The Galaxy Power Spectrum: 2dFGRS-SDSS Tension

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Galaxy and Mass Power Spectra
Shaun Cole ICC, University of Durham Main
Contributors Ariel Sanchez (Cordoba) Steve
Wilkins (Cambridge)
Imperial College London Outstanding Questions for
the Standard Cosmological Model March 2007
Photograph by Malcolm Crowthers
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Outstanding Question

• Do uncertainties in modelling non-linearity and
  galaxy bias compromise constraints on
  cosmological parameters coming from measurements
  of the galaxy power spectrum?

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Subsidiary Questions

• Do analysis techniques effect the results?
• Do differences in sample selection and
  completeness effect the results?

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Outline

• Motivation for comparing 2dF and SDSS
• Methods for parallel Analysis of 2dFGRS and SDSS
  DR5
• Modelling the selection functions
• (Comparison in the overlap region)
• Comparison of Power Spectra
• Understanding the differences
• Model Fits and Cosmological Parameters
• Conclusions and Future Prospects

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The Shape of 2dF and SDSS P(k) differ on large
scales

• Resulting parameter constraints
• 2dF (Cole et al 2005)
• SDSS (Tegmark et al 2004)

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Combined with CMB
Sanchez et al 2006
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Combined with CMB
Sanchez et al 2006
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Methods

• Use equivalent methods and modelling for both 2dF
  and SDSS so that direct comparisons can be made.

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2dFGRS data and selection function
Data, modelling and methods identical to Cole et
al 2005

• 2dFGRS final data release
• Completeness and magnitude limit masks from Cole
  et al 2005 using methods of Norberg et al 2002
• Selection function modelled via the luminosity
  function

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2dF Random Catalogue
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SDSS data and selection function

• DR5 public data (500k redshifts)
• Completeness and magnitude limit masks retaining
  450k redshifts
• Assign a redshift, magnitude and other properties
  by
• Selecting an object at random from the r17.77
  sample
• Keep/reject according to apparent magnitude limit
  map

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SDSS data and selection function

• DR5 public data (500k redshifts)
• Completeness and magnitude limit masks retaining
  450k redshifts
• Assign a redshift, magnitude and other properties
  by
• Selecting an object at random from the r17.77
  sample
• Keep/reject according to apparent magnitude limit
  map

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SDSS data and selection function

• DR5 public data (500k redshifts)
• Completeness and magnitude limit masks retaining
  450k redshifts
• Assign a redshift, magnitude and other properties
  by
• Selecting an object at random from the r17.77
  sample
• Keep/reject according to apparent magnitude limit
  map

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SDSS Random Catalogue
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SDSS Random Catalogue
Real and random redshift slices ?????
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2dFGRS and SDSS comparison
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2dFGRS and SDSS comparison
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2dF SDSS overlap
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2dF SDSS overlap
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Power Spectrum Estimation

• Weight galaxies as in Cole et al 2005 using PVP
  method
• Assign galaxies onto a grid and use FFTs
• Determine the spherically averaged power in bins
  of log(k)

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Optimum Weighting
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Optimum weight with bias
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Optimum weight with bias

• (Percival, Verde Peacock 2004)

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Adopted Colour and Luminosity dependent bias
relations
Convert SDSS magnitudes to 2dF bands and then
apply simple k-correction from Cole et al 2005
Split at restframe colour of 1.07 and adopt the
bias relations
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Determining Statistical Errors

• Log-Normal Random catalogues
• Realizations of random fields with log-normal
  density distributions, luminosity dependent
  clustering and realistic P(k).
• Used to determine statistical errors
• Used to test ability to recover input P(k)

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• Power Spectrum from 1000 LN mocks compared to the
  input P(k) convolved with the window function

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Window Function
The window function is computed directly from
the random catalogue and the spherically averaged
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• 2dF and SDSS P(k)
• Full samples
• Differing window functions
• Good match at high k

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• 2dF and SDSS P(k)
• Full samples
• Deconvolved
• Good match at high k
• Less large scale power in SDSS?
• Robust to selection cuts, mask details,
  incompleteness corrections

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2dF and SDSS P(k) Full samples Deconvolved Go
od match at high k Less large scale power in
SDSS? Robust to selection cuts, mask details,
incompleteness corrections Very similar P(k)
from Tegmark et al (2006)
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Parameter Constraints Direct comparison
of 2dFGRS and SDSS
Tegmark et al 2004
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Parameter Constraints Direct comparison
of 2dFGRS and SDSS But SDSS are red and 2dF
blue selected
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• All galaxies

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• Blue Galaxies

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• Red galaxies

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• Power Spectra of the red and blue galaxies in the
  same volume of space
• The errors on the ratio take account of the
  correlation this induces
• To first order they have a very similar shape and
  only differ in amplitude
• Only the shape differences on small scales are
  statistically significant

Cole et al 2005
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• 2dF and SDSS P(k)
• Red galaxies
• Deconvolved

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Evolution of the mass power spectrum
z0
non-linear evolution
z1
z2
z3
linear growth
z4
z0
z5
z1
large scale power is lost as fluctuations move to
smaller scales
z2
z3
z4
z5
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Non-linearity, scale dependent bias and redshift
space distortions Angulo et al 2007
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Non-linearity, scale dependent bias and redshift
space distortions Tegmark et al 2006
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• Model P(k)

Red galaxies are more strongly clustered and have
a larger value of Q. Our assumed linear bias
matches the amplitude around k0.1 h/Mpc
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Parameter Constraints Red galaxies only
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Conclusions I

• 2dFGRS and SDSS DR5 galaxy power spectra differ
  in shape at the 2 to 2.5s level.
• This is due to scale dependent bias which is
  largest for red (and more luminous) galaxies.
• It is an even larger effect for the SDSS LRG
  survey.
• A simple empirical model of the distortion
  appears to be robust.
• When marginalized over the distortion parameter
  Q, 2dFGRS, SDSS and SDSS-LRG constraints agree
  within the statistical noise.

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Conclusions II

• Galaxy surveys give robust constraints on the
  linear mass power spectrum
• Important for constraining the parameters of the
  standard model
• More important still for constraining
  non-standard models