exploring dark energy with galaxy cluster peculiar velocities lloyd knox & alan peel university...
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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)
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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
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