Cosmology from Galaxy Cluster Peculiar Velocities.

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Cosmology from Galaxy Cluster Peculiar Velocities.

• Suman Bhattacharya.
• Arthur Kosowsky
• Department of Physics and Astronomy.
• University of Pittsburgh.

Outstanding Questions in Cosmology. Imperial
College. March 07.
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Outline

• Sunyaev-Zeldovich effect.
• Whats wrong with peculiar velocities from
  Galaxy surveys?
• Theoretical outline Different velocity
  statistics.
• Results Constraints on parameters.

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Thermal Sunyaev-Zeldovich Effect

• CMB photons passing
• through galaxy clusters
• undergo collisions with
• electrons present within
• clusters causing a change
• in the spectrum (Thermal
• SZ effect).
• proportional to optical depth and gas
  temperature.
• 
  

Credit Carlstrom et al 2002
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Kinetic SZ effect

• This is due to scattering
• of photons off gas with bulk
• motion.
• Being Doppler shift,
• (approx.) spectrum of kSZ
• is still blackbody unlike tSZ.
• This effect is proportional
• to radial peculiar velocity and
• optical depth.
• Typically kSZ ( 10 µK ) ltlt
• tSZ ( 100 µK) in clusters of
• galaxies.
• .

Credit Carlstrom et al 2002
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Upcoming SZ measurements

• ACT (150 sq deg).
• (Kosowsky 2003 Fowler et al 2005).
• SPT (4000 sq deg).
• (Ruhl et al. 2004)
• designed to scan the microwave sky with very
  high sensitivity and arc minute resolution.
• ACT would have the nominal sensitivity (2-10 µK)
  to measure kSZ.
• ACT Telescope

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Q. Why are kSZ velocity surveys more reliable
than redshift based surveys?

• Redshift based velocity surveys need to estimate
  distance.
• Biases introduced in calibrating the distances.
  
• Error increases with z. Typically 15-20 of
  the distance.
• Velocity as a cosmology probe limited to near
  redshift z0.024 (Bridle et al 2001).
• Moreover galaxy velocity surveys probe into
  nonlinear scale which is difficult to model.

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On the other hand kSZ

• Use clusters of galaxies as tracers of cosmic
  velocity field.
• kSZ effect directly measures velocities with
  respect to the cosmic rest frame.
• These velocities respond only to larger scales
  which are mostly linear.
• Measured velocity is independent of redshift

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Velocity Statistics

• Probability distribution of radial velocities-gt
  number of clusters at each velocity bin at each
  redshift range.
• Plot shows normalized count in each velocity bin
  at z0.1.
• Use semi analytic halo model-gt2 halo term.
• (Sheth 2000, Hamana 2003, Cooray Sheth 2002)

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• Mean streaming velocity average relative
  velocity of all clusters at a fixed separation
  along the line joining them.
• V12(r) lt (V1 - V2 ) . r gt
• Plots shows mean streaming velocity at redshift
  0.3 as a function of separation.
• Use semi analytic halo model-gt2-halo term.
• (Sheth et al 2001, Cooray
  Sheth 2002).
  

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Halo model for PDF(v) and mean streaming velocity
V12(r)
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Cosmological Parameter space spanned by velocity
statistics.

• Om(DM b) 0.29 - 0.34.
• n 0.93 0.96.
• s8 0.68 0.79.
• h 0.7-0.76.
• w 0.9 1.15

• Matter density (CDM Baryons).
• power spectrum index.
• Amplitude of fluctuations
• Hubble parameter
• Dark Energy equation of state.

Current constraints from WMAP3 Spergel et al 2006
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Results Parameter constraints from two different
velocity statistics for a SPT like survey. (5000
sq deg sky area and mass limit Mmin1014 Msun )

• PDF
  Mean Streaming velocity

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Conclusion

• Constraints on s8 from f(v) itself is 5.8. A
  joint constraint from f(v) V12(r) gives 2.9
  accuracy. Adding priors (WMAP 3rd year (Spergel
  et al 2006) SNLS 1st year, (Astier et al 2006),
  this reduces to 0.7 and 0.5 respectively.
• Constraints on w from f(v) are 11.4 and 14.0
  for velocity error of 100 km/s and 300 km/s
  respectively. Adding priors the constraints
  decreases to around 4.0.
• Constraints on Om from V12(r) are 9.4 and 16
  for the two velocity errors. Adding priors these
  decreases to 3.0.

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Plot shows parameter degeneracy for velocity
(red), WMAP3SNLS1 (Green), velocity priors (
blue)
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Forecast for ACT(400 sq deg and Mmin 1014 Msun )

• Marginalised over ns (1.5 WMAP3) and h (8 HST
  Key project, Freedman et al 2000).
• PDF
  Mean streaming velocity
• Bhattacharya Kosowsky in prep.

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Conclusion

• s8 can be constrained to 4.5-6.5 accuracy with
  velocity only and 1.3-1.0 accuracy adding priors
  (WMAP 3rd year SNLS 1st year).
• Om can be obtained with 7.5-9.0 accuracy
  (velocity only) and 2.0-6.0 accuracy (priors).
• w can be obtained with 23-35 accuracy
  (velocity) and 4.7-5.0 accuracy ( priors).

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Plot shows velocity statistics is robust against
error in mass measurement.

• Mmin 1014 Msun (red) 1.2X1014 Msun (blue).
• 20 bias in measurement of minimum mass results
  3 change for the case of mean streaming
  velocity and 1 for PDF.

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Comparing with number density of clusters

• Bhattacharya Kosowsky in prep.
  
  (Francis, Bean Kosowsky 2005).
• Plot (right) of Om vs s8 shows a 20 bias in
  mass estimate leads to shift in parameter
  estimation by more than 4- s. Corresponding shift
  (left) in the case of velocity is insignificant.

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Effect of velocity errors on parameter
constraints for the case of PDF

• 
  Om
• 
  
• 
  h
• 
  w
• 
  
• 
  s8
• 
  ns

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Summary

• A future wide area SPT like velocity survey will
  provide competitive probe to various cosmological
  parameters independent of any other observations.
• ACT (400 sq deg) data WMAP3SNLS1 will provide
  5-6 times improvement on current constraints of
  s8 and Om . The constraint on w will be improved
  by 2-3 over existing accuracy.
• Velocity statistics is robust to error in minimum
  mass measurement. This is an advantage over
  number density.
• Will need to worry about other systematic error
  like point sources, relativistic tSZ, lensing,
  primary CMB..