Cosmoogica effects in the high-z universe inear redshift-space distortion coherence between density and veocity fieds finger-of-god noninear veocity f

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1 Custering statistics on a ight-cone in the cosmoogica redshift space Yasushi Suto Dept. of Phys. and RESCEU, The University of Tokyo, Japan November 7, 999 (The 4th RESCEU Symposium) based on the coaboration with Y.P. Jing, Tetsu Kitayama, Hiromitsu Magira, Takahiko Matsubara, Hiroaki Nishioka, Kazuhiro Yamamoto Contents Cosmoogica effects in the high-z universe 2 2 Cosmoogica redshift-space distortion 3 3 Cosmoogica ight-cone effect 7 4 Summary and concusions 5

2 Cosmoogica effects in the high-z universe inear redshift-space distortion coherence between density and veocity fieds finger-of-god noninear veocity fied in viriaized regions cosmoogica redshift-space distortion anisotropy due to the geometry of the universe ight-cone effect cosmoogica observations are on a ight-cone gravitationa ensing distortion due to the mass aong the ine-of-sight bias (uminous) objects 6= (dark) mass distribution + Noise? hampers the proper understanding of the custering in the universe Signa? provides additiona cosmoogica information Predictions of the two-point custering statistics on a ight-cone in the cosmoogica redshift space 2

3 2 Cosmoogica redshift-space distortion? separations in the redshift space parae to the ine-of-sight: x sk (z) = cffiz=h 0 perpendicuar to the ine-of-sight: x s? (z) = czffi =H 0 +? mapping to those in the rea (comoving) space with x k (z) = c k (z)x sk (z); c k (z) = x? (z) = c? (z)x s? (z); r Ω0 ( + z) 3 + ( Ω 0 0 )( + z) c? (z) = H 0( + z) D A (z;ω 0 ; 0 ) cz (Acock & Paczyński 979; Bainger, Peacock & Heavens 996; Matsubara & YS 996) Anisotropic power-spectrum in the cosmoogica redshift space P (CRD) (k s? ;k sk ; z) = c? (z) 2 c k (z) P (S) 0 k s? c? (z) ; k sk c k (z) ; z where k sk (z) = c k (z)k k (z), k s? (z) = c? (z)k? (z), and P (S) (k? ;k k ; z) = P (R) mass (k; z) b2 (z) fi(z) 0 k k k C A 7 5 D» k k ff p (z) C A ; 3

4 Ange-averaged P (k) in redshift space at z = 0 and 2:2 in SCDM, LCDM and OCDM theories vs. N-body simuations (N = ) Figure : Power spectra for representative CDM modes at z = 0 (upper panes) and z = 2:2 (ower panes) negecting the geometrica effect in the redshift-space distortion. The fuctuation ampitudes are normaized according to the custer abundances. (Magira, Jing & YS 2000) 4

5 2D contours of P (k) in redshift space at z = 2:2 in SCDM, LCDM and OCDM: inear theory (top panes) noninear mode (midde panes) N-body simuations (bottom panes) Figure 2: (Magira, Jing & YS 2000) 5

6 Expected confidence contours on Ω 0-0 pane at z = 2:2 in SCDM, LCDM and OCDM from cosmoogica redshift-space distortion: N = (upper panes) N = (midde panes) N = (bottom panes) Figure 3: (Magira, Jing, & YS 999) 6

7 3 Cosmoogica ight-cone effect? A cosmoogica observations are carried out on a nu hypersurface or a ight-cone. A fairy conventiona approximation is to repace the ight-cone by the constant-time hypersurface at z = 0 (at east for surveys with depth z < 0:). For z > 0:, however, this approximation apparenty breaks down. +? One shoud simutaneousy take account of the intrinsic evoution of the custering. future X-ray seected custers on-going wide-fied surveys of gaaxies and quasars incuding 2dF and SDSS count-in-ce statistics for higher-order moments Matsubara, YS, & Szapudi, ApJ 49(997)L perturbation anaysis for fi-parameter Nakamura, Matsubara & YS, ApJ 494(998)3 genera formuation Mataresse, Coes, Lucchin, Moscardini, MNRAS 286(997)5 Yamamoto & YS, ApJ 57(999) review YS, Magira, Jing, Matsubara & Yamamoto, Prog.Theor.Phys.Supp., 33(999)83 Stay tuned! the next tak by Yamamoto, and a poster by Nishioka 7

8 3. Two-point correation functions of X-ray seected custers Express custer properties in terms of the hao mass gas temperature T X viria equiibrium X-ray uminosity L X observed L-T reation + band correction X-ray fux S X uminosity distance bias parameter b(z;m) anaytic mode (Mo & White 996) + N-body simuations (Jing 998) seection function hao mass function from the Press- Schechter theory redshift-space distortion Kaiser (987), Peacock & Dodds (996), Magira et a. (2000) ight-cone effect Yamamoto & YS (999), Yamamoto, Nishioka & YS (999) Two-point correation functions of custers on the ightcone brighter than the X-ray fux-imit S im ο LC X c (R; > S im) = Z zmin z max dz dv c dz n2 0 (z)οs c (R; z(r); > S im) Z zmin z max dz dv c dz n2 0 (z) (YS, Yamamoto, Kitayama & Jing 999) 8

9 Mode predictions in SCDM, LCDM and OCDM of redshift-space distortion and ight-cone effect for X-ray custer correation functions z z Figure 4: (YS, Yamamoto, Kitayama & Jing 999) z

10 Difference due to various seection functions X-ray fux-, temperature-, uminosity-imit Figure 5: Left: S im = 0 3 (soid ines), 0 4 (dotted) and 0 5 erg/s/cm 2 (dashed). Center: T im = (soid), 3 (dotted) and 6keV (dashed) in the X- ray fux-imited sampe (S im = 0 4 erg/s/cm 2 ). Right: L > 0 45 (soid), 0 44 (dotted) and 0 43 h 2 erg/s/cm 2 (dashed) in the X-ray fux-imited sampe (S im = 0 4 erg/s/cm 2 ). 0

11 Ω 0 -dependence of X-ray custer correation engths defined by ο LC c (r c0 ; S im ) = Figure 6: The X-ray fux-imit S im is 0 3 (soid ines), 0 4 (dotted) and 0 5 erg/s/cm 2 (dashed). For each S im, we pot the case of 0 = Ω 0 in thick ines, and 0 = 0 in thin ines. Fuctuation ampitudes are normaized by the custer abundance.

12 3.2 Two-point correation functions and power spectra of SDSS gaaxy and QSO sampes Theoretica predictions which take into account the ightcone and cosmoogica distortion effects simutaneousy. Decompose P (CRD) (k; μ k ; z) into mutipoes P (CRD) (k; z) 2 +Z dμ kp (CRD) (k; μ k ; z)l (μ k ) Compute ο (CRD) (x; z) from P (CRD) (k; z) 2 ο (CRD) (x; z) = 2ß 2 i Z Average over the ight-cone P (LC;CRD) (k s ) = ο (LC;CRD) (x s ) = Z z min zmax Z z min zmax dz dv c 0 dz [ffi(z)ncom Z z min zmax dz dv c Z z min zmax P (CRD) (k; z)j (kx)k 2 dk 0 (z)] 2 c? (z) 2 c k (z)p (CRD) (k s ; z) dz dv c dz [ffi(z)ncom 0 (z)] 2 c? (z) 2 c k (z) dz [ffi(z)ncom 0 (z)] 2 c? (z) 2 c k (z)ο CRD (x s ; z) dz dv c dz [ffi(z)ncom 0 (z)] 2 c? (z) 2 c k (z) +? Evauate the effects for SDSS gaaxy (B < 9) and QSO (B < 20) sampes using the uminosity functions of Loveday et a. (992) and Boye, Shanks & Peterson (988)! ffi(z). (YS, Magira & Yamamoto 999) 2

13 Ange-averaged P (k) on the ight-cone in the cosmoogica redshift space divided by the inear theory prediction in rea space at z = 0: in SCDM (Left) and LCDM (Right) for Gaaxies (Upper) and QSOs (Lower) Figure 7: (YS, Magira & Yamamoto 999) 3

14 Ange-averaged ο(x) on the ight-cone in the cosmoogica redshift space divided by the inear theory prediction in rea space at z = 0: in SCDM (Left) and LCDM (Right) for Gaaxies (Upper) and QSOs (Lower) Figure 8: (YS, Magira & Yamamoto 999) 4

15 4 Summary and concusions In the statistica anaysis of custering at high redshifts, the cosmoogica redshift-space distortion and ight-cone effects pay an important roe both as signas and as noises. We have constructed a theoretica mode to describe those physica effects for the two-point spatia custering statistics (the gravitationa ensing effect is important for the anguar statistics, but not for the spatia one). except for the bias mode, which is unikey to be described by physics. correction for the systematic effects feasibe for a given cosmoogica mode (fuctuation spectrum and ampitude, cosmoogica parameters, bias mode, etc.) cosmoogica parameters can be constrained from the SDSS and 2dF QSO sampes provided that the bias is inear. scae-dependence and noninearity of bias with Ω 0 and 0 accuratey determined from MAP and PLANCK, the cosmoogica redshift-space distortion and ight-cone effects are essentia to mode the bias from observations. 5