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YinZhe Ma
Joined: 09 Oct 2008 Posts: 11 Affiliation: University of KwaZulu-Natal
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Posted: April 13 2013 |
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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 , since , .
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
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Posted: April 14 2013 |
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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
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Posted: April 14 2013 |
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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:
(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 in the end. |
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YinZhe Ma
Joined: 09 Oct 2008 Posts: 11 Affiliation: University of KwaZulu-Natal
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Posted: April 17 2013 |
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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: 84 Affiliation: Torun Centre for Astronomy, University of Nicolaus Copernicus
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Posted: July 16 2013 |
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As Maciej and Wojciech said, the discussion concerns linear perturbation theory, meaning . 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 , 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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