.175F .221. The Astrophysical Journal, 221:175-185, 1978 April 1 . © 1978. The American Astronomical Society. All rights reserved. Printed in U.S.A. 1978ApJ. EVOLUTION OF THE a CENTAURI SYSTEM Brian P. Flannery and Thomas R. Ayres Center for Astrophysics, Harvard College Observatory and Smithsonian Astrophysical Observatory Received 1977 July 11; accepted 1977 October 12 ABSTRACT Astrometric data and an analysis of available photometry suggest that the masses, luminosities, and temperatures of the A and B components of a Centauri are, respectively, (1.11, 0.92 [ ± 37J) M©, (1.51, 0.47 [±4%])L0, and (5800, 5300 [± 100]) K. By constructing consistent evolutionary models for the binary, relative to a solar fiducial sequence, we find Za/ZQ ~ 2, Ya — 70 = —0.01, and a system age of 6 billion years. A previous curve-of-growth analysis by French and Powell supports the conjecture that the A and B components have similar compositions, and that the system is slightly metal-rich compared to the Sun. This, coupled with the nearly identical galactic motions of a Centauri and the Sun, implies that if accretion of material from the interstellar medium has substantially altered the metallicity of the solar surface convection zone with respect to the interior, the bulk of the accretion must have occurred in a very small number of significant accumulations. Our results also suggest that the Sun and a Centauri do not obey the putative relation A T æ (3-5) AZ for the galactic enrichment of helium and metals. Subject headings: stars : abundances — stars : evolution — stars : individual — stars : interiors I. INTRODUCTION II. PHYSICAL PARAMETERS OF THE a CENTAURI SYSTEM The nearby triple system of a Centauri (G2 V + a) Astrometric Properties Kl V + dM5e) provides an excellent opportunity for In this section we discuss, and in some cases the comparison of stellar structure models against reanalyze, available data in order to derive accurate stars whose gross properties—mass, luminosity, tem- estimates for the stellar masses, luminosities, tempera- perature, chemical composition, rotation, etc.—can be tures, and chemical composition of a Cen. The astro- reliably determined. These properties are (or can be) metric properties of the binary are quite reliable reliably established for the A and B components of because they are based on a well observed visual orbit, the widely separated, i.e., noninteracting, double on a large parallax, and on additional information system. Unfortunately, the distant, active dMe available from measured radial velocity variations. component Proxima (see Haisch et al 1977) cannot be Several orbital solutions for the visual binary exist in included in our analysis because of its faintness and the literature (e.g., van de Kamp 1958; Gasteyer lack of a reliable orbit. The basic intent of this paper is 1966); here we adopt the values recently derived by similar to previous unsuccessful attempts to model the Kamper and Wesselink (1977), as listed in Table 1. visual binary stars in the Hyades cluster (see Iben 1967 The masses of the A and B components are 1.11 and and references therein). Given two points on an H-R 0.92 M0, respectively, and the binary distance is diagram plus the stellar masses, we seek to determine 1.34 pc. Because the period and semimajor axis are a consistent evolutionary history for the double star. very well known, the total and individual masses Unlike the Hyades cluster, a Cen will be shown to be should be accurate to about 370, corresponding to the somewhat evolved. possible 1% error in parallax, while the uncertainty The paper is divided as follows : in § II we discuss of the mass ratio is somewhat smaller, about 2J0, observational material available in the literature relevant to the evolutionary status of a Cen; in § III TABLE 1 we describe theoretical evolutionary sequences appro- Astrometric Properties of a Centauri* priate for the A and B components for two values of metallicity Z = 0.02 and 0.04, and a reference solar Period 80.089 years model (Z = 0.02); in § IV we present a partial Semi major axis 17''544, 23.5 AU reanalysis of the observed abundances, based on the Parallax 0''746 ± 0.008, 1.34 pc equivalent measurements of French and Powell (1971), Mb/Ma... 0.828 ± 0.007 (Ma + Mb)/M0. 2.03 ± 0.07 which provide a consistency check on the evolutionary M /M , M [Mq 1.11 ± 0.04, 0.92 ± 0.03 models ; finally, in § V we discuss and apply our results a 0 b in a more general context. * Kamper and Wesselink 1977. 175 © American Astronomical Society • Provided by the NASA Astrophysics Data System .175F .221. 176 FLANNERY AND AYRES . Vol. 221 b) Photometry, Luminosities and Colors a Lyr) ; therefore V0 cannot be determined directly. On Alpha Centauri A and B have been measured photo- the other hand, the absolute irradiance of the solar spectrum at the Earth is known very accurately (e.g., 1978ApJ. metrically in a variety of broad-band systems including Labs and Neckel 1970). In fact, we can estimate the the standard UBV (Johnson 1956; Cousins and 0 Lagerweij 1967; Eggen [see Thomas et al 1973]), the apparent visual luminosity of the Sun, «^ , indirectly long-wave RIJKLMN (Kron, Gascoigne, and White by folding a numerical representation of the F-filter 1957 ; Thomas, Hyland, and Robinson 1973 ; Alexander response function into the solar irradiance curve and Branch 1973), and the six-color UViBGRI (Powell (e.g., Labs 1975). If we also know the absolute flux, and French 1970). Narrow-band photometric indices in the same units, corresponding to the zero-point of are also available (Willstrop 1965; Rodgers [see the stellar magnitude scale (i.e., V = 0), we can Ayres et al. 1976]). Table 2 summarizes the photo- convert into magnitudes to obtain F©. We determine the F = 0 absolute flux using Vega metric data to be discussed in this subsection. aLyr The relative luminosities of the A and B com- as a transfer standard. To calibrate ^ in absolute ponents can be estimated to sufficient accuracy flux units, we adopt the Hayes and Latham (1975) according to the following identity: monochromatic calibration of Vega at 5556 Â, and apply the synthetic F-filter response described by Labs (1975) to the Schild, Peterson, and Oke (1971) energy aLyr (■) distribution. Finally, we convert ^ to^=0 using the measured apparent visual magnitude of Vega, with P«Lyr = +0-03 ± 0.02mag (Johnson et al. 1966; Blanco et al. 1970). In this fashion, we obtain, 9 2 1 1 AA ^=0 = 3.63 x 10" ± 3% ergs cm“ s“ “ (at the Earth). We have chosen to work relative to the apparent visual magnitude V; hence the expression in square The uncertainty in the zero-point absolute flux arises brackets is a differential bolometric correction (B.C.). equally from the Hayes and Latham monochromatic The sum is taken over the available photometry. A calibration and FaLyr. similar expression can be written for LA/L°, provided Applying the F-filter response to the solar irradiances that we can convert measured solar irradiances (e.g., tabulated by Beckers, Bridges, and Gilliam (1976; Labs and Neckel 1970) into stellar absolute magni- Labs and Neckel calibration), and converting to tudes. the stellar magnitude scale, we obtain, F = —26.76 ± 0.03 mag, i) The Apparent and Absolute Visual Magnitudes of 0 the Sun, a. Centauri A, and a Centauri B which implies In order to evaluate the leading term on the right- Mv° = +4.81 ± 0.03 mag, hand side of equation (1), we must determine the using the solar distance modulus cited by Allen (1973). absolute visual magnitudes Mv of the Sun, a Cen A, Combining the solar estimate with the values of Mv and a Cen B. These are obtained from apparent for a Cen A and B in Table 2, gives, magnitudes V and measured distances. However, the Sun is some 27 mag brighter than V/V> - 1.53 ± 4% , B standard photometric comparison standards (e.g., LV /LV° - 0.44 ± 4% . TABLE 2 Photometric Properties B— V V-I L/Lq Star V [Terr, S(B.C)] [reff, S(B.C.)] Mv [S(B.C.)] Sun — 26.76a 0.65a 0.87b 4.81 1.00 ±0.03 (5770,0.0) (5770,0.0) ±0.03 (0.00) a Cen B 0.88°, 0.91«e a,c 0.93a s 1.33 0.91 1.03 5.69 0.47 ±470 ±0.02 (5040,-0.20)f (5320,-0.10)f ±0.02 (-0.07) b b d a Cen A -0.01°,+0.01 0.68°, 0.69e ’ 0.72 (La/Lb = 3.18)* -0.01a 0.69a 0.87b 4.35 1.51 ±47, ±0.02 (5630,-0.01)f (5770,0.0)f ±0.02 ( + 0.01) * Using unrounded values for LA, LB. Notes.—a Adopted for this work. b Thomas et al. 1973. c Cousins and Lagerweij 1967. d This work, based on Rodgers (see Ayres et al. 1976) photometry. 6 This work, based on Willstrop 1965 photometry. f From Johnson 1966, as scaled to (B — F)©, (V— /)©. s Alexander and Branch 1973 (uncorrected). © American Astronomical Society • Provided by the NASA Astrophysics Data System .175F .221. No. 1, 1978 EVOLUTION OF a CEN SYSTEM 177 . ii) B —V Colors of the Sun, a Centaur i A, and a Centaur i B Finally we have applied the differential B.C. scheme We can modify the approach of the previous section represented by the brackets of equation (1) using the available broad- and narrow-band photometric indices. 1978ApJ. in order to estimate synthetic B — V colors for the A Sun, a Cen A, and a Cen B.