Peculiar Velocities

It is necessary to observe at large distances to determine the Hubble constant because we require a sample of galaxies that are far enough away that motions due to local gravitational influences are small. These are called peculiar motions and they represent deviations from the Hubble Law. That is, the Hubble flow is caused by the expansion of space, but in addition galaxies may move within the space. The latter is the peculiar motion. We have already seen two examples of peculiar motion, the influence of mass concentrations in the Local Supercluster on the Local Group, and the influence of the Great Attractor on all galaxies in our neighborhood.

The Hubble Law (2) ...

Determining the value of H is simple in principle, but complicated in practice. Two measurements are required. First, spectroscopic observations are used to determine the redshift, which can be related to the radial velocity. This is (relatively) easy. The second measurement is more difficult: the galaxy's precise distance from Earth must be determined by some means. As we have seen, precise distances can be difficult in astronomy, particularly if the distances are large.

Units for Hubble's Constant
We shall usually quote the value of the Hubble constant in units of "kilometers per second per megaparsec." In other words, the value of the Hubble constant tells us that for each megaparsec of distance the velocity of a distant galaxy appears to increase by some fixed number of kilometers per second. For example, if the Hubble constant was determined to be 65 km/s/Mpc, a galaxy at a distance of 10 Mpc would have a redshift corresponding to a radial velocity of 650 km/s since

v = Hd = (65 km/s/Mpc) x 10 Mpc = 650 km/s

Current Value of the Hubble Constant
The value of the Hubble constant initially obtained by Hubble was around 500 km/s/Mpc. It has since been revised downward by about a factor of 10 because initial distance determinations were underestimated. Modern determinations of the Hubble constant typically lie in the range 50-85 km/s/Mpc with recent analysis suggesting a more likely value of 60-70 km/s/Mpc. Where necessary to adopt a value of the Hubble constant for our discussion, we shall assume 65 km/s/Mpc.

Controversy over the Value of the Hubble Constant

The Hubble constant can be determined by comparing the recessional velocity of galaxies with their distances. This is difficult, because we must use galaxies at large distances to ensure that the motion is because of the expansion of space and not just local motion of the galaxy in space, and determining large distances in astronomy is often not easy. There has been controversy over the present value of the Hubble constant. Two camps consistently obtain values that are not consistent with each other within the expected uncertainty for the determination.

One group, led by American astronomer Alan Sandage and Swiss astronomer Gustav Tammann, favor a value H ~ 50 km/s/Mpc. A second group, led by French astronomer Gerard de Vaucouleurs, contends that the value of H is closer to 85 km/s/Mpc. Although this difference is not so large, we shall see that it implies significantly different ages for the Universe. However, we should set this controversy in perspective. It is remarkable that despite their differences, both camps would agree that we know the Hubble constant with an uncertainty that is less than a factor of two. This is a stunning achievement, because we shall see that this implies that we probably know the age of the Universe with the same degree of certainty. As noted above, most workers now use a value of the Hubble constant in the vicinity of 65 km/s/Mpc.

The Deceleration Parameter
The Hubble constant measures the present rate of expansion for the Universe. But the Hubble "constant" changes over time. The rate of change for the expansion of the Universe is expressed in terms of a second quantity called the deceleration parameter, which is usually denoted by the variable q. Over larger scales, both the Hubble constant and the deceleration parameter are required to determine the ultimate behavior of the Universe.

The adjacent left figure illustrates the effect of an increasing positive value of the deceleration parameter on the expansion of the Universe. The value q = 0 corresponds to an empty Universe with no mass to slow the expansion. In this case, the Hubble constant would really be a constant.

However, the Universe contains mass and this slows the expansion, causing the curve to tilt over (unless the Universe contains "dark energy" in addition to mass; see the comments below) and causing the Hubble constant to change with time. The value q = 1/2 corresponds to a flat Universe with the assumptions that we have made. Note that the deviations from the simple Hubble law implied by the deceleration are not peculiar motion since they still imply a recession caused by the expansion of space. They instead specify a time dependence in the Hubble constant that determines the rate at which space expands.

Can the Expansion Accelerate Rather than Decelerate?
We shall also see later that under certain conditions it is possible that q can become negative and then the Universe accelerates rather than decelerates (it expands even faster as time goes on). This strange behavior is possible if "empty space" takes on some ra ther peculiar properties that we shall explain in Chapter 18. The term dark energy has been coined to describe the component of the Universe's energy density responsible for such behavior. Remarkably, there is mounting evidence that the Universe contains such dark energy and is accelerating rather than declerating!