R. Smolec

An eclipsing-binary distance to the Large Magellanic Cloud accurate to two per cent.

In the era of precision cosmology, it is essential to determine the Hubble constant to an accuracy of three per cent or better. At present, its uncertainty is dominated by the uncertainty in the distance to the Large Magellanic Cloud (LMC), which, being our second-closest galaxy, serves as the best anchor point for the cosmic distance scale. Observations of eclipsing binaries offer a unique opportunity to measure stellar parameters and distances precisely and accurately. The eclipsing-binary method was previously applied to the LMC, but the accuracy of the distance results was lessened by the need to model the bright, early-type systems used in those studies. Here we report determinations of the distances to eight long-period, late-type eclipsing systems in the LMC, composed of cool, giant stars. For these systems, we can accurately measure both the linear and the angular sizes of their components and avoid the most important problems related to the hot, early-type systems. The LMC distance that we derive from these systems (49.97 ± 0.19 (statistical) ± 1.11 (systematic) kiloparsecs) is accurate to 2.2 per cent and provides a firm base for a 3-per-cent determination of the Hubble constant, with prospects for improvement to 2 per cent in the future.

Physical parameters and the projection factor of the classical Cepheid in the binary system OGLE-LMC-CEP-0227

A novel method of analysis of double-lined eclipsing binaries containing a radially pulsating star is presented. The combined pulsating-eclipsing light curve is built up from a purely eclipsing light curve grid created using an existing modeling tool. For every pulsation phase the instantaneous radius and surface brightness are taken into account, being calculated from the disentangled radial velocity curve of the pulsating star and from its out-of-eclipse pulsational light curve and the light ratio of the components, respectively. The best model is found using the Markov Chain Monte Carlo method. The method is applied to the eclipsing binary Cepheid OGLE-LMC-CEP-0227 (Ppuls = 3.80 d, Porb = 309 d). We analyze a set of new spectroscopic and photometric observations for this binary, simultaneously fitting OGLE V-band, I-band and Spitzer 3.6 µm photometry. We derive a set of fundamental parameters of the system significantly improving the precision comparing to the previous results obtained by our group. The Cepheid mass and radius are M1 = 4.165 ± 0.032M⊙ and R1 = 34.92± 0.34R⊙, respectively. For the first time a direct, geometrical and distance-independent determination of the Cepheid projection factor is presented. The value p =1.21 ± 0.03(stat.) ± 0.04(syst.) is consistent with theoretical expectations for a short period Cepheid and interferometric measurements for δ Cep. We also find a very high value of the optical limb darkening coefficients for the Cepheid component, in strong disagreement with theoretical predictions for static atmospheres at a given surface temperature and gravity.

THE ECLIPSING BINARY CEPHEID OGLE-LMC-CEP-0227 IN THE LARGE MAGELLANIC CLOUD: PULSATION MODELING OF LIGHT AND RADIAL VELOCITY CURVES

We performed a new and accurate fit of light and radial velocity curves of the Large Magellanic Cloud (LMC) Cepheid—OGLE-LMC-CEP-0227—belonging to a detached double-lined eclipsing binary system. We computed several sets of nonlinear, convective models covering a broad range in stellar mass, effective temperature, and chemical composition. The comparison between theory and observations indicates that current theoretical framework accounts for luminosity—V and I band—and radial velocity variations over the entire pulsation cycle. Predicted pulsation mass—M = 4.14 ± 0.06 M ☉—and mean effective temperature—Te = 6100 ± 50 K—do agree with observed estimates with an accuracy better than 1σ. The same outcome applies, on average, to the luminosity amplitudes and to the mean radius. We find that the best-fit solution requires a chemical composition that is more metal-poor than typical LMC Cepheids (Z = 0.004 versus 0.008) and slightly helium enhanced (Y = 0.27 versus 0.25), but the sensitivity to He abundance is quite limited. Finally, the best-fit model reddening—E(V – I) = 0.171 ± 0.015 mag—and the true distance modulus corrected for the barycenter of the LMC—μ0, LMC = 18.50 ± 0.02 ± 0.10 (syst) mag—agree quite well with similar estimates in the recent literature.

Double-mode radial–non-radial RR Lyrae stars in the OGLE photometry of the Galactic bulge

Non-radial modes are excited in classical pulsators, both in Cepheids and in RR Lyrae stars. Firm evidence come from the first overtone pulsators, in which additional shorter period mode is detected with characteristic period ratio falling in between 0.60 and 0.65. In the case of first overtone Cepheids three separate sequences populated by nearly 200 stars are formed in the Petersen diagram, i.e. the diagram of period ratio versus longer period. In the case of first overtone RR Lyrae stars (RRc stars) situation is less clear. A dozen or so such stars are known which form a clump in the Petersen diagram without any obvious structure. Interestingly, all first overtone RR Lyrae stars for which precise space-borne photometry is available show the additional mode, which suggests that its excitation is common. Motivated by these results we searched for non-radial modes in the OGLE-III photometry of RRc stars from the Galactic bulge. We report the discovery of 147 stars, members of a new group of double-mode, radial-non-radial mode pulsators. They form a clear and tight sequence in the Petersen diagram, with period ratios clustering around 0.613 with a signature of possible second sequence with higher period ratio (0.631). The scatter in period ratios of the already known stars is explained as due to population effects. Judging from the results of space observations this still mysterious form of pulsation must be common among RRc stars and with our analysis of the OGLE data we just touch the tip of the iceberg.

Pulsation models for the 0.26M_sun star mimicking RR Lyrae pulsator. Model survey for the new class of variable stars

We present non-linear hydrodynamic pulsation models for OGLE-BLG-RRLYR-02792 - a 0.26M_sun pulsator, component of the eclipsing binary system, analysed recently by Pietrzynski et al. The stars light and radial velocity curves mimic that of classical RR Lyrae stars, except for the bump in the middle of the ascending branch of the radial velocity curve. We show that the bump is caused by the 2:1 resonance between the fundamental mode and the second overtone - the same mechanism that causes the Hertzsprung bump progression in classical Cepheids. The models allow to constrain the parameters of the star, in particular to estimate its absolute luminosity (approx 33L_sun) and effective temperature (approx 6970K, close to the blue edge of the instability strip). We conduct a model survey for the new class of low mass pulsators similar to OGLE-BLG-RRLYR-02792 - products of evolution in the binary systems. We compute a grid of models with masses corresponding to half (and less) of the typical mass of RR Lyrae variable, 0.20M_sun<=M<=0.30M_sun, and discuss the properties of the resulting light and radial velocity curves. Resonant bump progression is clear and may be used to distinguish such stars from classical RR Lyrae stars. We present the Fourier decomposition parameters for the modelled light and radial velocity curves. The expected values of the phi_31 Fourier phase for the light curves differ significantly from that observed in RR Lyrae stars, which is another discriminant of the new class.

Blazhko-type modulation in the double-mode RR Lyrae stars of the OGLE Galactic bulge collection

We present the analysis of Blazhko-type modulation in double-mode RR Lyrae (RRd) stars found in the OGLE photometry of the Galactic bulge. Modulation is detected in 15 stars. Most of them have non-typical period ratio of the radial modes. In the Petersen diagram, at a given period of the fundamental mode, they are located significantly below or above the sequence formed by the majority of RRd stars. In the analysed sample we detect a variety of dynamic behaviours. Multi-periodic modulation is very frequent; two or three modulation periods are detected in 8 stars. Modulation periods vary from �20 to more than 300days. Radial mode amplitudes can be modulated by a few to nearly hundred per cent. Both radial modes may be modulated with the same period. More commonly however, dominant modulation for the fundamental mode has different period than dominant modulation for the first overtone. Quite often modulation of only one mode is detected in the data. In a few cases data are dense enough to follow time variation of radial mode amplitudes and phases. We find a clear feedback between pulsation amplitude of the dominant mode and mean stellar brightness: lower the pulsation amplitude, brighter the star. At phases of low pulsation amplitude, the mode periods are prone to fast changes. All the stars share the common feature: their pulsation properties are non-stationary. Amplitudes and phases of the radial modes vary irregularly on a long time-scale of a few hundred or thousand days. The short-term modulations are also irregular. One of the stars has switched the pulsation mode recently: from single-mode fundamental mode pulsation to RRd state. Interestingly, this dramatic change did not affect the modulation of the fundamental mode strongly. In other star the non-radial mode with characteristic � 0.61 period ratio to the first overtone is detected. This non-radial mode is likely modulated with the same period as the radial modes.

The Araucaria project: A study of the classical cepheid in the eclipsing binary system OGLE LMC562.05.9009 in the large magellanic cloud

We present a detailed study of the classical Cepheid in the double-lined, highly eccentric eclipsing binary system OGLE-LMC562.05.9009. The Cepheid is a fundamental mode pulsator with a period of 2.988 days. The orbital period of the system is 1550 days. Using spectroscopic data from three 4–8-m telescopes and photometry spanning 22 years, we were able to derive the dynamical masses and radii of both stars with exquisite accuracy. Both stars in the system are very similar in mass, radius, and color, but the companion is a stable, non-pulsating star. The Cepheid is slightly more massive and bigger (M1=3.70±0.03 Me, R1=28.6±0.2 Re) than its companion (M2=3.60±0.03 Me, R2=26.6±0.2 Re). Within the observational uncertainties both stars have the same effective temperature of 6030±150 K. Evolutionary tracks place both stars inside the classical Cepheid instability strip, but it is likely that future improved temperature estimates will move the stable giant companion just beyond the red edge of the instability strip. Within current observational and theoretical uncertainties, both stars fi to n a 205 Myr isochrone arguing for their common age. From our model, we determine a value of the projection factor of p=1.37±0.07 for the Cepheid in the OGLE-LMC562.05.9009 system. This is the second Cepheid for which we could measure its p-factor with high precision directly from the analysis of an eclipsing binary system, which represents an important contribution toward a better calibration of Baade-Wesselink methods of distance determination for Cepheids.

An RR Lyrae family portrait: 33 stars observed in Pisces with K2-E2

A detailed analysis is presented of 33 RR Lyrae stars in Pisces observed with the Kepler space telescope over the 8.9-day long K2 Two-Wheel Concept Engineering Test. The sample includes not only fundamental-mode and first overtone (RRab and RRc) stars but the first two double-mode (RRd) stars that Kepler detected and the only modulated first-overtone star ever observed from space so far. The precision of the extracted K2 light curves made it possible to detect low-amplitude additional modes in all subtypes. All RRd and non-modulated RRc stars show the additional mode at PX/P1 � 0.61 that was detected in previous space-based photometric measurements. A periodicity longer than the fundamental mode was tentatively identified in one RRab star that might belong to a gravity mode. We determined the photometric [Fe/H] values for all fundamental-mode stars and provide the preliminary results of our efforts to fit the double-mode stars with non-linear hydrodynamic pulsation models. The results from this short test run indicate that the K2 mission will be, and has started to be, an ideal tool to expand our knowledge about RR Lyrae stars. As a by-product of the target search and analysis, we identified 165 bona-fide double-mode RR Lyrae stars from the Catalina Sky Survey observations throughout the sky, 130 of which are new discoveries.

Amplitude saturation in β Cephei models

Although the driving mechanism acting in β Cephei pulsators is well known, problems concerning the identification of the amplitude limitation mechanism and the non-uniform filling of the theoretical instability strip remain to be solved. In the present analysis, these problems are addressed by non-linear modelling of radial pulsations of these stars. In this approach radial modes are treated as representative of all acoustic oscillations. Several models of different masses and metallicities were converged to limit cycles through the Stellingwerf relaxation technique. The resulting peak-to-peak amplitudes are of the order of � V = 0.3 mag. Such amplitudes are significantly larger than those observed in β Cephei pulsators. Assuming that all acoustic modes are similar, we show that collective saturation of the driving mechanism by several acoustic modes can easily lower predicted saturation amplitudes to the observed level. Our calculations predict a significant decrease in saturation amplitudes as we go to high-mass/high-luminosity models. However, this effect is not strong enough to explain the scarcity of high-mass β Cephei variables. A possible weakness of the collective saturation scenario is that the estimated line-broadening, resulting from excitation of many high-l modes, might be higher than that observed in some of the β Cephei stars. We argue that this difficulty can be overcome by allowing g-modes to participate in the saturation process. We also discuss robust double-mode (DM) behaviour, encountered in our radiative models. On a single evolutionary track we identify two DM domains with two different mechanisms responsible for DM behaviour. The non-resonant DM domain separates the first overtone and fundamental-mode pulsation domains. The resonant DM domain appears in the middle of the first overtone pulsation domain. Its origin can be traced to the 2ω1 = ω0 + ω2 parametric resonance, which destabilizes the first overtone limit cycle.

Survey of non-linear hydrodynamic models of type-II Cepheids

We present a grid on non-linear convective type-II Cepheid models. The dense model grids are computed for 0.6M_Sun and a range of metallicities ([Fe/H]=-2.0,-1.5,-1.0), and for 0.8M_Sun ([Fe/H]=-1.5). Two sets of convective parameters are considered. The models cover the full temperature extent of the classical instability strip, but are limited in luminosity; for the most luminous models violent pulsation leads to the decoupling of the outermost model shell. Hence, our survey reaches only the shortest period RV Tau domain. In the Hertzsprung-Russel diagram we detect two domains in which period doubled pulsation is possible. The first extends through the BL Her domain and low luminosity W Vir domain (pulsation periods ~2-6.5 d). The second domain extends at higher luminosities (W Vir domain; periods >9.5d). Some models within these domains display period-4 pulsation. We also detect very narrow domains (~10 K wide) in which modulation of pulsation is possible. Another interesting phenomenon we detect is double-mode pulsation in the fundamental mode and in the fourth radial overtone. Fourth overtone is a surface mode, trapped in the outer model layers. Single-mode pulsation in the fourth overtone is also possible on the hot side of the classical instability strip. The origin of the above phenomena is discussed. In particular, the role of resonances in driving different pulsation dynamics as well as in shaping the morphology of the radius variation curves is analysed.