# 5 Distances in extragalactic astronomy

Recall **Hubble's law**:

This relationship between **redshift**, *z*, of a distant galaxy which is given by

and its distance, *d*, from us arises because space is expanding. When the large redshifts of quasars were first discovered, there was naturally some reluctance to straightforwardly apply Hubble's law to them because the distances, and consequently the inferred luminosities were enormous. In fact, quasars are the most intrinsically luminous persistently bright objects we have discovered, and the most distant quasars are the most distant individual objects we know about. Consequently, active galaxies are of fundamental importance to **cosmology**, the study of the Universe as a whole. Cosmology is a huge subject and here in S381_1 we will focus on the active galaxies themselves, using only those cosmological ideas necessary to understand them.

The astronomical research required to determine the value of the Hubble constant, *H*_{0}, and thereby calibrate the extragalactic distance scale has filled entire textbooks, and we will not discuss it in this course, focusing instead on astrophysics. In this course we will generally adopt the same approach as Peterson, and use *h*_{0} to represent the value of the Hubble constant in units of 100 km s^{−1} Mpc^{−1}, i.e.

At the time of writing, astronomers favoured a value of around *H*_{0} = 60 km s^{−1} Mpc^{−1}, i.e. *h*_{0} = 0.6, but this is continuously being debated and refined as new observations are made. Wherever a result is strongly dependent on the value of the Hubble constant, *h*_{0} will appear explicitly.

The **Hubble time** is the inverse of *H*_{0}. If the Universe has always expanded at a constant rate, this is the time required for the Universe to expand from the Big Bang to its current size. The Hubble ‘constant’ has probably actually changed over time since the Big Bang, with the **deceleration parameter**, *q*_{0}, describing the change in the expansion rate.

## Question 3

What is meant by the ‘cosmological redshift’?

### Answer

Redshift refers to the shifting of the wavelength of a spectral line. Cosmological redshift indicates that this shifting in wavelength in the light emitted by a distant source occurs as a consequence of the overall expansion of the Universe. If a redshift is cosmological, Hubble's law can be used to infer the distance of the emitting object.