AGE-DIFFERENCES BETWEEN OLD STELLAR POPULATIONS FROM THE HB MORPHOLOGY METALLICITY DIAGRAM

Isochrones in the horizontal-branch (HB) morphology-metallicity diagram have been constructed on the basis of (1) detailed synthetic HB models, as recently presented by Catelan [A&AS, 98, 547 (1993a)], and herein extended to completely red and blue HB morphologies; and (2) the red giant branch (RGB) models of Sweigart & Gross [ApJS, 36, 405 (1978)]. The effect of variations in the several relevant input parameters that characterize the present (standard) isochrones-namely, main-sequence helium content (Y(MS)), abundances of the alpha-capture elements ([alpha/Fe]), and mean overall mass loss on the RGB (DELTAM)-has been extensively studied. We find that the age difference which may be estimated between any two (old) stellar populations from their distributions in the HB morphology-[Fe/H] plane, holding Y(MS), [alpha/Fe], and DELTAM fixed, depends strongly on the absolute values which are assumed for the latter quantities. In other words, unless the absolute values for such parameters can be accurately determined for the objects subject to examination, the HB morphology-[Fe/H] diagram does not constrain age differences in a reliable way. As examples, we have analyzed the following cases. (1) The classical ''second-parameter'' pair of globular clusters (GCs) NGC 288-NGC 362; (2) the (reportedly ''young'') GC Ruprecht 106; (3) the old LMC GCs; and (4) the bulge RR Lyrae population. Our isochrones for fixed Y(MS), [alpha/Fe], and DELTAM suggest that: (1) NGC 288 and NGC 362 may differ in age by any amount in the range approximately 3-14 Gyr; (2) Ruprecht 106 may be younger than the GCs inside the solar circle by approximately 3-12 Gyr; (3) the latter clusters may be older than the old LMC ones by approximately 2-8 Gyr; and, finally, (4) the RR Lyrae stars in the Galactic bulge may be older than the clusters in the inner halo by approximately 0.8-3.5 Gyr. The identification of the true second parameter that controls HB morphology (besides [Fe/H]) is thus seen to depend on the accurate determination of cluster-to-cluster differences in (at least) the three parameters listed above, whereas the magnitude of the problem itself depends on the absolute values of those parameters which may have been excluded as second-parameter candidates. We also find that similar age differences between any two populations, as obtained for different (Y(MS), [alpha/Fe], DELTAM) combinations, imply similar absolute ages for these populations. On the basis of this result, we show that the classical second-parameter pair NGC 288-NGC 362 can only be explained in terms of an age difference as small as congruent-to 3 Gyr {as found by VandenBerg et al. [AJ, 100, 445 (1990)] and others through independent age-dating methods}, if both clusters are younger than approximately 10 Gyr. This follows irrespective of the (Y(MS), [alpha/Fe], DELTAM) combination chosen which is capable of reproducing the reported age difference of 3 Gyr between these two clusters. The far-reaching implications of this result must clearly be further explored.