Ω, age, and H0 implications of recent Hubble Space Telescope data in the Coma Cluster

This paper presents a way of finding mutually consistent values of Omega(M), t(0), and H-0. This approach is illustrated using recent Coma Cluster distance data, together with recent Hipparcos data for RR Lyrae stars. The age of the universe is derived by two completely independent methods, both linked to the RR Lyrae stars. The two methods can be made to yield the same answer by adjustment of the RR Lyrae magnitude zero point. One of these two age determinations is based on stellar evolution in globular clusters, and the other is based on the Hubble constant derived from globular clusters as distance indicators calibrated in the Milky Way. If, for example, RR Lyrae stars are brighter than previously thought, the stellar evolution age is shortened, whereas the Hubble age is increased, so one can determine the RR Lyrae magnitude zero point that would make the stellar evolution age coincide with the Hubble age, and ask whether it is a reasonable value. The answer depends strongly on the mass density of the universe, Omega(M), which can therefore be derived simply by demanding that the two age determinations agree. For each straw-man value of Omega(M), we find the RR Lyrae zero point M-V(RR)(0) for which the two age determinations coincide. We then choose the Omega(M) value for which the implied RR Lyrae zero point best agrees with observations. In the present paper, the mean of six recent Hipparcos values, M-V(RR)(0) = 0.61 +/- 0.15, is used for illustration. For that choice, the coinciding of ages occurs at 12.5 +/- 1.5 Gyr. The corresponding value of the Hubble constant is H-0 = 61 +/- 5 km s(-1) Mpc(-1). In a zero-Lambda universe, the implied mass density is Omega(M) = 0.41 with only weak constraints on either higher or lower Omega(M) values. In a flat universe with Omega(M) + Omega(Lambda) = 1, however, the implied mass density is Omega(M) = 0.62, and the uncertainty in it is asymmetric. For example, a critical-density universe with Omega(M) = 1.0 and Omega(Lambda) = 0.0 (for which H-0 = 57 km s(-1) Mpc(-1) and t(0) = 11.4 Gyr) differs by only 0.7 sigma, and is therefore not strongly negated, whereas a low-density universe with Omega(M) = 0.1 and Omega(Lambda) = 0.9 (for which H-0 = 74 km s(-1) Mpc(-1) and t(0) = 17.0 Gyr) differs by 3 sigma, and therefore appears unlikely.