### 7. THE HUBBLE CONSTANT

Ever since Edwin Hubble's pioneering measurements in the 1920s (and to some extent even before that, since Vesto Slipher's measurements, that started in 1912; e.g., Slipher 1917), we knew that we live in an expanding universe (Hubble 1929, Hubble and Humason 1931). In the standard big bang theory the universe expands uniformly, with the recession velocity being related to the distance through the Hubble law, v = H0d. More generally, based on the "Cosmological Principle" (the assumption that the universe is homogeneous and isotropic on large scales), the expansion is governed by the Friedmann equation in the context of general relativity

 (24)

Here R(t) is the scale factor, H = / R measures expansion rate (with H0, the "Hubble Constant," giving the rate at present), M is the mass density, k is the curvature parameter and is Einstein's cosmological constant (which represents the energy density of the vacuum). Commonly, the density of matter and that associated with the vacuum are represented by the density parameters (at present) M = 8 G M / 3H20 and = c2 / 3H20, with which the Friedmann equation can be expressed as (kc2 / Ro2) = H20 (M + - 1). The Hubble Constant is thus the key parameter in determining the age of the universe (with M and also playing a role). Similarly, physical processes such as the growth of structure and the nucleosynthesis of light elements (H, D, 3He, 4He, Li), as well as critical epochs in the Universe's history, such as the transition from a radiation-dominated to a matter-dominated universe, depend on the cosmic expansion rate and thereby on the value of H0. It should therefore come as no surprise that the determination of the value of the Hubble Constant became a major observational goal for the past eight decades.

The first value for the Hubble Constant may have actually been derived by Lemaître (1927), who, on the basis of Slipher's radial velocity measurements and Hubble's mean absolute magnitude for galaxies ("nebulae") obtained H0 = 526 km s-1 Mpc-1. The next set of values by Hubble (1929) and Hubble and Humason (who produced a velocity-distance relation up to V ~ 20000 km s-1 and obtained H0 = 559 km s-1 Mpc-1 in 1931), were all around 500 km s-1 Mpc-1, with an uncertainty stated rather naively as "of the area of ten percent." About twenty years passed before Baade (1954) revised the distance to nearby galaxies, recognizing that Hubble confused two classes of "standard candles" (Population I Cepheids and Population II W Virginis stars), thereby reducing the value of H0 by about a factor two (a revision suggested also by Behr 1951). The value of the Hubble Constant first reached the range of values accepted today through the work of Alan Sandage (1958). Sandage demonstrated that Hubble mistakenly identified H II regions as bright stars, and he [Sandage] was able to revise the value further to H0 75 km s-1 Mpc-1 (recognizing that the uncertainty could still be by a factor 2).

In the three decades that followed, published values of the Hubble Constant varied by about a factor of two between ~ 100 and 50 km s-1 Mpc-1. Table 1, adapted from Trimble (1997), summarizes the early history of the constant.

 When Who Numerical value 1927 Lemaître 600 1929 Hubble 530-513-465 1931 Hubble & Humason 558 1936 Hubble 526 1946 Mineur 330 1951 Behr 250 1952 Baade, Thackeray 270 1956 Humas, Mayall & Sandage 180 1958 Holmberg 134 1958 Sandage 150-75-38 1959 McVittie 227-143 1960 Sersic 125 1960 van den Bergh 125 1960 van den Bergh 125 1961 Ambartsumyan 140-60 1961 Sandage 113-85 1964 de Vaucouleurs 125 1968-69 de Vaucouleurs 100 1969 van den Bergh 110-83 1968-76 Sandage & Tammann 50 1972 Sandage 55 1979 de Vaucoulers 100

Generally, since redshifts (and therefore radial velocities) can be determined relatively readily (this is, of course, not true for the most distant or faintest objects), the problem of determining the Hubble Constant has always been a problem of determining accurate astronomical distances. The availability of new instrumentation, and the Hubble Space Telescope in particular, have allowed for a dramatic improvement in distance determinations.