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What is the meaning of bias and galaxy overdensity?
 
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YinZhe Ma



Joined: 09 Oct 2008
Posts: 11
Affiliation: University of KwaZulu-Natal

PostPosted: April 13 2013  Reply with quote

Hi Guys,

I am confused about the bias and galaxy overdensity.

First, galaxy overdensity is related to matter density contrast through:
δg = b * δm, where b is the bias. δm cannot be less than −1, because it is defined as (\rho-\overline{\rho})/\overline{\rho}, since \rho \geq 0, \delta_{\rm{m}} \geq -1.

However, b can take any value. It can be − 3, − 2 (void), or very positive number, such as 2 in Table 5 and 6 of 1303.4486. Therefore, δg can be any value. For example, If δm = − 0.8, b = 2, then δg = − 1.6. Then what is the definition of δg if it can take any value?

It certainly cannot be defined as the matter density contrast because it can be less than −1. Then how to understand its physical meaning?

Thanks.
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Maciej Bilicki



Joined: 12 May 2010
Posts: 19
Affiliation: University of Cape Town

PostPosted: April 14 2013  Reply with quote

The bias as defined here is linear. Voids with δ=−0.8 are pretty non-linear.

Galaxy underdensity, as any other underdensity, cannot – by definition – be smaller than −1.

You can find more basics on the bias in for instance the classic review by Strauss & Willick (1995).

I am quite sure that the bias can't be negative.
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Wojciech Hellwing



Joined: 17 May 2006
Posts: 1
Affiliation: Institute for Computational Cosmology, Durham

PostPosted: April 14 2013  Reply with quote

A negative bias would be totally unphysical when one concerns density. However an anti-bias (0<b<1) is possible and in the fact is present for small galaxies/haloes.

As Maciej had noticed You have used a definition of the linear bias. In general we have:

δg = f(δ)

in particular we can express the non-linear function f in Tylor series:
\delta_g = \sum_{k=0}^\infty {b_k\over k!}  \delta^k
(see e.g. Fry&Gaztanaga 1994)
hence in regions where b1 > 1 and δ < 0.8 rest of the bias parameters will have values making the \delta_g\geq -1 in the end.
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YinZhe Ma



Joined: 09 Oct 2008
Posts: 11
Affiliation: University of KwaZulu-Natal

PostPosted: April 17 2013  Reply with quote

However, what if b=3 (positive bias), but delta_m=−0.5? In this case, delta_g=b*delta_m=−1.5, still < − 1.
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Boud Roukema



Joined: 24 Feb 2005
Posts: 82
Affiliation: Torun Centre for Astronomy, University of Nicolaus Copernicus

PostPosted: July 16 2013  Reply with quote

As Maciej and Wojciech said, the discussion concerns linear perturbation theory, meaning |\delta| \ll 1. Your value of δm = − 0.5 is highly non-linear, so the linear theory is no longer valid. If you apply it anyway, then you get unphysical results.

Similarly, when the overall virialisation fraction at low redshifts fvir(z) fails to satisfy f_{vir}(z) \ll 1, the underlying homogeneity assumption fails and an artefact - would-be "dark energy" - arises if the homogeneous (FLRW) metric is used to interpret the observations despite the invalidity of the homogeneity assumption (1303.4444).
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