699 HIPPARCOS SUBDWARFS AND GLOBULAR CLUSTERS: TOWARDS RELIABLE ABSOLUTE AGES 1 2 3 F. Pont , C. Charb onnel , Y. Lebreton 1 3 4 M. Mayor ,C.Turon , D.A. VandenBerg 1 Observatoire de Gen eve, Sauverny, Switzerland 2 Lab oratoire d'Astrophysique de Toulouse, CNRS URA 5572, Toulouse, France 2 DASGAL/URA CNRS 335, Observatoire de Paris-Meudon, France 3 DepartmentofPhysics and Astronomy, University of Victoria, Canada tted to lo cal sub dwarfs of known distances and sim- ABSTRACT ilar metallicities, and their distance mo duli can be determined indep endently of any mo del assumption. The distance and age of the key globular cluster We shall fo cus here on M92 NGC 6341 as a repre- M92 are determined with Hipparcos eld sub dwarfs. sentative of the oldest GC p opulation. M92 is one of [Fe/H] values for sub dwarfs we re measured with the the most metal-p o or GC, with a small and uncontro- Coravel sp ectrometer. The distance mo dulus of M92 versial value of foreground reddening, a well-known is obtained by tting the cluster sequence to sub d- metallicity, and a sequence measured with great accu- warfs of a similar metallicity, and the age by compar- racy down to M > 8 mag Stetson & Harris 1988. ison of the turno magnitude with up-to-date evolu- V It has b een recognized by several study of relative tion mo dels. Particular attention is given to system- ages as among the oldest GCs Stetson et al. 1996. atic and selection biases, and to the e ect of bina- ries. Field sub dwarfs evolved past the turno stage are also considered. 2. HIPPARCOS SUBDWARF SAMPLE Our b est estimate of the distance mo dulus of M92 is =14:61 0:08 mag, using 17 Hipparcos sub dwarfs 0 with [Fe/H]< 1:8. The age obtained is 141.2 Gyr, The sample on which this study is based is the union implying an age of at least 14 Gyr for the Universe. of two separate Hipparcos prop osals: The value of the small colour shift needed in the mo d- els to t the M92 sequence is con rmed with an in- { a set of 330 stars previously known to b e sub dwarf dep endent set of intermediate-metallicity Hipparcos candidates from various sources. sub dwarfs. { ab out 300 stars revealed to b e markedly b elow the solar-metallicity ZAMS according to Hipparcos data. Key words: globular clusters; sub dwarfs; ages glob- 1 ular clusters, Universe. Coravel [Fe/H] measurements were gathered for most stars in the sample, and p o oled with other reli- able metallicity determinations for sub dwarfs Schus- ter & Nissen 1989, Ryan & Norris 1991, Axer et al. 1. INTRODUCTION 1994, Carney et al. 1994. The result is a set of 506 sub dwarf candidates with go o d parallax = < 20 per cent, magnitude, colour and [Fe/H] data, The dep endence of turno luminosity on age for glob- from which smaller samples can b e selected for sp e- ular clusters GC is a very robust prediction of stel- ci c studies. lar evolution mo dels. It is directly related to main- sequence lifetimes for 1M stars, and avoids the delicate problems asso ciated with the mo del tem- p erature and colour predictions age from turno 3. CORAVEL [FE/H] DETERMINATION colour or with advanced stages of evolution age from horizontal-branch p osition. The cross-correlation function equivalent width de- Up to now, the main obstacle to the application of the noted W given by the radial velo city scanner Coravel turno luminosity metho d to determine reliable ab- is a tight function of T and [Fe/H] for dwarfs. e solute ages for GCs has b een the uncertain de nition For F dwarfs, the determination of [Fe/H] from W of the sub dwarf intrinsic luminosity scale. Hipparcos 1 The Coravel radial velo city scanner is describ ed in parallaxes for nearby sub dwarfs now allow a new cal- Baranne et al. 1979. ibration of this scale. GC sequences can b e directly 700 5. SYSTEMATICS BIASES Imp ortant systematic biases are known to a ect lumi- nosities computed from parallax data see the often- quoted mo delisation of Lutz & Kelker 1973, or the elab oration by Smith 1987. Other biases also a ect the calculation of the mean luminosity of a set of stars of given intrinsic characteristics. From Monte Carlo simulations of the whole selection and treatment pro cedure, we nd that the global bias on globular cluster distances from Hipparcos sub d- warfs acts in a direction opposite to the classic Lutz- Kelker bias. In the sp eci c case of Hipparcos sub d- warfs selected with a = < lim criteria and tted to GC sequences, the total bias can b e schematically broken down into three comp onents: 1. the classical Lutz-Kelker bias: the interaction of the steep parallax distribution Figure 3a with Figure 1. Hipparcos distances compared to previous es- the parallax uncertainties causes a systematic timates from Zinn & West 1981, for the eight subd- underestimation of luminosity; warfs most often used to determine the subdwarf lumi- 2. a luminosity bias favouring brighter stars, aris- nosity scale. Most distances were importantly underesti- ing from the strong dep endence of the paral- mated. lax uncertainty on magnitude in Hipparcos data Figure 3b; was calibrated using the meticulous study of Ed- 3. a Lutz-Kelker typ e bias on [Fe/H]; the interac- vardsson et al. 1993. The resulting disp ersion, tion of the steep [Fe/H] distribution for sub- [Fe/H] [Fe/H] , is 0.06 dex if T is known dwarfs Figure 3c with the errors on [Fe/H] Coravel E 93 e indep endently, or 0.09 dex if the BV colour index causes a systematic underestimation of metal- is taken as a temp erature indicator. These values in- licity. dicate that the Coravel determination is at least as precise as go o d sp ectroscopic values. Moreover, 2 and 3 couple strongly, so that at a given [Fe/H] and colour, more metal-rich stars more For G dwarfs and sub dwarfs, the W index is cal- numerous and brighter have a signi cantly higher ibrated using the comprehensive study by Carney probabilitytobe included in the sample than more et al. 1994. The resulting disp ersion is higher, metal-p o or stars, causing a net overestimation of =0:17 dex, probably re ecting the lower accuracy mean luminosity. of Carney et al. [Fe/H] values. From our Monte Carlo simulations, we nd a resul- Some other sub dwarf studies, such as Axer et tant correction of 0.07 mag towards fainter magni- al. 1994, have advo cated signi cantly more com- tudes for main-sequence sub dwarfs, and of 0.11 to- pressed [Fe/H] scales for sub dwarfs i.e. shifted to- 2 wards brighter magnitudes for subgiants . wards higher metallicities. The e ect of adopting sucha [Fe/H] scale [Fe/H] for our sample is also 2 considered. 6. BINARIES Several binaries were detected in the sample, either 4. LUMINOSITY OF VERY METAL-POOR by radial velo cityvariations or by Hipparcos. Unre- SUBDWARFS solved binaries can b e up to 0.75 mag brighter than the single-star sequence, and thus imp ortantly af- fect the luminosity determination. Along with the Previously, only 8 to 15 sub dwarfs of all metallicities usual pro cedure of removing detected binaries, we had reliable parallaxes. Even for this small sample, also consider the results obtained by applying an av- the Hipparcos data reveals imp ortant systematic er- erage magnitude correction to all detected binaries rors Figure 1. The abundance of very metal-p o or | a correction calculated from the p osition of the sub dwarfs in our sample allows a separation into sev- binary star sequence in the Praesep e cluster from eral metallicityintervals, thus reducing the need for Bolte 1991. This last pro cedure may b e more jus- shifts in colour to bring all ob jects to a common ti ed than simply rejecting detected binaries, since [Fe/H] Figure 2. The data show, for the rst time, it also statistically accounts for undetected binaries the p osition of the turno and the subgiant branch of remaining in the sample. the eld subdwarfs. The sequence is esp ecially clear 2 for the most metal-p o or stars. These plots provide a Note that LK-typ e corrections should still b e applied if very strong constraint on the sub dwarf sequence lu- individual magnitudes are needed. The corrections that we derive are only valid for whole samples, and re ect the average minosity, the age of eld sub dwarfs themselves, and e ect of ob jects excluded by the selection pro cedure. the distance to globular clusters. 701 a Fe/H < 1.8 dex b 1:8 < Fe=H < 1:1 dex Figure2. Position in the HR diagram of the most metal-poor subdwarfs, divided in two [Fe/H] intervals. Detected binaries are shown as open symbols. The line is the Hyades sequence. a Distribution of parallaxes for a b Dep endence of the parallax un- c Distribution of metallicity for the volume-limited sample. certainty on magnitude for Hipparcos sub dwarf sample. data. Figure3. Three signi cant sources of biases. 702 Table 1. Data for subdwarfs with [Fe/H] < 1.8 and = <15 per cent. B V is the colour shift used to bring the 1 data to [Fe/H] = {2.2. 1 HIP Name B V EB-V M [Fe/H] [Fe/H] B V Binarity Note 0 V M 1 2 V 14594 HD 19445 0.48 0.01 5.07 0.09 2.20 1.96 0.000 C 16404 BD +66 258 0.60 0.06 5.94 0.17 2.10 1.87 0.005 CSH 21609 HD 29907 0.61 0.03 5.92 0.12 2.28 2.03 0.004 SB 24316 HD 34328 0.47 0.03 5.15 0.14 1.88 1.67 0.014 C 38541 HD 64090 0.62 0.00 6.01 0.06 1.92 1.71 0.015 SV 44124 BD 03 2525 0.44 0.04 5.00 0.28 1.94 1.73 0.008 SB2 46120 CPD80 349 0.54 0.02 6.12 0.12 2.26 2.01 0.003 C 48152 HD 84937 0.39 0.01 3.78 0.17 2.21 1.97 0.000 C 60632 HD 108177 0.44 0.00 4.86 0.24 1.91 1.70 0.009 C 65201 HD 116064 0.42 0.03 4.66 0.19 2.39 2.13 0.006 H2 68464 HD 122196 0.41 0.05 3.53 0.27 2.22 1.98 0.002 C 72461 BD +26 2606 0.44 0.00 4.79 0.28 2.58 2.30 0.012 SB 73385 HD 132475 0.44 0.06 3.53 0.21 1.95 1.74 0.020 C 76976 HD 140283 0.44 0.04 3.29 0.11 2.41 2.15 0.034 C 98532 HD 189558 0.50 0.07 3.36 0.15 1.84 1.64 0.064 C 99267 BD +42 3607 0.50 0.01 5.48 0.19 2.13 1.90 0.002 C 106924 BD +59 2407 0.58 0.05 6.12 0.16 1.91 1.70 0.017 C Binarity notes { C: constant radial velo city; SB: sp ectroscopic binary; SB2: double-line sp ectroscopic binary; SV: p ossible small radial velo cityvariations; SH: susp ected non-single from Hipparcos catalogue; H2: two comp onents resolved by Hipparcos.