Seyfert Galaxies: How does this statistical deduction about the age of their nucleus make sense?

Question

As per this book, An Introduction to Active Galactic Nuclei by Bradley Peterson:

The nuclear emission must last more than $10^8$ years, because Seyfert galaxies constitute about 1 in 100 spiral galaxies. This is a simple argument. One extreme scenario is that galaxies which are Seyferts are always Seyferts, in which case their lifetime is the age of the Universe ($10^{10}$ years). The opposite extreme is one where all spirals pass through a Seyfert phase (or phases) - since 1 spiral in 100 is currently in the Seyfert phase, it must last of order $10^{10} / 100 = 10^8$ years.

I can't seem to grasp this justification for the age of nuclear emissions. Could someone explain?

Answer 1

Suppose the Seyfert phenomenon occurs randomly at some point during every galaxy's life. If 1 in a 100 galaxies currently are seen to be exhibiting the phenomenon then you could guess that it lasts about $\sim 10^{10}/100$ years, where $\sim 10^{10}$ years is the age of a typical galaxy.

On the other hand, suppose the Seyfert phenomenon is peculiar just to 1% of galaxies. In which case it must be happening in those galaxies all the time so that we see 1 in a 100 as Seyfert galaxies. In which case, the lifetime of the phenomenon in those galaxies must be similar to the age of those galaxies, i.e. $\sim 10^{10}$ years.

The argument appears to be that the truth must be somewhere between these scenarios and so the lifetime of the phenomenon must be at least $10^8$ years.

It seems to me there is wriggle-room in this argument. For example, what if the Seyfert phenomenon was some sort of semi-regular event that lasted for a short time? The total duration of these events would have to be at least $10^8$ years, but the phenomenon itself could be more short-lived than that if it was repeated lots of times in the same galaxy.