A&A 413, 251–256 (2004) Astronomy DOI: 10.1051/0004-6361:20031527 & c ESO 2003 Astrophysics The diameter and evolutionary state of Procyon A Multi-technique modeling using asteroseismic and interferometric constraints P. Kervella1,F.Th´evenin2,P.Morel2,G.Berthomieu2,P.Bord´e3, and J. Provost2 1 European Southern Observatory, Casilla 19001, Vitacura, Santiago 19, Chile 2 D´epartement Cassini, UMR CNRS 6529, Observatoire de la Cˆote d’Azur, BP 4229, 06304 Nice Cedex 4, France 3 LESIA, Observatoire de Paris-Meudon, 5, place Jules Janssen, 92195 Meudon Cedex, France Received 19 May 2003 / Accepted 20 August 2003 Abstract. We report the angular diameter measurement obtained with the VINCI/VLTI instrument on the nearby star Procyon A (α CMi A, F5IV–V), at a relative precision of 0:9%. We obtain a uniform disk angular diameter in the K band of θ = ± UD 5:376 0:047 mas and a limb darkened value of θLD = 5:448 0:053 mas. Together with the hipparcos parallax, this gives a linear± diameter of 2:048 0:025 D . We use this result in combination± with spectroscopic, photometric and asteroseismic constraints to model this star± with the CESAM code. One set of modeling parameters that reproduces the observations within their error bars are an age of 2314 Myr, an initial helium mass fraction Yi = 0:301 and an initial mass ratio of heavy elements to Z hydrogen ( X )i = 0:0314. We also computed the adiabatic oscillation spectrum of our model of Procyon A, giving a mean large frequency separation of ∆ν0 54:7 µHz. This value is in agreement with the seismic observations by Marti´c et al. (1999, 2001). The interferometric diameter≈ and the asteroseismic large frequency spacing together suggest a mass closer to 1.4 M than to 1.5 M . We conclude that Procyon is currently ending its life on the main sequence, as its luminosity class indicates. Key words. stars: individual: α CMi – stars: fundamental parameters – stars: evolution – techniques: interferometric 1. Introduction and metallicity Z of the star. We note that among the com- puted models only their model b is close to the mean large α Procyon A ( CMi, HD 61421, HIP 37279) is among the frequency spacing measured by M99–M01. Because numerous brightest stars in the sky and is easily visible to the naked new studies and observational constraints (like the direct di- eye. This made it an ideal target for a number of spectro- ameter) exist today, we re-examine the status of Procyon A in photometric calibration works. It is also a visual binary star helium content Y and in age. We first review and present the (ADS 6251A) classified F5 IV–V, with a white dwarf (WD) adopted fundamental parameters of Procyon A in Sect.2, part companion orbiting the main component in 40 years. The in- of them being used for the limb-darkening in Sect. 3, where fluence of this massive companion on the apparent motion of we present our new interferometric observations and the asso- Procyon was discovered by Bessel (1844). Girard et al. (2000) ciated data processing. In Sect. 4, we detail several models of have measured precisely the orbit of the pair, and obtained Procyon computed with the CESAM code (Morel 1997). These masses of 1:497 0:037 M and 0:602 0:015 M , respec- ± ± models are constrained using the spectroscopic effective tem- tively for Procyon A and B. It has also been an asteroseismic perature and the linear diameter value that we derived from the target since a decade and Martic et al. (1999 and 2001 here- VINCI/VLTI observations. Thus, we avoid to fit the luminosity after M99 and M01) have measured a large frequency spac- for which bolometric corrections are rather uncertain for stellar µ ing of respectively 55 and 54 Hz. These asteroseismic obser- luminosity class IV–V.A study of the asteroseismic frequencies vations provide strong constraints on stellar interior models, is then presented in Sect. 5, before the conclusion. and on macroscopic stellar parameters like mass and radius. Comparing the direct interferometric measurements of this star to its model diameter is therefore important to cross-validate both approaches. Matching Procyon’s position in the HR diagram has been 2. Fundamental parameters recognized as of great difficulty by Guenther & Demarque (1993, hereafter GD93). The reason is the poorly known mass Physical properties of Procyon A are well known thanks to the carefully measured orbit of the system and accurate hippar- Send offprint requests to: P. Kervella, cos parallax. Its mass has been recently measured by Girard e-mail: [email protected] et al. (2000) at MA = 1:497 0:037 M , adopting a parallax of ± Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20031527 252 P. Kervella et al.: The diameter and evolutionary state of Procyon A 283:2 1:5 mas. This mass is computed using a large number Table 1. Relevant parameters of α CMi (Procyon) and its calibra- of observations± of inhomogeneous quality. The same authors, tor α CMa (Sirius). For Sirius, see also Kervella et al. (2003d). when they limit their observation sample to the excellent im- ages obtained with the WFPC2, found MA = 1:465 0:041 M . α CMi α CMa If we replace the parallax used by Girard et al. (2000)± by the HD 61421 HD 48915 parallax from the hipparcos catalogue, 285:93 0:88 mas, mV 0.34 1:47 ± m 0:65 −1:31 the sum of the masses of the binary decreases by 2.9%. K − − Spectral Type F5IV–V A1Vm Consequently, masses become respectively MA = 1:42 ± M(M )1:42 0:04 2:12 0:02 0:04 M for Procyon A and MB = 0:575 0:017 M for the ± ± ± T (K) 6530 50 9900 200 white dwarf Procyon B. Allende Prieto et al. (2002, hereafter eff ± ± log g 3.96 4.30 AP02), using the hipparcos parallax of Procyon A, have esti- [Fe=H] 0:05 0:03 0:50 0:20 mated its mass to be 1:42 0:06 M . From these works, we can − ± ± ± v sin i 3:16 0:50 16:0 1:0 conclude that the mass of Procyon is probably between 1.4 and πa (mas) 285:93± 0:88 379:22± 1:58 ± ± 1.5 M . Consequently, we investigate these two values in our θ (mas) 5:376 0:047 5:94 0:02b UD ± ± b study. The other adopted stellar parameters are summarized in θLD (mas) 5:448 0:053 6:04 0:02 Table 1. ± ± The bolometric luminosity is given by Steffen (1985) a Parallax values from hipparcos (Perryman et al. 1997). b Sirius θUD and θLD are taken from Kervella et al. (2003d). log(L?=L ) = 0:85 0:06. The photospheric properties of Procyon have been carefully± studied by AP02, who derived an effective temperature Teff = 6512 K. This value is based on the angular diameter measured in the visible by the Mark III except if the two stars have filled their Roche lobe, the mass of optical interferometer (Mozurkewich et al. 1991). Detailed 3D Procyon A has only been changed by a negligible amount. stellar atmosphere simulations have led AP02 to correct this The projected rotational velocity of Procyon A has been value of Teff by 80 K. Following their results, we adopt Teff = determined by many authors who derived values smaller 1 6530 50 K in our computations with a surface gravity of than 5.0 km s− . Considering in particular the value proposed ± 1 log g = 3:96 0:02. It is interesting to notice that over the last by AP02, v sin i = 3:2 0:5kms− , we conclude that twenty years,± the effective temperature estimates for Procyon Procyon A is a slow rotator± and we neglect the rotational ve- are spread between 6545 and 6811 K (Cayrel et al. 1997). locity in our modeling of its internal structure. The semi-major Adopting a color index of B V = 0:421 and using the cal- axis of the Procyon orbit being α 4: 5 (Girard et al. 2000), − ' 00 ibration by Alonso (1996) we find Teff = 6551 K which is very the distance between the two companions amounts to 16 au. close to the value proposed by AP02. The tidal interaction between the two components is therefore' The iron abundance at surface of [Fe=H] = 0:05 negligible. 0:03 dex with respect to the solar one is also taken from− AP02.± Therefore we adopt for the modeling of the internal structure 3. Interferometric angular diameter of Procyon A a chemical mixture which is calculated from the iron abundance using the approximation: 3.1. Instrumental setup and data processing ZFe Z ZFe The European Southern Observatory’s Very Large Telescope [Fe=H]s log + log log (1) Interferometer (Glindemann et al. 2000) is operated on top of ≡ Z s X s − X Z Z the Cerro Paranal, in Northern Chile, since March 2001. The log log observations reported here were done with two test siderostats ' X s − X (0.35 m aperture) and the VINCI beam combiner (Kervella et al. 2000, 2003a). The Procyon visibility measurements were where ZFe is the iron mass fraction within Z.Weusethesolar Z s all obtained on the B3–D3 baseline, 24 m in ground length. We Z mixture of Grevesse & Noels (1993) then X = 0:0245. As used a regular K band filter (λ = 2:0 2:4 µm) for these obser- we shall see in Sect.