The Galaxy−Dark Matter Connection cosmology & galaxy formation with the CLF
Frank C. van den Bosch (MPIA) Outline
• Statistical Description of Large Scale Structure • Galaxy Bias & The Galaxy-Dark Matter Connection • The Halo Model, Halo Bias & Halo Occupation Statistics • The Conditional Luminosity Function (CLF) • The Universal Relation between Light and Mass • Constraining Cosmological Parameters with the CLF • Halo Occupation Statistics from Galaxy Groups • Constraining Galaxy Formation with Galaxy Ecology • Conclusions Correlation Functions
ρ(~x) ρ¯ Define the dimensionless density perturbation field: − δ(~x) = ρ¯
For a Gaussian random field, the one-point probability function is: 2 1 δ P (δ)dδ = exp 2 dδ √2πσ − 2σ h i δ = δP (δ)dδ = 0 h i δ2 = δ2P (δ)dδ = σ2 h i R Define n-point probability functionR : P (δ ,δ , ,δ ) dδ dδ dδ n 1 2 ··· n 1 2 ··· n Gravity induces correlations between δi so that n Pn (δ1,δ2, ,δn) = P (δi) ··· 6 i=1 Q Correlations are specified via n-point correlation function: δ δ δ = δ δ δ P (δ ,δ , ,δ ) dδ dδ dδ h 1 2 ··· ni 1 2 ··· n n 1 2 ··· n 1 2 ··· n In particular, we willR often use the two-point correlation function
ξ(x) = δ δ with x = ~x ~x h 1 2i | 1 − 2| Galaxy Bias
Consider the distribution of matter and galaxies, smoothed on some scale R
ρ(~x) ρ¯ ngal(~x) n¯gal δ(~x) = − δgal(~x) = − ρ¯ n¯gal xxxxxxxxx Mass distribution xxxxxxxxx Galaxy distribution
ξ(r) = δ(~x1)δ(~x2) ξ (r) = δ (~x1)δ (~x2) h i gal h gal gal i
• There is no good reason why galaxies should trace mass.
Ratio is galaxy bias: b(~x) = δ (~x)/δ(~x) gal • • One can distinguish various types of bias: linear, deterministic: δgal = bδ gal non-linear, deterministic: δ δgal = b(δ) δ stochastic: δ = δ δ gal 6 h gal| i • Real bias probably non-linear and stochastic Dekel & Lahav 1999
Bias also depends on smoothing scale R δ • Since δgal = δgal(L, M , ...) bias also depends on galaxy properties • ∗ Handling Bias
Bias is an imprint of galaxy formation, which is poorly understood • Consequently, little progress constraining cosmology with LSS •
Q: How can we constrain and quantify galaxy bias in a convenient way? Handling Bias
Bias is an imprint of galaxy formation, which is poorly understood • Consequently, little progress constraining cosmology with LSS •
Q: How can we constrain and quantify galaxy bias in a convenient way?
A: With Halo Model plus Halo Occupation Statistics!
The Halo Model describes CDM distribution in terms of halo building blocks, under assumption that every CDM particle resides in virialized halo
On small scales: δ(~x) reflects density distribution of haloes (NFW profiles) • On large scales: δ(~x) reflects spatial distribution of haloes (halo bias) •
PARADIGM: All galaxies live in Cold Dark Matter Haloes.
galaxy bias = halo bias + halo occupation statistics Halo Model Ingredients