Searching for visual companions of close Cepheids. VLT/NACO lucky imaging of Y~Oph, FF~Aql, X~Sgr, W~Sgr and η\eta~Aql

Aims: High-resolution imaging in several photometric bands can provide color and astrometric information of the wide-orbit component of Cepheid stars. Such measurements are needed to understand the age and evolution of pulsating stars. In addition, binary Cepheids have the potential to provide direct and model-independent distances and masses. Methods: We used the NAOS-CONICA adaptive optics instrument (NACO) in the near-infrared to perform a deep search for wide components around the classical Cepheids, Y~Oph, FF~Aql, X~Sgr, W~Sgr, and $\eta$~Aql, within a field of view (FoV) of $1.7"\times 1.7"$ ($3.4"\times 3.4"$ for $\eta$~Aql). Results: We were able to reach contrast $\Delta H = 5$-8\,mag and $\Delta K_\mathrm{s} = 4$-7\,mag in the radius range $r > 0.2"$, which enabled us to constrain the presence of wide companions. For Y~Oph, FF~Aql, X~Sgr, W~Sgr, and $\eta$~Aql at $r > 0.2"$, we ruled out the presence of companions with a spectral type that is earlier than a B7V, A9V, A9V, A1V, and G5V star, respectively. For $0.1"< r < 0.2"$, no companions earlier than O9V, B3V, B4V, B2V, and B2V star, respectively, are detected. A component is detected close to $\eta$~Aql at projected separation $\rho = 654.7 \pm 0.9$\,mas and a position angle $PA = 92.8 \pm 0.1^\circ$. We estimated its dereddened apparent magnitude to be $m_H^0 = 9.34 \pm 0.04$ and derived a spectral type that ranges between an F1V and F6V star. Additional photometric and astrometric measurements are necessary to better constrain this star and check its physical association to the $\eta$~Aql system.Comment: Accepted for publication in Astronomy and Astrophysic

Investigating Cepheid ℓ\ell Carinae's Cycle-to-cycle Variations via Contemporaneous Velocimetry and Interferometry

Baade-Wesselink-type (BW) techniques enable geometric distance measurements of Cepheid variable stars in the Galaxy and the Magellanic clouds. The leading uncertainties involved concern projection factors required to translate observed radial velocities (RVs) to pulsational velocities and recently discovered modulated variability. We carried out an unprecedented observational campaign involving long-baseline interferometry (VLTI/PIONIER) and spectroscopy (Euler/Coralie) to search for modulated variability in the long-period (P $\sim$ 35.5 d) Cepheid Carinae. We determine highly precise angular diameters from squared visibilities and investigate possible differences between two consecutive maximal diameters, $\Delta_{\rm{max}} \Theta$. We characterize the modulated variability along the line-of-sight using 360 high-precision RVs. Here we report tentative evidence for modulated angular variability and confirm cycle-to-cycle differences of $\ell$ Carinae's RV variability. Two successive maxima yield $\Delta_{\rm{max}} \Theta$ = 13.1 $\pm$ 0.7 (stat.) {\mu}as for uniform disk models and 22.5 $\pm$ 1.4 (stat.) {\mu}as (4% of the total angular variation) for limb-darkened models. By comparing new RVs with 2014 RVs we show modulation to vary in strength. Barring confirmation, our results suggest the optical continuum (traced by interferometry) to be differently affected by modulation than gas motions (traced by spectroscopy). This implies a previously unknown time-dependence of projection factors, which can vary by 5% between consecutive cycles of expansion and contraction. Additional interferometric data are required to confirm modulated angular diameter variations. By understanding the origin of modulated variability and monitoring its long-term behavior, we aim to improve the accuracy of BW distances and further the understanding of stellar pulsations.Comment: Accepted for publication in MNRAS. 19 pages, 13 figures, 10 table

Cepheid limb darkening, angular diameter corrections, and projection factor from static spherical model stellar atmospheres

Context. One challenge for measuring the Hubble constant using Classical Cepheids is the calibration of the Leavitt Law or period-luminosity relationship. The Baade-Wesselink method for distance determination to Cepheids relies on the ratio of the measured radial velocity and pulsation velocity, the so-called projection factor and the ability to measure the stellar angular diameters. Aims. We use spherically-symmetric model stellar atmospheres to explore the dependence of the p-factor and angular diameter corrections as a function of pulsation period. Methods. Intensity profiles are computed from a grid of plane-parallel and spherically-symmetric model stellar atmospheres using the SAtlas code. Projection factors and angular diameter corrections are determined from these intensity profiles and compared to previous results. Results. Our predicted geometric period-projection factor relation including previously published state-of-the-art hydrodynamical predictions is not with recent observational constraints. We suggest a number of potential resolutions to this discrepancy. The model atmosphere geometry also affects predictions for angular diameter corrections used to interpret interferometric observations, suggesting corrections used in the past underestimated Cepheid angular diameters by 3 - 5%. Conclusions. While spherically-symmetric hydrostatic model atmospheres cannot resolve differences between projection factors from theory and observations, they do help constrain underlying physics that must be included, including chromospheres and mass loss. The models also predict more physically-based limb-darkening corrections for interferometric observations.Comment: 8 pages, 6 figures, 2 tables, accepted for publication in A&

The long-period Galactic Cepheid RS Puppis - III. A geometric distance from HST polarimetric imaging of its light echoes

As one of the most luminous Cepheids in the Milky Way, the 41.5-day RS Puppis is an analog of the long-period Cepheids used to measure extragalactic distances. An accurate distance to this star would therefore help anchor the zero-point of the bright end of the period-luminosity relation. But, at a distance of about 2 kpc, RS Pup is too far away for measuring a direct trigonometric parallax with a precision of a few percent with existing instrumentation. RS Pup is unique in being surrounded by a reflection nebula, whose brightness varies as pulses of light from the Cepheid propagate outwards. We present new polarimetric imaging of the nebula obtained with HST/ACS. The derived map of the degree of linear polarization pL allows us to reconstruct the three-dimensional structure of the dust distribution. To retrieve the scattering angle from the pL value, we consider two different polarization models, one based on a Milky Way dust mixture and one assuming Rayleigh scattering. Considering the derived dust distribution in the nebula, we adjust a model of the phase lag of the photometric variations over selected nebular features to retrieve the distance of RS Pup. We obtain a distance of 1910 +/- 80 pc (4.2%), corresponding to a parallax of 0.524 +/- 0.022 mas. The agreement between the two polarization models we considered is good, but the final uncertainty is dominated by systematics in the adopted model parameters. The distance we obtain is consistent with existing measurements from the literature, but light echoes provide a distance estimate that is not subject to the same systematic uncertainties as other estimators (e.g. the Baade-Wesselink technique). RS Pup therefore provides an important fiducial for the calibration of systematic uncertainties of the long-period Cepheid distance scale.Comment: 14 pages, 14 figures, accepted for publication in Astronomy & Astrophysic

Using limb darkening to measure fundamental parameters of stars

Context. Limb darkening is an important tool for understanding stellar atmospheres, but most observations measuring limb darkening assume various parameterizations that yield no significant information about the structure of stellar atmospheres. Aims. We use a specific limb-darkening relation to study how the best-fit coefficients relate to fundamental stellar parameters from spherically symmetric model stellar atmospheres. Methods. Using a grid of spherically symmetric Atlas model atmospheres, we compute limb-darkening coefficients, and develop a novel method to predict fundamental stellar parameters. Results. We find our proposed method predicts the mass of stellar atmosphere models given only the radius and limb-darkening coefficients, suggesting that microlensing, interferometric, transit and eclipse observations can constrain stellar masses. Conclusions. This novel method demonstrates that limb-darkening parameterizations contain important information about the structure of stellar atmospheres, with the potential to be a valuable tool for measuring stellar masses.Comment: 8 pages, 6 figures, 2 tables, A&A accepte

Mid-infrared interferometry with K band fringe-tracking I. The VLTI MIDI+FSU experiment

Context: A turbulent atmosphere causes atmospheric piston variations leading to rapid changes in the optical path difference of an interferometer, which causes correlated flux losses. This leads to decreased sensitivity and accuracy in the correlated flux measurement. Aims: To stabilize the N band interferometric signal in MIDI (MID-infrared Interferometric instrument), we use an external fringe tracker working in K band, the so-called FSU-A (fringe sensor unit) of the PRIMA (Phase-Referenced Imaging and Micro-arcsecond Astrometry) facility at VLTI. We present measurements obtained using the newly commissioned and publicly offered MIDI+FSU-A mode. A first characterization of the fringe-tracking performance and resulting gains in the N band are presented. In addition, we demonstrate the possibility of using the FSU-A to measure visibilities in the K band. Methods: We analyzed FSU-A fringe track data of 43 individual observations covering different baselines and object K band magnitudes with respect to the fringe-tracking performance. The N band group delay and phase delay values could be predicted by computing the relative change in the differential water vapor column density from FSU-A data. Visibility measurements in the K band were carried out using a scanning mode of the FSU-A. Results: Using the FSU-A K band group delay and phase delay measurements, we were able to predict the corresponding N band values with high accuracy with residuals of less than 1 micrometer. This allows the coherent integration of the MIDI fringes of faint or resolved N band targets, respectively. With that method we could decrease the detection limit of correlated fluxes of MIDI down to 0.5 Jy (vs. 5 Jy without FSU-A) and 0.05 Jy (vs. 0.2 Jy without FSU-A) using the ATs and UTs, respectively. The K band visibilities could be measured with a precision down to ~2%.Comment: 11 pages, 13 figures, Accepted for publication in A&

Calibrating the projection factor for Galactic Cepheids

The projection factor (p), which converts the radial velocity to pulsational velocity, is an important parameter in the Baade-Wesselink (BW) type analysis and distance scale work. The p-factor is either adopted as a constant or linearly depending on the logarithmic of pulsating periods. The aim of this work is to calibrate the p-factor if a Cepheid has both the BW distance and an independent distance measurement, and examine the p-factor for delta Cephei -- the prototype of classical Cepheids. We calibrated the p-factor for several Galactic Cepheids that have both the latest BW distances and independent distances either from Hipparcos parallaxes or main-sequence fitting distances to Cepheid-hosted stellar clusters. Based on 25 Cepheids, the calibrated p-factor relation is consistent with latest p-factor relation in literature. The calibrated p-factor relation also indicates that this relation may not be linear and may exhibit an intrinsic scatter. We also examined the discrepancy of empirical p-factors for delta Cephei, and found that the reasons for this discrepancy include the disagreement of angular diameters, the treatment of radial velocity data, and the phase interval adopted during the fitting procedure. Finally, we investigated the impact of the input p-factor in two BW methodologies for delta Cephei, and found that different p-factors can be adopted in these BW methodologies and yet result in the same angular diameters.Comment: 6 pages, 6 figures and 2 tables. A&A accepte

Stellar parameters of Be stars observed with X-shooter

Aims. The X-shooter archive of several thousand telluric star spectra was skimmed for Be and Be-shell stars to derive the stellar fundamental parameters and statistical properties, in particular for the less investigated late type Be stars, and the extension of the Be phenomenon into early A stars. Methods. An adapted version of the BCD method is used, utilizing the Balmer discontinuity parameters to determine effective temperature and surface gravity. This method is optimally suited for late B stars. The projected rotational velocity was obtained by profile fitting to the Mg ii lines of the targets, and the spectra were inspected visually for the presence of peculiar features such as the infrared Ca ii triplet or the presence of a double Balmer discontinuity. The Balmer line equivalent widths were measured, but due to uncertainties in determining the photospheric contribution are useful only in a subsample of Be stars for determining the pure emission contribution. Results. A total of 78 Be stars, mostly late type ones, were identified in the X-shooter telluric standard star archive, out of which 48 had not been reported before. The general trend of late type Be stars having more tenuous disks and being less variable than early type ones is confirmed. The relatively large number (48) of relatively bright (V > 8.5) additional Be stars casts some doubt on the statistics of late type Be stars; they are more common than currently thought: The Be/B star fraction may not strongly depend on spectral subtype.Comment: Accepted for publication in A&