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

We study the perturbations of a relatively close third star on a tidally distorted eccentric eclipsing binary. We consider both the observational consequences of the variations of the orbital elements and the interactions of the stellar rotation with 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. 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 interactions with a tertiary. We also integrated numerically simultaneously the orbital and rotational equations for the possible hierarchical triple stellar system AS Camelopardalis. We find that there is a significant domain of the possible hierarchical triple system configurations, where both the dynamical 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 plane 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 rate varies during the dissipation-driven synchronization process...Comment: 33 pages, 12 figures (reduced quality!), accepted for publication for Astronomy and Astrophysic

Szociálisan hátrányos helyzetű gyermekek testnevelési teljesítményének vizsgálata

Fő kérdésünk az, hogy megnézzük, milyen hatással van a család szocio-ökonómiai helyzete és a szülők (az anya) iskolai végzettsége a diákok sportolási és higiéniás szokásaira, valamint ezek hogyan befolyásolják a testtömeg-index alakulását, az iskolai teljesítményt (bizonyítvány átlaga) és a fizikai teherbírást (Cooper-teszt és az erőnléti feladatok). Az eredményekre támaszkodva olyan mozgásanyagot kívánunk összeállítani, amely eltér az eddigiektől és tükrözi az egészségfejlesztés új irányvonalát. Szeretnénk olyan hasznos gyakorlatanyaggal szolgálni, amelyet ki-ki az általa képviselt területre adaptálhat. A mai kor igényeit kielégítő tartalmakat és módszereket, eszközöket kívánunk biztosítani. A fejlesztendő tananyag jellemzője az interdiszciplináris megközelítés. Az alkalmazandó eszközök között szerepel a zene, a mozgás, és valamilyen fizikai eszköz használata. Figyelembe véve az iskolák szer-készletét, ennek megfelelően kívánjuk alakítani a délutáni mozgásprogramok anyagát

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.Comment: Submitted to Astronomy and Astrophysics; Revised versio

On the apsidal motion of BP Vulpeculae

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.Comment: accepted for New Astronomy; two figure

Long-term photometry of three active red giants in close binary systems: V2253 Oph, IT Com and IS Vir

We present and analyze long-term optical photometric measurements of the three active stars V2253 Oph, IT Com and IS Vir. All three systems are single-lined spectroscopic binaries with an early K giant as primary component but in different stages of orbital-rotational synchronization. Our photometry is supplemented by 2MASS and WISE near-IR and mid-IR magnitudes and then used to obtain more accurate effective temperatures and extinctions. For V2253 Oph and IT Com, we found their spectral energy distributions consistent with pure photospheric emission. For IS Vir, we detect a marginal mid-IR excess which hints towards a dust disk. The orbital and rotational planes of IT Com appear to be coplanar, contrary to previous findings in the literature. We apply a multiple frequency analysis technique to determine photometric periods, and possibly changes of periods, ranging from days to decades. New rotational periods of 21.55+-0.03d, 65.1+-0.3d, and 23.50+-0.04d were determined for V2253 Oph, IT Com, and IS Vir, respectively. Splitting of these periods led to tentative detections of differential surface rotations of delta P/P ~0.02 for V2253 Oph and 0.07 for IT Com. Using a time-frequency technique based on short-term Fourier transforms we present evidence of cyclic light variations of length ~10yrs for V2253 Oph and 5-6yrs for IS Vir. A single flip-flop event has been observed for IT Com of duration 2-3yrs. Its exchange of the dominant active longitude had happened close to a time of periastron passage, suggesting some response of the magnetic activity from the orbital dynamics. The 21.55-d rotational modulation of V2253 Oph showed phase coherence also with the orbital period, which is 15 times longer than the rotational period, thus also indicating a tidal feedback with the stellar magnetic activity.Comment: 13 pages, 14 figures, accepted to A

Observational Detection of Higher Order Secular Perturbations in Tight Hierarchical Triple Stars

In this work, we search for observational evidence of higher-order secular perturbations in three eclipsing binaries. These are slightly eccentric binaries, and they form the inner pairs of tight, compact, hierarchical triple star systems. We analyze simultaneously the high precision satellite ($Kepler$ and $TESS$) light curves, eclipse timing variations, combined spectral energy distributions (through catalog passband magnitudes) and, where available, radial velocities of KICs 9714358, 5771589 and TIC 219885468. Besides the determination of robust astrophysical and dynamical properties of the three systems, we find evidence that the observed unusual eclipse timing variations of KIC 9714358 are a direct consequence of the octupole-order secular eccentricity perturbations forced by an unusual, resonant behaviour between the lines of the apsides of the inner and outer orbital ellipses. We also show that, despite its evident cyclic eclipse depth variations, KIC~5771589 is an almost perfectly coplanar system (to within $0.3^\circ$), and we explain the rapid eclipse depth variations with the grazing nature of the eclipses. Finally, we find that the inner pair of TIC~219885468 consists of two twin stars and, hence, in this triple there are no octupole order three-body perturbations. Moreover, we show that this triple is also coplanar on the same level as the former one, but due to its deep eclipses, it does not exhibit eclipse depth variations. We intend to follow this work up with further analyses and a quantitative comparison of the theoretical and the observed perturbations.Comment: Accepted for publication in the journal Universe, special issue The Royal Road: Eclipsing Binaries and Transiting Exoplanets, 33 page

The Anticorrelated Nature of the Primary and Secondary Eclipse Timing Variations for the Kepler Contact Binaries

We report on a study of eclipse timing variations in contact binary systems, using long-cadence lightcurves in the Kepler archive. As a first step, 'observed minus calculated' (O-C) curves were produced for both the primary and secondary eclipses of some 2000 Kepler binaries. We find ~390 short-period binaries with O-C curves that exhibit (i) random-walk like variations or quasi-periodicities, with typical amplitudes of +/- 200-300 seconds, and (ii) anticorrelations between the primary and secondary eclipse timing variations. We present a detailed analysis and results for 32 of these binaries with orbital periods in the range of 0.35 +/- 0.05 days. The anticorrelations observed in their O-C curves cannot be explained by a model involving mass transfer, which among other things requires implausibly high rates of ~0.01 M_sun per year. We show that the anticorrelated behavior, the amplitude of the O-C delays, and the overall random-walk like behavior can be explained by the presence of a starspot that is continuously visible around the orbit and slowly changes its longitude on timescales of weeks to months. The quasi-periods of ~50-200 days observed in the O-C curves suggest values for k, the coefficient of the latitude dependence of the stellar differential rotation, of ~0.003-0.013.Comment: Published in The Astrophysical Journal, 2013, Vol. 774, p.81; 14 pages, 12 figures, and 2 table

Tidally Induced Oscillations and Orbital Decay in Compact Triple-Star Systems

We investigate the nature of tidal effects in compact triple-star systems. The hierarchical structure of a triple system produces tidal forcing at high frequencies unobtainable in binary systems, allowing for the tidal excitation of high frequency p-modes in the stellar components. The tidal forcing exists even for circular, aligned, and synchronized systems. We calculate the magnitude and frequencies of three-body tidal forcing on the central primary star for circular and coplanar orbits, and we estimate the amplitude of the tidally excited oscillation modes. We also calculate the secular orbital changes induced by the tidally excited modes, and show that they can cause significant orbital decay. During certain phases of stellar evolution, the tidal dissipation may be greatly enhanced by resonance locking. We then compare our theory to observations of HD 181068, which is a hierarchical triply eclipsing star system in the Kepler field of view. The observed oscillation frequencies in HD 181068 can be naturally explained by three-body tidal effects. We then compare the observed oscillation amplitudes and phases in HD 181068 to our predictions, finding mostly good agreement. Finally, we discuss the past and future evolution of compact triple systems like HD 181068.Comment: 19 pages, 8 figures, published in MNRA

Szociálisan hátrányos helyzetű gyermekek testnevelési teljesítményének vizsgálata

Fő kérdésünk az, hogy megnézzük, milyen hatással van a család szocio-ökonómiai helyzete és a szülők (az anya) iskolai végzettsége a diákok sportolási és higiéniás szokásaira, valamint ezek hogyan befolyásolják a testtömeg-index alakulását, az iskolai teljesítményt (bizonyítvány átlaga) és a fizikai teherbírást (Cooper-teszt és az erőnléti feladatok). Az eredményekre támaszkodva olyan mozgásanyagot kívánunk összeállítani, amely eltér az eddigiektől és tükrözi az egészségfejlesztés új irányvonalát. Szeretnénk olyan hasznos gyakorlatanyaggal szolgálni, amelyet ki-ki az általa képviselt területre adaptálhat. A mai kor igényeit kielégítő tartalmakat és módszereket, eszközöket kívánunk biztosítani. A fejlesztendő tananyag jellemzője az interdiszciplináris megközelítés. Az alkalmazandó eszközök között szerepel a zene, a mozgás, és valamilyen fizikai eszköz használata. Figyelembe véve az iskolák szer-készletét, ennek megfelelően kívánjuk alakítani a délutáni mozgásprogramok anyagát