an example of that. On the other hand, we show for fluids with weak variation of mass density and conductivity that the meridional and azimuthal decay rates do not drop significantly below those of free decay.Comment: Revised version, 28 pages, 1 figur

Axisymmetric dynamo action produced by differential rotation, with anisotropic electrical conductivity and anisotropic magnetic permeability

The effect on dynamo action of an anisotropic electrical conductivity conjugated to an anisotropic magnetic permeability is considered. Not only is the dynamo fully axisymmetric, but it requires only a simple differential rotation, which twice challenges the well-established dynamo theory. Stability analysis is conducted entirely analytically, leading to an explicit expression of the dynamo threshold. The results show a competition between the anisotropy of electrical conductivity and that of magnetic permeability, the dynamo effect becoming impossible if the two anisotropies are identical. For isotropic electrical conductivity, Cowling's neutral point argument does imply the absence of an azimuthal component of current density, but does not prevent the dynamo effect as long as the magnetic permeability is anisotropic.Comment: 19 pages, 6 figure

Spot activity of late-type stars : a study of II Pegasi and DI Piscium

All stars that have outer convection zones show magnetic activity. This activity strengthens with angular velocity and depth of the convection zone. Cool starspots are believed to be caused by local magnetic field concentrations on the surfaces of stars. They show up as dark regions against a bright photosphere and are observable manifestations of the internal dynamo activity. Therefore the solar dynamo is not unique, only one example of a cyclic dynamo. This makes studies of magnetic activity in other stars important. The convection zone is believed to be the source area of the solar dynamo. The distributed dynamo paradigm is relying on magnetic field generation throughout the convection zone, while the flux-transport paradigm is based on the Babcock-Leighton -effect near the surface in which the mean poloidal field is produced by the merging of twisted magnetic loops. Mean-field dynamo models can produce many observed features both of the solar cycle and some of the features seen in active rapid rotators, but it remains yet under debate which dynamo paradigm is correct. Especially in the case of the Sun, the kinematic mean-field models of different types can lead to a satisfactory reproduction of the solar cycle main properties. These two prevailing dynamo paradigms are briefly introduced in this thesis, as well as their current challenges. For II Peg our time series covers both states of high and low activity. Furthermore we discover a drift of the active region. This drift is also confirmed from photometry, with the carrier fit analysis. The most natural explanation for it would be an azimuthal dynamo wave. DI Psc is a rapidly rotating single giant, which has an interestingly high lithium concentration. We examine the spot behaviour for a two years time-span, and retrieve changes in the activity, which could indicate a fast activity cycle of only a few years.Tähdet, joilla on ulkoinen konvektiokerros, ovat magneettisesti aktiivisia. Tähtien magneettikenttä syntyy konvektiokerroksessa, joka on eräänlainen pohjalta kuumennettu kaasukerros. Kuuman kaasun ylös-alas suuntautuva liike yhdessä tähden pyörimisen kanssa aiheuttaa virtauksen, jossa syntyy magneettikenttää. Magneettikentän syntyprosessia kutsutaan dynamoprosessiksi. Auringossa ja Auringon kaltaisissa tähdissä magneettinen aktiivisuus ilmenee muun muassa pilkkuina, eli paikallisten magneettikenttien synnyttäminä kylmempinä alueina tähtien pinnalla. Näitä pilkkuja voidaan mallintaa epäsuorasti inversiomenetelmin, joiden avulla saadaan tuotettua lämpötilakartta tähden pinnasta. Tähdenpilkut ovat havaittuja todisteita tähtien sisäisestä dynamotoiminnasta. Auringon dynamo ei ole siten ainutlaatuinen vaan ainoastaan yksi esimerkki syklisestä dynamosta. Tästä syystä muiden tähtien magneettisen aktiivisuuden tutkimus on tärkeätä. Samat magneettisen aktiivisuuden ilmiöt kuin Auringossa näkyvät myös auringonkaltaisissa tähdissä. Tutkimusprojektissa keskitytään tutkimaan nopeasti pyörivien tähtien magneettista aktiivisuutta. Näissä tähdissä on pilkkuja, jotka ovat kooltaan paljon auringonpilkkuja suurempia ja ovat keskittyneet yleensä ekvaattorin sijaan korkeammille latitudeille ja näiden tähtien aktiivisuus on huomattavasti suurempi kuin Auringossa. Tutkimusprojektissa hyödynnetään spektroskooppisia havaintoja, jotka on otettu kohteistamme Nordic Optical Telescopella La Palmalla. Pisin keskeytymätön havaintosarjamme II Pegille kattaa noin 20 vuotta, minkä aikana tähden magneettinen aktiivisuustaso muuttuu. Havainnoista pystyimme määrittämään yhden ensimmäisistä havaituista dynamoaalloista, mikä avasi uusia ovia teoreettiselle tutkimukselle. Toinen kohteemme DI Psc on nopeasti pyörivä jättiläistähti, jolla on korkea litiumpitoisuus. Tutkimme pilkkujen käyttäytymistä kahden vuoden aikasarjalla ja havaitsimme muutoksia aktiivisuustasoissa, mikä indikoi nopeata muutaman vuoden aktiivisuussykliä

Dissipative heating and nonthermal distributions in black hole accretion flaring events

The center of the Milky Way galaxy contains a supermassive black hole called Sgr A*, which has been observed at radio, mm, X-ray, and near infrared (NIR) wavelengths. The NIR emission flares about once per day with the flaring state being about an order of magnitude brighter than the non-flaring state. These flares have a flat spectrum that drops off at high frequency much slower than would be expected from thermal emission alone. This thesis describes work to model these flares using general relativistic magnetohydrodynamics (GRMHD) and radiative transfer calculations with a nonthermal kappa distribution function (which effectively adds a power-law tail to the thermal distribution) for electrons accelerated by resistive heating in reconnecting current sheets. This approach is well supported by the literature on the acceleration of electrons in magnetized plasma, which shows that current sheets do accelerate electrons and those electrons can have a distribution function similar to a kappa distribution. In axisymmetric (two dimensional) simulations presented here, a model with a constant fraction of electrons in the kappa distribution is able to enhance NIR emission but is unable to produce any substantial variability in the NIR flux density. Similar models that heat electrons through resistive dissipation are able to produce flares. In three-dimensional standard and normal evolution (SANE) and magnetically arrested disk (MAD) models, the total current in the simulation showed only small variability. This resulted in some small-scale variability in the light curve, but no flares are observed. In all cases, nonthermal models were able to reproduce the observed spectral slope of Sgr A* in the NIR region

Symmetries in the Kinematic Dynamos and Hydrodynamic Instabilities of the ABC Flows

This thesis primarily concerns kinematic dynamo action by the 1:1:1 ABC flow, in the highly conducting limit of large magnetic Reynolds number Rm. The flow possesses 24 symmetries, with a symmetry group isomorphic to the group O24 of orientation-preserving transformations of a cube. These symmetries are exploited to break up the linear eigenvalue problem into five distinct symmetry classes, which we label I-V. The thesis discusses how to reduce the scale of the numerical problem to a subset of Fourier modes for a magnetic field in each class, which then may be solved independently to obtain distinct branches of eigenvalues and magnetic field eigenfunctions. Two numerical methods are employed: the first is to time step a magnetic field in a given symmetry class and obtain the growth rate and frequency by measuring the magnetic energy as a function of time. The second method involves a more direct determination of the eigenvalue using the eigenvalue solver ARPACK for sparse matrix systems, which employs an implicitly restarted Arnoldi method. The two methods are checked against each other, and compared for efficiency and reliability. Eigenvalue branches for each symmetry class are obtained for magnetic Reynolds numbers Rm up to 10^4 together with spectra and magnetic field visualisations. A sequence of branches emerges as Rm increases and the magnetic field structures in the different branches are discussed and compared. All symmetry classes are found to contain a dynamo, though dynamo effectiveness varies greatly between classes, suggesting that the symmetries play an important role in the field amplification mechanisms. A closely related problem, that of linear hydrodynamic stability, is also explored in the limit of large Reynolds number Re. As the same symmetry considerations apply, the five symmetry classes of the linear instability can be resolved independently, reducing the size of the problem and allowing exploration of the effects of the symmetries on instability growth rate. Results and visualisations are obtained for all five classes for Re up to 10^3, with comparisons drawn between the structures seen in each class and with those found in the analogous magnetic problem. For increasing Re, multiple mode crossings are observed within each class, with remarkably similar growth rates seen in all classes at Re=10^3, highlighting a lack of dependence on the symmetries of the instability, in contrast with the magnetic problem. This thesis also investigates the problem of large-scale magnetic fields in the 1:1:1 ABC flow through the introduction of Bloch waves that modify the periodicity of the magnetic field relative to the flow. Results are found for a field with increased periodicity in a single direction for Rm up to 10^3; it is established that the optimal scale for dynamo action varies as Rm increases, settling on a consistent scale for large Rm. The emerging field structures are studied and linked with those of the original dynamo problem. On contrasting this method with a previous study in which the flow is instead rescaled, it is shown that the use of Bloch waves drastically increases the range of possible scales, whilst cutting required computing time. Through a multiple-scale analysis, the contribution from the alpha-effect is calculated for the 1:1:1 ABC flow and is seen in growth rates for Rm << 1.The Leverhulme Trus

Stellar Magnetism in Theory and Observation

The universe is populated with magnetically active stars. This magnetic activity is thought to be generated by dynamos operating in turbulent stellar convection zones, a process by which kinetic energy is converted into magnetic energy. The solar dynamo is but one dynamo type possible for stars. Rapidly rotating late-type stars are observed to have large spots, activity cycles, flip-flops, and active longitudes, all indicating a different dynamo mechanism may be responsible. Numerical simulations provide a tool for better understanding some of the mechanisms responsible for these dynamos. In this thesis, direct numerical simulations in spherical wedges are used to study dynamo mechanisms in the stellar convection zone. These spherical wedges are used to investigate the dependence of the resulting magnetic field on input parameters such as the density stratification and rotation rate. Mean-field models are used to evaluate the assumption that the wedges can be used to approximate full spheres. As rotation increases, differential rotation decreases in the models, in agreement with observations where more rapidly rotating stars have smaller estimates for differential rotation. As density stratification approaches more realistic values, a lat- itudinal dynamo wave with equatorward propagation is found. The impact of the domain size in the azimuthal direction on the results is explored. When the domain size is increased to 2pi in the azimuthal direction, a non-axisymmetric m = 1 mode is excited. This non-axisymmetry is reminiscent of the field configurations of rapidly rotating late-type stars. The azimuthal dynamo wave rotates nearly independently of latitude and depth, and its rotation rate is slower than that of the mean rotation of the model. This azimuthal dynamo can provide a possible explanation for the observed rotational difference of spots from the mean rotation observed on stars. The wedges use the perfect conductor boundary conditions at the latitudinal boundary to compensate for the omission of polar regions due to the time step becoming prohibitively small there. Simple mean-field models with only a latitudinal extent and perfectly conducting boundaries do not oscillate when the model is extended to the poles. Thus oscillations near the polar region may be an artifact of the boundary condition. However, when the alpha effect from mean-field dynamo theory and magnetic diffusivity are concentrated towards lower latitudes, oscillatory solutions with equatorward migration are found. When sufficient shear is added, oscillatory solutions are again found, and the Parker-Yoshimura rule for latitudinal dynamo wave propagation is obeyed. It is concluded that numerical simulations where the alpha effect and diffusivity are found to be stronger at lower latitudes and simulations with sufficient shear are considered good approximations of full spheres. These numerical simulations are put into context with stellar observations. Two young solar analogs are selected, V352 Canis Majoris and LQ Hydrae. V352 CMa is considered an active star, while LQ Hya is classified as a super-active star. The continuous period search method is applied to the low-amplitude light curves of V352 CMa. Stable active longitudes with rotation periods of 7.157 days are found. This is faster than the mean rotation of 7.24 days. Such active longitudes may be due to the underlying magnetic structure with azimuthal dynamo waves competing with differential rotation. LQ Hya rotates even more rapidly with a rotation period of only 1.600 days. A carrier period is selected of 1.605 days using the D2 statistical analysis. Primary and secondary light curve minima are found with the carrier fit analysis. No stable active longitudes are found, instead, there is only a short period spanning a few years where an active longitude may exist, but the rotation period is poorly defined. Several possible flip-flop events are identified. The azimuthal dynamo waves in numerical simulations with comparable rotation rates have a similar chaotic nature. The Doppler Imaging technique is applied to LQ Hya to examine the latitudinal spot structure. Spots at high and low latitudes are in agreement with the bimodal structure of the D2 statistic used in the carrier fit analysis. Temperature maps of LQ Hya spanning four years show an increase and a decrease in spot coverage, but no cycle can be found. Because LQ Hya is a rapidly rotating star, differential rotation is estimated to be very small. The azimuthal dynamo wave presents a new possible explanation for the jumps and trends of the spots in observations of this star