Integral group ring of the McLaughlin simple group

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the McLaughlin sporadic group McL. As a consequence, we confirm for this group the Kimmerle’s conjecture on prime graphs

Integral group ring of the first Mathieu simple group

We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Mathieu group M11. As a consequence, for this group we confirm the conjecture by Kimmerle about prime graphs

Amplitude variations of modulated RV Tauri stars support the dust obscuration model of the RVb phenomenon

Context. RV Tauri-type variables are pulsating post-AGB stars that evolve rapidly through the instability strip after leaving the Asymptotic Giant Branch. Their light variability is dominated by radial pulsations. Members of the RVb subclass show an additional variability in form of a long-term modulation of the mean brightness, for which the most popular theories all assume binarity and some kind of circumstellar dust. Here we address if the amplitude modulations are consistent with the dust obscuration model. Aims. We measure and interpret the overall changes of the mean amplitude of the pulsations along the RVb variability. Methods. We compiled long-term photometric data for RVb-type stars, including visual observations of the American Association of Variable Star Observers, ground-based CCD photometry from the OGLE and ASAS projects and ultra-precise space photometry of one star, DF Cygni, from the Kepler space telescope. After converting all the observations to flux units, we measure the cycle-to-cycle variations of the pulsation amplitude and correlate them to the actual mean fluxes. Results. We find a surprisingly uniform correlation between the pulsation amplitude and the mean flux: they scale linearly with each other for a wide range of fluxes and amplitudes. It means that the pulsation amplitude actually remains constant when measured relative to the system flux level. The apparent amplitude decrease in the faint states has long been noted in the literature but it was always claimed to be difficult to explain with the actual models of the RVb phenomenon. Here we show that when fluxes are used instead of magnitudes, the amplitude attenuation is naturally explained by periodic obscuration from a large opaque screen, one most likely corresponding to a circumbinary dusty disk that surrounds the whole system.Comment: 8 pages, 6 figures, accepted for publication in A&

Kimmerle conjecture for the Held and O'Nan sporadic simple groups

Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held simple group and also derive for both groups some extra information relevant to the classical Zassenhaus conjecture

Covering theorems for Artinian rings

The covering properties of Artinian rings which depend on their additive structure only, are investigated

Physical properties of galactic RV Tauri stars from Gaia DR2 data

We present the first period-luminosity and period-radius relation of Galactic RV Tauri variable stars. We have surveyed the literature for all variable stars belonging to this class and compiled the full set of their photometric and spectroscopic measurements. We cross-matched the final list of stars with the Gaia DR2 database and took the parallaxes, G-band magnitudes and effective temperatures to calculate the distances, luminosities and radii using a probabilistic approach. As it turned out, the sample was very contaminated and thus we restricted our study to those objects for which the RV Tau-nature was securely confirmed. We found that several stars are located outside the red edge of the classical instability strip, which implies a wider pulsational region for RV Tau stars. The period-luminosity relation of galactic RV Tauri stars is steeper than that of the shorter-period Type II Cepheids, in agreement with previous result obtained for the Magellanic Clouds and globular clusters. The median masses of RVa and RVb stars were calculated to be 0.45-0.52 M$_{\odot}$ and 0.83 M$_{\odot}$, respectively.Comment: 10 pages, accepted to Ap

The contact binary VW Cephei revisited: surface activity and period variation

Context. Despite the fact that VW Cephei is one of the well-studied contact binaries in the literature, there is no fully consistent model available that can explain every observed property of this system. Aims. Our motivation is to obtain new spectra along with photometric measurements, to analyze what kind of changes may have happened in the system in the past two decades, and to propose new ideas for explaining them. Methods. For the period analysis we determined 10 new times of minima from our light curves, and constructed a new O$-$C diagram of the system. Radial velocities of the components were determined using the cross-correlation technique. The light curves and radial velocities were modelled simultaneously with the PHOEBE code. All observed spectra were compared to synthetic spectra and equivalent widths of the H$\alpha$ line were measured on their differences. Results. We have re-determined the physical parameters of the system according to our new light curve and spectral models. We confirm that the primary component is more active than the secondary, and there is a correlation between spottedness and the chromospheric activity. We propose that flip-flop phenomenon occurring on the primary component could be a possible explanation of the observed nature of the activity. To explain the period variation of VW Cep, we test two previously suggested scenarios: presence of a fourth body in the system, and the Applegate-mechanism caused by periodic magnetic activity. We conclude that although none of these mechanisms can be ruled out entirely, the available data suggest that mass transfer with a slowly decreasing rate gives the most likely explanation for the period variation of VW Cep.Comment: 13 pages, 18 figures, 9 tables, accepted for publication in Astronomy and Astrophysic

CoRoT-TESS eclipsing binaries with light-travel-time effect

Identifying long-period eclipsing binaries with space-based photometry is still a challenge even in the century of space telescopes due to the relatively short observation sequences and short lifetime of these missions. The Transiting Exoplanet Survey Satellite (TESS) space telescope is an appropriate tool to supplement previous space-based observations. In this paper we report the first results of the eclipse timing variation (ETV) analyses of eclipsing binaries (EBs) measured by CoRoT and TESS space telescopes. Among the 1428 EB candidates we found 4 new potential triple candidates, for which ETV was analysed and fitted by the well-known light-travel-time effect (LTTE). One of them shows significant phase shift in its folded light curve which required extra care. In this paper we also present some other systems showing significant ETV signals that could be explained by mass transfer or apsidal motion.Comment: 6 pages, 5 figures, accepted for publication in MNRAS. Table 3 is available as online supplementary materia

The clockwork is moving on - a combined analysis of TESS and Kepler measurements of Kepler-13Ab

Kepler-13Ab (KOI-13) is an exoplanet orbiting a rapidly rotating A-type star. The system shows a significant spin-orbit misalignment and a changing transit duration most probably caused by the precession of the orbit. Here, we present a self-consistent analysis of the system combining Kepler and Transiting Exoplanet Survey Satellite (TESS) observations. We model the light curves assuming a planet transits a rotating oblate star that has a strong surface temperature gradient due to rotation-induced gravity darkening. The transit chord moves slowly as an emergent feature of orbital precession excited by the oblate star with a decline rate in the impact parameter of db/dt = -0.011 yr-1, and with an actual value of b = 0.19 for the latest TESS measurements. The changing transit duration that was measured from Kepler Q2 and Q17 quarters and the TESS measurements indicates a linear drift of the impact parameter. The solutions for the stellar spin axis suggest a nearly orthogonal aspect, with inclination around 100°

Chaotic dynamics in the pulsation of DF Cygni, as observed by Kepler

Pulsations of RV Tauri-type variable stars can be governed by chaotic dynamics. However, observational evidence for this happening is usually hard to come by. Here we use the continuous, 4-yr-long observations of the Kepler space telescope to search for the signs of chaos in the RVb-type pulsating supergiant, DF Cygni. We use the Global Flow Reconstruction method to estimate the quantitative properties of the dynamics driving the pulsations of the star. The secondary, long-term light variation, i.e. the RVb phenomenon, was removed in the analysis with the empirical mode decomposition method. Our analysis revealed that the pulsation of DF Cyg could be described as a chaotic signal with a Lyapunov dimension of ∼2.8. DF Cyg is only the third RV Tau star, and the first of the RVb subtype, where the non-linear analysis indicates that low-dimensional chaos may explain the peculiarities of the pulsation