Astrophysical Uncertainties in the Sunyaev-Zel’dovich ...clust10/presentations/Nagai_Daisu… ·...

Astrophysical Uncertainties in the Sunyaev-Zel’dovich power spectrum

Daisuke NagaiYale University

Garching, July 27th 2010

astro-ph/1006.1945: Laurie Shaw, DN, Suman Battacharya, Erwin Lau

Friday, August 27, 2010

Cosmology with Galaxy Clusters

σ8=0.813(ΩM/0.25)-0.47±0.013w0=-0.99±0.045ΩDE=0.740±0.012

A. Vikhlinin’s talk

Mass within radius enclosing overdensity of 500 times the critical density ρcrit(z) derived using the low-scatter mass proxy, Yx (Kravtsov et al. 2006)

Contribution of dark energy to the energy-density of the universe in units of the critical density

Local (z<0.1) sample of 49 clusters + 37 high-z clusters from the400d X-ray selected cluster sample (http://hea-www.harvard.edu/400d/)

ΩDE

Vikhlinin et al. 2009


Measurements of SZ power spectrum

homog. reion. kSZpatchy reion. kSZ

Residual Poisson Sources

Thermal SZ effect

W. Holzapfel’s talk

Amplitude of SZ power spectrum has very sensitive dependence on matter power spectrum normalization, σ8


Tension in σ8 measurementsCluster Abundance SZ power spectrum

σ8 = 0.80±0.02

Rozo et al. (2009)

σ8 = 0.746±0.017

Lueker et al. (2009)

In tension at 3σ level!Friday, August 27, 2010

Tension in σ8 measurementsCluster Abundance SZ power spectrum

σ8 = 0.80±0.02

Rozo et al. (2009)

σ8 = 0.746±0.017

Lueker et al. (2009)

I argue that the current SZ template is overpredicting the amplitude by 50-100%Missing Key Physics: Gas Motions in Outskirts of Groups and Clusters


Gastrophysical Uncertainty• Thermal SZ power spectrum

contains significant contribution from outskirts of low mass (M<3x1014 Msun), high-z (z>1) groups at l~3000

• However, high-redshift groups are poorly studied observationally.

• Impact of star-formation, AGN, SNe, difficult to evaluate.

• Additional effects not incorporated in semi-analytic models (e.g. bulk and turbulent motions) !

D!

[µK

2]

103

104

0

2

4

6

8

10

12

14

Semi-analytic models

Arnaud et al. X-ray derived profile

Hydro sims

Better understanding of cluster physics is critical in era of precision cluster cosmology!

Dl = l (l+1) Cl / 2 π


Predicting the Power Spectrum• Analytic calculations

• take ‘universal’ mass function (e.g. Tinker et al. 08)

• assume spherical gas pressure profiles (e.g. Komatsu and Seljak 02)

• approximately capture cluster physics, but important for parameter estimation (need to vary both cluster physics + cosmology)

Cl = g2ν

� zmax

0dz

dV

dz

� Mmax

0dM

dn(M, z)dM

|yl(M, z)|2

• Numerical simulations• don’t need to ‘assume profiles’ (Talk by D. Bond; also poster by N. Battaglia)

• follow detailed hydrodynamical evolution of gas in clusters (+ star-formation, AGN, bulk+turbulent gas motions...)

• need both large simulation boxes and high-resolution to resolve relevant sub-grid cluster physics. Prohibitably expensive!!

volume integral cluster mass function(e.g. Tinker et al 08)

electron pressure profiles


• Dark Matter Halos - NFW density profiles

• Gas resides in hydrostatic equilibrium in dark matter halos

• Polytropic equation of state for the ICM: Ptot=P0(ρgas/ρ0)Γ with Γ=1.2 and Ptot(r)=Ptherm(r)+Pnt(r)

• Assume that some fraction of the gas has radiatively cooled and formed stars. Adopt the stellar mass fraction (Gonzalez et al. 2007).

Toward realistic cluster gas model

Duffy et al. 2008AC = 1

c.f., Ostriker et al. 2005; Bode & Ostriker et al. 2007


Cluster Astrophysics

• Energy feedback from Supernovae/AGN: εf ~ 10-6-10-5

• Dynamical heating by mergers: εDM ~ 0.05• Non-thermal pressure due to gas motions in galaxy clusters

2h-1 Mpc

Major Merger Minor Merger

0.82h-1 Mpc

Gas motions (bulk+turbulent) are ubiquitous in ΛCDM clustersFriday, August 27, 2010

Cluster Astrophysics

• Energy feedback from Supernovae/AGN: εf ~ 10-6-10-5

• Dynamical heating by mergers: εDM ~ 0.05• Non-thermal pressure support: α0, β, nnt

where α(z)=α0(1+z)β

AMR simulations of 16 groups and clusters

Lau, Kravtsov, Nagai 2009

z=0

P

nt/P

tot

Calibrate with hydro simulations: α0=0.18, β=0.5, nnt=0.8

enhanced at high-z

enhanced toward outskirts18% at R500 at z=0


Gas Model Parametersfiducial min. max.

energy feedback (εf)

10-6 0 10-5

dynamical heating (εDM)

0.05 0 0.1

non-thermalamplitude (α0)

0.18 0 0.3

non-thermalz-evolution (β)

0.5 -1 1

cDM-M relation(AC)

1.0Duffy et al. 2008

0.8 1.2


Matching to fgas-M observations at z~0

fgas ≡ Mgas/MtotNo feedback model with εf = εDM = 0

Miximal feedback model with εf =10-5 and εDM = 0.1

εf = 10-7, 10-6, 5x10-6, 10-5

εDM = 0.05varying εf 10-7-10-5


Impact of Energy Feedback on Pressure Profiles

Energy feedback does NOT significantly modify the electron pressure profiles of massive clusters.

r/R500

Pe/P

500(r

/R500)3

1 2 3 410 2

10 1

Black: M=3x1014 h-1 Msun

Universal electron pressure profile (Arnaud et al. 2009)

20% scatter

εf = 10-7, 10-6, 5x10-6, 10-5

Hydrodynamical simulations without AGN feedback (r>R500)

X-ray observations (r<R500)


Impact of Energy Feedback on Pressure Profiles

εf = 10-7, 10-6, 5x10-6, 10-5

Black: M=3x1014 h-1 MsunRed: M=3x1013 h-1 Msun

But, significant impact on groups!


Impact of Gas Motions on Pressure Profiles

Black: M=3x1014 h-1 MsunRed: M=3x1013 h-1 Msun

α0: 0-30% with a step of 6% at R500

Non-thermal pressure due to gas motions suppress electron pressure in outskirts of both groups and clusters.


Redshift Evolution

Black: M=3x1014 h-1 Msun

At high-z, electron pressure is lower primarily due to enhanced non-thermal pressure.


Impact of Cluster Physics on the SZ Power Spectrum

Non-thermal pressure 0 ⇒ 18% ⇒ 30% @ R500

εf :10-7⇒ 10-6 ⇒10-5 0.8⇒ 1.0 ⇒ 1.2

-1⇒ 0.5 ⇒ 1

No feedback model

Miximal feedback model

z-evolution

enhanced gas motions toward high-z

Red: Fiducial model


Comparison to Komatsu & Seljak (2002)

Our fiducial model

KS02 model predicts larger power by roughly a factor of 2 at all scales, compared to our model. The differences are due to lack of

star formation, feedback, and non-thermal pressure in the KS model.

No star formationNo feedbackNo dynamical heatingNo non-thermal pressure


Comparison to non-radiative hydrodynamical simulations

Our fiducial model

No star formation,but include non-thermal pressure and dynamical heating

Non-radiative hydrodynamical simulations by ART code by D. Rudd

The overall amplitude is in reasonable agreement, but our model predicts less power at small scales (l > 4000)

compared to the simulation. Friday, August 27, 2010

Comparison to the universal pressure profile model by Arnaud et al. (2009)

Our fiducial model

The predicted power spectra match at large scales, but our model is below that of the A09 profile at small scales

due to enhanced non-thermal pressure at high-z.

Calibrated based on X-ray observations of massive, low-z clusters. Assumes self-similar evolution.


Comparison to the Sehgal et al. SZ template

Our new model with radially-dependent non-thermal pressure profile

No non-thermal pressure. This is a template used in SPT and ACT analyses.

Non-thermal pressure causes reduction of power by 50-60% at all scales.

Our fiducial model


A model with εf =5x10-6 (e.g., Battaglia et al. 2010) + non-thermal pressure predicts the SZ power lower by

a factor of 2 (100%) at l~3000-5000, relative to the current Seghal et al. template.

This physically plausible model can completely remove the tension in σ8 measurements from cluster abundance and SZ power spectrum.


Future Prospects✦ The SZ power spectrum contains useful information about poorly known high-z, low-mass clusters and groups.

✦The SZ power spectrum is complimentary to cluster abundance measurements of massive clusters.

✦ Many exciting activities are underway!!– Next generation of experiments:

• X-ray (e.g., Astro-H, eROSITA, WFXT)• SZE (e.g., ACT, SPT, Planck)• Optical/IR (e.g., DES, LSST)

– More sophisticated computational modeling of galaxy clusters with AGN feedback and plasma physics are underway (many talks in this conference)

SZ lightcone simulation

Hydro simulations of merging cluster


Astrophysical Uncertainties in the Sunyaev-Zel’dovich ...clust10/presentations/Nagai_Daisu… ·...

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