From Far East to Far Infra-Red: galaxy clustering and Galactic extinction map redshift 2.0 1.6 1.2 4000 3000 0.8 0.4 2000 1000 distance [h -1 Mpc] 0.2 0.15 0.1 0.05 100 500 400 200 300 [h -1 Mpc] 0.05 0.04 0.03 0.02 140 100 60 [h -1 Mpc] Yasushi Suto Department of Physics, University of Tokyo
Recent work related to SDSS at University of Tokyo: 鶏口牛後 genus statistics and phase correlation of SDSS galaxies (Hikage et al. 2003, 2004,2005; Hikage, Matsubara, and Suto 2004; Park et al. 2005) 3pt correlation functions of SDSS galaxies (Kayo, Suto, Nichol et al. 2004) 2pt correlation functions of SDSS quasars and cosmological constant (Yahata et al. 2005) constraints on the deviation from Newton s law of gravity from SDSS galaxy power spectrum (Shirata, Shiromizu, Yoshida & Suto 2005; Yamamoto et al. 2006) testing the Galactic dust map against SDSS galaxy number counts (Yahata et al. 2006) Bispectrum and nonlinear biasing (Nishimichi et al. 2006)
How galaxies trace mass? galaxy biasing SDSS significantly advanced our knowledge of galaxy distribution on large scales how to relate it to mass (dark matter) distribution? empirical perturbation expansion b2 2 δ = b δ + δ +L gal 1 mass 2 mass often consider the linear term alone (for twopoint statistics, or in linear regimes) higher-order terms? higher-order statistics
3pt correlation functions of SDSS galaxies in redshift space Q gal 1/b 1 Clear luminosity, morphology and color dependences of (2pt) bias disappear in 3pt amplitude Kayo et al. PASJ 56(2004) 415
nonlinearity of galaxy bias required if linear bias: δ gal = b1δ mass Qgal = Q b mass this is clearly inconsistent with SDSS data! even in nonlinear bias: b 2 2 1 b δ gal = b1δ mass + δ mass + L Qgal = Qmass + 2 b1 b still, dependence on b 1 is expected 1 2 1 Q=Q(b 1 ) correlation between b 1 & b 2
b 2 /b 1 against b 1 for SDSS galaxies and halo-occupation-distribution model estimated from P(k) & bispectra (or Q) Nishimichi et al. (2006) both observations and HOD models suggest a clear trend of b 2 /b 1 vs. b 1 fairly insensitive to bias models generic correlation in gravitational instability picture?
Constraints on deviation from Newton s law of gravity at cosmological scales Shirata, Yoshida, Shiromizu & Suto (2005, 2006) Parameter: α, λ V(r) G(1+α)/r Current model r r >> λ : V ( r) << λ : G(1 + α ) M r G/r V ( r) G M r r/λ
Modified shape of power spectrum Shirata et al. (2005) 10 6 α = +1.0 λ = 5h -1 Mpc Newton, Non Linear α=+1.0, Linear α=+1.0, Non Linear P(k) 10 4 10 2 modified Newtonian effect Non-linear effect 10-2 10-1 10 0 10 1 k [hmpc -1 ]
Constraint on (α,λ) from P(k) of SDSS galaxies (Tegmark et al, 2004) 1 box=500h -1 Mpc k<0.15hmpc -1 α α 0.5 0-0.5-1 1 σ 2 σ 3 σ theory Simulation analytic method (a) Δχ 2, P(k) 0 5 10 15 20 25 30 λ [h [Mpc/h] -1 Mpc] Shirata et al. (2006)
Modified gravity vs. Cosmological constant: from SDSS to WFMOS Yamamoto, Bassett, Nichol, Suto & Yahata PRD in press, astro-ph/0605278 modified Friedmann equation (spatially flat) H n=2: DGP model, n= : cosmological constant r c : key parameter ~1/H 0 r<r c : 4D space-time, r>r c : 5D space-time if spatially flat 2/ n 8 H πg 2 r 2 2/ n c ( H = r 0 c ) 3 ρ 2/ n 2 = 1 Ω m
The cosmological constant vs. the modified DGP model comoving distance Hubble parameter ratios relative to the cosmological constant model (spatial flatness is assumed) Yamamoto et al. astro-ph/0605278
Predicted shifts of BAO peaks purely linear theory, observation in ΛCDM assumed Yamamoto et al. astro-ph/0605278
Current constraints from the SDSS LRG sample data from Hütsi (astro-ph/0409278) fit to linear theory for k<0.2hmpc -1 observation in ΛCDM assumed Yamamoto et al. astro-ph/0605278
Expected constraints from future WFMOS z=1 sample Yamamoto et al. astro-ph/0605278
Galactic extinction map vs. galaxy number counts Galactic extinction map by Schlegel, Finkbeiner & Davis (1998: SFD) dust extinction estimated from IR emission can be used for absorption correction??? independent consistency check is needed
DR4 survey area vs. A SFD SDSS DR4 Imaging ~10 7 galaxies,6600 deg 2
Estimating Galactic extinction from galaxy number count SDSS DR4 survey area (color coded according to A SFD ) high extinction medium extinction low extinction divide the SDSS DR4 survey area into many small regions according to A SFD combine those un-contiguous regions into 69 bins with ~100 deg 2 each compare the galaxy number density S gal for those bins
Cumulative distribution function of A r,sfd 68 % of the survey area has A r,sfd < 0.1 30 % of the survey area has A r,sfd < 0.05
galaxy surface density Sgal vs. SFD extinction ASFD If A SFD is perfect smaller S gal at larger A SFD before correction constant S gal after correction S gal [deg -2 ] after correction before correction confirmed for A SFD >0.1, but quite the opposite for A SFD <0.1 68% of the SDSS survey area has A SFD <0.1! What s wrong? A r,sfd [mag] Yahata, Yonehara, Suto, Turner, Broadhurst & Finkbeiner (2006)
Origin of the anomaly? A SFD is estimated assuming that the reddening is proportional to the Farinfrared emission flux (100μm) the anomaly indicates the positive correlation between galaxy surface density and the FIR flux at least where the real extinction is small 100μm flux = Galactic dust + galaxies contamination by the FIR emission from galaxies???
comparison with A HI from HI map A r,sfd < 0.05 で 同じ HI の強度でも銀河の密度が高い程 A r,sfd が大きい事がはっきりと見られる A SFD >A HI at A SFD <0.1 (unphysical binning effect at A SFD <0.02) stronger trend for larger S gal regions Yahata et al. (2006) astro-ph/0607098
simulations to test the hypothesis Gaussian distributed galaxies over the survey area (a bit confusingly) assume that A SFD represents the true Galactic extinction add galaxy FIR contribution according to Smock [deg -2 ] A C =A SFD +c(s mock -<S mock >) A c applied A SFD applied The use of A C indeed reproduces the observed trend! ASFD or Ac [mag] Yahata et al. (2006) astro-ph/0607098
Tiny but systematic error in A SFD a typical amplitude of the systematic error in A SFD is ~0.01mag c.f., mean flux of the background IR which was removed in making the SFD map is ~ 0.04 mag this is tiny, but systematic S gal A dust S gal becomes even larger after correction for A dust systematically overestimates the contrast of real structure maybe important for precision measurements
Summary: 世皆塵 statistically significant clustering of SDSS activities detected in the Far East this week hopefully not an artifact due to the Far Infrared contamination in the extinction map