# Estimating the abundance of type-Ia supernovae using magnitude limited survey

I would like to estimate the fraction of type-Ia supernovae in a magnitude limited survey (only including those supernovae that are brighter than a certain than a given fixed apparent magnitude).

I currently have the following information:

1. Type-Ia supernovae are usually around 2.5 magnitudes brighter than core-collapse supernovae.

2. Volume limited surveys found that 30% of supernovae within a fixed distance from us are type-Ia.

How can I solve this problem using the above information? The formula for apparent magnitude $$m = -2.512\log_{10}(d/10\mathrm{pc})+c$$ seems like an obvious starting point, but doesn't seem to lead anywhere. A worked solution would be very helpful.

• Are you asking us to do your homework for you? – Mike G Aug 22 '19 at 1:07
• Hardly likely during the summer... – user29126 Aug 22 '19 at 14:09

## 1 Answer

The rudiments of a solution would be take your apparent magnitude limit and work out how far away you can see type Ia supernovae and how far away you can see core collapse supernovae.

Within the latter distance, 30% of the supernovae would be type Ia. Beyond that distance, all of the observed supernovae would be type Ia.

You then need to be assuming something about the density of supernova progenitors and thinking about any spread in their absolute magnitudes. And you didn't mention any observational uncertainties.

• I follow most of the logic here, but why must it be the case that "beyond that distance, all of the observed supernovae would be type Ia"? Surely, if type 1a novae are 2.5 magnitudes brighter, then they would be closer? – user29126 Aug 22 '19 at 14:10
• @user29126 It is the absolute magnitude that is 2.5 mag brighter. The apparent magnitude of course depends on how far away they are, so no generalisation is possible. – Rob Jeffries Aug 22 '19 at 15:04
• Ah, I see. What sort of fraction of Ia novae would you usually expect to find in this case? Would it be very high? – user29126 Aug 22 '19 at 17:30
• @user29126 obviously it will depend on the magnitude limit. Type Ia supernovae differ in other respects too and so it will depend on how one sets out to find them. – Rob Jeffries Aug 22 '19 at 22:07