Disentangling dynamic and Disentangling dynamic and geometric distortionsgeometric distortions

Federico MarulliFederico MarulliDipartimento di Astronomia, Università di BolognaDipartimento di Astronomia, Università di Bologna

Marulli, Bianchi, Branchini, Guzzo, Moscardini and Angulo2012, arXiv:1203.1002

Bianchi, Guzzo, Branchini, Majerotto, de la Torre, Marulli, Moscardini and Angulo

2012, arXiv:1203.1545

Bologna cosmology/clustering Bologna cosmology/clustering groupgroup

Carmelita Carbone:

Victor Vera (PhD):

Fernanda Petracca (PhD):

Carlo Giocoli:

Roberto Gilli:

Michele Moresco:

Lauro Moscardini:

Andrea Cimatti:

Federico Marulli:

N-body with DE and neutrinos + forecasts

BAO with new statistics

DE and neutrino constraints from ξ(rp,π)

HOD and HAM (Halo Abundance Matching)

AGN clustering

P(k)

clustering of galaxy clusters

galaxy/AGN evolution

RSD + Alcock-Paczynski test + clustering of galaxies/AGN

Redshift space distortionsRedshift space distortions

Ra, Dec, Redshift comoving coordinates

the real comoving distance is:

the observed galaxy redshift:

zc : cosmological redshift due to the Hubble flowv||: component of the galaxy peculiar velocity parallel to the line-of-sight

c

z+c

v+z=z v||

cobs

1

cc z

cM

cz

c

z

dz

H

c

zH

dzcr

0 30

0||)1()(

How to constract a 3D map

Geometric Geometric distortionsdistortions

ObservationObservational al

distortionsdistortions

Dynamic Dynamic distortionsdistortions

Dynamic and geometric distortionsDynamic and geometric distortionsThe two-point correlation function

DM

galaxygalaxyb

VVrnrP

2

212 )(1)(

geometrigeometricc

distortiodistortionsns

no no distortionsdistortions

dynamicdynamic distortiodistortio

nsns

dynamicdynamic++geomegeometrictric distortions distortions

geometrigeometricc

distortiodistortionsns

dynamicdynamic++geomegeometrictric distortions distortions

Modelling the dynamical Modelling the dynamical distortionsdistortions

212

2

12

1212

exp

||||

exp1

)(

||2exp

2

1)(

))(/)(/,()(),(

vvf

vvf

zazHvrrvdvfrr

gauss

lin

4

05

2

03

2

4

2

2

2

0

442200||

)(5

)(

)(3

)(

)(2

7)(

2

5)(

35

8)(

)()(7

4

3

4)(

)(53

21)(

)()()()()()(),(

rrdrr

r

rrdrr

r

rrrs

rrs

rs

sPssPssPsrr

r

r

lin

linear model

non-linear model

ad

Ddf

zbzb

zkfzk

ln

ln

)()(

),(),(

and 545.0

12

model

parameters

The “dispersion” model

Statistical errors on the growth Statistical errors on the growth raterate

nb

nVCb

β

δβ 0.7200.5 exp

5.15.12

3340

109.4

107.1

MpchC

Mpchn

bias density

δβ

/β

Bianchi et al. 2012

Effect of redshift errors on Effect of redshift errors on ββ and and σσ1212Only dynamic

distortions

δz small sistematic error

on βδβ ~ 5% for all δz

Dynamic distortions + δz

Dynamic distortions + δz

Effect of geometric distortionsEffect of geometric distortions

Error on β

Error on the bias

Error on ξ(s)/ξ(r)

GD δβ is negligible

Spurious scale

dependence in b(r)

The Alcock-Paczynski testThe Alcock-Paczynski test

Steps of the method1. Choose a cosmological model to

convert redshifts into comoving coordinates

2. Measure ξ3. Model onlyonly the dynamical

distortions4. Go back to 1. using a different

test cosmology

……next futurenext future

10 N-body simulations with massive neutrinos (L=2 Gpc/h)

(1e6 CPU hours at CINECA)for:

all-sky mock galaxy catalogues via HOD and box-stacking

all-sky shear maps via box-stacking and ray-tracing

all-sky CMB weak-lensing maps

end-to-end simulations for BAO and RSD statistics

reference skies for future galaxy/shear/CMB-lensing probes

ISW/Rees-Sciama implementation/analysis

PI Carmelita Carbone

ConclusionsConclusions

• systematic error on β of up to 10%, for small bias objects

• small systematic errors for haloes with more than ~1e13 Msun

• scaling formula for the relative error on β as a function of survey parameters

• the impact of redshift errors on RSD is similar to that of small-scale velocity dispersion

• large redshift errors (σv >1000km/s) introduce a systematic error on β, that can be accounted for by modelling f(v) with a gaussian form

• the impact of GD is negligible on the estimate of β

• GD introduce a spurious scale dependence in the bias

• AP test joint constraints on β and ΩM

BASICC simulation by Raul AnguloGADGET-2 code

• ~1448^3 DM particles with mass 5.49e10 Msun/h

• periodic box of 1340 Mpc/h on a side

• ΛCDM “concordance” cosmological framework (Ωm=0.25, Ωb=0.045, ΩΛ=0.75, h=0.73, n=1, σ8=0.9)

• DM haloes: FOF M>1e12 Msun/h

• Z=1

Mock halo cataloguesMock halo catalogues

Systematic errors on the growth Systematic errors on the growth raterate

Errors onErrors on β β on different mass on different mass ranges ranges

• Small masses [M<5e12 Msun/h] systematic error on β ~ 10%

• Intermediate masses [5e12<M<2e13 Msun/h] systematic error is small the linear model works accurately

• Large masses [M>2e13 Msun/h] large random errors

Statistical errors vs VolumeStatistical errors vs Volume

Effect of redshift errors on Effect of redshift errors on ββ and and σσ1212

Effect of geometric distortionsEffect of geometric distortions

1D correlation function deprojected

correlation

Effect of redshift errors on 1D Effect of redshift errors on 1D ξξ