Structure growth & redshi0-space distor4ons around voids - PowerPoint PPT Presentation

Structure growth & redshi0-space distor4ons around voids Yan-Chuan Cai Y. Cai, A. Taylor, J. Peacock, N. Pad illa, arXiv:1603.05184 V. Demchenko, Y. Cai, C. Heymans & J. Peacock, arXiv:1605.05286 XII th Rencontres du Vietnam, Large Scale Structure and Galaxy Flows 07.07.2016, Quy Nhon, Vietnam

Outline • Voids • Why RSD around voids • What should voids look like in z-space • Measuring the linear growth • Summary

Spherical expansion Sheth & van de Weygaert, 2004 In LCDM, shell-crossing occurs at R f /R int ∼ 1 . 7 Y. Cai 3

Spherical evolu4on model w = − 0 . 5 Demchenko, Cai, Heymans & Peacock, 2016

Voids in Simula4ons The Aspen–Amsterdam void finder comparison project 40 Mpc/h Millennium Simula4on ZOBOV Spherical overdensity Colberg et al. 2008 Y. Cai 5

Voids in observa4ons • SDSS voids from Pan et al. 2012 Sueer et al. 2012 Cai et al. 2014 Nadathur et al. 2014 Pan et al. 2012 Mao et al. 2016 … Nadathur et al. 2014 Sueer et al. 2012 Y. Cai 6

Tes4ng gravity with voids f(R) voids are emp4er than GR voids Cai, Li & Padilla 2015 f(R) voids expand faster 7 Y. Cai

Alcock-Pasczynski test with voids IF voids are spherical LOS distance transverse distance Voids are distorted in redshi0 space 14% flaeening in redshi0 space, Lavaux & Wandelt (2012)

Linear Redshi0 Space Distor4on (RSD) r obs = r + v pec /aH Kaiser 1987, Hamilton 1997

RSD for void ? Maeda, Sakai & Triay, 2011 µ = cos θ

Void-halo correla4on func4on

ξ s ( r, µ ) = ξ ( r ) + 1 3 β ¯ ξ ( r ) + β µ 2 [ ξ ( r ) − ¯ β = f/b ξ ( r )] ξ s ( r, 1) = (1 + β ) ξ ( r ) − 2 (line of sight) Z r ¯ ξ ( r ) = 3 ξ ( r ) ¯ ξ ( r 0 ) r 0 2 dr 0 3 r 3 ξ s ( r, 0) = ξ ( r ) + 1 0 3 β ¯ (transverse LOS) ξ ( r )

Void-halo correla4on func4on

Extrac4ng the linear growth ξ s 2 β G ( β ) = s = 0 − ¯ 3 + β ξ s ξ s 0 m o n o p o l e q u a d r u p o l e

m o n o p o l e q u a d r u p o l e quasi-linear model

Summary * Diverse shapes of voids in z-space * Complicates Alcock-Paczynski test * Unbiased linear growth at 12 Mpc/h * 5% constraint for with 3 Gpc/h 3 β

Gravita4onal Redshi0 from Stacked Clusters Yan-Chuan Cai, Nick Kaiser & Shaun Cole , in prep.

Gravita4onal Redshi0: Φ /c ∝ GM/R Neighbour Neighbour Line of sight Neighbour satellite satellite Neighbour Central Gravita4onal redshi0 Galaxy satellite satellite Neighbour Neighbour Neighbour Neighbour

The observed redshi0 Φ 0 cluster centre To the lowest order of the poten4al and peculiar velocity Φ g galaxy In the weak field limit in GR cz = Hx + v x − Φ /c Stacking to beat velocity dispersion < cdz > = < cz g − cz 0 > = < Φ 0 − Φ g > /c

Wojtak, Hansen & Hjorth, 2011 7800 Clusters from SDSS DR7 line-of-sight veloci4es Projected Radius from the Composite Cluster

Wojtak, Hansen & Hjorth, 2011, Nature 477:567-569 7800 Clusters from line-of-sight veloci4es SDSS DR7 Projected Radius from the Composite Cluster

Wojtak, Hansen & Hjorth, 2011

• Individual clusters are not spherical symmetric , but the average from stacking large number of clusters should be symmetric • isotropic weigh4ng vs. galaxy weigh4ng

Isotropic weigh4ng Mass weigh4ng

isotropic weigh4ng

Mass weigh4ng isotropic weigh4ng Impact of neighbourghs

real space vs. v-space

Cluster-mass correla4on func4on space v space Φ + v Φ cz = v x − Φ / c cz = − Φ / c cz = v x Real space observed v space

Redshi0 in the past light cone Φ 0 cluster centre η 0 Photons emieed at 4me and at are received at the same 4me η η 0 Φ g Galaxy moves : the trajectory of a galaxy galaxy η Conformal 4me interval The Universe expand : expand off the redshi0 around η 0 sta4onary observer rela4ve to the cluster centre in conformal coordinates

The observed poten4al profile Real space Observed without sample variance, with light cone effect Observed v space

Summary • biases for modelling gravita4onal redshi0: (1) substructures, neighbours (2) peculiar velocity (3) light cone effects