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


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

Galaxy Clustering

• We see galaxies, not dark matter

• Galaxy formation is difficult to model

• Dark matter halos are the habitat of galaxies

• Galaxy bias


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


0b

“Red State”

Tegmark et al. 2006

“Blue State”, in fact.“Red State”

Tegmark et al. 2006

Tegmark et al. 2006

Scale-Dependent Bias


)()()( 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


Tegmark et al. 2006

Questions

• Is the Q-model an accurate description?

• Can the value of Q be predicted?


Our Approach

• Alternative, more robust approach

• Recovering the shape of power spectrum

• Based on the halo occupation distribution


Halo Occupation Distribution (HOD)

• Nonlinear relation between galaxies and matter

• Probability P(N|M) that a halo of mass M can contain N galaxies


Berlind et al. 2003

Probability Distribution P(N|M) Mean Occupation



Mass

Num

ber

of

Gala

xie

s

Mean o

ccupati

on

SPH simulation


• Halo population is independent of galaxy formation process

• It can be determined empirically


Can be determined from clustering measurements

Zehavi et al. 2005



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)


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


Real-Space and Redshift-Space

)(kPR)(0 kP

)(kP RZ


Redshift-Space Distortion


Hamilton 1997

Large scale

Small scale

Finger-of-God

Finger-of-God


SDSS galaxies

Redshift distance

Analytic and Numerical Models

N-body test shape comparison


• Scale-dependent bias relations : where• Q-model prescription is not an accurate description

Recovering Linear Matter Power Spectrum)(/)()( linobs

2 kPkPkb )(),(),()( 0obs kPkPkPkP RZR


Luminous Red Galaxies

SDSS Main SDSS LRG

Tegmark

Test of Analytic Model


N-body test

• Q-model prescription for LRG?• Tegmark et al. (2006) marginally inconsistent

LRG Bias Shapes


• Linear bias relation works on large scales, but Accuracy is challenged by measurement precision

• Accurate description of scale-dependent bias

• Based on complementary measurements


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


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 ?


Galaxy Clustering

gg

gg

,, gmgg

Can you tell the difference?


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


)()( rr

Galaxy-Galaxy Lensing

Linear Bias Approximation

• ,

•

• For a given (fixed) ,

• Nonlinearity? and stochasticity?


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


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)


Separation

Test of Analytic Model• The analytic model provides accurate predictions for

consistent with N-body results.


Separation

N-body test

Predictions


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


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


8m

New Results!• HOD parameters from clustering measurements• Predictions


New Results!


• 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


Probing Dark Energywith Cluster-Galaxy Weak Lensing

• Angular diameter distance is closer

• Volume of survey area is smaller

Expansion History


Fiducial model vs Comparison model with w=-0.8

• Larger structure in the past

• Massive halos are more abundant

Growth Rate of Structure


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


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


• Scatter in mass-observable relation

Cluster Mass-Observable Relation

• Robust to the scatter

• Stacked sample

very close to

most massive clusters


• Advantages :

• No irregularity of individual halos

• Higher S/N ratio of lensing measurements

• Lensing measurements at multiple radii

Upside and Downside


• Disadvantages :

• Small but nonzero impact of the scatter

• Weak lensing systematic errors

• Statistical uncertainties in galaxy shape

Upside and Downside


• 50 most rich clusters at z=0.3 from SDSS catalog

• Stacked samples are different!

Sensitivity


Changing only one parameter

Sensitivity


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



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


• 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


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


Conclusion

• Complementary measurements

• Comprehensive analysis will provide a unique opportunity to understand

the true nature of 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

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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