arXiv subjects

P. Kervella

Publications and source records attributed to P. Kervella.

At least 163 records · Page 9Linked to original sources

arXiv2017

Dynamical masses of Cepheids from the GAIA parallaxes

The mass of a Cepheid is a fundamental parameter for studying the pulsation and evolution of intermediate-mass stars. But determining this variable has been a long-standing problem for decades. Detecting the companions (by spectroscopy or imaging) is a difficult task because of the brightness of the Cepheids and the close orbit of the components. So most of the Cepheid masses are derived using stellar evolution or pulsation modeling, but they differ by 10-20%. Measurements of dynamical masses offer the unique opportunity to make progress in resolving this mass discrepancy. The first problem in studying binary Cepheids is the high contrast between the components for wavelengths longer than 0.5 μm, which make them single-line spectroscopic binaries. In addition, the close orbit of the companions (< 40 mas) prevents us from spatially resolving the systems with a single-dish 8m-class telescope. A technique able to reach high spatial resolution and high- dynamic range is long-baseline interferometry. We have started a long-term program that aims at detecting, monitoring and characterizing physical parameters of the Cepheid companions. The GAIA parallaxes will enable us to combine interferometry with single-line velocities to provide unique dynamical mass measurements of Cepheids.

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arXiv2017

Four years' interferometric observations of Galactic binary Cepheids

We give an update on our long-term program of Galactic Cepheids started in 2012, whose goal is to measure the visual orbits of Cepheid companions. Using the VLTI/PIONIER and CHARA/MIRC instruments, we have now detected several com- panions, and we already have a good orbital coverage for several of them. By combining interferometry and radial velocities, we can now derive all the orbital elements of the systems, and we will be soon able to estimate the Cepheid masses.

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arXiv2017

The inhomogeneous sub-millimeter atmosphere of Betelgeuse

The mechanisms responsible for heating the extended atmospheres of early-M spectral-type supergiants are poorly understood. So too is the subsequent role these mechanisms play in driving the large mass-loss rates of these stars. Here we present ALMA long (i.e., $\sim$16 km) baseline 338 GHz (0.89 mm) continuum observations of the free-free emission in the extended atmosphere of the M2 spectral-type supergiant Betelgeuse. The spatial resolution of 14 mas exquisitely resolves the atmosphere, revealing it to have a mean temperature of 2760 K at $\sim$1.3 R$_{\star}$, which is below both the photospheric effective temperature ($T_{\textrm{eff}} = 3690$ K) and the temperatures at $\sim$$2 $R$_{\star}$. This is unambiguous proof for the existence of an inversion of the mean temperature in the atmosphere of a red supergiant. The emission is clearly not spherically symmetric with two notable deviations from a uniform disk detected in both the images and visibilities. The most prominent asymmetry is located in the north-east quadrant of the disk and is spatially resolved showing it to be highly elongated with an axis-ratio of 2.4 and occupying $\sim$$5\%$ of the disk projected area. Its temperature is approximately 1000 K above the measured mean temperature at 1.3 R$_{\star}$. The other main asymmetry is located on the disk limb almost due east of the disk center and occupies $\sim$$3\%$ of the disk projected area. Both emission asymmetries are clear evidence for localized heating taking place in the atmosphere of Betelgeuse. We suggest that the detected localized heating is related to magnetic activity generated by large-scale photospheric convection.

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arXiv2017

An Updated 2017 Astrometric Solution for Betelgeuse

We provide an update for the astrometric solution for the Type II supernova progenitor Betelgeuse using the revised Hipparcos Intermediate Astrometric Data (HIAD) of van Leeuwen, combined with existing VLA and new e-MERLIN and ALMA positions. The 2007 Hipparcos refined abscissa measurements required the addition of so-called Cosmic Noise of 2.4 mas to find an acceptable 5-parameter stochastic solution. We find that a measure of radio Cosmic Noise should also be included for the radio positions because surface inhomogeneities exist at a level significant enough to introduce additional intensity centroid uncertainty. Combining the 2007 HIAD with the proper motions based solely on the radio positions leads to a parallax of $π= 5.27\pm 0.78$ mas ($190^{+33}_{-25}$ pc), smaller than the Hipparcos 2007 value of $6.56\pm 0.83$ mas ($152^{+22}_{-17}$ pc; van Leeuwen 2007). Furthermore, combining the VLA and new e-MERLIN and ALMA radio positions with the 2007 HIAD, and including radio Cosmic Noise of 2.4 mas, leads to a nominal parallax solution of $4.51 \pm 0.80$ mas ($222^{+48}_{-34}$ pc), which while only $0.7σ$ different from the 2008 solution of Harper et al. it is $2.6σ$ different from the solution of van Leeuwen. An accurate and precise parallax for Betelgeuse is always going to be difficult to obtain because it is small compared to the stellar angular diameter ($θ=44$ mas). We outline an observing strategy, utilizing future mm and sub-mm high-spatial resolution interferometry that must be used if substantial improvements in precision and accuracy of the parallax and distance are to be achieved.

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arXiv2017

First Light for GRAVITY: Phase Referencing Optical Interferometry for the Very Large Telescope Interferometer

GRAVITY is a new instrument to coherently combine the light of the European Southern Observatory Very Large Telescope Interferometer to form a telescope with an equivalent 130 m diameter angular resolution and a collecting area of 200 m$^2$. The instrument comprises fiber fed integrated optics beam combination, high resolution spectroscopy, built-in beam analysis and control, near-infrared wavefront sensing, phase-tracking, dual beam operation and laser metrology [...]. This article gives an overview of GRAVITY and reports on the performance and the first astronomical observations during commissioning in 2015/16. We demonstrate phase tracking on stars as faint as m$_K$ ~ 10 mag, phase-referenced interferometry of objects fainter than m$_K$ ~ 15 mag with a limiting magnitude of m$_K$ ~ 17 mag, minute long coherent integrations, a visibility accuracy of better than 0.25 %, and spectro-differential phase and closure phase accuracy better than 0.5°, corresponding to a differential astrometric precision of better than 10 microarcseconds (μas). The dual-beam astrometry, measuring the phase difference of two objects with laser metrology, is still under commissioning. First observations show residuals as low as 50 μas when following objects over several months. We illustrate the instrument performance with the observations of archetypical objects for the different instrument modes. Examples include the Galactic Center supermassive black hole and its fast orbiting star S2 for phase referenced dual beam observations and infrared wavefront sensing, the High Mass X-Ray Binary BP Cru and the Active Galactic Nucleus of PDS 456 for few μas spectro-differential astrometry, the T Tauri star S CrA for a spectro-differential visibility analysis, ξ Tel and 24 Cap for high accuracy visibility observations, and η Car for interferometric imaging with GRAVITY.

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arXiv2017

Accretion-ejection morphology of the microquasar SS433 resolved at sub-au scale

We present the first optical observation at sub-milliarcsecond (mas) scale of the microquasar SS 433 obtained with the GRAVITY instrument on the VLT interferometer. The 3.5 hour exposure reveals a rich K-band spectrum dominated by hydrogen Br$γ $ and \ion{He}{i} lines, as well as (red-shifted) emission lines coming from the jets. The K-band continuum emitting region is dominated by a marginally resolved point source ($<$ 1 mas) embedded inside a diffuse background accounting for 10\% of the total flux. The jet line positions agree well with the ones expected from the jet kinematic model, an interpretation also supported by the consistent sign (i.e. negative/positive for the receding/approaching jet component) of the phase shifts observed in the lines. The significant visibility drop across the jet lines, together with the small and nearly identical phases for all baselines, point toward a jet that is offset by less than 0.5 mas from the continuum source and resolved in the direction of propagation, with a typical size of 2 mas. The jet position angle of $\sim$80$^{\circ}$ is consistent with the expected one at the observation date. Jet emission so close to the central binary system would suggest that line locking, if relevant to explain the amplitude and stability of the 0.26c jet velocity, operates on elements heavier than hydrogen. The Br$γ $ profile is broad and double peaked. It is better resolved than the continuum and the change of the phase signal sign across the line on all baselines suggests an East-West oriented geometry alike the jet direction and supporting a (polar) disk wind origin.

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arXiv2017

Sub-milliarcsecond Optical Interferometry of the HMXB BP Cru with VLTI/GRAVITY

We observe the HMXB BP Cru using interferometry in the near-infrared K band with VLTI/GRAVITY. Continuum visibilities are at most partially resolved, consistent with the predicted size of the hypergiant. Differential visibility amplitude ($Δ|V| \sim 5\%$) and phase ($Δϕ\sim 2 °$) signatures are observed across the HeI $2.059 μ$m and Br$γ$ lines, the latter seen strongly in emission, unusual for the donor star's spectral type. For a baseline $B \sim 100$m, the differential phase RMS $\sim 0.2 °$ corresponds to an astrometric precision of $\sim 2 μ$as. A model-independent analysis in the marginally resolved limit of interferometry reveals asymmetric and extended emission with a strong wavelength dependence. We propose geometric models based on an extended and distorted wind and/or a high density gas stream, which has long been predicted to be present in this system. The observations show that optical interferometry is now able to resolve HMXBs at the spatial scale at which accretion takes place, and therefore probe the effects of the gravitational and radiation fields of the compact object on its environment.

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arXiv2017

VLTI/PIONIER images the Achernar disk swell

Context. The mechanism of disk formation around fast-rotating Be stars is not well understood. In particular, it is not clear which mechanisms operate, in addition to fast rotation, to produce the observed variable ejection of matter. The star Achernar is a privileged laboratory to probe these additional mechanisms because it is close, presents B-Be phase variations on timescales ranging from 6 yr to 15 yr, a companion star was discovered around it, and probably presents a polar wind or jet. Aims. Despite all these previous studies, the disk around Achernar was never directly imaged. Therefore we seek to produce an image of the photosphere and close environment of the star. Methods. We used infrared long-baseline interferometry with the PIONIER/VLTI instrument to produce reconstructed images of the photosphere and close environment of the star over four years of observations. To study the disk formation, we compared the observations and reconstructed images to previously computed models of both the stellar photosphere alone (normal B phase) and the star presenting a circumstellar disk (Be phase). Results. The observations taken in 2011 and 2012, during the quiescent phase of Achernar, do not exhibit a disk at the detection limit of the instrument. In 2014, on the other hand, a disk was already formed and our reconstructed image reveals an extended H-band continuum excess flux. Our results from interferometric imaging are also supported by several H-alpha line profiles showing that Achernar started an emission-line phase sometime in the beginning of 2013. The analysis of our reconstructed images shows that the 2014 near-IR flux extends to 1.7 - 2.3 equatorial radii. Our model-independent size estimation of the H-band continuum contribution is compatible with the presence of a circumstellar disk, which is in good agreement with predictions from Be-disk models.

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arXiv2017

Asymmetries on red giant branch surfaces from CHARA/MIRC optical interferometry

Context. Red giant branch (RGB) stars are very bright objects in galaxies and are often used as standard candles. Interferometry is the ideal tool to characterize the dynamics and morphology of their atmospheres. Aims. We aim at precisely characterising the surface dynamics of a sample of RGB stars. Methods. We obtained interferometric observations for three RGB stars with the MIRC instrument mounted at the CHARA interfer- ometer. We looked for asymmetries on the stellar surfaces using limb-darkening models. Results. We measured the apparent diameters of HD197989 (Epsilon Cyg) = 4.61+-0.02 mas, HD189276 (HR7633) = 2.95+-0.01 mas, and HD161096 (Beta Oph) = 4.43+-0.01 mas. We detected departures from the centrosymmetric case for all three stars with the tendency of a greater effect for lower logg of the sample. We explored the causes of this signal and conclude that a possible explanation to the interferometric signal is the convection-related and/or the magnetic-related surface activity. However, it is necessary to monitor these stars with new observations, possibly coupled with spectroscopy, in order to firmly establish the cause.

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arXiv2017

Proxima's orbit around Alpha Centauri

Proxima and Alpha Centauri AB have almost identical distances and proper motions with respect to the Sun. Although the probability of such similar parameters is in principle very low, the question as to whether they actually form a single gravitationally bound triple system has been open since the discovery of Proxima one century ago. Owing to HARPS high precision absolute radial velocity measurements and the recent revision of the parameters of the Alpha Cen pair, we show that Proxima and Alpha Cen are gravitationally bound with a high degree of confidence. The orbital period of Proxima is approximately 550 000 years. With an excentricity of 0.50 (+0.08 -0.09), Proxima comes within 4.3 (+1.1 -0.9) kau of Alpha Cen at periastron. Its orbital phase is currently close to apastron (13.0 +0.3 -0.1 kau). This orbital motion may have influenced the formation or evolution of the recently discovered planet orbiting Proxima as well as circumbinary planet formation around Alpha Cen.

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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

ALMA observations of the nearby AGB star L2 Puppis - I. Mass of the central star and detection of a candidate planet

Six billion years from now, while evolving on the asymptotic giant branch (AGB), the Sun will metamorphose from a red giant into a beautiful planetary nebula. This spectacular evolution will impact the Solar System planets, but observational confirmations of the predictions of evolution models are still elusive as no planet orbiting an AGB star has yet been discovered. The nearby AGB red giant L2 Puppis (d = 64 pc) is surrounded by an almost edge-on circumstellar dust disk. We report new observations with ALMA at very high angular resolution (18 x 15 mas) in band 7 (f ~ 350 GHz) that allow us to resolve the velocity profile of the molecular disk. We establish that the gas velocity profile is Keplerian within the central cavity of the dust disk, allowing us to derive the mass of the central star L2 Pup A, mA = 0.659 +/- 0.011 +/- 0.041 Msun (+/- 6.6%). From evolutionary models, we determine that L2 Pup A had a near-solar main sequence mass, and is therefore a close analog of the future Sun in 5 to 6 Gyr. The continuum map reveals the presence of a secondary source (B) at a radius of 2 AU contributing fB/ fA = 1.3 +/- 0.1% of the flux of the AGB star. L2 Pup B is also detected in CO emission lines at a radial velocity of vB = 12.2 +/- 1.0 km/s. The close coincidence of the center of rotation of the gaseous disk with the position of the continuum emission from the AGB star allows us to constrain the mass of the companion to mB = 12 +/- 16 MJup. L2 Pup B is most likely a planet or low mass brown dwarf with an orbital period around 5 years. Its continuum brightness and molecular emission suggest that it may be surrounded by an extended molecular atmosphere or an accretion disk. L2 Pup therefore emerges as a promising vantage point on the distant future of our Solar System.

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arXiv2016

Close stellar conjunctions of alpha Centauri A and B until 2050 - An mK = 7.8 star may enter the Einstein ring of alpha Cen A in 2028

The rapid proper motion of the alpha Cen pair (3.7 arcsec/yr) and its location close to the galactic plane on a rich stellar background combine to make them excellent candidates for stellar conjunctions with distant stars. Adding new astrometry to archival data, we have refined the orbital parameters, barycentric proper motion and parallax of alpha Cen and compute its apparent trajectory on sky over the coming decades. We present a catalog of the expected close conjunctions until 2050. An exceptional event will take place in early May 2028, when alpha Cen A will come within 0.015 +/- 0.135 arcseconds of the mK = 7.8 star 2MASS 14392160-6049528 (hereafter S5). In terms of impact parameter and contrast, this is the most favorable stellar conjunction of alpha Cen within at least the next three decades. With an angular diameter of LD = 0.47 +/- 0.05 mas, it is likely that S5 is a red giant or supergiant located at several kiloparsecs. The approached stars will act as moving light probes in transmission through the environment of alpha Cen. The observation of these close conjunctions holds great promises to search for planets and other low mass objects in the alpha Cen system using photometry and astrometry. The relativistic deflection of the approached star images will be in the milliarcsecond range. The small impact parameter of the conjunction with S5 means that this star has a probability of 45% of entering the Einstein ring of alpha Cen A. The gravitational amplification of the flux of S5 could reach a factor five for the combination of the two lensed images. The proper motion, orbital parameters and parallax of alpha Cen will be measurable with an extreme accuracy from differential astrometry with the S stars. This will be valuable, for example to prepare the Breakthrough Starshot initiative to send interstellar nanocrafts to alpha Centauri.

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arXiv2016

The radii and limb darkenings of Alpha Centauri A and B - Interferometric measurements with VLTI/PIONIER

The photospheric radius is one of the fundamental parameters governing the radiative equilibrium of a star. We report new observations of the nearest solar-type stars Alpha Centauri A (G2V) and B (K1V) with the VLTI/PIONIER optical interferometer. The combination of four configurations of the VLTI enable us to measure simultaneously the limb darkened angular diameter thetaLD and the limb darkening parameters of the two solar-type stars in the near-infrared H band (lambda = 1.65 microns). We obtain photospheric angular diameters of thetaLD(A) = 8.502 +/- 0.038 mas (0.43%) and thetaLD(B) = 5.999 +/- 0.025 mas (0.42%), through the adjustment of a power law limb darkening model. We find H band power law exponents of alpha(A) = 0.1404 +/- 0.0050 (3.6%) and alpha(B) = 0.1545 +/- 0.0044 (2.8%), which closely bracket the observed solar value (alpha_sun = 0.15027). Combined with the parallax pi = 747.17 +/- 0.61 mas recently determined, we derive linear radii of RA = 1.2234 +/- 0.0053 Rsun (0.43%) and RB = 0.8632 +/- 0.0037 Rsun (0.43%). The power law exponents that we derive for the two stars indicate a significantly weaker limb darkening than predicted by both 1D and 3D stellar atmosphere models. As this discrepancy is also observed on near-infrared limb darkening profile of the Sun, an improvement of the calibration of stellar atmosphere models is clearly needed. The reported PIONIER visibility measurements of Alpha Cen A and B provide a robust basis to validate the future evolutions of these models.

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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

Resolved astrometric orbits of ten O-type binaries

Our long term aim is to derive model-independent stellar masses and distances for long period massive binaries by combining apparent astrometric orbit with double-lined radial velocity amplitudes (SB2). We follow-up ten O+O binaries with AMBER, PIONIER and GRAVITY at the VLTI. Here, we report about 130 astrometric observations over the last 7 years. We combine this dataset with distance estimates to compute the total mass of the systems. We also compute preliminary individual component masses for the five systems with available SB2 radial velocities. Nine over the ten binaries have their three dimensional orbit well constrained. Four of them are known colliding wind, non-thermal radio emitters, and thus constitute valuable targets for future high angular resolution radio imaging. Two binaries break the correlation between period and eccentricity tentatively observed in previous studies. It suggests either that massive star formation produce a wide range of systems, or that several binary formation mechanisms are at play. Finally, we found that the use of existing SB2 radial velocity amplitudes can lead to unrealistic masses and distances. If not understood, the biases in radial velocity amplitudes will represent an intrinsic limitation for estimating dynamical masses from SB2+interferometry or SB2+Gaia. Nevertheless, our results can be combined with future Gaia astrometry to measure the dynamical masses and distances of the individual components with an accuracy of 5 to 15\%, completely independently of the radial velocities.

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arXiv2016

The red dwarf pair GJ65AB: inflated, spinning twins of Proxima

The nearby red dwarf binary GJ65AB (UB+BL Ceti, M5.5Ve+M6Ve) is a cornerstone system to probe the physics of very low mass stars. We present new interferometric measurements of the angular diameters of the two components of GJ65AB with the PIONIER instrument in the H band: thetaUD (A) = 0.558 +/- 0.008 +/- 0.020 mas and thetaUD (B) = 0.539 +/- 0.009 +/- 0.020 mas. They translate into limb-darkened angular diameters of LD (A) = 0.573 +/- 0.021 mas and LD (B) = 0.554 +/- 0.022 mas. From the known parallax, the radii are R(A) = 0.165 +/- 0.006 Rsun and R(B) = 0.159 +/- 0.006 Rsun (sigma(R)/R = 4%). We also observed GJ65AB with the VLT/NACO adaptive optics and refine the orbital parameters and infrared magnitudes of the system. We derive masses for the two components of m(A) = 0.1225 +/- 0.0043 Msun and m(B) = 0.1195 +/- 0.0043 Msun (sigma(m)/m = 4%). To derive the radial and rotational velocities of the two stars, as well as their relative metallicity with respect to Proxima, we also present new individual UVES high resolution spectra. Placing GJ65 A&B in the mass-radius diagram shows that their radii are larger respectively by 14 +/- 4% and 12 +/- 4% compared to expectations from the models by Baraffe et al. (2015). Following Chabrier et al. (2007), we propose that this discrepancy is caused by the inhibition of convective energy transport by a strong internal magnetic field generated by dynamo effect in these two fast rotating stars. A comparison with the almost identical twin but slowly-rotating Proxima strengthens this hypothesis, as the radius of Proxima does not appear inflated compared to models.

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arXiv2016

Multiplicity of Galactic Cepheids from long-baseline interferometry~III. Sub-percent limits on the relative brightness of a close companion of $δ$~Cephei

We report new CHARA/MIRC interferometric observations of the Cepheid archetype $δ$ Cep, which aimed at detecting the newly discovered spectroscopic companion. We reached a maximum dynamic range $ΔH $ = 6.4, 5.8, and 5.2 mag, respectively within the relative distance to the Cepheid $r < 25$ mas, $25 < r < 50$ mas and $50 < r < 100$ mas. Our observations did not show strong evidence of a companion. We have a marginal detection at $3σ$ with a flux ratio of 0.21\%, but nothing convincing as we found other possible probable locations. We ruled out the presence of companion with a spectral type earlier than F0V, A1V and B9V, respectively for the previously cited ranges $r$. From our estimated sensitivity limits and the Cepheid light curve, we derived lower-limit magnitudes in the $H$ band for this possible companion to be $H_\mathrm{comp} > 9.15, 8.31$ and 7.77 mag, respectively for $r < 25$ mas, $25 < r < 50$ mas and $50 < r < 100$ mas. We also found that to be consistent with the predicted orbital period, the companion has to be located at a projected separation $< 24$ mas with a spectral type later than a F0V star.

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