LAURO MOSCARDINI!DIP. ASTRONOMIA, UNIBO!LAURO.MOSCARDINI@UNIBO.IT !

Imprints of primordial non-Gaussianities on future cluster surveys

The Almost Gaussian Universe, Paris, 8th-11th June 2010

IN COLLABORATION WITH:!

Stefano Borgani – Univ. Trieste Enzo Branchini – Univ. Roma Tre Klaus Dolag – MPA Garching Cosimo Fedeli – Univ. Bologna Margherita Grossi – MPA Garching Francesca Iannuzzi – MPA Garching Sabino Matarrese – Univ. Padova Mauro Roncarelli – CESR Toulouse Piero Rosati – ESO Garching Barbara Sartoris – Univ. Trieste Jochen Weller – Univ. Munich

Mostly based on: - Fedeli, LM, Matarrese, 2009, MNRAS, 397, 1125 - Roncarelli et al., 2010, MNRAS, 402, 923 - Sartoris et al., 2010, MNRAS, in press, ArXiv:1003.0841

Primordial non-Gaussianity: mass function

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Φ =ΦG + fNL * ΦG2 − ΦG

2( )

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n M,z( ) = n G( ) M,z( )nPS M,z( )nPS

G( ) M,z( )

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Non-Gaussianity parametrized as

largest effects at high masses & redshifts: (high-z )clusters?

Matarrese et al. 2000; LoVerde et al. 2008;

Maggiore & Riotto 2009; D’Amico et al. 2010; …

Fedeli et al. 2009

Primordial non-Gaussianity: bias

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Φ =ΦG + fNL * ΦG2 − ΦG

2( )

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Non-Gaussianity parametrized as

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b M,z,k( ) =1+ bLG( ) M,z( ) 1+

Δb M,z,k( )bLG( ) M,z( )

for “local” NG, largest effects at large scales;

clusters?

Fedeli et al. 2009

Dalal et al. 2007; Matarrese & Verde 2008;

Slosar et al. 2008; Taruya et al. 2008; …

Tests with N-body simulations: mass function

Grossi et al. 2009; see also Pillepich et al., Desjacques et al., Valageas, Giannantonio & Porciani, …,

fNL=+100

fNL=-100

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δc → qδcModification required to the theoretical mass function: with q=0.75

Tests with N-body simulations: halo bias

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ΔbbLG ≈ 2 fNLδc z( )αM k( )q

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⇒ q = 0.75

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α k( )∝1/k 2

theory

simulations

Grossi et al. 2009; see also Pillepich et al., Desjacques et al. Giannantonio & Porciani, …,

Predictions for the future: X-ray and SZ

eROSITA 0.5 of the full sky; Slim=3.3 10-14

South Pole Telescope 0.1(+) of the full sky; S150Ghz,lim=5 mJy

Predictions: counts

Fedeli et al. 2009

Small differences visible mostly at

high-z

Confirmed in N-body simulations by

Roncarelli et al. 2010

Predictions: clustering

Fedeli et al. 2009

  Wide X-ray surveys are more promising   20-30% changes in the correlation length   <10% precision on P(k) amplitude is required

Forecasts: the general method (Sartoris et al. 2010)

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Fαβ = −∂ 2 lnL∂pα∂pβ

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Fisher Matrix method:

  abundance of galaxy clusters as a function of mass and redshift   clustering of galaxy clusters as a function of wavenumber and redshift   plus the Fisher Matrix of the Planck CMB experiment (DEFT)

Observables:

Forecasts only for ‘local’ shape

1. Cluster Number Counts (NC)

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FαβN =

∂Nl ,m

∂pα

∂Nl,m

∂pβl ,m∑ 1

Nl ,m

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The FM is:

l=1,60 z bins up to z=2

m mass bins with ΔlogM=0.1

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Nl.m = ΔΩ dz dVdzdΩzl

zl+1

∫ dMob dM0

∞

∫ n M,z( )M l .m

ob

M l .m+1ob

∫ p Mob ||M( )

1. Cluster Number Counts (NC)

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p Mob ||M( ) =exp −x 2 Mob( )( )

2πσ lnM2

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x Mob( ) =lnMob − BM − lnM

2σ lnM2

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Nl.m =ΔΩ2

dz dVdzdΩzl

zl+1

∫ dMn M,z( )0

∞

∫ erfc xm( ) − erfc xm+1( )[ ]

Two possible approaches:

Lognormal distrib.

(Lima & Hu 2005) - Self-calibration

- Direct measurement of mass proxies, but on a limited sample of brighter objects

2. (Average) Cluster Power Spectrum (PS)

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The FM is:

l z bins up to z=2 with Δz=0.2

m wavenumber bins with 0.3=kmax ≥k Mpc ≥0.001

Majumdar & Mohr 2004

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Fαβ =12π( )2

∂ lnP cl km ,zl( )∂pα

∂ lnP cl km ,zl( )∂pβl,m

∑ Vl ,meff km

2Δk

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Pcl k,z( ) = beff2 k,z( )P k,z( )

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P l,mcl k,zl( ) =

dz dVdz

N 2 z( )Pcl z( )zl

zl+1∫

dz dVdz

N 2 z( )zl

zl+1∫

The average power spectrum is defined as

with

Veff = effective volume

The Wide Field X-Ray Telescope (WFXT)

Collaboration US (JHU, Marshall, CfA) & Italy (Milano, Trieste, Bologna, Napoli,Roma); see Murray et al.

Main Characteristics: a large collecting area and field of view with a sharp PSF over the entire field ⇒  a large number of

clusters out to z=2 with the possibility of measuring

mass proxies like Yx=MgasTx and Mgas down

to low fluxes

WFXT

White paper on cluster science submitted to the NASA Decadal Survey:

Giacconi et al. arXiv:0902.4857

http://wfxt.pha.jhu.edu

in units of 10-14 erg s-1 cm-2

Selection function

Lx => M500 adopting the relation calibrated by Maughan (2007) using 115 clusters observed by Chandra

objects with M500< 5 1013 Msun/h are discarded because the relation is not reliable in that range

The “Reference model”

9 cosmological parameters: WMAP7 (Komatsu et al. 2010) plus 4 nuisance parameters for the

z-dependence of the fraction mass bias and of the intrinsic scatter

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BM = BM ,0 1+ z( )α

σ lnM z( ) =σ lnM ,0 1+ z( )β

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BM ,0 = −0.15α = 0

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σ lnM ,0 = 0.25β = 0

Ωm=0.28, Ωk=0., Ωb=0.046, σ8=0.81, w0=-0.99, wa=0,h=0.70, n=0.96, fNL=0

as suggested by observations and hydro-simulations

Reference values:

Redshift distribution

Detection samples Bright samples

in units of 10-14 erg s-1 cm-2

Constraints on cosmological parameters

Strong complementarity between number counts (NC) and power spectrum (PS) to constrain σ8 and fNL

NC: Weak sensibility of the high end of the mass function to non-Gaussianity and so on fNL

PS: Strong constraints on fNL thanks to the scale dependence of bias

Wide survey

68 per cent contour levels

Constraints on cosmological parameters

Combining the information obtainable from the three surveys

Most of the constraining power comes from the Wide survey: -  larger statistics out to z≈1 -  better sampling of the long-wavelength modes

Timing of structure formation:

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FoMSFT = det Cov σ 8, fNL( )[ ]( )−1/ 2

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ΔfNL ≈12FoMSFT ≈ 26with no prior

Changing the k-range considered for power spectrum

The best choice for kmax represents a compromise between adding more info and avoiding small-scale mode where non-linearity is in action

No significant changes for the resulting constraints

Power spectrum: contribution to FM information

Most of information comes from k≈0.01 Mpc-1 and z≈0.5

redshift wavenumber

Priors

weak prior:

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ΔBM ,0 → 0.05Δα →1

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Δσ lnM ,0 → 0.1Δβ →1

strong prior: nuisance parameters

perfectly known (ref. values)

fNL constraints are weakly sensitive to priors

(but FoMSFT worsens)

Which survey? Detection versus bright surveys

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ΔfNL ≈ 35FoMSFT ≈ 7

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ΔfNL ≈12FoMSFT ≈ 26

Detection surveys have more constraining power

The case of XMMU-J2235.3 (Jee et al. 2009)

M=5 x 1014 Msun detected at z≈1.4 in the initial 11 deg2 of the XMM Distant Cluster Project survey (Mullis et al. 2005)

Assuming the concordance Gaussian model, only 5 x 10-3 of such massive clusters are expected in that area!

An imprint of (positive) primordial non-Gaussianity?

Constraints on cosmological parameters

non-Gaussian mass function: LoVerde et al. (2008) => dot-dashed curves

Matarrese et al. (2000) => solid curves

curves (from right to left): 0.05, 0.2, 0.1 and 0.005 clusters

The case of the XMMU-J2235.3 cluster

If confirmed, this object remains a quite

unexpected event!!!

Summary

• Power spectrum and number counts of galaxy clusters are highly complementary tools to constrain fNL and σ8

• X-ray surveys of clusters like WFXT are very promising

• Most of the constraining power lies in the Wide survey

• Combining number counts and power spectrum information for the three surveys turns into ΔfNL≈12 for the local shape model (FoMSFT≈26)

• Constraints on fNL are weakly dependent on the prior assumptions for the nuisance parameters

• The presence of XMMU-J2235.3 @z1.4 is an unlikely event even when a large positive non-Gaussianity is assumed