Determining the Hubble constant

Of course, if we are going to apply Hubble's law to determine distances, we need an accurate value for the Hubble constant. This means that we need an independent way of measuring distances to objects that are far enough away to be in the Fig 18.12.

Expansion of the universe and random velocities of galaxies. (a) We see just the motion due to the expansion of the universe.The center can be any reference galaxy, such as our own.The red arrows show the motions of galaxies at different distances from us solely due to the expansion of the universe. Notice that all the red arrows are pointed directly away from us, and that they are longer as we look at more distant galaxies. (b) We add in the random motions of the galaxies (green arrows). The random motions point in any direction, and they are the same throughout the universe.The net motion of any galaxy is the sum of its random and expansion motions.

Fig 18.12.

Expansion of the universe and random velocities of galaxies. (a) We see just the motion due to the expansion of the universe.The center can be any reference galaxy, such as our own.The red arrows show the motions of galaxies at different distances from us solely due to the expansion of the universe. Notice that all the red arrows are pointed directly away from us, and that they are longer as we look at more distant galaxies. (b) We add in the random motions of the galaxies (green arrows). The random motions point in any direction, and they are the same throughout the universe.The net motion of any galaxy is the sum of its random and expansion motions.

Hubble flow. The importance of an object being far away is illustrated in Fig. 18.13. Suppose an object has a velocity of H0d from the Hubble flow and Av from other sources. This Av probably results from random motions of the galaxies, just as the gas in the room has random motions superimposed on any regular flow. Note that Av can be positive or negative. The actual radial velocity that we measure will be vr = H0d + Av (18.5)

In general, Av is independent of d. Thus, for more distant objects, H0d increases while Av stays the same. For more distant objects, Av represents a smaller fraction of H0d, and introduces a smaller fractional error into the determination of H0.

It would seem a simple task to get around this problem. All we have to do is use the most distant objects we can observe. Unfortunately, our distance indicators work best for nearby galaxies, where we can still see individual stars such as Cepheids. Therein lies the problem. We can measure distances more accurately for nearby objects, but we are not sure if they are in the Hubble flow. Arguments over the proper value of H0 center around these two points: (1) what are the correct distance indicators, and (2) where does the Hubble flow start?

We now turn to the problem of measuring distances to distant clusters of galaxies. The procedure involves using our most secure distance indicators to measure the distances to nearby galaxies, and then building up a series of distance indicators, useful at greater and greater distances. The problem can be involved, as shown in Table 18.1.

We start the process by looking at Cepheids to find the distances to nearby galaxies. Of course, we must calibrate the Cepheid period-luminosity relationship within our own galaxy. This involves starting with trigonometric parallax observations of nearby stars and moving cluster observations of nearby star clusters to produce a calibrated HR diagram. The calibrated HR diagram allows us to use spectroscopic parallax for individual stars, and for main sequence fitting for globular clusters containing Cepheids. This gives a calibrated period-luminosity relation for Cepheids as well as RR Lyrae stars. We can then use the Cepheids and RR Lyrae stars as distance indicators for galaxies that are close enough for us to see these stars individually.

Method_range (Mpc)

0 50 100

Distance (Millions of Parsecs)

HST has greatly expanded the distance over which we can study Cepheids up to 100 Mpc.

For galaxies that are somewhat farther away, we can still use individual objects within the galaxy, but they have to be brighter than Cepheids. We can, for example, measure the angular sizes of HII regions. Since we think we know what their linear sizes should be, this gives us a measure of distance. One promising technique is the use of supernovae. From the light curve we can tell whether the supernova is a type I or type II. Type I supernovae appear to have similar peak luminosities. By measuring their apparent magnitude at peak brightness, we can find the distances.

Eventually we reach a point where individual objects within galaxies cannot be measured. We must rely on being able to know the total luminosity of the galaxy. If we know the absolute magnitude of a given type of galaxy, and we measure

Method_range (Mpc)

 Cepheids
0 0