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Astron. Astrophys. 364, 102-136 (2000)

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10. Discussion

10.1. Comparison with previous observers

Table 13 compares model parameters and abundances found by us (KCCBHV) with those given by other authors. Stellar abundances are relative to the solar values from Grevesse et al. (1996), as given at the end of Table 10. Parameters from de Boer et al. (1997) (BTS) are only averages of previous determinations taken from the literature. Takeda & Sadakane (1997) estimated the stellar parameters of HD 161817 from the literature. They obtained a microturbulent velocity [FORMULA] = 4 km s-1 from an analysis of O I lines in this star and suggested that [FORMULA] is depth dependent.


Table 13. Comparison of stellar parameters and abundances from different authors.
KCCBHV: this paper; AP90, AP94, AP96: Adelman & Philip (1990, 1994, 1996a); GCP: Gray et al. (1996) BTS: de Boer at al. (1997); PB: Przybylski & Bessell (1974); TS: Takeda & Sadakane (1997)

The mean differences between our parameters and abundances and those found by Adelman & Philip (1990, 1994, 1996a) for the nine stars we have in common are:

  • [FORMULA] = +0.08[FORMULA]0.05 ([FORMULA]0.14)

  • [FORMULA] = -0.02[FORMULA]0.14 ([FORMULA]0.35)

  • [FORMULA] = +0.16[FORMULA]0.05 ([FORMULA]0.14)

  • [FORMULA]  = +331 K[FORMULA]75 K ([FORMULA]212 K)

  • [FORMULA]  = +0.10[FORMULA]0.10 ([FORMULA]0.27)

  • [FORMULA]   = +1.0[FORMULA]0.4 ([FORMULA]1.0)

where the numbers in parentheses are the rms differences between the individual determinations. The most significant difference is in [FORMULA] and this may well be traceable to different assumptions for interstellar reddening. The largest of these is the 800 K difference in [FORMULA] for HD 130095 for which there is a large range in the different estimates of [FORMULA]. In spite of this, the differences between the abundance estimates for this star are quite small. For further comments on HD 130095 see Sect. 10.6.

Gray et al. (1996) give stellar parameters for BHB stars that were determined from Philip's Strömgren photometry, classification-dispersion spectra and spectral synthesis. The mean differences between our parameters and theirs for the ten stars in common are:

  • [FORMULA] = -0.26[FORMULA]0.05 ([FORMULA]0.16)

  • [FORMULA]  = +40 K[FORMULA]91 K ([FORMULA]272 K)

  • [FORMULA]  = -0.09[FORMULA]0.02 ([FORMULA]0.06)

The systematic difference between our [FORMULA] and those of Gray et al. are much smaller than for those given by Adelman & Philip. The abundance estimates of Gray et al. from their low resolution spectra, however, average 0.2 to 0.3 dex more metal rich than ours.

10.2. Comparison of BHB abundances with those of other types of halo stars

Excluding BD +32 2188, BD +00 0145 and HD 16456, we have 28 stars that from their stellar parameters, abundances, [FORMULA] and kinematics have a very high probability of being BHB stars. HD 202759 has been classified as a type c RR Lyrae star, but its V-amplitude is so low ([FORMULA] 0.1 mag), and its [FORMULA] is so high (7500 K), that it has been included with the BHB stars. The [Fe/H] of these 28 stars lie in the range -0.99 (for HD 31943) to -2.95 (for HD 8376) with a mean value of -1.67[FORMULA]0.08 and an rms dispersion ([FORMULA]) about this mean of [FORMULA]0.42 11. We compare these parameters with those of other types of halo stars in Table 14. The small group of nearby red horizontal branch stars are taken from Pilachowski et al. (1996). The nearby RR Lyrae stars include those with abundances by Clementini et al. (1995) and by Lambert et al. (1996). The red giants are those within 600 pc from the sample given by Chiba & Yoshi (1998). The halo globular clusters are those listed by Armandroff (1989). The first sample is a subset of 21 of these clusters whose [Fe/H] has been given by Carretta & Gratton (1997). The second sample contains all those in Armandroff 's list, using Carretta & Gratton's abundances for 21 of the clusters while for the remainder, the abundances given by Armandroff (which are on the Zinn & West (1984) scale) were converted to the system of Carretta & Gratton using the quadratic relation given in their paper 12. The halo clusters, on the average, appear to be 0.1 or 0.2 dex more metal-rich than the field halo stars. On the Zinn & West scale, they would have had more comparable metallicities. The red giant sample contains a greater fraction of very metal-poor stars than the other groups. Thus, 30% of the red giants have [Fe/H][FORMULA]-2.00 while only between 5 and 10% of the globular clusters are this metal-poor; this difference is significant at better than the 1% level. This is possibly because many of the red giants were discovered in the objective-prism surveys of Bond (19701980) which, while being kinematically unbiased, tended to accentuate the discovery of the most metal-poor stars. The large subdwarf samples of Ryan & Norris (1991), although they contain stars in the range +0.01[FORMULA][Fe/H][FORMULA]-3.70 and presumably include thick disk stars, have a maximum frequency in [Fe/H] at -1.65. This is similar to what we find for the field halo stars but not for the halo globular clusters where the maximum frequency is [FORMULA]0.3 dex more metal-rich. Thus, although the [Fe/H] abundances which we have derived for the BHB stars is in general agreement with those found for other local halo stars, they are appreciably more metal-poor than those of the halo globular clusters. This discrepancy requires further investigation 13.


Table 14. Comparison of the distribution of [Fe/H] in our BHB stars with that of other samples of halo stars.
1) BHB stars (this paper).
2) Pilachowski et al. (1996).
3) Halo RR Lyraes (see text).
4) Chiba & Yoshii (1998) (Red Giants within 600 pc).
5) Halo globular clusters (see text).
6) Halo globular clusters (see text).

10.3. Comparison with ZAHB models

The [FORMULA] and [FORMULA] that we adopted for the analysis of the Kitt Peak and ESO-CAT spectra (Table 10) are plotted in Fig. 9. The 28 stars that have a high probability of being BHB stars are plotted as filled circles and the c-type RR Lyrae star HD 16456 as a filled triangle. For comparison we show the ZAHB models of Dorman et al. (1993) with [m/H] = -1.48 and [O/Fe] = 0.6, the models of Straniero et al. (1998, priv. comm.) with [m/H] = -1.3 (equivalent to [m/H] = -1.6 with [FORMULA]-enhancement +0.4, see Salaris et al. 1993) and the He-enhanced models of Sweigart (1997, 1999) ([FORMULA] = 0.0 and 0.10 14 with [m/H] = -1.56). We also show models by Bono & Cassisi (1999, priv. comm.) for [Fe/H] = -1.7 and -2.5; these illustrate the small metallicity dependence that is present. The agreement is generally satisfactory except for HD 130201 whose [FORMULA] is not very well determined. A similar plot for the BHB stars in globular clusters (both metal-poor and the metal-rich NGC 6388, NGC 6441, NGC 362, and 47 Tuc) has been given in Fig. 8 of the recent review by Moehler (1999). At [FORMULA] = 3.95, the metal-poor globular cluster BHB have [FORMULA] in the range 2.90 to 3.44 and are mostly concentrated in the range 3.10 to 3.40. We have eleven BHB with [FORMULA] in the range 3.93 to 3.97 and and their mean [FORMULA] is 3.27, so there is good agreement between the field and cluster BHB stars in the [FORMULA] vs [FORMULA]  plot. Both field and cluster BHB stars tend to lie slightly above the ZAHB, suggesting either that some evolution is present or that some He-enhancement is required. The difference is, however, comparable with the errors in the computed gravities so that no definitive conclusion is possible.

[FIGURE] Fig. 9. The 28 BHB stars (filled circles) and the RR Lyrae star HD 016456 (filled triangle) in the [FORMULA] - [FORMULA] plane using the mean values given in Table 11. The lines show the ZAHB O-enhanced models of Dorman et al.(1993) (1) and the models of Straniero et al. (priv. comm.) (2) and the He-enhanced models of Sweigart (1997, 1999) for [FORMULA] = 0.00 (3) and [FORMULA] = 0.10 (4). The models of Bono & Cassisi for [Fe/H] = - 2.5 and - 1.7 are shown by (5) and (6) respectively.

10.4. Projected rotational velocities ([FORMULA])

Peterson et al. (1983) measured the projected rotational velocities ([FORMULA]) of eight of the brighter field BHB stars from echelle spectra (resolution of 24 000) and found rotations of up to 30 km s[FORMULA]. Peterson (1983, 1985a and 1985b) also measured the [FORMULA] of HB stars in the globular clusters M3, M5, M13, M4 and NGC 288. More recently, the [FORMULA] of 67 HB stars in M3, M5, M13 and NGC 288 have been measured by Peterson et al. (1995, hereafter PRC). Also, Cohen & McCarthy (1997) have determined [FORMULA]  for 5 HB stars in M92 from HIRES Keck spectra. Behr et al. (2000) have also measured [FORMULA] for stars in M13. Rotations of up to 40 km s[FORMULA] were found in both M13 and M92 for HB stars whose [FORMULA] were less than 11 000 K. PRC could find no correlation between ([FORMULA]) and [FORMULA]. Cohen & McCarthy suspected a possible trend of [FORMULA] with abundance.

The resolution of most of our spectra (15 000) is not enough for us to make definitive measurements of [FORMULA], but we can distinguish quite easily between stars with a [FORMULA] of less than 15 km s[FORMULA] and those with a [FORMULA] [FORMULA] 30 km s[FORMULA] . We chose to use the Mg II  ([FORMULA] 4481) line 15 and measured its FWHM (F) with the IRAF routine that employs a simple gaussian fit. The [FORMULA] of seven field BHB stars observed by Peterson et al. (1983) were used to convert the FWHM to [FORMULA] with the relation:


where F is in Å and the constant K is 0.221 for the Kitt Peak spectra and 0.151 for the ESO CAT spectra. The fit for the Kitt Peak spectra is shown in Fig. 10. A number of early-type stars whose [FORMULA] are given in the IAU Transactions (1991) were also observed and they are shown by open circles. Their [FORMULA] follow the same trend with F as the calibrating BHB stars (filled circles) but their [FORMULA] are systematically lower for a given F. The reason for this discrepancy is not understood but we have chosen to follow the calibration defined by the observations of Peterson et al. (1983) because our main interest is to compare our [FORMULA] with those obtained by PRC for the BHB stars in globular clusters. We point out, however, that the use of our relation for [FORMULA] [FORMULA] 30 km s[FORMULA] does involve a small extrapolation beyond the range of the calibration. Had we used a calibration based on the IAU standards, our computed [FORMULA] would have been about 60% of those given in Table 15.

[FIGURE] Fig. 10. A plot of [FORMULA] against the FWHM of the Mg II  [FORMULA]4481 doublet for BHB stars observed by Peterson et al. (1983) (filled circles) and IAU standards (open circles). The adopted calibration is shown by the curve.


Table 15. The rotational velocity ([FORMULA]) for BHB star candidates[FORMULA] (determined from the Mg II  [FORMULA]4481 line). The Strömgren index [FORMULA] for the same stars determined both photometrically and from our spectra.
1) Determined from synthetic spectra.
2) Determined from FWHM of line (Sect. 9.4).
[FORMULA]) Omitting BD +00 0145 because of the poor quality of the spectrum.
a) Adopted photometric value (Table 1)
b) Determined from H[FORMULA] (Sect. 3).

In Fig. 11b, we compare the [FORMULA] that were determined from the FWHM of the Mg II  line with the estimates of the rotational broadening that were obtained in fitting the observed and computed Mg II  line profiles. There is a good correlation between the two for [FORMULA] [FORMULA] 15 km s[FORMULA] ; for smaller [FORMULA], the fractional errors in the estimates are greater and so there is a poorer correlation. In any case, we should not expect the two quantities to be identical since the [FORMULA] determined from the Mg II  line have been forced onto the system of another observer, whereas the rotational broadenings deduced from the model involve different assumptions. In Fig. 11a we compare the [FORMULA] that were obtained from the ESO-CAT spectra with those obtained for the same seven stars (six BHB stars and HD 140194) with the KPNO coudé feed. The good agreement between these independent estimates of [FORMULA] fully supports the conclusion that our data can be used to distinguish between stars with a [FORMULA] [FORMULA] 30 km s[FORMULA] and those of lower rotational velocity.

[FIGURE] Fig. 11. a A comparison of the [FORMULA] obtained (using the FWHM of the Mg II  doublet) from spectra taken with the ESO-CAT (ordinate) with those obtained from spectra of the same stars taken with the Kitt Peak coudé feed (abscissa). b A comparison of the [FORMULA] obtained (using the FWHM of the Mg II  doublet) for the Kitt Peak coudé feed spectra (ordinate) with that determined from the same line using the synthetic spectra. (abscissa).

The dependence of [FORMULA] on the metallicity is shown in panel (a) of Fig. 12. Although the six most metal-weak stars have lower than average [FORMULA], it is not thought that these data show any significant trend of [FORMULA] with metallicity. The middle and lower panels of Fig. 12 show plots of [FORMULA] against [FORMULA] for the HB stars in globular clusters (middle) and for our field BHB (below). The distributions in the clusters and in the field are similar and in neither case is there a trend seen between [FORMULA] and colour.

[FIGURE] Fig. 12. a A plot of [FORMULA] (ordinate) against [Fe/H] (abscissa) for our field BHB stars. b A plot of [FORMULA] (ordinate) against [FORMULA] (absicissa) for BHB stars in the globular clusters NGC 288 (open circles), M3 (filled circles) and M13 (filled triangles) from Peterson et al. (1995) and also M92 (crosses) from Cohen & McCarthy (1997). c A plot of [FORMULA] (ordinate) against [FORMULA] (abscissa) for our field BHB stars.

The interpretation of the observed distribution of [FORMULA] in terms of a randomly oriented population has been discussed by Chandrasekhar & Münch (1950) and by Brown (1950). Brown, in particular, points out that the true distribution of rotational velocities can only be determined from relatively large samples. It is possible to put some constraints on the true distribution using the expressions given by Chandrasekhar & Münch for the mean and mean square deviation of this distribution (their Eq. (20)). Table 16 gives the mean projected rotational velocity ([FORMULA]), the mean true rotational velocity ([FORMULA]) and the root mean square deviation of this true rotational velocity ([FORMULA]) in km s[FORMULA] for our sample of field BHB stars and for various samples of globular cluster HB stars. Bearing in mind that our measured [FORMULA] undoubtedly have somewhat larger observational errors than those of the globular cluster HB stars, the [FORMULA], [FORMULA] and [FORMULA] of our sample well match the whole sample of globular cluster HB stars. This suggests that the two subgroups of globular clusters with low [FORMULA] and [FORMULA] (M3 & NGC 288) and high [FORMULA] and [FORMULA] (M13 & M92) are fairly equally represented in the field. None of these samples show significant evidence for skewness so the characterization of the true velocity distribution in terms of [FORMULA] and [FORMULA] is sufficient. It is to be noted that the [FORMULA] of the low velocity group must be very largely produced by observational error so that the intrinsic dispersion in this subgroup must be very low.


Table 16. Mean [FORMULA] and deprojected rotational velocities in field and cluster stars.
a) Data from Peterson et al. (1995).
b) Data from Cohen & McCarthy (1997).

10.5. Abundances of the [FORMULA]-elements

It is well known that the [FORMULA]-elements are more abundant relative to iron in metal-poor halo stars than in disk stars with solar abundances (Wheeler et al. 1989). The exact form of this enhancement may differ somewhat from element to element. Thus Boesgaard et al. (1999) have found a linear relation between [O/H] and [Fe/H] in the range 0.0[FORMULA][Fe/H][FORMULA]-3.0, but the relation is less well-defined for other [FORMULA]-elements such as Mg and Ti. The mean abundances of these two elements (relative to iron) are given in Table 17 for the BHB stars in our sample and for a number of other samples of metal-poor stars of similar metallicity. All of these other samples are late-type halo stars except for the old metal-poor selection taken from the thick-disk stars of Edvardsson et al. (1993) and the halo RR Lyrae sample of Clementini et al. (1995). Some systematic differences may be expected between the abundance ratios found for the different samples because they are derived from different lines of these elements and also different ionization states and undoubtedly systematic errors are present in their assumed [FORMULA]. Also, the abundance determined from the Mg II  [FORMULA]4481 line can be quite sensitive to the assumed microturbulent velocity (Table 12). Under these circumstances, we consider that the [FORMULA]-element enhancement in our BHB sample is in reasonable agreement with other recent determinations for halo stars.


Table 17. Mean values of [Mg/Fe] and [Ti/Fe] from various sources.
(1) BHB stars (this paper).
(2) Edvardsson et al. (1993) (Thick disk: Age[FORMULA] 10 Gyr; Orbital Ecc. [FORMULA] 0.35; [Fe/H][FORMULA]-0.50).
(3) Clementini et al. (1995) (halo RR Lyraes).
(4) Gratton & Sneden (1991) (metal-poor dwarfs and giants).
(5) Pilachowski et al. (1996) (halo giants).
(6) Magain (1989) (halo dwarfs).
(7) Nissen et al. (1994) (metal-poor dwarfs and subgiants).
(8) Stephens (1999) (halo dwarfs: eccentric orbit).
(9) Clementini et al. (1999) (Hipparcos stars: [Fe/H][FORMULA]-0.50).

10.6. BHB binaries and HD 130095

Binaries may be expected among halo stars and a discussion of their possible effect on the abundances has been given by Edvardsson et al. (1993) and Clementini et al. (1999). We have no direct evidence from the spectra that there are any binaries in our sample except that HD 130095 may have a variable radial velocity although it does not appear to vary in light (ESA Hipparcos Catalogue 1997; Stetson 1991). Although the published radial velocities of this star (Table 18) show a spread of over 50 km s[FORMULA], more than half of these velocities lie in a 5 km s[FORMULA] range centered on +63 km s[FORMULA]. It does not seem entirely impossible that HD 130095 has a constant velocity of +63 km s[FORMULA] and that the errors of the velocities that are outside this range have been greatly underestimated. If, however, the spread is real, then a period of about seven months seems to be possible, although far from certain. Now if P is the period in years, a is the semi-major axis of the orbit (in A.U.) and [FORMULA] and [FORMULA] are the masses of the two components (in [FORMULA]), then



Table 18. Radial velocities of HD 130095.
(1) Przybylski & Kennedy (1965b)
(2) Hill (1971)
(3) Greenstein & Sargent (1974)
(4) Kodaira & Philip (1984)
(5) Peterson et al. (1983)
(6) Adelman & Philip (1990)
(7) This paper (ESO-CAT)
(8) This paper (KPNO coudé feed)

If we assume equal components with a combined mass of 1.2 [FORMULA], then the semi-major axis will be 0.74 A.U.; this is somewhat larger than the radius of the red giant progenitor of the HB star ([FORMULA]100[FORMULA]). The other component might possibly be an equally metal-poor subdwarf ([Fe/H] = -2.0) whose lines would not be easily detectable in the spectrum of HD 130095. Such a star would be much less luminous than but of comparable mass to the HB star. Such a companion would not be particularly bright in the infrared and so would not have been discovered in the survey for infrared-bright companions of halo stars by Carney (1983).

It is known (Smart 1931) that


where A is the semi-axis major (in km), T is the period (in days), e is the orbital eccentricity and ([FORMULA] + [FORMULA]) is the velocity amplitude. If we assume a velocity amplitude of 50 km s[FORMULA], then we find


which requires that [FORMULA] 0.75. Thus the published radial velocities are not incompatible with HD 130095 being a binary, but it does seem highly desirable to make new velocity measurements over a period of several months so that the reality of the variability can be confirmed and a period established. The star is relatively bright (V = 8.15) and at declination -27o; the observations would most easily be made in the southern hemisphere.

10.7. The RR Lyrae variable CS Eri (HD 16456)

Solano et al. (1997) observed CS Eri (HD 16456) with an Image Tube spectrograph (resolving power 19 000) on the SAAO 1.9-m telescope at Sutherland in July, 1995. They determined abundances by assuming a microturbulent velocity ([FORMULA]) of 3.6 km s[FORMULA] and a [FORMULA] of 2.75. A summary of their observations and ours is given in Table 19. Solano et al. found the phases of their observations from the ephemeris of CS Eri given in the General Catalogue of Variable Stars (Kholopov et al. 1985) (Column 2 of Table 19). We have calculated phases for all the observations using the more recent ephemeris given in the Hipparcos Catalogue (1997) (Column 3 of Table 1916. The effective temperatures which are given by Solano et al. and also the one which we derived from the Kitt Peak spectrum are given in Column 4. CS Eri is intermediate in metallicity and amplitude to the two c-type variables T Sex ([FORMULA]V = 0.42 mag) and TV Boo ([FORMULA]V = 0.60 mag) and has a similar period. Using the [FORMULA] given for these stars by Liu & Janes (1990), we deduce that the maximum and minimum [FORMULA] for CS Eri should be 7475 K and 6725 K respectively. This minimum [FORMULA] is in good agreement with the [FORMULA] determined from the Kitt Peak spectrum which was taken near minimum (phase 0.42). The abundance deduced from the ESO-CAT spectrum (phase 0.92, near maximum) assuming [FORMULA] = 7500 K agrees well with that deduced from the Kitt Peak spectrum; their mean is [Fe/H] = -1.67. Table 20 also gives the [Fe/H] that was derived for the Fe II  lines alone since, at the [FORMULA] of RR Lyrae stars, the strengths of these lines are less sensitive both to [FORMULA] and NLTE effects than those of Fe I  (Fernley & Barnes 1997). Our abundances for [Fe/H] are therefore [FORMULA]0.2 dex lower than those found by Solano et al. (1997).


Table 19. Spectroscopic observations of CS Eri (HD 16456).
a) from the equivalent widths of both the Fe I  and Fe II  lines.
b) from the equivalent widths of the Fe II  lines only.
c) [FORMULA] = 3.0

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Online publication: December 15, 2000