Infer the distance of a closest neighbor galaxy from correlation

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fab13
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I am trying to estimate the distance of closest galaxy neighbor knowing the expression of number of neighbors into a volume ##\text{d}V##, the mean density ##n_\text{gal}## and the correlation function, i.e with this expression :

##\text{d}N=n_{\text{gal}}\,\text{d}V\,(1+\xi(r))##

with ##\xi(r)=\bigg(\dfrac{r}{r_{0}}\bigg)^{-\gamma}\quad\text{with}\quad\gamma\,\sim\,1.77 \quad\text{and}\,r_{0}\,\sim\,5\,\text{Mpc}##.

I take into my calculation the following value for ##n_{\text{gal}}=0.0420\,\text{h}^{-3}\,\text{Mpc}^{-3}##

How could I infer the distance of the closest galaxy from us ?

Regards
 
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Hello PeterDonis,

the formula :

##\text{d}N=n_{\text{gal}}\,\text{d}V\,(1+\xi(r))## is well known from what I have seen.

But for ##n_{\text{gal}}=0.0420\,\text{h}^{-3}\,\text{Mpc}^{-3}##, I have taken it from astrophysics litterature.

Do you know a simple way to estimate ##n_{\text{gal}}## and then the closest neighbour galaxy ?
 
fab13 said:
is well known from what I have seen

Then you should have no trouble producing a reference.

fab13 said:
I have taken it from astrophysics litterature.

That's not a reference. A reference is a specific textbook or peer-reviewed paper.
 
@PeterDonis

You can find the first formula on this link (slide 14) : http://www.bo.astro.it/~school/school09/Presentations/Students/Contreras.pdf

Author takes as value ##\gamma \sim 1.7 ## and ##r_{0}\sim 4.5\,\text{Mpc}\,h^{-1}##

and for the galaxy number density : see http://www.astro.ljmu.ac.uk/~ikb/research/h-units.html

number density of galaxies is taken as : ##2.92\,h^3\,\text{Mpc}^{-3}\,\sim\,1\,\text{Mpc}^{-3}##

I just want to take roughly values, what interests me is the physical underslying issues for this estimation of density galaxy number.

Have you got any clues to compute closest galaxies from us with 2 points correlation function above ? regards
 
fab13 said:
You can find the first formula on this link (slide 14) :

These slides leave out a lot of information. In particular, they don't say what the two-point correlation function they are talking about means.

fab13 said:
and for the galaxy number density :

I'm not sure the values quoted on this page are actual formulas used in cosmology. Do you really think the number density of galaxies for ##h = 0.7## really magically turns out to be exactly one galaxy per cubic megaparsec?

fab13 said:
what interests me is the physical underslying issues for this estimation of density galaxy number.

Neither of the references you give talk about this at all. Do you have any other references?

fab13 said:
compute closest galaxies from us

I would not expect the general formulas for this to give accurate numbers for the closest galaxy from us, because our galaxy is part of a bound system of multiple galaxies (the Local Group), which is in turn part of a larger galaxy cluster. The general formulas assume that galaxies are evenly distributed throughout the universe, which they aren't, and that no systems of multiple galaxies gravitationally bound together exist, which they do.

Why do you want to compute this?
 
Why do you want to compute this ?

Because from the beginning, you don't want to help me, there are always things which are not right with you. I didn't wait after you to have useful informations about my issue. Other guys tried to help me with good intentions, not like you who don't give informations, except saying "What's your reference? it's not good etc ...

I explained that what interests me is the physics underlying this problem : I am not locked on a strict value, I just want to have an order of value for the equations that I am using.

fortunately, other persons on this forum gave me more constructive ideas.
 
fab13 said:
other persons on this forum gave me more constructive ideas.

Meaning you have another thread open on this same topic? Can you give a link? If there is another open thread, we can just close this one, since you're only supposed to have one thread on a given topic.
 
fab13 said:
Because from the beginning, you don't want to help me ...
You misunderstand the point of this forum. We are not a Q&A forum where you just ask a question and get an answer. We are a forum dedicated to helping people figure out for them selves how to get their answers. That is what Peter is attempting to do.
 
fab13 said:
Because from the beginning, you don't want to help me

It's not that I don't want to help you. It's that I don't understand what you are trying to do or why, or how the references you give relate to what you are trying to do or why. I can't help you if I don't understand what you're doing.

I see that there is indeed another open thread on a similar topic:

https://www.physicsforums.com/threa...f-galaxies-and-problematic-expression.962128/

Therefore, this thread is now closed, and further discussion should be done in the other thread.