Gravitational-darkening of Altair from interferometry

Received / Accepted Abstract. Several interferometric observations revealed that the rapid rotator Altair is a ∞attened star with a non-centrally symmetric intensity distribution. In this work we perform for the flrst time a physically consistent analysis of all interferometric data available so far, corresponding to three difierent interferometers operating in several spectral bands. These observations include new data (squared visibilities in the H and K bands from VLTI- VINCI) as well as previously published data (squared visibilities in the K band from PTI and squared visibilities, triple amplitudes, and closure phases in the visible between 520 nm and 850 nm from NPOI). To analyze these data we perform a ´ 2 minimization using an interferometry-oriented model for fast rotators, which includes Roche approximation, limb-darkening, and von Zeipel-like gravity-darkening. Thanks to the rich interferometric data set available and to this physical model, the main uniqueness problems were avoided. As a main result we show that observations can only be explained if Altair has a gravity-darkening compatible with the expected value for hot stars, i.e., the von Zeipel efiect (Tefi / g 0:25 ).

[1]  J.-M. Mariotti,et al.  Deriving object visibilities from interferograms obtained with a fiber stellar interferometer , 1997 .

[2]  Pierre Kervella,et al.  First observations with an H-band integrated optics beam combiner at the VLTI , 2004 .

[3]  F. Royer,et al.  Altair's inclination from line profile analysis , 2004, astro-ph/0408194.

[4]  Eduardo Janot-Pacheco,et al.  Modelling rapid rotators for stellar interferometry , 2002 .

[6]  Eduardo Janot-Pacheco,et al.  Stellar differential rotation and inclination angle from spectro-interferometry , 2004 .

[7]  The interferometric diameter and internal structure of Sirius A , 2003, astro-ph/0306604.

[8]  A. Renzini,et al.  The Stellar Populations of Galaxies , 1992 .

[9]  David Mozurkewich,et al.  Comparison of Stellar Angular Diameters from the NPOI, the Mark III Optical Interferometer, and the Infrared Flux Method , 2001 .

[10]  C. Soubiran,et al.  Catalogue of [Fe/H] determinations for FGK stars: 2001 edition , 2001, astro-ph/0106438.

[11]  L. Girardi,et al.  Theoretical isochrones in several photometric systems I. Johnson-Cousins-Glass, HST/WFPC2, HST/NICMOS, Washington, and ESO Imaging Survey filter sets , 2002, astro-ph/0205080.

[12]  Ivan Hubeny,et al.  A computer program for calculating non-LTE model stellar atmospheres , 1988 .

[13]  Robert C. Smith,et al.  Gravity-darkening in Stars for General Rotation Laws , 1974 .

[14]  Robert L. Kurucz,et al.  Model Atmospheres for Population Synthesis , 1992 .

[15]  D. Segransan,et al.  Data reduction methods for single-mode optical interferometry Application to the VLTI two-telescopes beam combiner VINCI , 2004 .

[16]  R. G. Petrov.  The near infrared VLTI instrument AMBER , 2003 .

[17]  E. Friel,et al.  A catalogue of [Fe/H] determinations: 1996 edition , 1992, astro-ph/9705206.

[18]  Mark R. Kidger,et al.  Spectral Irradiance Calibration in the Infrared. X. A Self-Consistent Radiometric All-Sky Network of Absolutely Calibrated Stellar Spectra , 1999 .

[19]  H. Zeipel,et al.  The Radiative Equilibrium of a Rotating System of Gaseous Masses , 1924 .

[20]  et al,et al.  The Palomar Testbed Interferometer , 1999 .

[21]  N. Morrell,et al.  The Relation between Rotational Velocities and Spectral Peculiarities among A-Type Stars , 1995 .

[22]  Y. Kondo,et al.  Chromospheric models for Altair (A7 IV-V) , 1995 .

[23]  R. Townsend,et al.  Spectroscopic modelling of non-radial pulsation in rotating early-type stars , 1997 .

[24]  Mark R. Kidger,et al.  High-Precision Near-Infrared Photometry of a Large Sample of Bright Stars Visible from the Northern Hemisphere , 2003 .

[25]  A. Reiners,et al.  On the feasibility of the detection of differential rotation in stellar absorption profiles , 2002 .

[26]  D. Ciardi,et al.  Altair’s Oblateness and Rotation Velocity from Long-Baseline Interferometry , 2001 .

[27]  F. Paresce,et al.  The spinning-top Be star Achernar from VLTI-VINCI , 2003, astro-ph/0306277.

[28]  P. North,et al.  Automated spectroscopic abundances of A and F-type stars using echelle spectrographs - II. Abundances of 140 A-F stars from ELODIE and CORALIE , 2002, astro-ph/0210065.

[29]  J. Armstrong,et al.  The Navy Prototype Optical Interferometer , 1998 .

[30]  T. Conrow,et al.  Altair: The Brightest δ Scuti Star , 2004, astro-ph/0405127.

[31]  W. Geroge,et al.  Continuum Emission from a Rotating Non-Gray Stellar Atmosphere. , 1965 .

[32]  G. Perrin,et al.  A catalogue of calibrator stars for long baseline stellar interferometry , 2002 .

[33]  P. Kervella,et al.  Tests of stellar model atmospheres by optical interferometry. VLTI/VINCI limb-darkening measurements of the M4 giant ψ Phe , 2004 .

[34]  Nicholas M. Elias,et al.  Navy Prototype Optical Interferometer Observations of the Double Stars Mizar A and Matar , 1998 .

[35]  Sebastien Morel,et al.  The VLTI -- A Status Report , 2003, SPIE Astronomical Telescopes + Instrumentation.

[36]  T. R. Stoeckley.  Determination of Aspect and Degree of Differential Rotation, From Line Profiles in Rapidly Rotating Stars , 1968 .

[37]  Tyler E. Nordgren,et al.  ASYMMETRIC SURFACE BRIGHTNESS DISTRIBUTION OF ALTAIR OBSERVED WITH THE NAVY PROTOTYPE OPTICAL INTERFEROMETER , 2004 .

[38]  F. Thevenin,et al.  The angular sizes of dwarf stars and subgiants Surface brightness relations calibrated by interferometry , 2004, astro-ph/0404180.

[39]  Ivan Hubeny,et al.  Non-LTE line-blanketed model atmospheres of hot stars. 1: Hybrid complete linearization/accelerated lambda iteration method , 1995 .