Tamas Borkovits

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.

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.

On the apsidal motion of BP Vulpeculae

Abstract BP Vulpeculae is a bright eclipsing binary system showing apsidal motion. It was found in an earlier study that it shows retrograde apsidal motion which contradicts theory. In this paper we present the first BV light curve of the system and its light curve solution as well as seven new times of the minima from the years 1959–1963. This way we could expanded the baseline of the investigation to five decades. Based on this longer baseline we concluded that the apsidal motion is prograde agreeing with the theoretical expectations and its period is about 365 years and the determined internal structure constant is close to the theoretically expected one.

CHARA and e-VLBI observations of Algol

The CHARA Array is funded by the National Science Foundation through NSF grants AST-0307562 and AST06006958 and by Georgia State University through the College of Arts and Sciences and the Office of the Vice President for Research. e-VLBI developments in Europe are supported by the EC DG-INFSO funded Communication Network Developments project ’EXPReS’, Contract No. 02662 (http://www.expres-eu.org/). The European VLBI Network (http://www.evlbi.org/) is a joint facility of European, Chinese, South African and other radio astronomy institutes funded by their national research councils.