### What is the meaning of bias and galaxy overdensity?

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**April 13 2013**Hi Guys,

I am confused about the bias and galaxy overdensity.

First, galaxy overdensity is related to matter density contrast through:

[tex]\delta_{\rm{g}}=b*\delta_{\rm{m}}[/tex], where [tex]b[/tex] is the bias. [tex]\delta_{\rm{m}}[/tex] cannot be less than -1, because it is defined as [tex](\rho-\overline{\rho})/\overline{\rho}[/tex], since [tex]\rho \geq 0[/tex], [tex]\delta_{\rm{m}} \geq -1[/tex].

However, [tex]b[/tex] can take any value. It can be [tex]-3, -2[/tex] (void), or very positive number, such as [tex]2[/tex] in Table 5 and 6 of 1303.4486. Therefore, [tex]\delta_{\rm{g}}[/tex] can be any value. For example, If [tex]\delta_{\rm{m}}=-0.8[/tex], [tex]b=2[/tex], then [tex]\delta_{\rm{g}}=-1.6[/tex]. Then what is the definition of [tex]\delta_{\rm{g}}[/tex] 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.

I am confused about the bias and galaxy overdensity.

First, galaxy overdensity is related to matter density contrast through:

[tex]\delta_{\rm{g}}=b*\delta_{\rm{m}}[/tex], where [tex]b[/tex] is the bias. [tex]\delta_{\rm{m}}[/tex] cannot be less than -1, because it is defined as [tex](\rho-\overline{\rho})/\overline{\rho}[/tex], since [tex]\rho \geq 0[/tex], [tex]\delta_{\rm{m}} \geq -1[/tex].

However, [tex]b[/tex] can take any value. It can be [tex]-3, -2[/tex] (void), or very positive number, such as [tex]2[/tex] in Table 5 and 6 of 1303.4486. Therefore, [tex]\delta_{\rm{g}}[/tex] can be any value. For example, If [tex]\delta_{\rm{m}}=-0.8[/tex], [tex]b=2[/tex], then [tex]\delta_{\rm{g}}=-1.6[/tex]. Then what is the definition of [tex]\delta_{\rm{g}}[/tex] 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.