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

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

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

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

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.Comment: 4 page

Triple-Star Candidates Among the Kepler Binaries

We present the results of a search through the photometric database of eclipsing Kepler binaries (Prsa et al. 2011; Slawson et al. 2011) looking for evidence of hierarchical triple star systems. The presence of a third star orbiting the binary can be inferred from eclipse timing variations. We apply a simple algorithm in an automated determination of the eclipse times for all 2157 binaries. The "calculated" eclipse times, based on a constant period model, are subtracted from those observed. The resulting O-C (observed minus calculated times) curves are then visually inspected for periodicities in order to find triple-star candidates. After eliminating false positives due to the beat frequency between the ~1/2-hour Kepler cadence and the binary period, 39 candidate triple systems were identified. The periodic O-C curves for these candidates were then fit for contributions from both the classical Roemer delay and so-called "physical" delay, in an attempt to extract a number of the system parameters of the triple. We discuss the limitations of the information that can be inferred from these O-C curves without further supplemental input, e.g., ground-based spectroscopy. Based on the limited range of orbital periods for the triple star systems to which this search is sensitive, we can extrapolate to estimate that at least 20% of all close binaries have tertiary companions.Comment: 19 pages, 13 figures, 3 tables; ApJ, 2013, 768, 33; corrected Fig. 7, updated references, minor fixes to tex