dark matter density profiles
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2 LSS & CDM 2
3 LSS & CDM 3
4 SPH simulation: movie SPH simulation in CDM : dark matter hot gas galaxy (Yoshikawa, Taruya, Jing & Suto 2001) LSS & CDM 4
5 Confronting elements of the CDM paradigm Global cosmological parameters Fairly well established confirmed by WMAP Large-scale structure Galaxy biasing with respect to CDM distribution Galaxy cluster abundance Amplitude of CDM density fluctuations Density profile of dark halos Cusp or core in the central region Substructures Formation efficiency of visible objects out of CDM halos LSS & CDM 5
6 δt T WMAP ( θ, ϕ ) = a Y lm lm( θ, ϕ ) l, m Ω b C = l a lm a * lm n s Spergel et al. astro-ph/ Ω Κ = Ω m +Ω -1 LSS & CDM 6
7 CMB NASA/WMAP Science Team LSS & CDM 7
8 WMAP 1st1 year LSS & CDM 8
9 WMAP LSS & CDM 9
10 NASA/WMAP Science Team = CDM LSS & CDM 10
11 Confronting elements of the CDM paradigm Global cosmological parameters Fairly well established confirmed by WMAP Large-scale structure Galaxy biasing with respect to CDM distribution Galaxy cluster abundance Amplitude of CDM density fluctuations Density profile of dark halos Cusp or core in the central region Substructures Formation efficiency of visible objects out of CDM halos LSS & CDM 11
12 CfA galaxy redshift survey: Geller, da Costa & Huchra (1992) Las Campanas redshift survey: Schectman et al. (1996) LSS & CDM 12
13 LSS & CDM 13
14 Tour in SDSS DR1 galaxies LSS & CDM 14
15 SDSS DR1 galaxies: morphology dependent clustering LSS & CDM 15
16 Morphology-dependent SDSS galaxy bias late-type type early-type average σ 8 : assumed fluctuation amplitude σ p : pair-wise velocity dispersion [km/s] ξ( galaxies)/ ξ( ΛCDM) galaxy bias is fairly scale-independent, if CDM (+ σ 8, σ p ) assumed. clear morphology dependence; early -types are positively biased relative to mass, while late -types types are anti-biased. Kayo, Suto, Fukugita,, Nakamura, et al., in preparation LSS & CDM 16 b
17 Large-scale structure and mass density of the universe LSS & CDM 17
18 Confronting elements of the CDM paradigm Global cosmological parameters Fairly well established confirmed by WMAP Large-scale structure Galaxy biasing with respect to CDM distribution Galaxy cluster abundance Amplitude of CDM density fluctuations Density profile of dark halos Cusp or core in the central region Substructures Formation efficiency of visible objects out of CDM halos LSS & CDM 18
19 8 from the Xray-cluster abundance best-fit mass-temperature relation + X-ray cluster abundance in Ω 0 =0.3, λ 0 =0.7, h=0.7 CDM σ 8 =0.82 (Press-Schechter mass function) σ 8 =0.75 (Jenkins et al. mass function) (Shimizu, Kitayama, Sasaki + YS 2003) LSS & CDM 19
20 Confronting elements of the CDM paradigm Global cosmological parameters Fairly well established confirmed by WMAP Large-scale structure Galaxy biasing with respect to CDM distribution Galaxy cluster abundance Amplitude of CDM density fluctuations Density profile of dark halos Cusp or core in the central region Substructures Formation efficiency of visible objects out of CDM halos LSS & CDM 20
21 Why density profiles of dark halos? Theoretical interest: what is the final state of the cosmological self- gravitating system? forget cosmological initial conditions? keep initial memory somehow? Practical importance: testing cosmology and/or nature of dark matter galactic rotation curve, gravitational lensing X-ray/SZ observations of clusters modeling the dark matter clustering LSS & CDM 21
22 Brief history (before NFW) 1970: Peebles; ; N-body N simulation (N=300). 1977: Gott; ; secondary infall model r -9/ : Hoffman & Shaham; ; predicted that density profile around density peaks is r 3(n+3)/(n+4). 1986: Quinn, Salmon & Zurek; ; N-body N simulations (N 10 4 ) confirmed r 3(n+3)/(n+4). 1988: Frenk,, White, Davis & Efstathiou; N-body simulations (N=32 3 ), showed that CDM model can reproduce the flat rotation curve out to 100kpc. 1990: Hernquist; ; proposed an analytic model with a central cusp for elliptical galaxies r 1 (r+r s ) : Navarro, Frenk & White; ; universal density profile for dark matter halos. LSS & CDM 22
23 NFW universal density profile log(density) shape of halo density profiles is insensitive to cosmological initial conditions! ρ( r) c vir ( M ) δ ( M ) c = ( r Navarro, Frenk & White (1997) δ cρcrit 2 / rs )(1 + r / rs ) rvir( M ) rs ( M ) Ω c 3[ln(1 + concentration parameter vir 0 c) 3 c /(1 + c)] log(radius) LSS & CDM 23
24 low mass/force resolutions shallower potential than real artificial disruption/overmerging (especially serious for small systems) ε = 1kpc ε = 7.5kpc central 500kpc region of a simulated halo in SCDM Moore (2001) LSS & CDM 24
25 ~ 5x10 12 M sun ~ 5x10 13 M sun ~ 3x10 14 M sun Jing & Suto (2000) LSS & CDM 25
26 Jing & Suto (2000) CDM r r -1.5! δ cρcrit ρ( r) = α α 3 α ( r / r ) (1 + r / r ) s 1.5 LSS & CDM 26 s
27 Rotation curves of DM dominated galaxies Predictions from CDM simulations Observed profile Moore et al. (1999) dwarf spirals to giant low surface brightness galaxies indicate the central cores rather than cusps! inconsistent with CDM simulations (?) (Moore et al. 1999; de Blok et al. 2000; Salucci & Burkert 2000) LSS & CDM 27
28 CL HST image reconstructed mass distribution (with 512 parameters) Z=0.39, L X = h -2 erg/s Tyson, Kochanski & Dell Antonio (1998) LSS & CDM 28
29 CL !! Tyson, Kochanski & Dell Antonio (1998) LSS & CDM 29
30 LSS & CDM 30
31 Constraining halo central density profiles with gravitational lensing Statistics of QSO multiple images (Wyithe,, Turner & Spergel 2001; Keeton & Madau 2001; Li & Ostriker 2001; Takahashi & Chiba 2001) Arc statistics of clusters of galaxies (Bartelmann et al. 1998; Molikawa & Hattori 2001; Oguri, Taruya + YS 2001, Oguri,, Lee + YS 2003) Time-delay statistics of QSO multiple images (Oguri, Taruya,, YS + Turner 2002) generally favor a steep cusp ( ( 1.5) LSS & CDM 31
32 Time-delay in QSO multiple images to probe the halo density profile Time-delay QSO among (source) QSO multiple images is very sensitive to the inner slope, but insensitive to cosmological halo (lens) parameters (except H 0!) Steeper inner profile larger observer time-delay conditional cumulative probability of time-delay as a function of image separation P > t θ, z ) ( s is a very sensitive measure of inner density profile of lensing objects Oguri, Taruya,, YS + Turner (2001) LSS & CDM 32
33 Tentative applications to 4 lens systems Inner slope of density profile Observed value of time-delay observed time-delay SIS Time-delays of existing lens systems are consistent with predicted time- delay probability when the density profile has a steep cusp r -1.5 Oguri, Taruya,, YS + Turner (2001) LSS & CDM 33
34 Self-interacting dark matter? Collisionless dark matter reproduces nicely the observed large-scale structure of the universe (r 1Mpc) problems on smaller scales (r<1mpc) LSB rotation curves, soft core in CL , prediction of a factor of ten more subhalos than observed in the Local Group Required scattering cross section for self- interacting dark matter 4 σ σ 2 10 ρ crit 1Mpc ( mn) l = 1 = 2cm / g m m ρcenter,cl l LSS & CDM 34
35 Collisional Dark Matter σ σ/m 1 cm /g Yoshida et al. (2000) LSS & CDM 35
36 Are Dark Halos Spherical? Collisionless CDM: NO Jing & Suto (2000) Yoshida et al. (2000) Collisional CDM: YES LSS & CDM 36
37 An improved model for dark matter halo: triaxial universal density profile Isodensity of a cluster-scale halo >100 >2000 >10000 ρ( R) R 2 ( ρ) δ cρcrit α ) (1 + R / R = 3 α ( R / Rs s ) 2 X + 2 a ( ρ) 2 Y + 2 b ( ρ) 2 Z 2 c ( ρ) Jing & Suto, ApJ, 574 (2002) 538 Non-spherical effects have several important implications for SZ, X- ray, and lensing observations. LSS & CDM 37
38 Lensed Arcs in Galaxy Clusters Cluster of galaxies distort the images of background galaxies by gravitational lensing radial arc (lensed) arcs ~30 giant arcs are observed so far tangential arc Hammer et al. (1997) LSS & CDM 38
39 Comparison with observed statistics Previous model predictions are known to be significantly smaller than the observed number of lensed arcs (Luppino et al. 1999) More realistic modeling of dark halos from simulations (inner slope of α=1.5 and non-sphericity) reproduces the observed frequency of arcs. (Oguri, Lee + YS 2003) LSS & CDM 39
40 Ω m 0.3, Ω Λ 0.7, h h 0.7 Ω m = , Ω Λ = , h= CDM LSS & CDM 40
41 SDSS LSS & CDM 41
42 WMAP NASA/WMAP Science Team LSS & CDM 42
43 CMB NASA/WMAP Science Team LSS & CDM 43
44 CMB NASA/WMAP Science Team LSS & CDM 44
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