We study the possibility of the detection of the low amplitude long (P') period perturbative effect of a distant third companion on the motion of a close binary. We give a new, more accurate analytical formula for this kind of perturbation affecting the moments of the times of minima in eclipsing binaries. The accuracy of this formula is tested by numerical integrations carried out for several initial configurations. We also describe a numerical method based on a non-linear Levenberg-Marquardt algorithm which makes it possible to separate this dynamical effect from the pure geometrical light-time effect in the eclipsing O-C diagram. The capabilities of this new method are demonstrated by the analysis of numerically simulated O-Cs for test systems having physical parameters very similar to Algol and IU Aur. The results show that the above mentioned effect would be detectable in these systems nowadays, observing almost each minima events in a 1–2 year-long interval.

Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

We report the discovery and complex analyses of the first two compact hierarchical triple star systems discovered with TESS in or near its southern continuous viewing zone during Year 1. Both TICs 167692429 and 220397947 were previously unknown eclipsing binaries, and the presence of a third companion star was inferred from eclipse timing variations exhibiting signatures of strong third-body perturbations and, in the first system, also from eclipse depth variations. We carried out comprehensive analyses, including the simultaneous photodynamical modelling of TESS and archival ground-based WASP light curves, as well as eclipse timing variation curves. Also, for the first time, we included in the simultaneous fits multiple star spectral energy distribution data and theoretical PARSEC stellar isochrones, taking into account Gaia DR2 parallaxes and catalogued metallicities. We find that both systems have twin F-star binaries and a lower mass tertiary star. In the TIC 167692429 system, the inner binary is moderately inclined (imut = 27°) with respect to the outer orbit, and the binary versus outer (triple) orbital periods are 10.3 versus 331 d, respectively. The mutually inclined orbits cause a driven precession of the binary orbital plane that leads to the disappearance of binary eclipses for long intervals. In the case of TIC 220397947, the two orbital planes are more nearly aligned and the inner versus outer orbital periods are 3.5 and 77 d, respectively. In the absence of radial velocity observations, we were unable to calculate highly accurate masses and ages for the two systems. According to stellar isochrones TIC 167692429 might be either a pre-main sequence (MS) or an older post-MS system. In the case of TIC 220397947, our solution prefers a young pre-MS scenario.

Several studies have examined the temporal variability of the solar activity, and many variations are reported in the literature. We also (re)analyse

One possible scenario for the origin of the solar tachocline, known as the “fast tachocline”, assumes that the turbulent diffusivity exceeds cm2 s-1. In this case the dynamics will be governed by the dynamo-generated oscillatory magnetic field on relatively short timescales. Here, for the first time, we present detailed numerical models for the fast solar tachocline with all components of the magnetic field calculated explicitly, assuming axial symmetry and a constant turbulent diffusivity η and viscosity ν. We find that a sufficiently strong oscillatory poloidal field with dipolar latitude dependence at the tachocline–convective zone boundary is able to confine the tachocline. Exploring the three-dimensional parameter space defined by the viscosity in the range –11, the magnetic Prandtl number in the range , and the meridional flow amplitude (-3 to +3 cm s-1), we also find that the confining field strength , necessary to reproduce the observed thickness of the tachocline, increases with viscosity ν, with magnetic Prandtl number , and with equatorward meridional flow speed. Nevertheless, the resulting values remain quite reasonable, in the range G, for all parameter combinations considered here. The thickness of the tachocline shows a marked dependence on both time and latitude. The latitude dependence is similar to that inferred by helioseismology, while the time dependence is within the observational errors.