# Formula for the large-scale bias of galaxies

• I
• fab13
In summary, the conversation discusses the equation given by the teacher which links the local and global number density of galaxies to the contrast of dark matter density. The article referenced defines the bias term and relates it to the contrast of density number and dark matter. The question is how to convert the equation in the article to the desired equation given by the teacher, specifically in regards to the presence of a second term in the equation.
fab13
TL;DR Summary
I would like to infer the relation between the local density of galaxies and the global density in Universe.
From this article : https://arxiv.org/pdf/1611.09787.pdf , I try to deduce the equation that my teacher told me which links 2 quantities :

1) the global number density of galaxies
2) the local number density of galaxies
3) the contrast of Dark matter density

The relation that I would like to find (the relation given by my teacher) is very simple :

where ##N_{1}## is the local number density of galaxies in Universe, ##n_{1}## is the global number density, ##b_{1}## is the bias (cosmological bias of galaxies) and ##\delta_{\text{DM}}## the contrast in dark matter density. When I say "local", I mean in the volume of scale that I consider (in a cluster of galaxies for example, doesn't it ?)

for the moment, I can't find this equation.

Into the article above, they define the bias by doing the relation ##(1.1)## :

with ##b_{1}## the bias.

As you can see, in this article, authors are reasoning with the contrast of density number of galaxies (##\delta_{g}(\vec{x}))## and the contrast of matter density of Dark matter (##\delta_{\text{DM}}(\vec{x})##).

I tried to modify this equation ##(2)## to get ##(1)## but I am stuck by the following difference : on one side, one takes number densities and on the other one, they take contrasts of density (with contrast density number and Dark matter contrast).

Multiplying the both by the volume ##V## is not enough since there is the value "-1" in the definition of contrast : ##\text{Global Number of galaxies} = \overline{n_{g}}\,V##. I think that I have to use the following relations : ##N_{g}\equiv N_{1}## and ##\overline{n_{g}}=n_{1}## in the relation of my teacher but I am not sure.

Anyone could help me to find the equation (1) from the equation (2) of article cited ?

Regards

Last edited:
The conversion is in the ##b_1## term which relates the number density contrast to the matter density contrast. I seem to remember this term being called the density bias.

Which ##b_{1}## do you talk about ? this of eq##(1)## or eq##(2)##. ?

If I take the relation eq##(2)##, I can write :

As you can see, ##(3)## is not equal to the equation ##(1)## that I would like to get (since a second term ##\overline{n_{g}}##)

How can I circumvent this issue ?

Any help is welcome, Regards

Given I have exceeded the edit deadline, I just wanted to add at the end of my post above :

Which ##b_{1}## do you talk about ? this of eq##(1)## or eq##(2)##. ?

If I take the relation eq##(2)##, I can write :

As you can see, ##(3)## is not equal to the equation ##(1)## that I would like to get (since a second term ##\overline{n_{g}}##)

With the notations of the equation##(1)##, in order to be coherent, I think that I have to assimilate ##N_{1}## to ##n_{g}(\vec{x})## (local density) and ##n_{1}## to ##\overline{n_{g}}## (global or mean density).

How can I circumvent this issue about the presence of this second term into eq##(3)## compared to eq##(1)## ?

Any help is welcome, Regards

I don't want to be insistent but I really need help about the issue between the eq##(3)## and eq##(1)##, especially how to suppress the presence of the second term of eq##(3)## in order to find equation##(1)##.

Thanks

## 1. What is the formula for the large-scale bias of galaxies?

The formula for the large-scale bias of galaxies is b(k) = √(P_gal(k)/P_m(k)), where b(k) represents the bias factor, P_gal(k) represents the power spectrum of galaxies, and P_m(k) represents the power spectrum of matter.

## 2. How is the large-scale bias of galaxies calculated?

The large-scale bias of galaxies is calculated by analyzing the distribution of galaxies in a particular region and comparing it to the distribution of matter in the same region. This is done by measuring the power spectrum of both galaxies and matter, and using the formula b(k) = √(P_gal(k)/P_m(k)) to determine the bias factor.

## 3. What does the large-scale bias of galaxies tell us about the universe?

The large-scale bias of galaxies provides insights into the distribution and clustering of matter in the universe. It helps us understand how galaxies are distributed in relation to the underlying dark matter structure, and how this structure evolves over time.

## 4. How does the large-scale bias of galaxies affect our understanding of cosmology?

The large-scale bias of galaxies is an important factor to consider in cosmology because it can impact our measurements and interpretations of the expansion rate of the universe, the distribution of matter, and the formation and evolution of galaxies. It also plays a role in testing and refining theories of cosmology.

## 5. Can the formula for the large-scale bias of galaxies be used to study other celestial objects?

Yes, the formula for the large-scale bias of galaxies can be applied to other celestial objects such as galaxy clusters, quasars, and even the cosmic microwave background. It can also be used to study the large-scale structure of the universe beyond just galaxies, providing valuable insights into the evolution and composition of the universe.

Replies
1
Views
951
Replies
9
Views
2K
Replies
0
Views
1K
Replies
1
Views
1K
Replies
7
Views
1K
Replies
4
Views
1K
Replies
6
Views
1K
Replies
15
Views
3K
Replies
1
Views
1K
Replies
11
Views
1K