4. Iron abundances

To determine the iron abundances we used the FeII lines at 6416.9 Å and 6432.7 Å. These lines have several useful attributes from the point of view of the present analysis. Firstly, they are strong enough to measure in even the most metal-poor stars in our sample. Secondly, their equivalent width (EW) is relatively insensitive to temperature over the temperature range covered by both RRab and RRc Lyraes during the pulsation. This is particularly important since it reduces one of the main sources of error in the abundances, that due to uncertainties in the temperature assignments. Finally, they are free of non-LTE effects (Lambert et al. 1995). The measured EWs are listed in Table 3.

Using the line data and procedures described in Fernley & Barnes (1996, hereafter FB96) we computed a grid of theoretical EWs for these two FeII lines over the range 5750-(250)-7250 K in , 0.0-(0.5)-2.0 in [M/H] and 2.5 and 3.0 in log g.

 

AT And 23 32 SU Dra 13 11 VZ Peg -- 10

CI And 85 -- SW Dra -- 29 DZ Peg 32 28

BR Aqr 64 79 BK Dra -- 23 AR Per 104 117

BH Aur 150 151 BB Eri 35 45 XX Pup 23 31

RS Boo 98 116 SZ Gem 19 25 HK Pup 36 41

AE Boo 20 22 SZ Hya 19 16 KZ Pup 108 --

UY Cam 13 18 XX Hya 41 37 VY Ser 9 9

Z CVn 14 17 DD Hya 48 57 AP Ser 17 18

SS CVn 36 47 ST Leo 34 48 T Sex 16 24

UZ CVn 23 22 AX Leo 34 -- SX UMa 16 18

AA CMi 122 127 BX Leo 26 26 TU UMa -- 21

V363Cas 103 102 TT Lyn -- 22 AB UMa 76 79

EZ Cep 116 136 TW Lyn -- 132 AF Vir -- 34

RR Cet 18 23 CN Lyr 99 106 BB Vir 29 27

RZ Cet 33 42 IO Lyr 51 59

U Com -- 27 KX Lyr 128 106

4.1. RRab Lyraes

As discussed in FB96, during the phase interval from 0.35-0.85, RRab Lyraes undergo an isothermal contraction and there is considerable evidence that the temperature variation from star to star during this phase interval is relatively small, i.e. K. To select the RR Lyrae spectra taken during this phase interval we firstly fitted the measured radial velocities to the standard velocity curve in order to obtain the true phases of our spectra and secondly examined the H profiles to select the ones that were narrowest and free of emission.

The measured EWs on these spectra were then matched with the synthetic EWs at K and (see discussion in FB96) in order to derive the abundances listed in the Appendix. We estimate the typical uncertainty in these abundances as dex, mainly due to the measurement error (). Our method of estimating the measurement error was to take the mean value of the abundance difference derived from the two Fe II lines. This showed a range of value between 0.00 and 0.28 dex with a mean value of 0.09. Smaller uncertainties arise from possible errors in the temperature of  K (), the gravity of dex () and the gf values ().

4.2. RRc Lyraes

RRc Lyraes have smaller temperature and gravity variations during the pulsation cycle and we have therefore adopted a different procedure for these stars than for the RRab Lyraes. For the RRab Lyraes we analysed only those spectra taken during the phases 0.35-0.85, to which we assigned a particular value of temperature K) and ) for all the stars. For RRc Lyraes we analysed all the spectra of all the stars, assuming a single value of temperature ( K) and ).

The value of temperature is based on the following work. Sandage (1981) calculated mean temperatures from (B-V) colours and an unpublished colour-temperature transformation of Bell for the RRc Lyraes in six globular clusters and this showed a range in mean of 6600-7500 K depending mainly on period but with a weaker dependence on metallicity. Amongst field stars the Baade-Wesselink analyses by Liu & Janes (1990) & Fernley et al. (1990) of the stars TV Boo (P = 0.31 days, [M/H] = -2.2), T Sex (P=0.32 days, [M/H] = -1.2) and DH Peg (P = 0.26 days, [M/H] = -0.9) give mean temperatures of 7020, 7105 and 7160 K using V-K colours and the calibration of V-K, (FB96) based on the ATLAS9 models of Kurucz (1992, private communication). T Sex is at the ``mid-point" of RRc Lyraes, both in terms of period and metallicity, and using the other two stars to set the temperature range as we vary metallicity at constant period (TV Boo) or vary period at constant metallicity (DH Peg) we adopt   K as representative of the mean temperature of all RRc Lyraes. This is consistent with, but narrower than, the temperature range found by Sandage (1981); however, the Sandage photometry is more difficult than the field star photometry (fainter stars, more crowded field) and B-V is subject to greater uncertainty than V-K for temperature determinations of RR Lyraes (Fernley 1993a)

Concerning log g, since we use spectra at all phases of the pulsation, then for our purposes the term cancels out and is given by the ``static" gravity. FB96 suggest that for RRab Lyraes . For RRc Lyraes this is higher from the following argument. Assuming the horizontal branch is horizontal than the higher mean temperatures of ``c" types ( K) imply lower radii ( 16%) and, assuming the masses of ``ab" and ``c" types are the same, hence higher gravities by 0.13 dex.

4.3. Comparison with previous work

Most previous work on RR Lyrae abundances expresses the results in the notation (Preston 1959). To facilitate comparison, both with this work and the very extensive analysis of Layden (1994), we have converted these values to [Fe/H] using the relation

which is the mean of the calibrations of Clementini et al. (1995), Lambert et al. (1996) and FB96, all of whom have recently made abundance analyses of a small sample of bright field RR Lyraes using intermediate to high-resolution optical spectra. The resulting comparison are shown in Fig. 1a (using results from various authors) and Fig. 1b (using the results of Layden).

In Fig. 1a it can be seen that there is reasonable agreement. Three stars are particularly discrepant (AB UMa, AT And and BK Dra) but if these are removed then we obtain

with a standard deviation of 0.19 dex. As discussed previously, the error on our abundances is dex and so this standard deviation suggests a similar level of error applies to other analyses. It should be noted that the fit in Eq. (2) is the bisector of the least squares fits of y upon x and x upon y (since the errors in x and y are approximately equal). This relation in Eq. (2) is plotted as the dotted line in Fig. 1a.

 
Figure 1: a) A comparison bewtween the [Fe/H] values of the present work and previous work (excluding Layden 1994). The solid line has intercept at zero and a slope of unity and the dotted line is the best-fit to the data. Over the range [Fe/H] 0 the difference between the two lines is always 0.05 in [Fe/H]

 
Figure 1: b) A comparison between the [Fe/H] values of the present work and those of Layden (1994). The solid line has intercept at zero and a slope of unity. The dots inserted in squares are for the stars used by Layden as calibrators. It can be seen that the [Fe/H] values of Layden and ourselves are in good agreement for the calibrating stars, whereas for the general sample of stars the Layden values are more metal-poor

Concerning the work of Layden (1994) it can be seen in Fig. 1b that his metallicities are systematically lower than ours. Three stars (UZ CVn, AX Leo and TW Lyn) are particularly discrepant. If these are excluded, the remaining 27 stars have a mean difference of 0.21 dex. Layden used a variation of the method in which a group of standard stars defined iso-abundance lines in the EW(CaIIK), EW(H) diagram. This diagram was then used to determine the metallicities of the survey stars. Five of Layden's standard stars were observed by us and comparing his adopted [Fe/H] values for these stars with our derived values shows close agreement (mean difference for the five stars is 0.02 dex, in the sense of Layden being more metal-poor). Given the good agreement between ourselves and Layden as to the metallicities of his calibrating stars, which cover the full range of metallicity, it is puzzling that the other stars are not in better agreement. The main difference between the calibrating stars and the other stars is, of course, that the calibrating stars are brighter and we show in Fig. 2 a plot of the difference as a function of the V magnitude. There is a clear trend in Fig. 2 with the fainter stars showing much larger differences.

As a further check we compared both our [Fe/H] values and Layden's [Fe/H] values with the compilation of Blanco (1992). He lists the ``best" values, from the literature, for a large number of field RR Lyraes. After converting these values to [Fe/H], using Eq. (1) of this paper, we find a mean difference between Blanco and ourselves of 0.02 (in the sense we are more metal-rich) from 19 stars in common and a mean difference between Blanco and Layden of 0.09 (in the sense Layden is more metal-poor) from 82 stars in common. However, plotting these differences (Blanco-us and Blanco-Layden) against V magnitude does not show any trend analogous to Fig. 2. Neither Layden (1996, private communication) nor ourselves have any convincing explanation for Fig. 2.

In summary, our metallicities are consistent with all previous work except that of Layden whose values appear to be systematically more metal-poor by between 0.1 and 0.2 dex.

 
Figure 2: The difference in metallicity derived by Layden and ourselves as a function of the V magnitude of the star. It can be seen that the brighter stars (which include the calibrating stars) have relatively small differences. Fainter than there is considerable scatter but the Layden metallicities are clearly shifted to lower metallicity