Question

A quasar is observed to be at redshift z=0.08 with an apparent magnitude of 19.5.

Assuming Hubble's constant to be 70 km/s/Mpc and that this redshift is in the non-relativistic regime, how far away is the quasar? Answer in Mpc

Answer 1

The redshift is the change in the frequency of the EM radiation that reaches earth. Redshifted means a shift towards the redder part of the spectrum. This happens if the source is moving away from us. In this case, the quasar is moving away from us due to expansion of the universe.

The redshift z in the non relativistic regime is simply:

Where c = speed of light = 3*10^8 m/s

and v =velocity of the source.

Using this, we get v = 2.4 *10 ^7 m/s

Now, the velocity of the quasar and the distance from us is given by this relationship:

where the constant H_0 is the hubble constant.

Now, using this to solve for D, we get the distance of the quasar as

D = (24000000 m/s ) / (70000 m/s /Mpc) = 342.8 Mpc

Which is the required answer.