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
Friday, August 27, 2010
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
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)
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
Friday, August 27, 2010
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
Friday, August 27, 2010
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
Friday, August 27, 2010
• 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
Friday, 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 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
Friday, August 27, 2010
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
Friday, August 27, 2010
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
Friday, August 27, 2010
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)
Friday, August 27, 2010
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!
Friday, August 27, 2010
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.
Friday, August 27, 2010
Redshift Evolution
Black: M=3x1014 h-1 Msun
At high-z, electron pressure is lower primarily due to enhanced non-thermal pressure.
Friday, August 27, 2010
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
Friday, August 27, 2010
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
Friday, August 27, 2010
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.
Friday, August 27, 2010
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
Friday, August 27, 2010
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.
Friday, August 27, 2010
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
Friday, August 27, 2010