Horizontal-branch models and the second-parameter effect. III. The impact of mass loss on the red giant branch and the case of M5 and Palomar 4/Eridanus

Deep Hubble Space Telescope (HST) photometry has recently been presented for the outer halo globular clusters Palomar 4 and Eridanus. The new high-precision color-magnitude diagrams obtained for these globulars have allowed a measurement of their ages relative to M5 (NGC 5904), which is a well-observed, much closer cluster. Assuming that the globular clusters share the same chemical composition, Pal 4/Eridanus have been reported to be younger than M5 by approximate to 1-2 Gyr, based on both the magnitude difference between the horizontal branch (HB) and the turnoff and the difference in color between the turnoff and the lower subgiant branch. In the present article, we address the following question: What age difference would be required to account for the difference in HE types between M5 and Pal 4/Eridanus, assuming age to be the "second parameter"? We find that, unless all these clusters (including M5) are younger than 10 Gyr, such an age difference is substantially larger than that based on an analysis of the cluster turnoffs. To reach such a conclusion, six different analytical mass-loss rate formulae (reported in an Appendix), all implying a dependence of mass loss on the red giant branch on age, were employed. Our results appear to be in conflict with claims that age can be the only second parameter in the Galactic globular cluster system.