Summary
We present interferometric observations and model atmosphere analyses of three stars: the F-type subgiant Procyon, the A-type supergiant Deneb, and the B-type supergiant Rigel. We use VLTI/VINCI and Mark III observations of Procyon to test recent multiwavelength limb-darkening predictions from 3-D hydrodynamic atmosphere simulations with no free parameters for convection. We also investigate the effects of different 1-D atmospheric convection treatments on limb-darkening predictions. We show that the 3-D model predictions are confirmed and we find that 1-D models fail to reproduce Procyon’s UV spectral energy distribution, a result consistent with models of granulation for Procyon’s surface. We use observations employing the longest baselines of the CHARA Array together with the FLUOR beam combiner to determine precise angular diameters for the two early-type supergiants and test limb-darkening predictions from expanding atmosphere models of these tars’ stellar winds. For Deneb, we derive angular diameters consistent with previous measurements, but which vary with position angle at the ≃3% level. Observations of the 2nd lobe of Deneb’s visibility curve are more consistent with expanding atmosphere predictions than hydrostatic atmosphere predictions. For Rigel, we derive from the CHARA/FLUOR observations a limb-darkened angular diameter consistent with a recent VLTI/IONIC measurement and 8% larger than reported from the Intensity Interferometer.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Mozurkewich et al. Angular Diameters of Stars from the Mark III Optical Interferometer. AJ, 126:2502–2520, 2003.
P. Kervella, F. Thé evenin, P. Morel, G. Berthomieu, P. Bordé, and J. Provost. The diameter and evolutionary state of Procyon A. Multi-technique modeling using asteroseismic and interferometric constraints. A&A, 413:251–256, 2004.
F.Abe et al.Probing the atmosphere of a solar-like star by galactic microlensing at high magnification. A&A, 411:L493–L496, 2003.
T.M. Girardet al.A Redetermination of the Mass of Procyon. AJ, 119:2428–2436, 2000.
C. Allende Prieto, M. Asplund, R.J.G. López, and D.L. Lambert. Signatures of Convection in the Spectrum of Procyon: Fundamental Parameters and Iron Abundance. ApJ, 567:544–565, 2002.
K.Schwarzschild. On the equilibrium of the sun’s atmosphere. In D.H. Menzel, editor, Selected Papers on the Transfer of Radiation. New York: Dover, 1966. Über das Gleichgewicht der Sonnenatmosphäre” Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen. Math.-phys. Kalsse (1906) 295, 41.
M. Asplund, N. Grevesse, A.J. Sauval, C. Allende Prieto, and D. Kiselman. Line formation in solar granulation. IV. [O I], O I and OH lines and the photospheric O abundance. A&A, 417:751–768, 2004.
J.B. Hearnshaw. The Analysis of Starlight: One Hundred and Fifty Years of Astronomical Spectroscopy. Cambridge: Cambridge University Press, 1990.
G.Müller. Die Photometrie der Gestirne. Leipzig: Wilhelm Engelmann, 1897.
J.B. Hearnshaw. The Measurement of Starlight, Two Centuries of Astronomical Photometry. Cambridge: Cambridge University Press, 1996.
C.H. Payne. Stellar Atmospheres. Number1 in Harvard Observatory Monographs. Cambridge: Harvard Observatory, 1925.
J.P. Aufdenberg, H.-G. Ludwig, and P. Kervella. On the Limb Darkening, Spectral Energy Distribution, and Temperature Structure fo Procyon. ApJ, 633, 424–439, 2005.
F.Castelli, R.G. Gratton, and R.L. Kurucz. Notes on the convection in the ATLAS9 model atmospheres. A&A, 318:841–869, 1997.
H.Neckel and D.Labs. Solar limb darkening 1986-1990 (λλ 303 to 1099nm). Solar Physics, 153:91–114, 1994.
M. Asplund, Å.Nordlund, and R. Trampedach. Confrontation of Stellar Surface Convection Simulations with Stellar Spectroscopy. In ASP Conf. Ser. 173: Stellar Structure: Theory and Tests of Convective Energy Transport, page 221, 1999.
M. Shao, M.M. Colavita, B.E. Hines, D.H. Staelin, and D.J. Hutter. The Mark III stellar interferometer. A&A, 193:357–371, 1988.
P.Kervellaet al.VINCI, the VLTI commissioning instrument: status after one year of operations at Paranal. In Proceedings of the SPIE, Volume 4838, pages 858–869, 2003.
P.H. Hauschildt, F.Allard, J. Ferguson, E. Baron, and D.R. Alexander. The NEXTGEN Model Atmosphere Grid. II. ApJ, 525:871, 1999.
B. Freytag, M. Steffen, and B. Dorch. Spots on the surface of Betelgeuse – Results from new 3D stellar convection models. AN, 323:213–219, 2002.
U. Heiter et al.New grids of ATLAS9 atmospheres I: Influence of convection treatments on model structure and on observable quantities. A&A, 392:619–636, 2002.
J.P. Aufdenberg et al.The Spectral Energy Distribution and Mass-loss Rate of the A-type Supergiant Deneb. ApJ, 570:344–368, 2002.
R.P. Kudritzki et al.The Wind Momentum-Luminosity Relationship of Galactic A- and B-Supergiants. A&A, 350:970, 1999.
J.P. Aufdenberg et al. CHARA/FLUOR Observations of B- and A-type Supergiants Rigel and Deneb. in preparation.
T.A. ten Brummelaar et al.First Results from the CHARA Array. II. A Description of the Instrument. ApJ, 628:453, 2005.
V. Coudé du Foresto et al.FLUOR fibered beam combiner at the CHARA array. In Proceedings of the SPIE, Volume 4838, pages 280–285, 2003.
S.R. Cranmer and S.P. Owocki. The effect of oblateness and gravity darkening on the radiation driving in winds from rapidly rotating B stars. ApJ, 440:308–321, 1995.
R.HanburyBrown, J.Davis, and L.R. Allen. The angular diameters of 32 stars. MNRAS, 167:121, 1974.
J.B LeBouquin et al. First observations with an H-band integrated optics beam combiner at the VLTI. A&A, 424:719–726, 2004.
A.Richichi and I. Percheron. CHARM: A Catalog of High Angular Resolution Measurements. A&A, 386:492–503, 2002.
A. Richichi, I.Percheron, and M. Khristoforova. CHARM2: An updated Catalog of High Angular Resolution Measurements. A&A, 431:773–777, 2005.
B. Baschek, M. Scholz, and R. Wehrse. The parameters R and Teff in stellar models and observations. A&A, 246:374, 1991.
M. Wittkowski, J.P. Aufdenberg, and P.Kervella. Tests of stellar model atmospheres by optical interferometry. VLTI/VINCI limb-darkening measurements of the M4 giant ψ Phe. A&A, 413:711–723, 2004.
R. Hanbury Brown, J. Davis, R.J.W. Lake, and R.J. Thompson. The Effects of Limb Darkening on Measurements of Angular Size with an Intensity Interferometer. MNRAS, 167:475, 1974.
A.R. Hajian et al.Direct Confirmation of Stellar Limb Darkening with the Navy Prototype Optical Interferometer. ApJ, 496:484, 1998.
A. Quirrenbach et al.Angular Diameter and Limb Darkening of Arcturus. A&A, 312:160, 1996.
D. Burns et al.The surface structure and limb-darkening profile of Betelgeuse. MNRAS, 290:L11, 1997.
G. Perrin et al.Interferometric observations of the supergiant stars α Orionis and α Herculis with FLUOR at IOTA. A&A, 418:675–685, 2004.
M.Wittkowski et al.Direct Multi-Wavelength Limb-Darkening Measurements of Three Late-Type Giants with the Navy Prototype Optical Interferometer. A&A, 377:981, 2001.
N. Ohishi, T.E. Nordgren, and D.J. Hutter. Asymmetric Surface Brightness Distribution of Altair Observed with the Navy Prototype Optical Interferometer. ApJ, 612:463–471, 2004.
A. Claret. A New Non-linear Limb-darkening Law for LTE Stellar Atmosphere Models. A&A, 363:1081–1190, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Aufdenberg, J.P. et al. (2007). Limb Darkening: Getting Warmer. In: Richichi, A., Delplancke, F., Paresce, F., Chelli, A. (eds) The Power of Optical/IR Interferometry: Recent Scientific Results and 2nd Generation Instrumentation. Eso Astrophysics Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74256-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-74256-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74253-1
Online ISBN: 978-3-540-74256-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)