constraining the dark side of the universe j aiyul y oo d epartment of a stronomy, t he o hio s tate...
TRANSCRIPT
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Constraining the Dark Side of the Universe
JAIYUL YOO
DEPARTMENT OF ASTRONOMY, THE OHIO STATE UNIVERSITY
Berkeley Cosmology Group, U. C. Berkeley, Nov, 14, 2006
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COLLABORATORS
David H. Weinberg (The Ohio State)
Jeremy L. Tinker (KICP)
Zheng Zheng (IAS)
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CONTENTS
Introduction
Part I : Improving Estimates of Power Spectrum
Part II : The Density and Clustering of Dark Matter
Part III : Galaxy Clusters and Dark Energy
Conclusion
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• In 1990s, models with a cosmological constant were gaining momentum
(e.g. Efstathiou et al. 1990, Krauss and Turner 1995, Ostriker and Steinhardt 1995)
• In the late 1990s, the first direct evidence for acceleration (Riess et al. 1998, Perlmutter et al. 1999)
• In 2000s, numerous observations strengthen the argument for dark energy
(CMB, galaxy power spectrum, Lya forest, BBN, and so on)
• Do we really understand the true nature of the dark side of the Universe?
CONSTRAINING THE DARK SIDE OF THE UNIVERSE
The Onset of the Dark
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• We develop analytic models
• Apply to the current and future surveys
• To constrain cosmological pameters
Goals (I Can Achieve)
wnsm ,,,, DE8
CONSTRAINING THE DARK SIDE OF THE UNIVERSE
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Refining the Power Spectrum Shape with HOD Modeling
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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Dark Matter Clustering
• Easy to predict given a cosmological model• Correlation function , power spectrum)(r )(kP
Millennium Simulation
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Linear Matter Power Spectrum
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Linear Matter Power Spectrum
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Linear Matter Power Spectrum
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Galaxy Clustering
• We see galaxies, not dark matter
• Galaxy formation is difficult to model
• Dark matter halos are the habitat of galaxies
• Galaxy bias
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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The city light traces the human population
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Linear Bias Approximation
•
• Linear bias factor (constant)
• Identical shape (just different normalization)
• How accurate on what scales?
)()( lin20gal kPbkP
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
0b
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“Red State”
Tegmark et al. 2006
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“Blue State”, in fact.“Red State”
Tegmark et al. 2006
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Tegmark et al. 2006
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Scale-Dependent Bias
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
)()()( lin2
gal kPkbkP •
•
• Bias factor is changing at each k
• Different shape
0)( bkb
Bias Shapes
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Q-Model Prescription
• Q-model prescription for scale-dependent bias (Cole et al. 2005)
• A is constant, Q is a free parameter
• Ad hoc functional form
Ak
Qkbkb
1
1)(
220
2
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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Tegmark et al. 2006
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Questions
• Is the Q-model an accurate description?
• Can the value of Q be predicted?
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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Our Approach
• Alternative, more robust approach
• Recovering the shape of power spectrum
• Based on the halo occupation distribution
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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Halo Occupation Distribution (HOD)
• Nonlinear relation between galaxies and matter
• Probability P(N|M) that a halo of mass M can contain N galaxies
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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Berlind et al. 2003
Probability Distribution P(N|M) Mean Occupation
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
Halo Occupation Distribution (HOD)
Mass
Num
ber
of
Gala
xie
s
Mean o
ccupati
on
SPH simulation
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Halo Occupation Distribution (HOD)
• Halo population is independent of galaxy formation process
• It can be determined empirically
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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Can be determined from clustering measurements
Zehavi et al. 2005
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
Halo Occupation Distribution (HOD)
Num
ber
of
Gala
xie
s
Projected correlation
separation
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Strategy
• Constrain HOD parameters
• Calculate scale-dependent bias shapes
• Based on complementary information
• Based on an adhoc functional form (Q-model)
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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Redshift-Space Distortion
• Deprojection (e.g., Padmanabhan et al. 2006, Blake et al. 2006)
• Angle-average (monopole) (e.g., Cole et al. 2005, Percival et al. 2006)
• Linear combination of monopole, quadrupole, hexadecapole (Pseudo real-space)
(e.g., Tegmark et al. 2004, 2006)
• Investigate bias shapes for all of these
)(kPR
)(0 kP
)(kP RZ
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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Real-Space and Redshift-Space
)(kPR)(0 kP
)(kP RZ
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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Redshift-Space Distortion
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
Hamilton 1997
Large scale
Small scale
Finger-of-God
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Finger-of-God
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
SDSS galaxies
Redshift distance
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Analytic and Numerical Models
N-body test shape comparison
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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• Scale-dependent bias relations : where• Q-model prescription is not an accurate description
Recovering Linear Matter Power Spectrum)(/)()( linobs
2 kPkPkb )(),(),()( 0obs kPkPkPkP RZR
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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Luminous Red Galaxies
SDSS Main SDSS LRG
Tegmark
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Test of Analytic Model
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
N-body test
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• Q-model prescription for LRG?• Tegmark et al. (2006) marginally inconsistent
LRG Bias Shapes
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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• Linear bias relation works on large scales, but Accuracy is challenged by measurement precision
• Accurate description of scale-dependent bias
• Based on complementary measurements
CONSTRAINING THE DARK SIDE OF THE UNIVERSE
PART I: Improving Estimates of the Linear Matter Power Spectrum
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• Smaller systematic errors, better statistical constraints than fitting linear theory or Q-model
• Can use data to k=0.4 before systematic uncertainties are too large
• It can be further refined with better constraints from more precise correlation measurements
CONSTRAINING THE DARK SIDE OF THE UNIVERSE
PART I: Improving Estimates of the Linear Matter Power Spectrum
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From Galaxy-Galaxy Lensing to Cosmological Parameters
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
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• Statistically robust measurements of galaxy clustering
• Information on the galaxy formation process
• Can we do cosmology just with ?
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
Galaxy Clustering
gg
gg
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,, gmgg
Can you tell the difference?
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
The Universe can fool you!
Separation
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,, gmgg
m = 0.1, 8 = 0.95 m = 0.63, 8 = 0.6
m = 0.3, 8 = 0.80Tinker et al. (2005)
Light Galaxies! Heavy Galaxies!
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,, gmgg
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• Weak distortion of background galaxy shapes
• Higher S/N and more reliable than cosmic shear
• Information on the matter distribution around foreground lensing galaxies
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
)()( rr
Galaxy-Galaxy Lensing
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Linear Bias Approximation
• ,
•
• For a given (fixed) ,
• Nonlinearity? and stochasticity?
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
28
20
20 )()( brbr mmgg )()( 0g rbr mmm
0/bggmgmm
8mgg
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Strategy
• Find the best-fit HOD parameters with observed galaxy clustering measurements
• Predict
• Comparison to lensing measurement determines and
• No need for an unknown coefficient
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
m 8
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,, gmgg
m = 0.1, 8 = 0.95 m = 0.63, 8 = 0.6
m = 0.3, 8 = 0.80Tinker et al. (2005)
Light Galaxies! Heavy Galaxies!
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Test of HOD Calculations• Dependence of a halo’s large-scale environments:
A flaw of the standard HOD?(e.g. Gao et al. 2005, Wechsler et al. 2005, Croton et al. 2005)
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
Separation
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Test of Analytic Model• The analytic model provides accurate predictions for
consistent with N-body results.
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
Separation
N-body test
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Predictions
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
m8 =0.6 --- 1.0 =0.2 --- 0.4
SeparationSeparation
• Lensing signals are different
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• Is it linear?
• Accuracy of the linear bias approximation
Test of Linear Bias Scaling
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
75.024.08
FID
m8m
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PART II: THE DENSITY AND CLUSTERING OF DARK MATTER
• Combination constrains
• Better exploitation of data on nonlinear scales
• Application to SDSS measurements
CONSTRAINING THE DARK SIDE OF THE UNIVERSE
8m
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New Results!• HOD parameters from clustering measurements• Predictions
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
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New Results!• HOD parameters from clustering measurements• Predictions
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
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New Results!
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
• HOD parameters from clustering measurements• Predictions (this is not a fit)
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New Results!
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
• HOD parameters from clustering measurements• Predictions (this is not a fit)
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Probing Dark Energy with Cluster-Galaxy Weak Lensing
PART III : GALAXY CLUSTERS AND DARK ENERGY
Work in progress
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• “Is it a cosmological constant?”
• Dark energy observable: the expansion history of the Universe the growth rate of structure
PART III : GALAXY CLUSTERS AND DARK ENERGY
Probing Dark Energywith Cluster-Galaxy Weak Lensing
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• Angular diameter distance is closer
• Volume of survey area is smaller
Expansion History
PART III : GALAXY CLUSTERS AND DARK ENERGY
Fiducial model vs Comparison model with w=-0.8
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• Larger structure in the past
• Massive halos are more abundant
Growth Rate of Structure
PART III : GALAXY CLUSTERS AND DARK ENERGY
Fiducial model vs Comparison model with w=-0.8
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• Number of massive clusters
• from halo mass function
• from physical volume of survey area
• Accurate mass measurement is crucial
Galaxy-Cluster Method
PART III : GALAXY CLUSTERS AND DARK ENERGY
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X-rays X-rays ++ OpticalOptical
Sunyaev-Zel'dovich effectSunyaev-Zel'dovich effect
Weak LensingWeak Lensing
SZA image of A1914SZA image of A1914
Temperature map Temperature map ++
strong lensingstrong lensing
Andrey Kravtsov
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nearby clusters
Alexey Vikhlinin
distant clusters (z ~ 0.6)
Chandra X-ray images of clusters
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• Alternative method, robust to the scatter
• Cluster-galaxy weak lensing
• Monotonic relation of mass-observables
• Stacked sample of the most rich clusters
Our Method
PART III : GALAXY CLUSTERS AND DARK ENERGY
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• Scatter in mass-observable relation
Cluster Mass-Observable Relation
• Robust to the scatter
• Stacked sample
very close to
most massive clusters
PART III : GALAXY CLUSTERS AND DARK ENERGY
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• Advantages :
• No irregularity of individual halos
• Higher S/N ratio of lensing measurements
• Lensing measurements at multiple radii
Upside and Downside
PART III : GALAXY CLUSTERS AND DARK ENERGY
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• Disadvantages :
• Small but nonzero impact of the scatter
• Weak lensing systematic errors
• Statistical uncertainties in galaxy shape
Upside and Downside
PART III : GALAXY CLUSTERS AND DARK ENERGY
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• 50 most rich clusters at z=0.3 from SDSS catalog
• Stacked samples are different!
Sensitivity
PART III : GALAXY CLUSTERS AND DARK ENERGY
Changing only one parameter
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Sensitivity
PART III : GALAXY CLUSTERS AND DARK ENERGY
Changing only one parameter
• 50 most rich clusters at z=0.3 from SDSS catalog
• Stacked samples are different!
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Sensitivity with Priors• Flat universe & LSS Distance
cosmological parameters are not independent
• Dark energy density is lower
PART III : GALAXY CLUSTERS AND DARK ENERGY
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PART III : GALAXY CLUSTERS AND DARK ENERGY
Sensitivity with Priors• Flat universe & LSS Distance
cosmological parameters are not independent
• Dark energy density is lower
• “20% scatter” in the mass-observable relation
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PART III: GALAXY CLUSTERS AND DARK ENERGY
CONSTRAINING THE DARK SIDE OF THE UNIVERSE
• Cluster-galaxy lensing best constrains
• Constrain w with combination of others
• Robust to the scatter
• For an observational program
• It can be applied to future imaging surveys at no extra observational cost
m8
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• Analytic models
• To improve estimates of power spectrum
• To estimate the density and clustering of DM
• To predict the dependence of cluster-galaxy lensing signals
CONSTRAINING THE DARK SIDE OF THE UNIVERSE
Conclusion
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• New, multi-band, wide-field imaging surveys (PanSTARRS, DES, LSST, SNAP)
• Power spectrum recovery from LRG (SDSS-II, SDSS-III BAO, WFMOS, ADEPT)
• Joint analysis of galaxy and shear
• Constraing dark energy with galaxy clusters
CONSTRAINING THE DARK SIDE OF THE UNIVERSE
Conclusion
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• Complementary measurements
• Comprehensive analysis will provide a unique opportunity to understand
the true nature of the dark side of the Universe
CONSTRAINING THE DARK SIDE OF THE UNIVERSE
Conclusion
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Constraining the Dark Side of the Universe
JAIYUL YOO
DEPARTMENT OF ASTRONOMY, THE OHIO STATE UNIVERSITY
Berkeley Cosmology Group, U. C. Berkeley, Nov, 14, 2006