Constraining the Dark Side of the Universe J AIYUL Y OO D EPARTMENT OF A STRONOMY, T HE O HIO S TATE...
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Transcript of Constraining the Dark Side of the Universe J AIYUL Y OO D EPARTMENT OF A STRONOMY, T HE O HIO S TATE...
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
COLLABORATORS
David H. Weinberg (The Ohio State)
Jeremy L. Tinker (KICP)
Zheng Zheng (IAS)
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
• 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
• 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
Refining the Power Spectrum Shape with HOD Modeling
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
Dark Matter Clustering
• Easy to predict given a cosmological model• Correlation function , power spectrum)(r )(kP
Millennium Simulation
Linear Matter Power Spectrum
Linear Matter Power Spectrum
Linear Matter Power Spectrum
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
The city light traces the human population
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
“Red State”
Tegmark et al. 2006
“Blue State”, in fact.“Red State”
Tegmark et al. 2006
Tegmark et al. 2006
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
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
Tegmark et al. 2006
Questions
• Is the Q-model an accurate description?
• Can the value of Q be predicted?
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
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
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
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
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
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
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
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
Real-Space and Redshift-Space
)(kPR)(0 kP
)(kP RZ
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
Redshift-Space Distortion
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
Hamilton 1997
Large scale
Small scale
Finger-of-God
Finger-of-God
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
SDSS galaxies
Redshift distance
Analytic and Numerical Models
N-body test shape comparison
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
• 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
Luminous Red Galaxies
SDSS Main SDSS LRG
Tegmark
Test of Analytic Model
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
N-body test
• Q-model prescription for LRG?• Tegmark et al. (2006) marginally inconsistent
LRG Bias Shapes
PART I : IMPROVING ESTIMATES OF LINEAR MATTER POWER SPECTRUM
• 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
• 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
From Galaxy-Galaxy Lensing to Cosmological Parameters
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
• 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
,, gmgg
Can you tell the difference?
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
The Universe can fool you!
Separation
,, 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!
,, gmgg
• 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
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
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
,, 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!
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
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
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
• 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
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
New Results!• HOD parameters from clustering measurements• Predictions
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
New Results!• HOD parameters from clustering measurements• Predictions
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
New Results!
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
• HOD parameters from clustering measurements• Predictions (this is not a fit)
New Results!
PART II : ESTIMATING THE DENSITY AND CLUSTERING OF DARK MATTER
• HOD parameters from clustering measurements• Predictions (this is not a fit)
Probing Dark Energy with Cluster-Galaxy Weak Lensing
PART III : GALAXY CLUSTERS AND DARK ENERGY
Work in progress
• “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
• 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
• 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
• 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
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
nearby clusters
Alexey Vikhlinin
distant clusters (z ~ 0.6)
Chandra X-ray images of clusters
• 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
• 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
• 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
• 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
• 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
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!
Sensitivity with Priors• Flat universe & LSS Distance
cosmological parameters are not independent
• Dark energy density is lower
PART III : GALAXY CLUSTERS AND DARK ENERGY
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
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
• 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
• 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
• 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
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