Essay

PECULIAR MOTIONS

Adapted from P. Coles, 1999, The Routledge Critical Dictionary of the New Cosmology, Routledge Inc., New York. Reprinted with the author's permission. To order this book click here: http://www.routledge-ny.com/books.cfm?isbn=0415923549

The large-scale motions of galaxies are described in broad terms by Hubble's law. The pattern of motions resulting from this law is often called the Hubble flow: all observers see themselves as the centre of expansion, so that all motions are radially outward, and galaxies are moving away at a speed proportional to their distance. This behaviour is readily explained in the standard cosmological models as being a consequence of the homogeneity and isotropy of the Universe as embodied in the cosmological principle (see also expansion of the Universe).

However, the real pattern of galaxy motions is not exactly of this form. This is because, while the cosmological principle might hold in a broad sense on large scales, the Universe is not exactly homogenous: it contains galaxies distributed in a complicated hierarchy of large-scale structure. Local fluctuations in the density from the uniformity required of a completely homogeneous Universe give rise to fluctuations in the local gravitational field from place to place. These gravitational fluctuations tend to deflect galaxies from the paths they would follow in a pure Hubble flow.

These departures from the pure Hubble expansion are usually called peculiar motions, though there is nothing particularly peculiar about them: their occurrence is entirely expected given the observed inhomogeneous nature of the real Universe. Peculiar motions modify the form of Hubble's law by adding a term to the right-hand side:

v = H₀ d + v_p

where v_p is that component of the peculiar motion that lies in the line-of-sight direction from the galaxy to the observer. Unlike the pure Hubble expansion, which is radial, the peculiar motions are generally randomly directed in space. Since the total velocity v is inferred from the redshift, however, only the part that lies in the radial direction can be detected directly from the spectrum. The typical peculiar motions of galaxies are several hundred kilometres per second, so we can see from the above equation that peculiar motions can swamp the Hubble flow entirely for nearby objects. Some nearby galaxies, such as the Andromeda Galaxy, are even moving towards the Milky Way. At large distances, however, the discrepancies are very small compared with the Hubble flow.

Peculiar motions are one cause of the observed scatter in the Hubble diagram of velocity against distance. This scatter might suggest that their presence is merely an irritation, but peculiar motions are very important because they raise the possibility of measuring the amount of matter responsible for their generation (see dark matter). This is possible because the size of the peculiar motion depends on the density field, and is not simply a random error. Basically, the more matter there is in the Universe - in other words, the higher the value of the density parameter Omega - the larger should be the size of any peculiar motions.

There are two basic ways to study peculiar motions. In the first, and simplest, they are measured not directly but by using a redshift survey of a large number of galaxies to make a map in `redshift space'. In other words, we measure the redshift and hence the total velocity of a sample of galaxies, and then assume that Hubble's law holds exactly. The presence of peculiar motions will distort the map, because velocity is not simply proportional to distance, but also depends to some extent on the matter density. This manifests itself in two ways. In very dense regions of strong gravitational forces, the peculiar velocities are large and random (see virial theorem). All the galaxies are in a small volume in real space, but because of their huge peculiar motions they are spread out in redshift space. What we see in a redshift survey are therefore not near-spherical blobs (which is what clusters really are), but `fingers' stretched along the line-of-sight to the observer. These features are called, somewhat irreverently, the fingers of God. In more extended systems such as superclusters, the peculiar motions are not so large but they are discernible because they are coherent. Imagine a spherical supercluster which is gradually collapsing. Consider what happens to objects on the edge of the structure: galaxies on the far side of the structure will be falling towards the observer, while those on the near side will be falling away from the observer. This squashes the structure in redshift space compared with what it is like in real space. We can use statistical arguments to quantify the distortions present in redshift-space maps, and hence attempt to work out how much mass there is causing them.

The second way of studying peculiar motions is to attempt to measure them directly. This requires us to measure the distance to the galaxy directly (thus introducing all the difficulties inherent in the extragalactic distance scale), and then to subtract the Hubble flow to obtain the peculiar velocity v_p. This technique has been used for many years to map the flow of relatively nearby galaxies, and some interesting features have emerged. The Local Group of galaxies, for example, is moving towards the centre of the Virgo Cluster of galaxies at about 200 km/s; this is essentially the kind of infall motion discussed above. On larger scales, coherent peculiar motions are expected to be smaller than this, but there is evidence of flows on quite large scales. For example, a study of the motions of a sample of spiral galaxies by Vera Rubin and co-workers in 1976 revealed an apparent anisotropy in the expansion of the Universe on a scale of around 100 million lightyears. This has become known as the Rubin-Ford effect.

The fact that we do not see a purely isotropic expansion reflects the fact that the Universe is not homogeneous on these scales. It has been claimed that there is motion on scales much larger than this. Astronomers have postulated a Great Attractor - a hypothetical concentration of matter with a mass of more than 10¹⁶ solar masses, located about 150 million light years from our Galaxy in the direction of the borders of the constellations Hydra and Centaurus - which may be pulling surrounding galaxies, including the Milky Way, into itself. Although there is clearly a concentration of galaxies at the place where the Great Attractor has to be located to account for these large-scale galaxy motions, more recent studies indicate that no single object is responsible, and that the observed bulk flows of galaxies are probably caused by the concerted gravitational effect of several distinct clusters of galaxies.

An alternative approach to the study of peculiar motions is to look at the properties of the dipole anisotropy of the cosmic microwave background radiation. Because of our motion with respect to the frame of reference in which this radiation is isotropic, we see a characteristic cosine variation in the temperature on the sky. The size of this variation is roughly v/c, because of the Doppler effect, and the direction of maximum temperature gives the direction of our motion. The microwave background therefore supplies us with the best measured peculiar motion in cosmology: our own!