Lloyd Knox & Alan Peel University of California, Davis Exploring Dark Energy With Galaxy Cluster Peculiar Velocities
Exploring D.E. with cluster v pec Philosophy Advertisement Cluster velocity velocity correlation functions as probes of dark energy POTENT on 100 Mpc scales
Dark Energy Models Dark Energy Parameters ρ, w ( z) = w + w z x x x x 0 0 1 Expansion rate, H(z) m ρ 0 Primordial P(k) ρ, d (1100), Ω m 0 A 2 bh, zreion, f ν CMB C l d A ( z) Angular-diameter distance Alcock-Paczynski tests with forest correlations Ly α Redshift-space correlations Evolution of angular clustering dl( z) Luminosity distance mz ( ) m ( z) obs Observed apparent magnitude of SNe Ia M Calibration parameters noise Dz ( ) Growth factor lensing C l dv dzdω Volume element N ( M, z ) N( ysz, z) halo N( M, z) lens N( I, z) x-ray Nv (, z) Dark Energy Does Not Exist In A Vacuum rot
Advertisement Advertisement Advertisement Advertisement Advertisement Advertisement Advertisem Kaplinghat, Knox and Skordis (2002) DASh (The Davis Anisotropy Shortcut) Dash is a combination of numerical computation with analytic and semi analytic approximations which achieve fast and accurate C l computation. How fast? How accurate? Applications: About 30 times faster than CMBfast rms error parameter estimation (Knox, Christensen & Skordis 2001, note: age and mcmc) error forecasting
continuity equation On to peculiar velocities δ & = ikv δ η = η δ η ( x, ) D( ) ( x, ) 0 v D & For z< 0.5, D& is much less dependent on the nature of the dark energy than is the case for Dz ( ) or r( z). Peculiar velocities may be helpful in breaking degeneracies. Ω m, w
Solid lines are for w=-1 Growth factor vs. z (normalized to standard CDM) Time derivative of growth factor vs. z Dotted lines are for w=-0.7.
Thermal Measuring with the SZ effect v pec Spectral distortion characterized by Compton y parameter y = kσ mc dlt () l n () l T e 2 e e 2 e mc e Iν = yf ( x) ; x = I ν As x 0, f( x) 2 τ kt hν kt CMB Kinetic x Iν v e δt v = τ x x = τ I c e 1 T c ν SZ kte ( δt / T ) SZ Combine to get velocity: v/ c = 2 mc y e Sunyaev & Zeldovich 1980
Kinetic SZ Thermal 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 T e ) Follow up with optical photometric or spectroscopic redshifts
How well can be measured? v pec Holzapfel et al. (1997): Abell 2163: v =+ 490 km/ s r + 1370 880 Abell 1689: v =+ 170 km/ s r + 815 630 σ 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. v 25 km/sec (.01/ τ) ( T ) + ( T ) CMB 2 2 noise 2µ K Haehnelt & Tegmark (1996) Becker et al. (2001)
What Are The Expected Signals? observer θ r v 1 r v 2 Cluster 1 v v C Cluster 2 v( θ, z1, z2) < vr( r1) vr( r2) > v v v v ( r1 r)( r2 r) =Ψ perp( r)cos( θ ) + ( Ψpara( r) Ψperp( r)) 2 rrr DD & & 1 2 j1( kr) Ψ perp() r = dkp 2 0() k 2π kr DD & & 1 2 j1( kr) Ψ para( r) = dkp 2 0( k)[ j0( kr) 2 ] 2π kr 12 r v
* Expected correlation of radial component of velocities for clusters with the same redshift but in different directions C z z v( θ, 1 = 1, 2 = 1) 200 km/sec errors (16 micro-k for tau=0.01) 100 km/sec errors (8 micro-k for tau=0.01) 10 15 30 60 *Pierpaoli, Scott & White (2001)
C z z z v( θ = 0, 1 = 1, 2 = ) Expected correlation of radial component of velocities for clusters in the same direction but with different redshifts 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 Why? We can reconstruct the gravitational potential from cluster peculiar velocities, as has been done with galaxy peculiar velocities, but with much cleaner velocity measurements. Use as input for better modeling of cluster and galaxy formation. Combine with other surveys to directly measure large scale bias. * Bertschinger & Dekel 1989
Gravitational Potential Reconstruction Φ = Φ% ( 2 r, θ, φ ) dkk ( ) ( ) (, ) lm, lm k jl kr Ylm θ φ Reconstruction weight: k k' W lmk l m k k k drr X r w r j kr j k r H δ δ 3 3 2 2 (, ' ' ') = ' ' ' ll mm ( ) ( ) l '( ) l '( ' ) Φ% H0 0 X() r 2 3 dd da Ω m / a+ω Λ a Ω m 2
Gravitational Potential Reconstruction w () v r = dn dr 1 1 σ r 2 2 v From G. Holder 350 km/s 4 kpφ ( k) l = 20,50,75,125, 225 k 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 D& ( z) instead of D( z) At z < 0.5, D& ( z) is much more dependent on Ωm than w. 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. Thanks to G. Holder and S. Meyer for useful conversations