6 Metallicity estimate of the RR Lyrae population

6.1 Period-Metallicity relations

Some indication on the metallicity of the RR Lyrae population in Sgr can be inferred from its period distribution. In a study of cluster and field RR Lyrae stars spanning a wide range of metallicities, Sandage (1993) related the average periods of RR Lyrae stars to their metallicities:

$${\rm [Fe/H]_{ZW}}=(-{\rm log}\langle P_{\rm ab}\rangle-0.389)/0.092$$ (2)

$${\rm [Fe/H]_{ZW}}=(-{\rm log}\langle P_{\rm c}\rangle-0.670)/0.119$$ (3)

where $\langle P_{\rm ab}\rangle$ and $\langle P_{\rm c}\rangle$ are the average periods of RRab and RRc stars respectively. Although these relations were derived from cluster and field RR Lyraes, Siegel & Majewski (2000, their Fig. 6) showed that RR Lyrae populations in Dsph followed the same relation. Applying Eqs. (2) and (3) to Sgr yields an average metallicity of ${\rm [Fe/H]}=-1.61$ and -1.49 dex respectively.

The location of the blue and red fundamental edge of the instability strip are functions of metallicity. The shortest and longest period RR Lyraes are thus indicative of the metallicity boundaries of the RR Lyrae population which are given as (Sandage 1993):

$${\rm [Fe/H]_{ZW}}^{\rm (\rm max)}=[-{\rm log}(P^{\rm min}_{\rm ab})-0.500]/0.122-0.2$$ (4)

$${\rm [Fe/H]_{ZW}}^{\rm (min)}=[-{\rm log}(P^{\rm max}_{\rm ab})-0.280]/0.090-0.2$$ (5)

where $P^{\rm min}_{\rm ab}$ and $P^{\rm max}_{\rm ab}$ are the minimum and maximum periods of RRab stars respectively. We added the constant terms in Eqs. (4) and (5) in order to rescale the metallicity to the Zinn & West (1984) scale, whose zero point is $\sim$0.2 dex more metal-poor than the Butler & Blanco metallicity scale (Blanco 1992) on which these equations are based. The shortest RRab period is 0.41531$^{\rm d}$, yielding an upper limit of [Fe/H]=-1.17 dex, whereas the longest period of 0.84400$^{\rm d}$ implies a lower limit of [Fe/H]=-2.49 dex. These values suggest a considerable spread in the metallicity of the RR Lyrae population.

6.2 Period-amplitude-metallicity relation

Alcock et al. (2000a) provide a period-amplitude-metallicity relation calibrated with high-quality V-band light curves of RR Lyrae stars in several globular clusters:

$${\rm [Fe/H]}=-8.85\,{\rm log}(P_{\rm ab}+0.15\,A_{V})-2.60$$ (6)

where A_V is the amplitude in the V-band. The resulting metallicity distribution of Sgr RRab member stars is presented in Fig. 8b. The peak-value is at ${\rm [Fe/H]}\,\simeq\,-1.65$ dex, close to the estimate inferred from the Sandage relations. This is also similar to the value found in the LMC with the same relation ( ${\rm [Fe/H]}\,\simeq\,-1.6$; Alcock et al. 2000a).

The best Gaussian fit to the metallicity distribution is given by $y\propto {\rm e}^{-\frac{1}{2}\big(\frac{x+1.65}{0.24}\big)^{2}}$. As can be seen in Fig. 8b, this function fits the distribution relatively well, except for ${\rm [Fe/H]} \lesssim -$2.0 dex where the presence of a significant metal-poor subpopulation is apparent.

6.3 Petersen diagram

The strong metallicity spread in the RR Lyrae population seems confirmed by the distribution of RRd stars in the Petersen diagram, although a dispersion in the star masses could also be responsible for the spread. The dotted lines in Fig. 7 represent metallicities for a specific model of RRd with a mass of 0.75 $M_{\odot}$, a luminosity log( $L/L_{\odot}$)=1.72, a hydrogen abundance $X=\,$0.76 and an effective temperature of 6900, 6800 and 6700 K for [Fe/H]=1.3, -1.5 and -1.8 dex respectively. This model has been taken from Kovács (2000). The positions of the RRd stars are in good agreement with the above estimate of mean metallicity and metallicity spread of the RR Lyrae population.

A clump of RRd stars is apparent in Fig. 7 at ${\rm [Fe/H]} < -$1.8 dex, suggesting the presence of a minor but significant population of low metallicity and/or high mass RR Lyraes. The loci of the long period RRd stars in the Petersen diagram is similar to those found in OoII systems. Table 7 summarizes all the systems with known RRd pulsators. One sees that qs all these OoII systems have a metallicity within -2.0 and -2.2 dex, supporting the assumption that a fraction of RR Lyrae stars in Sgr has this abundance.

The existence of a very low metallicity population in Sgr has been suggested by Bellazzini et al. (1999a, 1999b) who detected a star count excess in a region of the CMD that could represent a very blue horizontal branch. Furthermore, in a period-amplitude diagram of RR Lyrae stars towards the globular cluster M 54, Layden & Sarajedini (2000) noted that a fraction of RR Lyrae stars could be consistent with a contamination by Sgr field stars of metallicity ${\rm [Fe/H]}=-2.1$ dex.