the apparent magnitude, we have a measure of the distance. The problem is to come up with independent indicators of galactic luminosity. Hubble made the simple assumption that all galaxies have the same absolute visual magnitude. We know that this is not the case. Instead, it has been suggested that the brightest ellipticals in each cluster have the same absolute magnitude. The luminosities of the brightest ellipticals seem to vary, however. For this reason, rather than using the brightest elliptical in a cluster, we use the second or third brightest elliptical in a cluster.

With the recent recognition that galaxies have luminosity classes, much effort has gone into finding luminosity class indicators. In this way, we can observe a galaxy, determine its morphological type (Sa, Sb, etc.), and then have some indicator of its luminosity class. If we know absolute magnitude as a function of morphological type and luminosity classes, and we measure the apparent magnitude, we can convert the difference into a distance.

Another recent discovery, indicated in Fig. 18.14, is that the width of the 21 cm line in a galaxy seems

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Distance (Millions of Parsecs)

Fig 18.13.

Sources of error in measuring the Hubble constant. For both nearby and distant galaxies, uncertainties are indicated schematically by error bars. Straight lines from the origin are then drawn at the widest angle that can still lie within one of the error bars.The error bar that determines this widest angle is the one that generates the largest uncertainty in H0 since H0 would be determined by the slope of a line from our measured point to the origin.

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