Exploring Dark Energy

With Galaxy Cluster Peculiar Velocities

Lloyd Knox & Alan Peel

University of California, Davis

Exploring D.E. with cluster

• Philosophy

• Advertisement

• Cluster velocity—velocity correlation functions as probes of dark energy

• POTENT on 100 Mpc scales

pecv

Observed apparent magnitude of SNe Ia

0m

Dark Energy Parameters

0 0 1, ( )x x x xw z w w z

Expansion rate, H(z)

Primordial P(k)

( )Ad z

Angular-diameter distance

( )Ld zLuminosity distance

( )D zGrowth factor

dV

dzdVolume element

0

2reion

, (1100),

, ,

mA

b

d

h z f

CMBlC

( )m zM

obs( )m z

Calibration parameters

noise

halo( , )N M z ( , )SZN y z

x-ray( , )N I z

lensinglC

Evolution of angular clustering

Alcock-Paczynski tests with

forest correlationsLy

Redshift-space correlations rot( , )N v zlens( , )N M z

Dark Energy

Models

Dark Energy Does Not Exist In A Vacuum

DASh (The Davis Anisotropy Shortcut)Dash is a combination of numerical computation with analytic and semi—analytic approximations which achieve fast and accurate computation.lC

How fast?About 30 times faster than CMBfast

How accurate?

rms error

Applications:

• parameter estimation (Knox, Christensen

& Skordis 2001, note: age and mcmc)

• error forecasting

Kaplinghat, Knox and Skordis (2002)

Advertisement Advertisement Advertisement Advertisement Advertisement Advertisement Advertisement

On to peculiar velocities…

ikv 0( , ) ( ) ( , )x D x

v D

For 0.5, is much less dependent on the nature

of the dark energy than is the case for ( ) or r( ).

z D

D z z

Peculiar velocities may be helpful in breaking degeneracies.

,m w

continuity equation

Growth factor vs. z

(normalized to standard CDM)

Time derivative of growth factor vs. z

Dotted lines are for w=-0.7.

Solid lines are for w=-1

Measuring with the SZ effect pecv

Thermal

Kinetic

2 2

CMB

Spectral distortion characterized by Compton y parameter

( ) ( )

( ) ;

As 0, ( ) 2

T ee e

e e

k kTy dlT l n l

m c m c

I hyf x x

I kT

x f x

1

x

xSZ

I v e T vx

I c e T c

2

( / )Combine to get velocity: / e SZ

e

kT T Tv c

m c y

Sunyaev & Zeldovich 1980

Thermal SZKinetic SZ

Holzapfel et al. (1997)

A possible survey strategy

• Survey large area with large detector array at 30 GHz to find clusters.

• Follow up with a smaller array of detectors at 150 GHz and 220 GHz targeting the clusters. (Or maybe even FTS to get )

• Follow up with optical photometric or spectroscopic redshifts

eT

How well can be measured?pecv

Aghanim et al. (2001): Planck will result in cluster peculiar velocities with errors of 500 to 1,000 km/s.

These large errors are due to Planck’s big 5’ beam and noisy maps.

With a smaller beam a cluster stands out better against the confusing background of CMB anisotropy and other clusters.

1370880

815630

Abell 2163: 490 /

Abell 1689: 170 /

r

r

v km s

v km s

Holzapfel et al. (1997):

2 2CMB noise( ) ( )

25 km/sec (.01/ )2 Kv

T T

Haehnelt & Tegmark (1996)

Becker et al. (2001)

What Are The Expected Signals?

observer

Cluster 1

Cluster 2

1r

2r

r

1 2 1 2

1 22

1 2

( , , ) ( ) ( )

( )( ) ( )cos( ) ( ( ) ( ))

v r r

perp para perp

C z z v r v r

r r r rr r r

r r r

1 2 102

1 2 10 02

( )( ) ( )

2

( )( ) ( )[ ( ) 2 ]

2

perp

para

D D j krr dkP k

kr

D D j krr dkP k j kr

kr

10’ 15’ 30’ 60’

Expected correlation of radial component of velocities for clusters with the same redshift but in different directions

200 km/sec errors (16 micro-K for tau=0.01)

100 km/sec errors (8 micro-K for tau=0.01)

*Pierpaoli, Scott & White (2001)

*

1 2( , 1, 1)vC z z

Expected correlation of radial component of velocities for clusters in the same direction but with different redshifts1 2( 0, 1, )vC z z z

Note: redshifts may need to be determined to better than .01!

Velocity Bias

• Our calculations were for randomly selected locations in the Universe, but measurements will be made where clusters are bias

• Velocity bias not calculated yet (unpublished work by Sheth)

• Easily calculable.

POTENT on 100 Mpc scales

Bertschinger & Dekel 1989

We can reconstruct the gravitational potential from cluster peculiar velocities, as has been done with galaxy peculiar velocities, but with much cleaner velocity measurements.

*

*

Why?

• Use as input for better modeling of cluster and galaxy formation.

• Combine with other surveys to directly measure large—scale bias.

Gravitational Potential Reconstruction

2

,( , , ) ( ) ( ) ( , )lm l lml mr dkk k j kr Y

3 3 2 2' '

0 0

'( , ' ' ') ' ( ) ( ) '( ) '( ' )ll mm l l

k kW lmk l m k k k drr X r w r j kr j k r

H H

2/2( )

3m

m

a adDX r

da

Reconstruction weight:

Gravitational Potential Reconstruction

2 2

1 1( )v

v

dNw r

dr r

From G. Holder

350 km/s

k

4 ( )k P k

20,50,75,125,225l

Ignore these

Conclusions

• CMB is important for breaking degeneracies between dark energy parameters and other parameters

• DASh will be available soon.• Peculiar velocities are sensitive to• At • Cluster peculiar velocities can be measured very well (in

principle) for z > 0.2, well enough to measure the velocity correlations and reconstruct the large—scale gravitational potential.

• Theory/observable relationship is even more straightforward than other uses of clusters such as dN/dz.

( ) instead of ( )D z D z

0.5, ( ) is much more dependent on than .mz D z w

Thanks to G. Holder and S. Meyer for useful conversations