E. Forgács-Dajka

Transit timing variations in eccentric hierarchical triple exoplanetary systems I. Perturbations on the time scale of the orbital period of the perturber

We study the long-term time-scale (i.e. period comaprable to the orbital period of the outer perturber object) transit timing variations in transiting exoplanetary systems which contain a further, more distant (a_2>>a_1) either planetary, or stellar companion. We give an analytical form of the O-C diagram (which describes such TTV-s) in trigonometric series, valid for arbitrary mutual inclinations, up to the sixth order in the inner eccentricity. We show that the dependence of the O-C on the orbital and physical parameters can be separated into three parts. Two of these are independent of the real physical parameters (i.e. masses, separations, periods) of a concrete system, and depend only on dimensionless orbital elements, and so, can be analyzed in general. We analyze these dimensionless amplitudes for different arbitrary initial parameters, as well as for two particular systems CoRoT-9b and HD 80606b. We find in general, that while the shape of the O-C strongly varies with the angular orbital elements, the net amplitude (departing from some specific configurations) depends only weakly on these elements, but strongly on the eccentricities. As an application, we illustrate how the formulae work for the weakly eccentric CoRoT-9b, and the highly eccentric HD 80606b. We consider also the question of detection, as well as the correct identification of such perturbations. Finally, we illustrate the operation and effectiveness of Kozai cycles with tidal friction (KCTF) in the case of HD 80606b.

A BABCOCK–LEIGHTON SOLAR DYNAMO MODEL WITH MULTI-CELLULAR MERIDIONAL CIRCULATION IN ADVECTION- AND DIFFUSION-DOMINATED REGIMES

Babcock–Leighton type-solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock–Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that the presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in the butterfly diagram, whereas the presence of a second cell in depth reverses the tilt of the butterfly wing to an antisolar type. A butterfly diagram constructed from the middle of convection zone yields a solar-like pattern, but this may be difficult to realize in the Sun because of magnetic buoyancy effects. Each of the above cases behaves similarly in higher and lower magnetic diffusivity regimes. However, our dynamo with a meridional circulation containing four cells in latitude behaves distinctly differently in the two regimes, producing solar-like butterfly diagrams with fast cycles in the higher diffusivity regime, and complex branches in butterfly diagrams in the lower diffusivity regime. We also find that dynamo solutions for a four-celled pattern, two in radius and two in latitude, prefer to quickly relax to quadrupolar parity if the bottom flow speed is strong enough, of similar order of magnitude as the surface flow speed.

Tidal and rotational effects in the perturbations of hierarchical triple stellar systems - II. Eccentric systems – the case of AS Camelopardalis

Aims. We study the perturbations of a relatively close third star o n a tidally distorted eccentric eclipsing binary. We consid er both the observational consequences of the variations of the orbital elements and the interactions of the stellar rotation w ith the orbital revolution in the presence of dissipation. We concentrate mainly on the effect of a hypothetical third companion on both the real, and the observed apsidal motion period. We investigate how the observed period derived mainly from some variants of the O‐C relates to the real apsidal motion period. Methods. We carried out both analytical and numerical investigations and give the time variations of the orbital elements of the binary both in the dynamical and the observational reference frames. We give the direct analytical form of an eclipsing O‐C affected simultaneously by the mutual tidal forces and the gravitational i nteractions with a tertiary. We also integrated numericall y simultaneously the orbital and rotational equations for the possible hiera rchical triple stellar system AS Camelopardalis. Results. We find that there is a significant domain of the possible hiera rchical triple system configurations, where both the dynami cal and the observational effects tend to measure longer apsidal advance rate than is expected theoretically. This happens when the mutual inclination of the close and the wide orbits is large, and the orbital plane of the tertiary almost coincides with the plan e of the sky. We also obtain new numerical results on the interaction of the orbital evolution and stellar rotation in such triplets. The most important fact is that resonances might occur as the stellar rotational rat e varies during the dissipation-driven synchronization pr ocess, for example in the case when the rotational rate of one of the stars reache s the average Keplerian angular velocity of the orbital revolution.

Tidal and rotational effects in the perturbations of hierarchical triple stellar systems - I. Numerical model and a test application for Algol

A new numerical integrator has been developed for studying the orbital and spin evolution of hierarchical triple stellar systems. The code includes equilibrium tide approximations with arbitrary direction of rotational axes. The variation of the orbital elements (e.g. the inclination of the close - eclipsing - binary) and its observational consequences according to the distorted models with different mass-distributions of the stars, as well as with and without dissipation are studied in the case of the well-known eclipsing triple system Algol. We found that, in the absence of the tidal dissipation, the presence of the third star may cause sudden fluctuations in the orbital elements and the stellar rotation of the binary members even in the previously synchronized case, too. The dissipation can eliminate these fluctuations, nevertheless some variations which would produce observable effects in the same order which have been measured in several eclipsing binaries are also present.

Long-term variation in distribution of sunspot groups

We studied the relation between the distribution of sunspot groups and the Gleissberg cycle. As the magnetic field is related to the area of the sunspot groups, we used area-weighted sunspot group data. On the one hand, we confirm the previously reported long-term cyclic behaviour of the sum of the northern and southern sunspot group mean latitudes, although we found a somewhat longer period (P ∼ 104 years). We introduced the difference between the ensemble average area of sunspot groups for the two hemispheres, which turns out to show similar behaviour. We also investigated a further aspect of the Gleissberg cycle where while in the 19th century the consecutive Schwabe cycles are sharply separated from each other, one century later the cycles overlap each other more and more.

Surface velocity network with anti‐solar differential rotation on the activeK‐giant σ Geminorum

We demonstrate the power of the local correlation tracking technique on stellar data for the first time. We recover the spot migration pattern of the long-period RS CVn-type binary

Dynamics of the fast solar tachocline. II. Migrating field

\sigma

Magnetoacoustic surface gravity waves at a spherical interface

Gem from a set of six Doppler images from 3.6 consecutive rotation cycles. The resulting surface flow map suggests a weak anti-solar differential rotation with

The dynamical solar atmosphere

\alpha\approx-0.0022\pm0.0016

Rotation–differential rotation relationships for late-type single and binary stars from Doppler imaging

, and a coherent poleward spot migration with an average velocity of