Binary Cepheids from optical interferometry

Classical Cepheid stars have been considered since more than a century as reliable tools to estimate distances in the universe thanks to their Period-Luminosity (P-L) relationship. Moreover, they are also powerful astrophysical laboratories, providing fundamental clues for studying the pulsation and evolution of intermediate-mass stars. When in binary systems, we can investigate the age and evolution of the Cepheid, estimate the mass and distance, and constrain theoretical models. However, most of the companions are located too close to the Cepheid (1-40 mas) to be spatially resolved with a 10-meter class telescope. The only way to spatially resolve such systems is to use long-baseline interferometry. Recently, we have started a unique and long-term interferometric program that aims at detecting and characterizing physical parameters of the Cepheid companions, with as main objectives the determination of accurate masses and geometric distances.Comment: 8 pages, Proceeding of the conference "Setting a new standard in the analysis of binary stars", September 2013, Leuven, Belgiu

Extended envelopes around Galactic Cepheids IV. T Monocerotis and X Sagittarii from mid-infrared interferometry with VLTI/MIDI

Aims. We study the close environment of nearby Cepheids using high spatial resolution observations in the mid-infrared with the VLTI/MIDI instrument, a two-beam interferometric recombiner. Methods. We obtained spectra and visibilities for the classical Cepheids X Sgr and T Mon. We fitted the MIDI measurements, supplemented by B, V, J, H, K literature photometry, with the numerical transfer code DUSTY to determine the dust shell parameters. We used a typical dust composition for circumstellar environments. Results. We detect an extended dusty environment in the spectra and visibilities for both stars, although T Mon might suffer from thermal background contamination. We attribute this to the presence of a circumstellar envelope (CSE) surrounding the Cepheids. This is optically thin for X Sgr (tau(0.55microns) = 0.008), while it appears to be thicker for T Mon (tau(0.55micron) = 0.15). They are located at about 15-20 stellar radii. Following our previous work, we derived a likely period-excess relation in the VISIR PAH1 filter, f(8.6micron)[%]= 0.81(+/-0.04)P[day]. We argue that the impact of CSEs on the mid-IR period-luminosity (P-L) relation cannot be negligible because they can bias the Cepheid brightness by up to about 30 %. For the K-band P-L relation, the CSE contribution seems to be lower (< 5 %), but the sample needs to be enlarged to firmly conclude that the impact of the CSEs is negligible in this band.Comment: Accepted for publication in Astronomy and Astrophysic

Multiplicity of Galactic Cepheids from long-baseline interferometry. II. The Companion of AX Circini revealed with VLTI/PIONIER

Aims: We aim at detecting and characterizing the main-sequence companion of the Cepheid AX Cir ($P_\mathrm{orb} \sim$ 18 yrs). The long-term objective is to estimate the mass of both components and the distance to the system. Methods: We used the PIONIER combiner at the VLT Interferometer to obtain the first interferometric measurements of the short-period Cepheid AX Cir and its orbiting component. Results: The companion is resolved by PIONIER at a projected separation $\rho = 29.2 \pm 0.2$ mas and projection angle $PA = 167.6 \pm 0.3^{\circ}$. We measured $H$-band flux ratios between the companion and the Cepheid of $0.90 \pm 0.10$ % and $0.75 \pm 0.17$ %, respectively at a pulsation phase for the Cepheid $\phi = 0.24$ and 0.48. The lower contrast at $\phi = 0.48$ is due to increased brightness of the Cepheid compared to the $\phi = 0.24$. This gives an average apparent magnitude $m\mathrm{_H (comp)} = 9.06 \pm 0.24$ mag. The limb-darkened angular diameter of the Cepheid at the two pulsation phases was measured to be $\theta_\mathrm{LD} = 0.839 \pm 0.023$ mas and $\theta_\mathrm{LD} = 0.742 \pm 0.020$ mas, respectively at $\phi = 0.24$ and 0.48. A lower limit on the total mass of the system was also derived based on our measured separation, we found $M_\mathrm{T} \geq 9.7 \pm 0.6 M_\odot$.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

GCIRS 7, a pulsating M1 supergiant at the Galactic centre. Physical properties and age

The stellar population in the central parsec of the Galaxy is dominated by an old (several Gyr) population, but young, massive stars dominate the luminosity function. We have studied the most luminous of these stars, GCIRS 7, in order to constrain the age of the recent star formation event in the Galactic Centre and to characterise it as an interferometric reference for observations of the Galactic Centre with the instrument GRAVITY, which will equip the Very Large Telescope Interferometer in the near future. We present the first H-band interferometric observations of GCIRS 7, obtained using the PIONIER visitor instrument on the VLTI using the four 8.2-m unit telescopes. In addition, we present unpublished K-band VLTI/AMBER data, build JHKL light-curves based on data spanning 4 decades, and measured the star's effective temperature using SINFONI spectroscopy. GCIRS 7 is marginally resolved at H-band (in 2013: uniform-disk diameter=1.076+/-0.093mas, R=960+/-92Rsun at 8.33+/-0.35kpc). We detect a significant circumstellar contribution at K-band. The star and its environment are variable in brightness and in size. The photospheric H-band variations are well modelled with two periods: P0~470+/-10 days (amplitude ~0.64mag) and long secondary period LSP~2700-2850 days (~1.1mag). As measured from CO equivalent width, =3600+/-195K. The size, periods, luminosity (=-8.44+/-0.22) and effective temperature are consistent with an M1 supergiant with an initial mass of 22.5+/-2.5Msun and an age of 6.5-10Myr (depending on rotation). This age is in remarkable agreement with most estimates for the recent star formation event in the central parsec. Caution should be taken when using this star as an interferometric reference as it is variable in size, is surrounded by a variable circumstellar environment and large convection cells may form on its photosphere.Comment: Accepted for publication in A&A. 10 pages, 12 figure

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

Observational calibration of the projection factor of Cepheids

Context. The distance to pulsating stars is classically estimated using the parallax-of-pulsation (PoP) method, which combines spec- troscopic radial velocity (RV) measurements and angular diameter (AD) estimates to derive the distance of the star. A particularly important application of this method is the determination of Cepheid distances in view of the calibration of their distance scale. How- ever, the conversion of radial to pulsational velocities in the PoP method relies on a poorly calibrated parameter, the projection factor (p-factor). Aims. We aim to measure empirically the value of the p-factors of a homogeneous sample of nine bright Galactic Cepheids for which trigonometric parallaxes were measured with the Hubble Space Telescope (HST) Fine Guidance Sensor by Benedict et al. (2007). Methods. We use the SPIPS algorithm, a robust implementation of the PoP method that combines photometry, interferometry, and radial velocity measurements in a global modeling of the pulsation of the star. We obtained new interferometric angular diameter mea- surements using the PIONIER instrument at the Very Large Telescope Interferometer (VLTI), completed by data from the literature. Using the known distance as an input, we derive the value of the p-factor of the nine stars of our sample and study its dependence with the pulsation period. Results. We find the following p-factors: p = 1.20 ± 0.12 for RT Aur, p = 1.48 ± 0.18 for T Vul, p = 1.14 ± 0.10 for FF Aql, p = 1.31 ± 0.19 for Y Sgr, p = 1.39 ± 0.09 for X Sgr, p = 1.35 ± 0.13 for W Sgr, p = 1.36 ± 0.08 for β Dor, p = 1.41 ± 0.10 for ζ Gem, and p = 1.23 ± 0.12 for ` Car. Conclusions. The values of the p-factors that we obtain are consistently close to p = 1.324 ± 0.024. We observe some dispersion around this average value, but the observed distribution is statistically consistent with a constant value of the p-factor as a function of the pulsation period (χ2 = 0.669). The error budget of our determination of the p-factor values is presently dominated by the uncertainty on the parallax, a limitation that will soon be waived by Gaia

Observational calibration of the projection factor of Cepheids

Context. The distances of pulsating stars, in particular Cepheids, are commonly measured using the parallax of pulsation technique. The different versions of this technique combine measurements of the linear diameter variation (from spectroscopy) and the angular diameter variation (from photometry or interferometry) amplitudes, to retrieve the distance in a quasi-geometrical way. However, the linear diameter amplitude is directly proportional to the projection factor (hereafter p-factor), which is used to convert spectro- scopic radial velocities (i.e., disk integrated) into pulsating (i.e., photospheric) velocities. The value of the p-factor and its possible dependence on the pulsation period are still widely debated. Aims. Our goal is to measure an observational value of the p-factor of the type-II Cepheid κ Pavonis. Methods. The parallax of the type-II Cepheid κ Pav was measured with an accuracy of 5% using HST/FGS. We used this parallax as a starting point to derive the p-factor of κ Pav, using the SPIPS technique (Spectro-Photo-Interferometry of Pulsating Stars), which is a robust version of the parallax-of-pulsation method that employs radial velocity, interferometric and photometric data. We applied this technique to a combination of new VLTI/PIONIER optical interferometric angular diameters, new CORALIE and HARPS radial velocities, as well as multi-colour photometry and radial velocities from the literature. Results. We obtain a value of p = 1.26 ± 0.07 for the p-factor of κ Pav. This result agrees with several of the recently derived Period-p-factor relationships from the literature, as well as previous observational determinations for Cepheids. Conclusions. Individual estimates of the p-factor are fundamental to calibrating the parallax of pulsation distances of Cepheids. Together with previous observational estimates, the projection factor we obtain points to a weak dependence of the p-factor on period