The 8th Pacific Rim Conference on Stellar Astrophysics ASP Conference Series, Vol. 404, c 2009 B. Soonthornthum, S. Komonjinda, K. S. Cheng, and K.-C. Leung, eds.

Canopus Angular Diameter Revisited by the AMBER Instrument of the VLT Interferometer

P. Bendjoya,1 A. Domiciano de Souza,1 F. Vakili,1 F. Millour,2 and R. Petrov1

Abstract. We used the VLTI/AMBER instrument to obtain interferometric data on the F0I star Canopus (visibilities and closure phases in the H and K bands with spectral resolution of 35). The adopted baselines (100 m) and the high quality of the VLTI/AMBER observations allowed us to measure fringe visibilities up to the third visibility lobe of Canopus.The angular diameter has been measured from the visibility and set to be (6.95 0.15) mas. From this measured angular diameter we derive a stellar radius R±= (72 4)R and an ± effective temperature Teff = (7272 107)K or Teff = (7570 250)K depending⊙ on the considered bolometric flux± and its precision. Contrarily± to the theory, our VLTI/AMBER data do not reveal any limb darkening on Canopus in the near-IR. Our observations set new constraints on the physical parameters of this star.

1. Introduction

The evolved star Canopus (α Carinae, HD45348) is a F0 supergiant (F0Ib) star, the second brightest star (V = 0.72) in the night sky, just after Sirius. During their evolution, intermediate− mass stars like Canopus (M 10 M ) leave the red giant branch (RGB) and enter the blue-giant region, significantly≃ ⊙ increasing their effective temperature and performing the so-called blue loop. There are still puzzling questions concerning this phase of the stelar evolution (e.g. Xu & Li 2004). To constrain evolutionary models it is quite important to have precise measurements of fundamental stellar parameters, such as the effective temperature, luminosity, radius R. It is surprising to note that even such a bright star as Canopus does not have a radius determination with a high precision. The most precise angular diameter θ measurements can be obtained by modern long baseline interferometers. In this work we present precise measurements of the angular diameter (and other derived physical parameters) of Canopus obtained with the AMBER beam- combiner instrument (Petrov et al. 2007), installed at the ESO-VLTI (Glinde- mann et al. 2004) located at Cerro Paranal in Chile.

1Lab. H. Fizeau, CNRS UMR 6525, Univ. de Nice-Sophia Antipolis, Observatoire de la Cˆote d’Azur, F-06108 Nice cedex 2, France 2Max-Planck-Institut f¨urRadioastronomie, Auf dem H¨ugel69, 53121 Bonn, Germany 330 Precise Canopus Diameter Measured by AMBER-VLTI 331

Figure 1. VLTI/AMBER visibility amplitudes and uncertainties in the H (clear error bars) and K bands (black error bars). The model visibilities (squares) where calculated with a linear limb-darkened disk model fitted to the data (Table 1). As a reference we also show the theoretical visibilities (dashes for H and solid for K) expected for Canopus from a linear limb- darkened disk with parameters ǫH = 0.28 and ǫK = 0.24, interpolated from the grids given by Claret (2000). Clearly these theoretical models do not account for the observations, especially after the first minimum.

2. Observations and Data reduction

The AMBER observations were performed at spectral resolution R = λ/∆λ 35 in the H and K bands, using three Auxiliary Telescopes (ATs) placed on≃ the VLTI stations A0, K0, and G1. A relatively complete uv-plane coverage was obtained thanks to observa- tions carried over 3 nights (2007 April 6, 7, 8) spanning several hour angles and spatial frequencies. Each AMBER observing file consists of 1000 frames (one in- terference and three photometric channels) recorded with an integration time of 0.026 s. The calibrator star is HD 79917. A complete AMBER observing block is typically composed by five observing files recorded on the target followed by another five files recorded on the calibrator. These files allow the measure of one set of calibrated squared visibilities (one at each baseline) and closure phases in the H and K bands. The data reduction was performed using the standard routines of the AM- BER Data Reduction Software (a.k.a. amdlib) version 2.11. Tatulli et al. (2007) describe the principles of the AMBER-DRS routines allowing the conversion of raw-data frames into individual complex visibilities. The best individual complex visibilities of an observing block are then se- lected and averaged to obtain uncalibrated visibilities and closure phases. Data selection is necessary mainly because of VLTI vibrations and the determina-

1Routines and user guide are available at ”http://www.jmmc.fr/data processing amber.htm” 332 Bendjoya et al. tion of the selection parameters is an important part of the data reduction. Calibrated visibilities (V ) and closure phases are then obtained from the se- lected and averaged visibilities and closure phases from the target and calibra- tor files of each observing block. The visibility uncertainty (σV (λ)) has been computed from the several observations of the calibrator star, averaging over the three baselines. Depending on the night and on the wavelength the rela- tive uncertainty was estimated as σV (λ)/V (λ) 0.03 0.09 in the H band and σ (λ)/V (λ) 0.02 0.06 in the K band. ≃ − V ≃ −

Table 1. Measured parameters (and uncertainties) for a linear limb- darkened disk model and physical parameters of Canopus derived from our angular diameter θ estimate.

Fitted parameter Derived parameter θ = 6.95 0.15 mas R/R = 72 4.0a ± ± b ǫH = 0.01 0.01 Teff =⊙7272 107 K ǫ = 0.17± 0.01 T = 7570 ± 250 Kc K − ± eff ± a From the Hipparcos distance d = 95.9 ± 4.9 pc (Perryman et al. 1997). b From the bolometric flux of Code et al. (1976): f = (45.0 ± 1.8) × 10−6 erg cm−2 s−1. c Obtained by using values from Smiljanic et al. (2006) and references therein (visual apparent magnitude V = −0.72, extinction AV = 0.08, visual bolometric correction BCV = 0.0) and from Drilling & Arlo (2000) (L⊙ and bolometric magnitude). The uncertainty in Teff was estimated from σθ and considering a conservative cumulative error of 0.1 in V , AV , and BCV .

3. Results

All measured closure phases lie in the range between -10◦to 10◦, with an uncer- tainty of a few degrees. This indicates that Canopus can be considered having a centrally-symmetric intensity distribution, as a first approximation. We have thus fitted a linear limb-darkened disk model to the observed H and K visibilities, simultaneously. The free parameters of the model are the limb-darkened angular diameter θ, the H and K linear limb-darkening coefficients ǫH and ǫK . The esti- mated parameters and corresponding uncertainties obtained from a Levenberg- Marquardt least-squares fit are given in Table 1. The model visibilities is shown in Fig.1.

Acknowledgments. This research is based on observations performed at the European Southern Observatory, Chile under ESO Programs 079.D-0507

References

Claret, A. 2000, A&A, 363, 1081 Code, A. D., Bless, R. C.,Davis, J., and Brown, R. H. 1976, ApJ, 203, 417 Glindemann, A., Albertsen, M., Andolfato, L. et al. 2004, Proceedings SPIE, 5491, 447 Drilling, J. & Arlo, U. L. 2000, in Allen’s Astroph. Quantities, 4th Ed., Cox (Springer) Perryman, M. A. C., et al., The Hipparcos Catalogue, 1997, A&A, 323, 49 Petrov, R. G., Malbet, F., Weigelt, G. et al. 2007, A&A, 464, 1 Smiljanic, R., Barbuy, B., de Medeiros, J. R., and Maeder, A. 2006, A&A, 449, 655 Precise Canopus Diameter Measured by AMBER-VLTI 333

Tatulli, E., Millour, F., Chelli, A., et al. 2007, A&A, 464, 29 Xu, H.Y and Li, Y. 2004, A&A, 418, 225