# Euclidean differential number counts of supernovae

• I
• resurgance2001
In summary, the conversation discusses the topic of deriving an expression for the differential number count of supernovae in a flat, non-expanding space. The person is confused by the question and is seeking help. They mention that supernovae are events rather than objects and question how they can be counted. The conversation also touches on the different types of supernovae and the possibility of computing supernova candidates. The conversation ends with a discussion about the concept of differential number count and how it relates to observing stars and supernovae.
resurgance2001
Hi

I am working on an assignment which is has asked us to derive an expression for a differential number count of supernovae in a euclidean flat non-expanding space.

I am bit perplexed by this question and am wondering whether it is a trick question. We are allowed to do research to find an answer outside the textbook we have so long as we quote any sources. I have dug around on the net and can't find anything at the moment that seems useful.

I am stuck because my understanding was/is that supernovae are events rather than 'objects'. I have read somewhere that it is estimate that there is a supernovae once every second in the whole universe. Supernovae only last for a few weeks before they die out, so I don't see exactly how one could count them - at least not in the same way as one might count galaxies or some specific type of star. Since this whole topic is quite new to me, I could be completely wrong and am barking up the wrong tree. Any way, any pointers or suggestions would be greatly welcome. For one thing I am actually still trying to understand properly what a differential number count is. Thanks

I think you are correct. Supernova is the explosion event where a heavy star is exploding to became a neutron star or a black hole.
In fact where are at least two types of supernovae. They are distinguished by whether or not a iron core is formed or not, i.e. type I and II. Astrophysicists are also characterizing them in further subgroups.

However, some types people are speaking of supernovae as objects. But, in that case what is meant is supernova candidates, meaning stars which finally will end their lives in a supernova explosion. I'm not sure but maybe your assignment is to compute this sort of candidates.

resurgance2001 said:
I have read somewhere that it is estimate that there is a supernovae once every second in the whole universe. Supernovae only last for a few weeks before they die out, so I don't see exactly how one could count them - at least not in the same way as one might count galaxies or some specific type of star.

Check out the intermediate Palomar Transient Factory (iPTF): "a fully-automated, wide-field survey for a systematic exploration of the optical transient sky"

eys_physics said:
I think you are correct. Supernova is the explosion event where a heavy star is exploding to became a neutron star or a black hole.
In fact where are at least two types of supernovae. They are distinguished by whether or not a iron core is formed or not, i.e. type I and II. Astrophysicists are also characterizing them in further subgroups.

However, some types people are speaking of supernovae as objects. But, in that case what is meant is supernova candidates, meaning stars which finally will end their lives in a supernova explosion. I'm not sure but maybe your assignment is to compute this sort of candidates.
Thanks - I was wondering about that also.

stoomart said:
Check out the intermediate Palomar Transient Factory (iPTF): "a fully-automated, wide-field survey for a systematic exploration of the optical transient sky"

Thank you . I will check out that link.

resurgance2001 said:
I am actually still trying to understand properly what a differential number count is
This seems to be the most important bit. What is your current understanding of it? Have you ever used it in some other context?

(for the record, I'm not sure I understand it myself, but maybe we'll come up with something together)

resurgance2001 said:
Supernovae only last for a few weeks before they die out, so I don't see exactly how one could count them - at least not in the same way as one might count galaxies or some specific type of star.
But there's no essential difference in this regard between a SN and some type of star - both are transient, albeit with vastly different lifetimes. Yet, when you make observations at any given time, you'll observe a specific number of both.
This is the same as e.g. with observations of dwarf stars and giants - the latter live orders of magnitude shorter than the former, which has the result that at any given time there is more dwarfs than giants to observe (and there's more giants than supernovae).

Bandersnatch said:
This seems to be the most important bit. What is your current understanding of it? Have you ever used it in some other context?

(for the record, I'm not sure I understand it myself, but maybe we'll come up with something together)But there's no essential difference in this regard between a SN and some type of star - both are transient, albeit with vastly different lifetimes. Yet, when you make observations at any given time, you'll observe a specific number of both.
This is the same as e.g. with observations of dwarf stars and giants - the latter live orders of magnitude shorter than the former, which has the result that at any given time there is more dwarfs than giants to observe (and there's more giants than supernovae).
Thanks

What I have got so far is that in a flat non-expanding space there is a formula of the form: dN/dS is proportional to S^-5/2 Where N is the number of stars and S is the flux of the star. But I have to admit I don't have much of a clue about what it means! I take your point about stars and supernova being the same apart from having different (vastly) lifetimes, and that helps. I will let you know how I get on as I continue to research.

## 1. What are Euclidean differential number counts of supernovae?

Euclidean differential number counts of supernovae is a method of measuring the distribution of supernovae in the universe based on their luminosity and redshift.

## 2. How are Euclidean differential number counts of supernovae calculated?

Euclidean differential number counts of supernovae are calculated by dividing the observed number of supernovae in a certain luminosity and redshift range by the expected number based on a simple Euclidean model of the universe and the observed luminosity function of supernovae.

## 3. What is the significance of Euclidean differential number counts of supernovae?

The significance of Euclidean differential number counts of supernovae lies in its ability to provide important information about the large-scale structure of the universe and the expansion rate of the universe.

## 4. How does the concept of Euclidean differential number counts of supernovae relate to the cosmological principle?

The cosmological principle states that the universe is homogeneous and isotropic on large scales. Euclidean differential number counts of supernovae follow this principle by assuming a uniform distribution of supernovae in the universe and using a simple model to calculate their expected numbers.

## 5. What are some current research topics related to Euclidean differential number counts of supernovae?

Some current research topics related to Euclidean differential number counts of supernovae include using these counts to study the properties of dark energy, comparing the predicted counts with observed data to test cosmological models, and improving the accuracy of the calculations by accounting for other factors such as gravitational lensing.

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