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. 1992b, ApJ 392, 328
with metallicities log [Me=H] = 0:28, and 0:20,
Hearnshaw, J.B. 1972, Mem. Roy. Astr. So c. 77, 55
resp ectively. Interp olating these two tracks for the
Hyi p osition, one nds ages of 6.83 and 6.64 Gy.
Hearnshaw, J.B. 1973, in G. Cayrel de Strob el,
A.M. Delplace, eds., L'^age des etoiles, IAU
Coll. 17, p. XLI{1
Jenkins, L.F. 1952, General Catalogue of Trigono-
5. CONCLUSIONS
metric Stellar Parallaxes, Yale Univ. Obs.
No els, A., Grevesse, N. 1993, in W.W. Weiss,
A. Baglin, eds., Inside the Stars, IAU Coll. 137,
Although the stellar luminosity implied by the new
ASPC 40, p. 410
Hipparcos parallax leads to a signi cant reduction of
the age and a slight increase in mass , compared to
Perrin, M.N., Hejlesen, P.M., Cayrel de Strob el, G.,
previous estimates, Hyi do es remain an old star.
Cayrel, R. 1977, A&A 54, 779
Rogers, F.J., Iglesias, C.A. 1992, ApJS 79, 507
Since the evolutionary tracks near the p osition of
van Altena, W.F., Lee, J.T., Hoeit, E.D. 1995, The
Hyi in the M = log T diagram run nearly hor-
V e
General Catalogue of Trigonometric Stellar Par-
izontally, the exact value for its e ective temp era-
allaxes, Fourth Ed., Yale Univ. Obs., Vol. I
ture has almost no e ect on its inferred prop erties.
This is indeed why Hyi is such an attractive star to
VandenBerg, D.A. 1992, ApJ 391, 685
study: there is probably no other single star b esides
VandenBerg, D.A., Swenson, F.J., Rogers, F.J., Igle-
the Sun , for whichit is p ossible to determine such
sias, C.A., Alexander, D.R. 1997, in preparation
a precise mass and age and further improvements
will now require a more precise determination of its
metallicity .
As a nal caveat, we note that all the ab ove dis-
cussion is p erformed within the paradigm of stellar
evolutionary mo dels, as calibrated b efore Hipparcos.
In case Hipparcos data would systematically change,
e.g. the future calibration of stellar luminosities, that
might lead to revisions of stellar evolution mo deling,
and p erhaps also a ect age determinations.
ACKNOWLEDGMENTS
The Swedish part of this pro ject was supp orted
by the Swedish National Space Board and by the
Swedish Natural Science Research Council. DAV is
grateful for the supp ort of a Killam ResearchFellow-
ship and an op erating grant from the Natural Sci-
ences and Engineering Research Council of Canada.