The effects of assembly bias on galaxy clustering predictions Arnau Pujol, Enrique Gaztañaga Marseille, July 15th, 2014 � Pujol & Gaztañaga 2014, MNRAS, 442, 1939 Pujol et al. 2014, MNRAS, 438, 3205 Institut d’Estudis Espacials de Catalunya Institut de Ciències de l’Espai (IEEC-CSIC)
Galaxies vs matter? haloes + HOD dark matter SDSS Semi Analytical Model (SAM)
HOD model N ( M ) = N c ( M ) + N s ( M ) •HOD is based on the halo model ✓ log M − log M min ◆� N c ( M ) = 1 •Galaxy populations described 1 + erf 2 σ log M according to halo proper ties ◆ α ✓ M − M 0 N s ( M ) = N c ( M ) × (commonly mass) M 1 •We can model clustering to measure Zheng et al. 2005 HOD •HOD can be used for measuring dark ξ gal ( r ) = ξ 1 halo gal ξ Lin ( r ) + b 2 dm ( r ) gal matter haloes •We need to know (or model) bias Coupon et al. 2012
HOD model Assumptions ? ξ gal = ξ 1 halo gal ξ Lin ( r ) + b 2 m ( r ) gal 1 k 3 P ( k )sin( kr ) Z dk ξ ( r ) = 2 π 2 kr k dMn ( M ) N 2 ( M ) Z | u h ( k | M ) | 2 P 1 h ( k ) = n 2 gal � 2 Z dMn ( M ) N ( M ) P 2 h ( k ) = P Lin ( k ) × b h ( M, r ) | u h ( k | M ) | m n gal
HOD model Assumptions ? • The galaxy occupation is only ξ gal = ξ 1 halo gal ξ Lin ( r ) + b 2 m ( r ) dependent on halo mass gal 1 k 3 P ( k )sin( kr ) Z dk ξ ( r ) = 2 π 2 kr k dMn ( M ) N 2 ( M ) Z | u h ( k | M ) | 2 P 1 h ( k ) = n 2 gal � 2 Z dMn ( M ) N ( M ) P 2 h ( k ) = P Lin ( k ) × b h ( M, r ) | u h ( k | M ) | m n gal
HOD model Assumptions ? • The galaxy occupation is only ξ gal = ξ 1 halo gal ξ Lin ( r ) + b 2 m ( r ) dependent on halo mass gal • Galaxies follow an NFW profile 1 k 3 P ( k )sin( kr ) Z dk ξ ( r ) = 2 π 2 kr k dMn ( M ) N 2 ( M ) Z | u h ( k | M ) | 2 P 1 h ( k ) = n 2 gal � 2 Z dMn ( M ) N ( M ) P 2 h ( k ) = P Lin ( k ) × b h ( M, r ) | u h ( k | M ) | m n gal
HOD model Assumptions ? • The galaxy occupation is only ξ gal = ξ 1 halo gal ξ Lin ( r ) + b 2 m ( r ) dependent on halo mass gal • galaxies follow an NFW profile 1 k 3 P ( k )sin( kr ) Z dk ξ ( r ) = 2 π 2 kr k dMn ( M ) N 2 ( M ) Z | u h ( k | M ) | 2 P 1 h ( k ) = n 2 gal Pujol et al. 2014 � 2 Z dMn ( M ) N ( M ) P 2 h ( k ) = P Lin ( k ) × b h ( M, r ) | u h ( k | M ) | m n gal
HOD model Assumptions ? •The galaxy occupation is only ξ gal = ξ 1 halo gal ξ Lin ( r ) + b 2 m ( r ) dependent on halo mass gal •Galaxies follow an NFW profile 1 k 3 P ( k )sin( kr ) Z dk •Correct model for halo bias ξ ( r ) = 2 π 2 kr k •No assembly bias dMn ( M ) N 2 ( M ) Z | u h ( k | M ) | 2 P 1 h ( k ) = n 2 gal � 2 Z dMn ( M ) N ( M ) P 2 h ( k ) = P Lin ( k ) × b h ( M, r ) | u h ( k | M ) | m n gal
Reconstruction method ? Millennium Simulation dMb h ( M ) n ( M ) N g ( L, M ) Z b g ( L ) = n g ( L ) n = 1 Λ CDM σ 8 = 0 . 9 Ω m = 0 . 25 Advantages Ω Λ = 0 . 75 h = 0 . 73 V = (500 h − 1 Mpc ) 3 •Linear and constant bias, no m p = 8 . 6 × 10 8 M � scale dependence Assumptions •only 2-halo term dominates •No density profile assumptions •No assembly bias needed •galaxy occupation only mass •No bias model needed if we dependent measure halo bias
Halo and galaxy bias •Halo bias consistent with theoretical predictions •Tinker et al. 2010 is the most consistent model s FOF bias Guo et al. 2011 bias ξ g,h ( r ) b g,h ( r ) = ξ m ( r ) fitted as constant at r = [20 − 30] h − 1 Mpc Bower 2006 bias halo bias Pujol & Gaztañaga 2014
HOD measurements Guo et al. 2011 HOD Bower 2006 HOD Number of galaxies per halo of mass Mh at different luminosity thresholds (solid) vs SDSS DR-7 (dashed) from Zehavi et al. 2011 dMb h ( M ) n ( M ) N g ( L, M ) Z b g ( L ) = n g ( L ) Pujol & Gaztañaga 2014
HOD measurements Guo et al. 2011 HOD Bower 2006 HOD Number of galaxies per halo of mass Mh at different luminosity thresholds (solid) vs SDSS DR-7 (dashed) from Zehavi et al. 2011 dMb h ( M ) n ( M ) N g ( L, M ) Z b g ( L ) = n g ( L ) Pujol & Gaztañaga 2014
bias reconstructions Results •Underprediction of galaxy bias of 5-10% •FOF mass obtain better reconstructions than gravitationally bound masses Consequences reconstructed vs real bias for FOF •Assembly bias •Galaxy population correlated with assembly bias dMb h ( M ) n ( M ) N g ( L, M ) Z b g ( L ) = n g ( L ) Pujol & Gaztañaga 2014 reconstructed vs real bias for bound haloes
Assembly bias effects •Galaxy bias > halo bias for low mass haloes •HOD not compatible with galaxy clustering for halo masses < 10^12Msun •Indication of low mass haloes with high clustering galaxy bias (lines) and halo bias (grey) vs mass •Strong subhalo abundance dependence of halo bias for fixed mass. Indication of assembly bias •For a fixed mass bin, haloes (or main haloes) with more subhaloes (and more galaxies) have more clustering. •Correlation between halo occupation and halo bias for fixed mass, independent of the SAM. halo bias vs mass for different subhalo occupations Pujol & Gaztañaga 2014
Assembly bias vs galaxy properties •Assembly bias can be related to galaxy properties, in this case the colour of the central galaxy. � •As a consequence the bias reconstruction does not make a good prediction of bias � •we are not able to predict the occupation of halo bias vs mass for different central colours these galaxies from the HOD assumptions, we can get large errors because of the misinterpretation of clustering � •Care must be taken when measuring the properties of haloes or galaxy occupations if we assume the HOD model reconstructed vs real bias for red central galaxies
Conclusions � •We used the Millennium Simulation to measure the linear bias at large scales and test the HOD model, where no assumptions for the profile of the galaxies in haloes are needed. •We find underprediction of galaxy bias of 5-10%, an indication of assembly bias. •FOF mass obtain better reconstructions than gravitationally bound masses. •For fixed host halo mass <10^12Msun, galaxy bias > halo bias, inconsistent with the HOD assumptions. •Strong subhalo abundance dependence of halo bias for fixed mass. This is independent of the galaxy formation model. •Care must be taken when using HOD to estimate the mass of haloes or galaxy occupations. Pujol et al. 2014, MNRAS 438, 3205 Pujol & Gaztañaga 2014, MNRAS 442, 1939
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