Peculiar Motions

All of the techinques I've talked about up until now, lead to Omega < 1. However, there is a strong theoretical prejudice that Omega = 1 (due to the notion of an inflationary universe). This seems to fly in the face of the data. However, Omega = 1 is still a possibility because of the following.

LENGTH SCALES

The Cosmological Principle says that the Universe is homogeneous and isotropic on some appropriately large length scale. This means that if we divide the Universe into large boxes and then mix up (smooth) the contents of the boxes, the set of smeared out chunks of the Universe will make a smooth Universe which appears homogeneous and isotropic to all observers in the Universe.

It is apparent that on small scales the Universe is not isotropic and homogeneous, e.g., the Solar System is clearly lumpy. Thus, the question is On what scale does the Universe become smooth?, because it is on this scale and larger that we measure the average density of the Universe.

So far all of the measurements of the mass (density) of the Universe have relied on galaxies. Our measurements are thus local in that we measure the mass of the Universe where we can easily see mass. What are the consequences of this procedure?

• Galaxies: M ~ 10**11 M(Sun) and R ~ 50,000 light years ===> rho(gal) ~ 4 x 10**(-25) grams per cubic centimeter >> rho(crit)

  Does this mean that the Universe is closed? No. The galaxy is a very overdense region of the Universe and we need to average over a larger box. The Milky Way resides in the Local Group where the large galaxies are separated by around 10 million light years. What is the density of material when smeared out over this larger volume?

  rho(Local Group) ~ 5 x 10**(-32) grams per c.c. << rho(crit) as claimed!

  The problem is, is the space between galaxies really empty?

• Clusters of Galaxies: M ~ 10**15 M(Sun) and R ~ 10 million light years ===> rho(cluster) ~ 6 x 10**(-28) >> rho(crit), and so, clusters of galaxies are still not large enough to make us feel confident that we are measuring the average mass of the Universe.

  clusters are separated by ~ 30 million light years ===> rho(cluster of cluster) ~ 2 x 10**(-29) on the order of rho(crit).

If we start measuring the mass of the Universe on length scales on the order of clusters of clusters of galaxies or greater, then maybe we can start to feel fairly confident that we are actually measuring the average mass of the Universe and not simply the mass of the overdense parts.

MASS ESTIMATES BASED ON LARGE LENGTH SCALE ESTIMATES

Peculiar Velocities

• Recall:

  

  

  The overall Universe participates in the expansion, the Hubble flow, however, superimposed on the uniform expansion are smaller scale motions due to interactions between galaxies, clusters of galaxies, .... . These motions are referred to as peculiar velocities, streaming motions, ... . The significance of these peculiar velocities is that in order for them to have persisted over the lifetime of the Universe, they must be driven by something. If they were not being driven then they would have decayed away. The simplest explanation is that there are mass concentrations in the Universe which causes material to move around. For example, consider the

• anisotropy in the CMBR

  This anisotropy is naturally interpreted as due to a peculiar velocity of the Milky Way galaxy. The motion has a speed of 600 kilometers per second in the direction of the Hydra-Centaurus supercluster on the sky.

  Further (controversial) work showed that the Hydra-Centaurus cluster was also moving in the same direction at 800 kilometers per second and that more distant objects were actually approaching the same point. How did they know this? Well, consider the following Hubble plot. At d < D, the galaxies appear to have higher velocities than the Hubble relation. For d > D, the galaxies appear to have lower velocities than suggested by the Hubble relation.

  How can we interpret this result? Well, imagine that there is a large mass concentration at D (the so-called, Great Attractor). This mass will then pull nearby objects toward it. So, things with d < D, will have enhanced velocities and objects with d > D will have decreased velocities compared to their Hubble flow values.

  Results: G.A. at 130 million light years and M(GA) ~ 3 x 10**16 M(Sun).

• Estimates of Omega from Peculiar Velocities

  The peculiar velocities are due to mass concentrations which pull on things causing deviations from the Hubble flow. It is clear that the size of the perturbation (the size of the peculiar velocities) will depend upon how much mass pulls on the object. A detailed analysis leads to

  Models ===> v(peculiar) ~ Omega**0.6 (delta rho/rho) [W H(now)]

  • delta rho / rho tells you the size of the mass perturbation compared to the average density in the Universe. We only consider perturbations because the smooth part of the Universe will not cause peculiar motions. Why?
  • W is the size in kilometers of the perturbation. We need to know such things in order to calculate the mass (because we are so far only given the density).
  • Omega tells us the overall mass of the Universe. Since (delta rho / rho) only tells us how big the perturbation is compared to the average density of Universe, we need to know the density of the Universe to figure out how much mass is actually involved in the perturbation. For example, if Omega ~ 0, then even if (delta rho / rho) = 1,000,000 the amount of mass in the perturbation, strictly speaking is ~ 0.

  People have many peculiar velocities and based on infrared surveys of the sky, people have inferred (delta rho / rho) ===> Omega ~ 1 x b with an uncertainty of 0.3.

  The factor b arises because the surveys actually tell us (delta number of galaxies / number of galaxies). That is, they count galaxies and then try to relate this to mass densities. This is a tricky proposition and so they simply say (delta rho / rho) = [delta N(gal) / N(gal)] / b . The simplest assumption is to say that b = 1, however, we really don't know what value b is supposed to have.

  This is a very interesting result in that it, so far, is the only method which suggests that Omega ~ 1.