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Beta Hydri G2 Iv : a Revised Age for the Closest Subgiant

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Beta Hydri G2 Iv : a Revised Age for the Closest Subgiant 397 BETA HYDRI G2 IV: A REVISED AGE FOR THE CLOSEST SUBGIANT 1 1 2 Dainis Dravins , Lennart Lindegren , Don A. VandenBerg 1 Lund Observatory,Box 43, SE-22100 Lund, Sweden 2 DepartmentofPhysics and Astronomy, Univ. of Victoria, P.O. Box 3055, Victoria, B.C., Canada V8W 3P6 2. BETA HYDRI | THE STAR ABSTRACT The characteristics of Hyi are typical of the old The secular evolution of solar-typ e atmospheres may Galactic disk p opulation: e.g. a feeble chromospheric be studied through comparisons of the current Sun activity and an eccentric Galactic orbit. As exp ected with old solar-typ e stars of known age. Among the for an old star, Hyi is slightly metal p o or, with few such stars in the solar Galactic neighborhood, log Fe/H determinations relative to the Sun around Hydri G2 IV stands out as a normal single star 0:2. While the abundances of heavier metals are with an advanced age. Previous age determinations low, lithium is abundant a signature shared with ' 9:5 Gy were based on the old ground-based other older subgiants, p ermitting analyses of stellar parallax of 153 mas. The new Hipparcos value of internal evolution in the p ost-main-sequence stages. 133:78 0:51 mas implies an absolute magnitude Various determinations set the e ective temp erature M = 3:43 0:01, 0.3 mag brighter than previ- V to 5800 100 K, equal to the commonly accepted ously b elieved. New evolutionary calculations pro- value for the Sun of T = 5780 30 K. For a re- e duce b est- t mo dels with ages around 6.7 Gy. Al- view of the basic stellar parameters, see Dravins et though the Hipparcos data thus lead to a signi cant al. 1993a. reduction of its age, Hyi remains an old star. Key words: space astrometry; stars: evolution; stars: 3. HIPPARCOS OBSERVATIONS individual; stars: late-typ e. Hipparcos data ESA 1997 for Hyi give the par- allax 133:78 0:51 mas. The prop er-motion mea- surements indicate a steady stellar motion, with no indications of duplicity or other irregularities. The 1. INTRODUCTION photometry gives Hp =2:9305 0:0003 mag, which for V I =0:68 mag corresp onds to V =2:801 mag, as transformed to the Johnson system. This is fully How do solar-typ e atmospheres evolve along with the consistent with the Hipparcos input catalogue value stellar evolution? Will the Sun still have a magnetic of V =2:82 mag. No photometric variability could activity cycle billions of years in the future, after it b e detected by Hipparcos, with an upp er amplitude has left the main sequence? Answers to questions limit of ' 0:004 mag. such as these may be found by studying old solar- typ e stars, taken to represent the future Sun. Such stars must have reliable age determinations, and b e 4. BETA HYDRI | THE AGE bright enough for detailed sp ectroscopy. Among old and single stars, accurate age determinations are p os- sible for G subgiants that haveevolved slightly o the 4.1. The Previous Old Age main sequence, yet are still suciently close to it to avoid ambiguities in stellar evolutionary tracks. The age of Hyi was previously determined bymod- eling evolutionary tracks across its lo cation in the The closest and brightest m = 2:8 among such V Hertzsprung-Russell diagram, as inferred from its stars in the solar Galactic neighb orho o d is Hydri parallax measured early in this century. The General HR 98; HD 2151; HIP 2021, of sp ectral typ e G2 IV. Catalogue of Trigonometric Stel lar Paral laxes listed Detailed studies of its photospheric structure, chro- the absolute parallax as 153 10 mas standard error, mospheric and transition zone emission, and of coro- probable error 7 mas; Jenkins 1952. After incorp o- nal X-ray uxes have b een made, making Hyi one of rating some additional observations, this value was the b est-studied individual stars other than the Sun slightly mo di ed to 150:1 7:2 mas in the latest edi- Dravins et al. 1993a,b,c; Dorren et al. 1995; Gudel tion van Altena et al. 1995. et al. 1997. 398 3 β Hyi 1.05 M 7 1.11 M 5 4 V 3 M 1 Gy Sun 5 3.80 3.75 3.70 log Teff [K] Figure 1. Stel lar evolution, and the age of Beta Hydri. Post-main-sequence tracks are shown for two representative models, passing through the post-Hipparcos position of Hyi in the M /log T plane black diamond. The position V e based on the old ground-basedparal lax is also marked grey diamond. Atbottom, a track for a solar model evolved until 4.6 Gy demonstrates that the present solar luminosity and temperatureareaccurately reproduced for the adoptedmodel parameters. of elements, and the same nuclear reaction rates as The most detailed previous age determination gave in standard solar mo dels Bahcall & Pinsonneault values around 9.5 Gy Dravins et al. 1993a. Also ear- 1992; Guenther et al. 1992a, b. It incorp orates low- lier work had arrived at ages in the 8{10 Gy range: temp erature opacities similar to those rep orted by Cayrel de Strob el 1981; Hearnshaw 1972, 1973; Per- Alexander & Ferguson 1994, and an equation of rin et al. 1977. Such an age ts well with that esti- state with Coulomb corrections and other non-ideal mated for the Galactic disk. The main observational e ects; see VandenBerg et al. 1997 for a detailed uncertaintywas due to the parallax error, while er- discussion of the adopted physics. These improve- rors in T play almost no role since Hyi is rapidly e ments lead to a solar helium abundance Y ' 0:27 evolving nearly horizontally in the HR diagram. rather than ' 0:28, when the Coulomb interaction is ignored. As b efore, the e ective temp erature was adopted as 5800 K. 4.2. The New Old Age A number of evolutionary tracks were computed, a few of which are shown in Figure 1. As a mo del veri - The availability of the new, and very much more ac- cation, a track for a standard solar mo del shows that curate, parallax from Hipparcos now p ermits a more the present luminosity M = 4:72; M = 4:84 precise determination of the evolutionary status for bol V and temp erature of the Sun are accurately repro- Hyi. The signi cance of such a new determination duced for the adopted choices of Y and mixing-length lies also in that the Hipparcos value rather signif- parameter. icantly by two standard errors deviates from the previous ground-based estimate. The Hipparcos par- Mo dels were computed for the slightly di erent allax yields the absolute magnitude M =3:430:01, V metallicities Z = 0:0100, 0.0125, and 0.0150, with some 0.3 mag brighter than previously b elieved. the same Y as needed to t the Sun. Another mo del for Z = 0:0125 had a helium abundance lower by New evolutionary calculations have b een made, us- Y =0:01. The four mo dels assume masses that are ing a considerably improved version of the program necessary, for the various choices of Z and Y ,tointer- co de used in previous calculations VandenBerg 1992; sect the p osition of Hyi in the M = log T plane. Dravins et al. 1993a; and references in these pap ers. V e The choices of Z should encompass the true metallic- This new version uses recentOPAL opacities Rogers ity corresp onding to the logarithmic values relative & Iglesias 1992 for the No els & Grevesse 1993 mix 399 REFERENCES Table 1. Interpolating in the tracks at the M ;T value V e of Hyi, one nds the ages [Gy]. Alexander, D.R., Ferguson, J.W. 1994, ApJ 437, 879 Bahcall, J.N., Pinsonneault, M.H. 1992, Rev. Mo d. Z Y [Me/H] Mass Age Phys. 64, 885 0.0100 0.2716 0:28 1.053 6.83 Cayrel de Strob el, G. 1981, Bull. Inform. CDS 20, 28 0.0125 0.2716 0:20 1.095 6.52 Dorren, J.D., Gudel, M., Guinan, E.F. 1995 ApJ 448, 0.0150 0.2716 0:10 1.228 6.31 431 0.0125 0.2616 0:20 1.109 6.64 Dravins, D., Lindegren, L., Nordlund, A., Vanden- Berg, D.A. 1993a, ApJ 403, 385 Dravins, D., Linde, P., Fredga, K., Gahm, G.F. 1993b, ApJ 403, 396 to hydrogen [Me=H] '0:28, 0:20, and 0:10, re- Dravins, D., Linde, P., Ayres, T.R., Linsky, J.L., sp ectively. Interp olating in the tracks for the age Monsignori-Fossi, B.,Simon, T., Wallinder, F. at the M ;T value of Hyi, one nds Figure 1 1993c, ApJ, 403, 412 V e and Table 1 that b est- t mo dels have parameters ESA, 1997, The Hipparcos and Tycho Catalogues, around: mass = 1:1 M ; Y =0:27, Z =0:011 cor- ESA SP{1200 resp onding to a metallicity log [Me=H] around 0:2; Gudel, M., Guinan, E.F., Skinner, S.L. 1997, ApJ, in T = 5800 K, and ages around 6.7 Gy. e press In Figure 1, the sup erp osed symb ols mark every bil- Guenther, D.B., Demarque, P., Kim, Y.C., Pinson- lion of years, starting from the pre-main-sequence neault, M.H. 1992a, ApJ 387, 372 zero age. The long-dashed curve is for a mo del with Guenther, D.B., Demarque, P., Pinsonneault, M.H., mass = 1:053 M , the dotted one for 1:109 M , Kim, Y.C.
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