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The Absolute Magnitude of RR Lyrae Stars Derived from the Hipparcos Catalogue

The present determination of the absolute magnitude $M_V(RR)$ of RR Lyrae stars is twofold, relying upon Hipparcos proper motions and trigonometric parallaxes separately. First, applying the statistical parallax method to the proper motions, we find $<M_V(RR)>=0.69\pm0.10$ for 99 halo RR Lyraes with $<$[Fe/H]$>$ =--1.58. Second, applying the Lutz-Kelker correction to the RR Lyrae HIP95497 with the most accurately measured parallax, we obtain $M_V(RR)$=(0.58--0.68)$^{+0.28}_{-0.31}$ at [Fe/H]=--1.6. Furthermore, allowing full use of low accuracy and negative parallaxes as well for 125 RR Lyraes with -- 2.49$\leq$[Fe/H]$\leq$0.07, the maximum likelihood estimation yields the relation, $M_V(RR)$=(0.59$\pm$0.37)+(0.20$\pm$0.63)([Fe/H]+1.60), which formally agrees with the recent preferred relation. The same estimation yields again $<M_V(RR)>$ = $0.65\pm0.33$ for the 99 halo RR Lyraes. Although the formal errors in the latter three parallax estimates are rather large, all of the four results suggest the fainter absolute magnitude, $M_V(RR)$$\approx$0.6--0.7 at [Fe/H]=--1.6. The present results still provide the lower limit on the age of the universe which is inconsistent with a flat, matter-dominated universe and current estimates of the Hubble constant.