arXiv subjects

D. Graczyk

Publications and source records attributed to D. Graczyk.

At least 37 records · Page 2Linked to original sources

arXiv2020

Calibrating the surface brightness - color relation for late-type red giants stars in the visible domain using VEGA/CHARA interferometric observations

The surface brightness - color relationship (SBCR) is a poweful tool for determining the angular diameter of stars from photometry. It was for instance used to derive the distance of eclipsing binaries in the Large Magellanic Cloud (LMC), which led to its distance determination with an accuracy of 1%. We calibrate the SBCR for red giant stars in the 2.1 < V-K < 2.5 color range using homogeneous VEGA/CHARA interferometric data secured in the visible domain, and compare it to the relation based on infrared interferometric observations, which were used to derive the distance to the LMC. Observations of eight G-K giants were obtained with the VEGA/CHARA instrument. The derived limb-darkened angular diameters were combined with a homogeneous set of infrared magnitudes in order to constrain the SBCR. The average precision we obtain on the limb-darkened angular diameters of the eight stars in our sample is 2.4%. For the four stars in common observed by both VEGA/CHARA and PIONIER/VLTI, we find a 1 sigma agreement for the angular diameters. The SBCR we obtain in the visible has a dispersion of 0.04 magnitude and is consistent with the one derived in the infrared (0.018 magnitude). The consistency of the infrared and visible angular diameters and SBCR reinforces the result of 1% precision and accuracy recently achieved on the distance of the LMC using the eclipsing-binary technique. It also indicates that it is possible to combine interferometric observations at different wavelengths when the SBCR is calibrated.

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arXiv2020

The TESS light curve of AI Phoenicis

Accurate masses and radii for normal stars derived from observations of detached eclipsing binary stars are of fundamental importance for testing stellar models and may be useful for calibrating free parameters in these model if the masses and radii are sufficiently precise and accurate. We aim to measure precise masses and radii for the stars in the bright eclipsing binary AI Phe, and to quantify the level of systematic error in these estimates. We use several different methods to model the TESS light curve of AI Phe combined with spectroscopic orbits from multiple sources to estimate precisely the stellar masses and radii together with robust error estimates. We find that the agreement between different methods for the light curve analysis is very good but some methods underestimate the errors on the model parameters. The semi-amplitudes of the spectroscopic orbits derived from spectra obtained with modern echelle spectrographs are consistent to within 0.1%. The masses of the stars in AI Phe are $M_1 = 1.1938 \pm 0.0008 M_{\odot}$ and $M_2 = 1.2438 \pm 0.0008M_{\odot}$, and the radii are $R_1 = 1.8050 \pm 0.0022 R_{\odot}$ and $R_2 = 2.9332 \pm 0.0023 R_{\odot}$. We conclude that it is possible to measure accurate masses and radii for stars in bright eclipsing binary stars to a precision of 0.2% or better using photometry from TESS and spectroscopy obtained with modern echelle spectrographs. We provide recommendations for publishing masses and radii of eclipsing binary stars at this level of precision.

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arXiv2019

Candidates for non-pulsating stars located in the Cepheid instability strip in the Large Magellanic Cloud based on Strömgren photometry

We present candidates for non-pulsating stars lying in the classical Cepheid instability strip based on OGLE photometric maps combined with Strömgren photometry obtained with the 4.1-m SOAR telescope, and Gaia DR2 data in four fields in the Large Magellanic Cloud. We selected 19 candidates in total. After analysis of their light curves from OGLE surveys we found that all these stars appear to be photometrically stable at the level of a few mmag. Our results show that non-pulsating stars might constitute to about 21%-30% of the whole sample of giant stars located in the classical instability strip. Furthermore, we identified potential candidates for classical Cepheids with hot companions based on their Strömgren colours.

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arXiv2019

Towards early-type eclipsing binaries as extragalactic milestones: I. Physical parameters of OGLE-LMC-ECL-22270 and OGLE-LMC-ECL-06782

In this first paper of the series we describe our project to calibrate the distance determination method based on early-type binary systems. The final objective is to measure accurate, geometrical distances to galaxies beyond the Magellanic Clouds with a precision of 2%. We start with the analysis of two early-type systems for which we have collected all the required spectroscopic and photometric data. Apart from catalog publications, these systems have not been studied yet, and it is the first time the modeling of light and radial velocity curves is performed for them. From the analysis we obtained precise physical parameters of the components, including the masses measured with precision of 0.6-1% and radii with precision of 0.4-3%. For one system we determined the $(V-K)$ color and estimated the distance using the bolometric flux scaling method (DM=18.47 $\pm$ 0.15 mag), which agrees well with our accurate determination of the distance to the LMC from late-type giants. For the same system we determined the surface brightness of individual stars using our model, and checked that it is consistent with a recent surface brightness -- color relation. We compared our results with evolution theory models of massive stars and found they agree in general, however, models with higher overshooting values give more consistent results. The age of the system was estimated to from 11.7 to 13.8 Myr, depending on the model.

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arXiv2019

The Araucaria Project: High-precision orbital parallax and masses of eclipsing binaries from infrared interferometry

Context. The precise determinations of stellar mass at $\sim$1% provide important constraints on stellar evolution models. Accurate parallax measurements can also serve as independent benchmarks for the next Gaia data release. Aims. We aim at measuring the masses and distance of binary systems with a precision level better than 1% using a fully geometrical and empirical method. Methods. We obtained the first interferometric observations for the eclipsing systems AI Phe, AL Dor, KW Hya, NN Del, $ψ$ Cen and V4090 Sgr with the VLTI/PIONIER combiner, which we combined with radial velocity measurements to derive their three-dimensional orbit, masses, and distance. Results. We determined very precise stellar masses for all systems, ranging from 0.04% to 3.3 % precision level. We combined these measurements with stellar effective temperature and linear radius to fit stellar isochrones models and determined the age of the systems. We also derived the distance to the systems with a precision level as high as 0.4%. Conclusions. The comparison of theoretical models with stellar parameters shows that stellar models are still deficient in simultaneously fitting the stellar parameters (Teff , R and M) with such level of precision on individual masses. This stresses the importance of precisely measuring the stellar parameters to better calibrate stellar evolution models. The precision of our model-independent orbital parallaxes varies from 24$μ$as as to 70$μ$as and they provide a unique opportunity to check on the future Gaia measurements for possible systematic errors.

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arXiv2019

Accurate stellar parameters and distance to two evolved eclipsing binary systems, OGLE-BLG-ECL-123903 and OGLE-BLG-ECL-296596, towards the Galactic bulge

Aim: Our aim is to obtain high-accuracy measurements of the physical and orbital parameters of two evolved eclipsing binary systems, and to use these measurements to study their evolutionary status. We also aim to derive distances to the systems by using a surface brightness - colour relation and compare these distances with the measurements provided by GAIA. Methods: We measured the physical and orbital parameters on both systems based on V-band and I-band photometry from OGLE, near-infrared photometry obtained with the NTT telescope and the instrument SOFI, as well as high-resolution spectra obtained at ESO 3.6m/HARPS and Clay 6.5/MIKE spectrographs. The light curves and radial-velocity curves were analysed with the Wilson-Devinney code. Results: We analysed two double-lined eclipsing binary systems OGLE-BLG-ECL-23903 and OGLE-BLG-ECL-296596 from the Optical Gravitational Lensing Experiment (OGLE) catalogue. Both systems have a configuration of two well-detached giant stars. The masses of the components ofOGLE-BLG-ECL-123903 are M_1= 2.045 $\pm$ 0.027 and M_2=2.074 $\pm$ 0.023 $M_\odot$ and the radii are R_1=9.540 $\pm$ 0.049 and R_2=9.052 $\pm$ 0.060 $R_\odot$. For OGLE-BLG-ECL-296596, the masses are M_1=1.093 $\pm$ 0.015 and M_2=1.125 $\pm$ 0.014 $M_\odot$, while the radii are R_1=18.06 $\pm$ 0.28 and R_2=29.80 $\pm$ 0.33 $R_\odot$. Evolutionary status was discussed based on the isochrones and evolutionary tracks from PARSEC and MESA codes. The ages of the systems were establishes to be around 1.3 Gyr for the OGLE-BLG-ECL-123903 and 7.7 Gyr for the OGLE-BLG-ECL-296596. We also determined the distance to both systems. For OGLE-BLG-ECL-123903 this is equal to d=2.95 $\pm$ 0.06 (stat.) $\pm$ 0.07 (syst.) kpc, while for the OGLE-BLG-ECL-296596 it is d=5.68 $\pm$ 0.07 (stat.) $\pm$ 0.14 (syst.) kpc. This is the first analysis of its kind for these unique evolved eclipsing binary systems.

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arXiv2019

A distance to the Large Magellanic Cloud that is precise to one per cent

In the era of precision cosmology, it is essential to empirically determine the Hubble constant with an accuracy of one per cent or better. At present, the uncertainty on this constant is dominated by the uncertainty in the calibration of the Cepheid period - luminosity relationship (also known as Leavitt Law). The Large Magellanic Cloud has traditionally served as the best galaxy with which to calibrate Cepheid period-luminosity relations, and as a result has become the best anchor point for the cosmic distance scale. Eclipsing binary systems composed of late-type stars offer the most precise and accurate way to measure the distance to the Large Magellanic Cloud. Currently the limit of the precision attainable with this technique is about two per cent, and is set by the precision of the existing calibrations of the surface brightness - colour relation. Here we report the calibration of the surface brightness-colour relation with a precision of 0.8 per cent. We use this calibration to determine the geometrical distance to the Large Magellanic Cloud that is precise to 1 per cent based on 20 eclipsing binary systems. The final distane is 49.59 +/- 0.09 (statistical) +/- 0.54 (systematic) kiloparsecs.

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arXiv2018

Metallicity estimates of young clusters in the Magellanic Clouds from Stromgren photometry of supergiant stars

We present results obtained from Stromgren photometry of 13 young (~30-220 Myr) Magellanic Cloud (MC) clusters, most of them lacking in the literature from direct metallicity measurements. We derived for them [Fe/H] values from a high-dispersion spectroscopy-based empirical calibration of the Stromgren metallicity sensitive index m1 for yellow and red supergiants (SGs). Particular care was given while estimating their respective uncertainties. In order to obtain the mean cluster metallicities, we used [Fe/H] values of selected SGs for which we required to be located within the cluster radii, placed in the expected SG region in the cluster colour-magnitude diagrams, and with [Fe/H] values within the FWHM of the observed cluster metallicity distributions. The resulting metallicities for nearly 75 per cent of the cluster sample agree well with the most frequently used values of the mean MCs' present-day metallicities. The remaining clusters have mean [Fe/H] values that fall near the edge of the MC present-day metallicity distributions. When comparing the cluster metallicities with their present positions, we found evidence that supports the claimed recent interaction of the MCs with the Milky Way, that could have caused that some clusters were scattered from their birthplaces. Indeed, we show examples of clusters with metal contents typical of the galaxy inner regions placed outward them. Likewise, we found young clusters, at present located in the inner regions of both MCs, formed out of gas that has remained unmixed since several Gyr ago.

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arXiv2018

A geometrical 1% distance to the short-period binary Cepheid V1334 Cygni

Cepheid stars play a considerable role as extragalactic distances indicators, thanks to the simple empirical relation between their pulsation period and their luminosity. They overlap with that of secondary distance indicators, such as Type Ia supernovae, whose distance scale is tied to Cepheid luminosities. However, the Period-Luminosity (P-L) relation still lacks a calibration to better than 5%. Using an original combination of interferometric astrometry with optical and ultraviolet spectroscopy, we measured the geometrical distance d = 720.35+/-7.84 pc of the 3.33 d period Cepheid V1334 Cyg with an unprecedented accuracy of +/-1 %, providing the most accurate distance for a Cepheid. Placing this star in the P-L diagram provides an independent test of existing period-luminosity relations. We show that the secondary star has a significant impact on the integrated magnitude, particularly at visible wavelengths. Binarity in future high precision calibrations of the P-L relations is not negligible, at least in the short-period regime. Subtracting the companion flux leaves V1334 Cyg in marginal agreement with existing photometric-based P-L relations, indicating either an overall calibration bias or a significant intrinsic dispersion at a few percent level. Our work also enabled us to determine the dynamical masses of both components, M1 = 4.288 +/- 0.133 Msun (Cepheid) and M2 = 4.040 +/- 0.048 Msun (companion), providing the most accurate masses for a Galactic binary Cepheid system.

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arXiv2018

The effect of metallicity on Cepheid Period-Luminosity relations from a Baade-Wesselink analysis of Cepheids in the Milky Way and Magellanic Clouds

The extragalactic distance scale builds on the Cepheid period-luminosity (PL) relation. In this paper, we want to carry out a strictly differential comparison of the absolute PL relations obeyed by classical Cepheids in the Milky Way (MW), LMC and SMC galaxies. Taking advantage of the substantial metallicity difference among the Cepheid populations in these three galaxies, we want to establish a possible systematic trend of the PL relation absolute zero point as a function of metallicity, and determine the size of such an effect in optical and near-infrared photometric bands. We are using the IRSB Baade-Wesselink type method as calibrated by Storm et al. to determine individual distances to the Cepheids in our samples in MW, LMC and SMC. For our analysis, we use a greatly enhanced sample of Cepheids in the SMC (31 stars) as compared to the small sample (5 stars) available in our previous work. We use the distances to determine absolute Cepheid PL relations in optical and near-infrared bands in each of the three galaxies.} {Our distance analysis of 31 SMC Cepheids with periods from 4-69 days yields tight PL relations in all studied bands, with slopes consistent with the corresponding LMC and MW relations. Adopting the very accurately determined LMC slopes for the optical and near-infrared bands, we determine the zero point offsets between the corresponding absolute PL relations in the 3 galaxies. We find that in all bands the metal-poor SMC Cepheids are intrinsically fainter than their more metal-rich counterparts in the LMC and MW. In the $K$ band the metallicity effect is $-0.23\pm0.06$~mag/dex while in the $V,(V-I)$ Wesenheit index it is slightly stronger, $-0.34\pm0.06$~mag/dex. We find some evidence that the PL relation zero point-metallicity relation might be nonlinear, becoming steeper for lower metallicities.

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arXiv2018

CRIRES high-resolution infrared spectroscopy of the long-period Cepheid l Car

The dynamical structure of the atmosphere of Cepheids has been well studied in the optical. Several authors have found very interesting spectral features in the J band, but little data have been secured beyond 1.6 um. However, such observations can probe different radial velocities and line asymmetry regimes, and are able to provide crucial insights into stellar physics. Our goal was to investigate the infrared line-forming region in the K-band domain, and its impact on the projection factor and the k-term of Cepheids. We secured CRIRES observations for the long-period Cepheid l Car, with a focus on the unblended spectral line NaI2208.969 nm. We measured the corresponding radial velocities (by using the first moment method) and the line asymmetries (by using the bi-Gaussian method). These quantities are compared to the HARPS visible spectra we previously obtained on l Car. The optical and infrared radial velocity curves show the same amplitude (only about 3% of difference), with a slight radial velocity shift of about 0.5 +/- 0.3 km s^-1 between the two curves. Around the minimum radius (phase ~ 0.9) the visible radial velocity curve is found in advance compared to the infrared one (phase lag), which is consistent with an infrared line forming higher in the atmosphere (compared to the visible line) and with a compression wave moving from the bottom to the top of the atmosphere during maximum outward velocity. The asymmetry of the K-band line is also found to be significantly different from that of the optical line.

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arXiv2018

Fundamental properties of red-clump stars from long-baseline H-band interferometry

Observations of 48 red-clump stars were obtained in the H band with the PIONIER instrument installed at the Very Large Telescope Interferometer. Limb-darkened angular diameters were measured by fitting radial intensity profile I(r) to square visibility measurements. Half the angular diameters determined have formal errors better than 1.2%, while the overall accuracy is better than 2.7%. Average stellar atmospheric parameters (effective temperatures, metallicities and surface gravities) were determined from new spectroscopic observations and literature data and combined with precise Gaia parallaxes to derive a set of fundamental stellar properties. These intrinsic parameters were then fitted to existing isochrone models to infer masses and ages of the stars. The added value from interferometry imposes a better and independent constraint on the R-Teff plane. Our derived values are consistent with previous works, although there is a strong scatter in age between various models. This shows that atmospheric parameters, mainly metallicities and surface gravities, still suffer from a non-accurate determination, limiting constraints on input physics and parameters of stellar evolution models.

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arXiv2017

HARPS-N high spectral resolution observations of Cepheids I. The Baade-Wesselink projection factor of δ Cep revisited

The projection factor p is the key quantity used in the Baade-Wesselink (BW) method for distance determination; it converts radial velocities into pulsation velocities. Several methods are used to determine p, such as geometrical and hydrodynamical models or the inverse BW approach when the distance is known. We analyze new HARPS-N spectra of delta Cep to measure its cycle-averaged atmospheric velocity gradient in order to better constrain the projection factor. We first apply the inverse BW method to derive p directly from observations. The projection factor can be divided into three subconcepts: (1) a geometrical effect (p0); (2) the velocity gradient within the atmosphere (fgrad); and (3) the relative motion of the optical pulsating photosphere with respect to the corresponding mass elements (fo-g). We then measure the fgrad value of delta Cep for the first time. When the HARPS-N mean cross-correlated line-profiles are fitted with a Gaussian profile, the projection factor is pcc-g = 1.239 +/- 0.034(stat) +/- 0.023(syst). When we consider the different amplitudes of the radial velocity curves that are associated with 17 selected spectral lines, we measure projection factors ranging from 1.273 to 1.329. We find a relation between fgrad and the line depth measured when the Cepheid is at minimum radius. This relation is consistent with that obtained from our best hydrodynamical model of delta Cep and with our projection factor decomposition. Using the observational values of p and fgrad found for the 17 spectral lines, we derive a semi-theoretical value of fo-g. We alternatively obtain fo-g = 0.975+/-0.002 or 1.006+/-0.002 assuming models using radiative transfer in plane-parallel or spherically symmetric geometries, respectively. The new HARPS-N observations of delta Cep are consistent with our decomposition of the projection factor.

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arXiv2016

VEGA/CHARA interferometric observations of Cepheids. I. A resolved structure around the prototype classical Cepheid delta Cep in the visible spectral range

The B-W method is used to determine the distance of Cepheids and consists in combining the angular size variations of the star, as derived from infrared surface-brightness relations or interferometry, with its linear size variation, as deduced from visible spectroscopy using the projection factor. While many Cepheids have been intensively observed by infrared beam combiners, only a few have been observed in the visible. This paper is part of a project to observe Cepheids in the visible with interferometry as a counterpart to infrared observations already in hand. Observations of delta Cep itself were secured with the VEGA/CHARA instrument over the full pulsation cycle of the star. These visible interferometric data are consistent in first approximation with a quasi-hydrostatic model of pulsation surrounded by a static circumstellar environment (CSE) with a size of theta_cse=8.9 +/- 3.0 mas and a relative flux contribution of f_cse=0.07+/-0.01. A model of visible nebula (a background source filling the field of view of the interferometer) with the same relative flux contribution is also consistent with our data at small spatial frequencies. However, in both cases, we find discrepancies in the squared visibilities at high spatial frequencies (maximum 2sigma) with two different regimes over the pulsation cycle of the star, phi=0.0-0.8 and phi=0.8-1.0. We provide several hypotheses to explain these discrepancies, but more observations and theoretical investigations are necessary before a firm conclusion can be drawn. For the first time we have been able to detect in the visible domain a resolved structure around delta~Cep. We have also shown that a simple model cannot explain the observations, and more work will be necessary in the future, both on observations and modelling.

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arXiv2016

A solar twin in the eclipsing binary LL Aqr

In the course of a project to study eclipsing binary stars in vinicity of the Sun, we found that the cooler component of LL Aqr is a solar twin candidate. This is the first known star with properties of a solar twin existing in a non-interacting eclipsing binary, offering an excellent opportunity to fully characterise its physical properties with very high precision. We used extensive multi-band, archival photometry and the Super-WASP project and high-resolution spectroscopy obtained from the HARPS and CORALIE spectrographs. The spectra of both components were decomposed and a detailed LTE abundance analysis was performed. The light and radial velocity curves were simultanously analysed with the Wilson-Devinney code. The resulting highly precise stellar parameters were used for a detailed comparison with PARSEC, MESA, and GARSTEC stellar evolution models. LL Aqr consists of two main-sequence stars (F9 V + G3 V) with masses of M1 = 1.1949$\pm$0.0007 and M2=1.0337$\pm$0.0007 $M_\odot$, radii R1 = 1.321$\pm$0.006 and R2 = 1.002$\pm$0.005 $R_\odot$, temperatures T1=6080$\pm$45 K and T2=5703$\pm$50 K and solar chemical composition [M/H]=0.02$\pm$0.05 dex. The absolute dimensions, radiative and photometric properties, and atmospheric abundances of the secondary are all fully consistent with being a solar twin. Both stars are cooler by about 3.5 $σ$ or less metal abundant by 5$σ$ than predicted by standard sets of stellar evolution models. When advanced modelling was performed, we found that full agreement with observations can only be obtained for values of the mixing length and envelope overshooting parameters that are hard to accept. The most reasonable and physically justified model fits found with MESA and GARSTEC codes still have discrepancies with observations but only at the level of 1$σ$.

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arXiv2016

Orbital and physical parameters, and the distance of the eclipsing binary system OGLE-LMC-ECL-25658 in the Large Magellanic Cloud

We present an analysis of a new detached eclipsing binary, OGLE-LMC-ECL-25658, in the Large Magellanic Cloud. The system consists of two late G-type giant stars on an eccentric orbit and orbital period of ~200 days. The system shows total eclipses and the components have similar temperatures, making it ideal for a precise distance determination. Using multi-color photometric and high resolution spectroscopic data, we have performed an analysis of light and radial velocity curves simultaneously using the Wilson Devinney code. We derived orbital and physical parameters of the binary with a high precision of < 1 %. The masses and surface metallicities of the components are virtually the same and equal to 2.23 +/- 0.02 M_sun and [Fe/H] = -0.63 +/- 0.10 dex. However their radii and rates of rotation show a distinct trace of differential stellar evolution. The distance to the system was calculated using an infrared calibration between V-band surface brightness and (V-K) color, leading to a distance modulus of (m-M) = 18.452 +/- 0.023 (statistical) +/- 0.046 (systematic). Because OGLE-LMC-ECL-25658 is located relatively far from the LMC barycenter we applied a geometrical correction for its position in the LMC disc using the van der Marel et al. model of the LMC. The resulting barycenter distance to the galaxy is d_LMC = 50.30 +/- 0.53 (stat.) kpc, and is in perfect agreement with the earlier result of Pietrzynski et al.(2013).

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arXiv2016

On the eclipsing binary ELHC 10 with occulting dark disc in the Large Magellanic Cloud

We investigate the luminous star ELHC 10 located in the bar of the Large Magellanic Cloud, concluding that it is a SB1 long-period eclipsing binary where the main eclipse is produced by an opaque structure hiding the secondary star. For the more luminous component we determine an effective temperature of 6500 $\pm$ 250 $K$, log\,g = 1.0 $\pm$ 0.5 and luminosity 5970 L$_{\sun}$. From the radial velocities of their photospheric lines we calculate a mass function of 7.37 $\pm$ 0.55 M$_{\sun}$. Besides Balmer and forbidden N II emission, we find splitting of metallic lines, characterized by strong discrete absorption components (DACs), alternatively seen at the blue and red side of the photospheric spectrum. These observations hardly can be interpreted in terms of an structured atmosphere but might reflect mass streams in an interacting binary. The primary shows signatures of s-process nucleosynthesis and might be a low-mass post-AGB star with a rare evolutionary past if the binary is semi-detached. The peak separation and constancy of radial velocity in H$α$ suggest that most of the Balmer emission comes from a circumbinary disc.

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arXiv2015

The Araucaria Project: High-precision orbital parallax and masses of the eclipsing binary TZ~Fornacis

Context: Independent distance estimates are particularly useful to check the precision of other distance indicators, while accurate and precise masses are necessary to constrain evolution models. Aim: The goal is to measure the masses and distance of the detached eclipsing-binary TZ~For with a precision level lower than 1\,\% using a fully geometrical and empirical method. Method: We obtained the first interferometric observations of TZ~For with the VLTI/PIONIER combiner, which we combined with new and precise radial velocity measurements to derive its three-dimensional orbit, masses, and distance. Results: The system is well resolved by PIONIER at each observing epoch, which allowed a combined fit with eleven astrometric positions. Our derived values are in a good agreement with previous work, but with an improved precision. We measured the mass of both components to be $M_1 = 2.057 \pm 0.001\,M_\odot$ and $M_2 = 1.958 \pm 0.001\,M_\odot$. The comparison with stellar evolution models gives an age of the system of $1.20 \pm 0.10$\,Gyr. We also derived the distance to the system with a precision level of 1.1\,\%: $d = 185.9 \pm 1.9$\,pc. Such precise and accurate geometrical distances to eclipsing binaries provide a unique opportunity to test the absolute calibration of the surface brightness-colour relation for late-type stars, and will also provide the best opportunity to check on the future Gaia measurements for possible systematic errors.

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