A Phase Transition for Circle Maps and Cherry Flows

We study $C^{2}$ weakly order preserving circle maps with a flat interval. The main result of the paper is about a sharp transition from degenerate geometry to bounded geometry depending on the degree of the singularities at the boundary of the flat interval. We prove that the non-wandering set has zero Hausdorff dimension in the case of degenerate geometry and it has Hausdorff dimension strictly greater than zero in the case of bounded geometry. Our results about circle maps allow to establish a sharp phase transition in the dynamics of Cherry flows

The Araucaria project: High-precision orbital parallaxes and masses of binary stars. I. VLTI/GRAVITY observations of ten double-lined spectroscopic binaries

We aim to measure very precise and accurate model-independent masses and distances of detached binary stars. Precise masses at the $< 1$% level are necessary to test and calibrate stellar interior and evolution models, while precise and independent orbital parallaxes are essential to check for the next Gaia data releases. We combined RV measurements with interferometric observations to determine orbital and physical parameters of ten double-lined spectroscopic systems. We report new relative astrometry from VLTI/GRAVITY and, for some systems, new VLT/UVES spectra to determine the radial velocities of each component. We measured the distance of ten binary systems and the mass of their components with a precision as high as 0.03% (average level 0.2%). They are combined with other stellar parameters (effective temperatures, radii, flux ratios, etc.) to fit stellar isochrones and determine their evolution stage and age. We also compared our orbital parallaxes with Gaia and showed that half of the stars are beyond $1\sigma$ with our orbital parallaxes; although, their RUWE is below the frequently used cutoff of 1.4 for reliable Gaia astrometry. By fitting the telluric features in the GRAVITY spectra, we also estimated the accuracy of the wavelength calibration to be $\sim 0.02$% in high and medium spectral resolution modes. We demonstrate that combining spectroscopic and interferometric observations of binary stars provides extremely precise and accurate dynamical masses and orbital parallaxes. As they are detached binaries, they can be used as benchmark stars to calibrate stellar evolution models and test the Gaia parallaxes.Comment: Accepted for publication in A&

The Araucaria Project. OGLE-LMC-CEP-1718: An exotic eclipsing binary system composed of two classical overtone Cepheids in a 413-day orbit

We have obtained extensive high-quality spectroscopic observations of the OGLE-LMC-CEP-1718 eclipsing binary system in the Large Magellanic Cloud which Soszynski et al. (2008) had identified as a candidate system for containing two classical Cepheids in orbit. Our spectroscopic data clearly demonstrate binary motion of the Cepheids in a 413-day eccentric orbit, rendering this eclipsing binary system the first ever known to consist of two classical Cepheid variables. After disentangling the four different radial velocity variations in the system we present the orbital solution and the individual pulsational radial velocity curves of the Cepheids. We show that both Cepheids are extremely likely to be first overtone pulsators and determine their respective dynamical masses, which turn out to be equal to within 1.5 %. Since the secondary eclipse is not observed in the orbital light curve we cannot derive the individual radii of the Cepheids, but the sum of their radii derived from the photometry is consistent with overtone pulsation for both variables. The existence of two equal-mass Cepheids in a binary system having different pulsation periods (1.96 and 2.48 days, respectively) may pose an interesting challenge to stellar evolution and pulsation theories, and a more detailed study of this system using additional datasets should yield deeper insight about the physics of stellar evolution of Cepheid variables. Future analysis of the system using additional near-infrared photometry might also lead to a better understanding of the systematic uncertainties in current Baade-Wesselink techniques of distance determinations to Cepheid variables.Comment: accepted to be published in Ap