The Clustering of Dark Matter in ΛCDM on Scales Both Large and Small

Transcription

1 The Clustering of Dark Matter in ΛCDM on Scales Both Large and Small Large Scales by Chris Orban May 19, 2008 Galaxy-redshift Survey Small Scales

2 0. Dark Matter Exists! 1. Large-Scale Structure What is P(k)? Theory/Observations 2. N-body Simulations Usefulness, Limitations Self-similarity Outline 3. Small Scales Local Group Tidal Streams Strong Gravitational Lensing 4. Summary

3 Dark Matter Exists! (Part 1) M33: A Spiral Galaxy M33 Rotation Curve V = 23 V c r Dark Matter! Gas Stars Observationally: M tot (< r) ~ r, at large r M light (< r) ~ constant, at large r

4 Dark Matter Exists! (Part 2) The Coma Cluster Mass Estimate: M guess ~ N gal x M gal ~ M sun Right Answer: M virial ~ R V 2 /G ~ 4 x M sun M virial >> M guess dunkle Materie in sehr viel grösserer Dichte vorhanden ist als leuchtende Materie[!!!] - Fritz Zwicky, 1933

5 Dark Matter Exists! (Part 3) Constraints on Matter Cross Section Cross Section The Bottom Line: Cross section is small enough to not be important for clustering! (Mack et al. 2007) Allowed Region Mass

6 Large-Scale Structure Dark Matter Density Field

7 The Power Spectrum: P(k) x 2 π 2 k 3 P(k) Scale λ Density Contrast Wavenumber k = 2 π λ Fourier Transform Wavenumber k Power Spectrum δ(x) = ρ(x) ρ m,avg ρ m,avg δ(k) P(k)

8 What is P(k) Good for? Ω m ; total amount of dark matter in the universe H(a) = H o (Ω m a -3 + Ω Λ ) 1/2 = expansion rate k eq = 2 1/2 H o Ω m c Ω r 1/2 earlier epoch smaller horizon smaller modes Higher Ω m of equality scale at a eq survive higher k eq

9 A Tale of Two Universes CMB predicts this Dark Matter galaxy surveys see this 100 Mpc 100 Mpc Low σ 8 High σ 8 σ 8 ; total amount of clustering

10 Dark Matter A Galaxy Factory Halo Formation Galaxy Formation Galaxy Field Collapse Theory N-body Simulations δ h (x) = b(m) δ(x)

11 Biased Galaxy-Galaxy Power Spectrum Observations Correction! Weak Gravitational Lensing Lyman-α Forest

12 N-body Simulations Large Scales Small Scales Useful for: Limitations: More precise understanding of halo formation P(k) for k > k nl = 0.2 h Mpc -1 Small scale dark matter dynamics Finite box size Finite number of particles

13 Self-Similarity Initial Conditions: P(k) = A k n, Ω m = 1 Well-understood time-scaling Linear Regime k nl (from Efstathiou et al. 1988)

14 Small Scales Map of Galaxies in the Local Group N-body Simulation (Kravtsov, Gnedin & Kylpin 2004)

15 Missing! Options: Keep Looking? Not likely to find enough Maybe they re not there? e.g. Zentner & Bullock 2003, Kamionkowski & Liddle 2000 Reward: Ph.D. Thesis Last Seen: N-body Simulations Maybe they re just dark? e.g. Kravtsov, Gnedin & Klypin 2004, Madau & Diemand 2008, Thoul & Weinberg 1996, Orban et al. 2008

16 Observations M31 Tidal Streams Theory (Johnston et al. 2002) (Ibata et al. 2001) (Bullock & Johnston 2005) (Martinez-Delgado et al. 2003)

17 Strong Gravitational Lensing Four-image Quasar Lens System Substructure Likelihood anomaly!! (Inada et al. 2003) f sat (Dalal & Kochanek 2002) f sat = fraction of mass in substructure

18 Summary The existence of dark matter is indisputable (e.g. galaxy rotation curves, virial relation arguments) Perturbation theory and N-body simulations make definite predictions for the clustering of dark matter; also give better understanding of halo formation and bias Observationally, we have a very good idea of how the dark matter clusters on cosmological scales On the scale of the Local Group the clustering of dark matter is harder to asses observationally; strong gravitational lensing may have detected dark matter substructure

19 Not the Only Game in Town Two-Point Correlation Function Correlation Function Power Spectrum ξ(r) P(k) Fourier Transform ξ(r) = (increased) likelihood that at a patch of dark matter there will be another patch distance, r, away More formally: ξ(r) = δ(x)δ(x+r) Statistical Ensemble