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. Padilla, arXiv:1603.05184
• V. Demchenko, Y. Cai, C. Heymans & J. Peacock, arXiv:1605.05286

XIIth 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

• Y. Cai

3

Sheth & van de Weygaert, 2004

Rf/Rint ∼ 1.7

In LCDM, shell-crossing occurs at

Spherical evolu4on model

Demchenko, Cai, Heymans & Peacock, 2016

w = −0.5

Voids in Simula4ons

The Aspen–Amsterdam void finder comparison project

• Y. Cai

5

ZOBOV Spherical overdensity Millennium Simula4on Colberg et al. 2008 40 Mpc/h

Voids in observa4ons

• SDSS voids from

Pan et al. 2012 Sueer et al. 2012 Cai et al. 2014 Nadathur et al. 2014 Mao et al. 2016

…

• Y. Cai

6

Pan et al. 2012 Nadathur et al. 2014 Sueer et al. 2012

Tes4ng gravity with voids

• Y. Cai

7

f(R) voids are emp4er than GR voids f(R) voids expand faster Cai, Li & Padilla 2015

Alcock-Pasczynski test with voids

IF voids are spherical

Voids are distorted in redshi0 space

LOS distance transverse distance 14% flaeening in redshi0 space, Lavaux & Wandelt (2012)

Kaiser 1987, Hamilton 1997

Linear Redshi0 Space Distor4on (RSD)

robs = r + vpec/aH

RSD for void

µ = cos θ

Maeda, Sakai & Triay, 2011 ?

Void-halo correla4on func4on

ξs(r, 1) = (1 + β)ξ(r) − 2 3 ¯ ξ(r)

ξs(r, µ) = ξ(r) + 1 3β ¯ ξ(r) + βµ2[ξ(r) − ¯ ξ(r)]

(line of sight) (transverse LOS)

¯ ξ(r) = 3 r3 Z r ξ(r0)r02dr0

β = f/b

ξs(r, 0) = ξ(r) + 1 3β ¯ ξ(r)

Void-halo correla4on func4on

Extrac4ng the linear growth

G(β) = ξs

s

ξs

0 − ¯

ξs = 2β 3 + β

m

• n
• p
• l

e q u a d r u p

• l

e

q u a d r u p

• l

e m

• n
• p
• 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/h3

β

Gravita4onal Redshi0 from Stacked Clusters

Yan-Chuan Cai, Nick Kaiser & Shaun Cole, in prep.

Line of sight Central Galaxy

satellite

Neighbour Neighbour Neighbour Neighbour Neighbour Neighbour Neighbour Neighbour

satellite satellite satellite

Gravita4onal redshi0 Gravita4onal Redshi0: Φ/c ∝ GM/R

The observed redshi0

To the lowest order of the poten4al and peculiar velocity In the weak field limit in GR cz = Hx + vx − Φ/c galaxy

Φ0

Φg

cluster centre

< cdz >=< czg − cz0 >=< Φ0 − Φg > /c

Stacking to beat velocity dispersion

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

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

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

Mass weigh4ng Isotropic weigh4ng

isotropic weigh4ng

Mass weigh4ng Impact of neighbourghs isotropic weigh4ng

real space vs. v-space

Cluster-mass correla4on func4on space

Φ

v space

Φ + v

cz = vx − Φ/c

cz = −Φ/c

cz = vx

v space Real space

• bserved

sta4onary observer rela4ve to the cluster centre in conformal coordinates Galaxy moves: the trajectory of a galaxy galaxy

Φ0

Φg

cluster centre

Redshi0 in the past light cone

η0

η

Photons emieed at 4me and at are received at the same 4me

η0

η

Conformal 4me interval The Universe expand: expand off the redshi0 around

η0

Observed Observed without sample variance, with light cone effect Real space v space

The observed poten4al profile

Summary

• biases for modelling gravita4onal redshi0:

(1) substructures, neighbours (2) peculiar velocity (3) light cone effects