Homework - Interparticle distance between galaxies

[fab13]

Homework Statement

[/B]
I have the following questions as homeworks and I would like to get help.

Question 1) Give the formal expression of the total number density of galaxies. Why is this expressoin problematic in practice?

Question 2) In practice one uses a numerical value for the number density of galaxies and for their typical luminosity. Explain why and how.

Question 3) Using the above typical values, infer an estimation of $l_{g}$ ,
the inter galaxy distance.

Question 4) Using a powerlaw correlation function, give the formal expression of the total number neighbours of a galaxy.

Question 5) Infer the distance of the inter galaxy distance

Question 6) From the number of neigbours infer the density contrast it represents

Homework Equations

: equations concerned are not provided into this homework[/B]

The Attempt at a Solution

Question 1) I saw from my research different expressions for the total density of galaxies (as a function of Luminosity or Mass), but which one could correspond to this question 1 ? What is this formal expression ?

Then, why this total density is problematic ?

Question 2) It seems to be related to the problematic above.

Can I use, for a sample of galaxies $S$, with $L$ luminosity :

$\Phi_{s}(L) = \dfrac{n_{s}(L)}{V_{s}(L)}$ which is the number of galaxies in S per unit luminosity ?

? If yes, why have I got to use $\Phi_{s}(L)$ compared to formula in question 1 ?

Question 3): How can I infer an estimation of inter galaxy distance from expressions into question 1 and question 2 above ?

Question 4): I didn't see the expression of the total number neighbours of a galaxy : anyone could give me help about the expression to apply in this case ?

Question 5): If I knew the formula of question 4, I could compute the average distance between two galaxies

Question 5): I must estimate the number of neighbours of main galaxy up to a distance $r$and so estimate the density contrast that represents.
I don't see how to estimate this density contrast since I have not the expression asked on question 5.
Sorry if the answers are simple but I am a beginner in galactic and extra-galactic matters.

Even short answers or suggestions could help me to solve these different questions.

Thanks

 

[haruspex]

Question 1) I saw from my research different expressions for the total density of galaxies (as a function of Luminosity or Mass), but which one could correspond to this question 1 ? What is this formal expression ?

I am only guessing here, but what you find online will mostly be concerned with estimating the value from observations, whereas "formal expression" sounds like they are asking for a definition.
How would you define the term?

 

[fab13]

@haruspex

I wonder if the expression of this "total density of galaxies" has to imply luminosity distribution or mass distribution. But the clue is that expression has to be problematic from a physical point of view (from what is said in homework).

So if someone could give me indications to find the appropriate relation of "total density of galaxies". Regards