Question

Assume a typical galaxy in the Coma cluster moves at a speed approximately equal to the cluster’s velocity dispersion, 977 km s−1 , and the diameter of the Coma cluster is 6 Mpc.

a) [5 pts] Estimate how long a galaxy in the Coma cluster would take to travel from one side to the other.

b) [2 pts] How does this compare to the present-day Hubble time, tH?

c) [3 pts] If there are 1000 galaxies in the Coma cluster, what is the average separation between two galaxies in the cluster today (at z ≈ 0)?

d) [5 pts] Now, put the Coma cluster at a redshift of 2. What is the average separation between two galaxies in the cluster at this redshift, and what does this imply about the size of the cluster at z = 2?

e) [5 pts] If the virial mass of the Coma cluster is the same at z =0 as it is as z = 2, calculate the velocity dispersion of the Coma cluster at z = 2.

Answer 1

using t = D/v

here D = 6 Mpc

= 18.48 x 10¹⁹ km

t = 18.48 x 10¹⁹ / 977

t = 6 x 10⁹ year

the Hubble time is t_H = 13.8 x 10⁹ year

t/t_H = 6 x 10⁹ year / 13.8 x 10⁹

t/t_H = 0.43

t = 0.43 t_H.