Question

Distances to very remote galaxies are estimated based on their apparent type, which indicate the number of stars in the galaxy, and their measured brightness. Explain how the measured brightness would vary with distance. Would there be any correction necessary to compensate for the red shift of the galaxy (all distant galaxies have significant red shifts)? Discuss possible causes of uncertainties in these measurements.

Short answer

The brightness would vary with distance in the same way that a candle appears less and less bright as we move further away. The difference is that we must account for the galaxy's redshift. Uncertainties could arise from additional blue/redshifts caused by the galaxy's rotation, an incorrect estimate of the galaxy's type, or instrument flaws.

Step-by-step solution

How the measured brightness vary with distance? 

We can calculate the absolute output brightness of a galaxy by estimating the number of stars - luminous objects in it. This brightness decreases with distance, similar to how a candle appears less and less bright as we move further away. The energy of a photon, on the other hand, decreases with frequency decrease, i.e. redshift, so a galaxy with redshifted radiation would have lower brightness and appear further away.

We must account for the redshift of the radiation, which we do by calculating the velocity of the galaxy, for example, by comparing known radiation spectra (such as a hydrogen or calcium spectrum) to their redshifted counterparts. This way, we can calculate the amount of redshift and compensate for it.

The relation between brightness and absolute brightness is given by,

\(m - M = {5^{{\rm{log}}\left( {{\rm{D/10}}} \right)}}\)

Here \(m\) is the brightness, \(M\) is the absolute brightness and \(D\) is the distance from the star.

Possible causes of uncertainties:

Further blue/red shifts

Because the galaxy is likely to be oriented in such a way that half of it is rotating towards us while the other is rotating away from us, the half that is rotating towards us will be blue-shifted while the half that is rotating away from us will be redshifted.