Virialized structures in the Universe produce velocity perturbations of galaxies which are located near them. The amplitude of these perturbations (delta v)/v depends on the background density of the Universe (OMEGA) and the density contrast ( delta rho/rho ) interior to the shell upon which the galaxy is located. The unperturbed velocity in this case is given by v = Hr where r is the distance from the source which is causing the perturbation.

The linear approximation to this perturbation, which works in the limit of small delta rho/rho is the following:

We can apply this equation to the case of Virgo Infall as schematically shown below:

The Virgo cluster is a nearby cluster or region of mass overdensity. Our galaxy feels the gravitational pull of Virgo and therefore our expansion velocity, with respect to Virgo is retarded. The diagram above shows three components:

• Our infall to Virgo
• The CMB Dipole Anistropy --> note that its direction is not pointed at Virgo and the amplitude is larger than our Infall into Virgo. Therefore, the Virgo cluster alone is not causing this motion.

• Possible motion of the entire Local Supercluster towards the next nearest supercluster, Hydra-Centaurus (HC): We will discuss this is more detail below

For now ,let's just consider our infall into Virgo.

• The distance to Virgo is 15 Mpc. If we use H = 100, then the predicted expansion velocity is 1500 km/s.

• The observed velocity of Virgo, however, is 1200 km/s

• The difference represents our infall of 300 km/s to Virgo

• delta v/v = 300/1500 = .2

• We can now determine OMEGA if we can measure delta rho/rho that is interior to us in the direction of Virgo.

  But we can only measure delta rho/rho in light when its really delta rho/rho in mass that is causing our velocity perturbation. Hence bias or the b parameter becomes important.

  The measured delta rho/rho in light is 1.9. If we assume there is no bias then we have:

  .2 = (1/3)(1.9)(OMEGA^.6)

  which yields OMEGA = 0.15

  Suppose there is bias such that we really area measuring

  .2 = (1/3)(1.9(OMEGA^.6/b)

  and hence we only have (OMEGA)/b = 0.15

  For OMEGA = 1 this would require b = 6.6 - which is a huge bias; in practice b =2.4 is the maximum which is allowed by observation and this yields OMEGA = 0.36. Recent data, however, strongly suggests that b is not larger than 1.5 which is OMEGA = 0.23.

  Hence, small scale infall values are generally too small to be consistent with OMEGA = 1. However, let's be insistent that OMEGA=1 and ask then what the density constrast must be:

  .2 = (1/3)(1/b)( delta rho/rho )
  .6b = delta rho/rho

  if b = 1 then delta rho/rho = 0.6 but delta rho/rho = 1.9 in light and hence there must be bias to recover OMEGA = 1. But the bias would have to be too large.

  What about larger scales? Next time we will journey to the Great Attractor to see what we can learn.

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  The Electronic Universe Project
  e-mail: nuts@moo.uoregon.edu