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
Outstanding Question:
Do uncertainties in modelling non-linearity and galaxy bias compromise constraints on cosmological parameters coming from measurements of the galaxy power spectrum?
Subsidiary Questions:
Do analysis techniques effect the results?
Do differences in sample selection and completeness effect the results?
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
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)
046.0185.0/
016.0168.0
mb
m
h
17.0/
023.0213.0
mb hm
Methods
• Use equivalent methods and modelling for both 2dF and SDSS so that direct comparisons can be made.
2dFGRS data and selection function
• 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
Data, modelling and methods Data, modelling and methods identical to Cole et al 2005identical to Cole et al 2005
SDSS data and selection function
• DR5 public data (500k redshifts)DR5 public data (500k redshifts)• Completeness and magnitude limit masks Completeness and magnitude limit masks
retaining 450k redshiftsretaining 450k redshifts
• Assign a redshift, magnitude and other Assign a redshift, magnitude and other properties byproperties by1.1.Selecting an object at random from the Selecting an object at random from the
r=17.77 sampler=17.77 sample2.2.Keep/reject according to apparent Keep/reject according to apparent
magnitude limit mapmagnitude limit map
SDSS data and selection function
• DR5 public data (500k redshifts)DR5 public data (500k redshifts)• Completeness and magnitude limit masks Completeness and magnitude limit masks
retaining 450k redshiftsretaining 450k redshifts
• Assign a redshift, magnitude and other Assign a redshift, magnitude and other properties byproperties by1.1.Selecting an object at random from the Selecting an object at random from the
r=17.77 sampler=17.77 sample2.2.Keep/reject according to apparent Keep/reject according to apparent
magnitude limit mapmagnitude limit map
SDSS data and selection function
• DR5 public data (500k redshifts)DR5 public data (500k redshifts)• Completeness and magnitude limit masks Completeness and magnitude limit masks
retaining 450k redshiftsretaining 450k redshifts
• Assign a redshift, magnitude and other Assign a redshift, magnitude and other properties byproperties by1.1.Selecting an object at random from the Selecting an object at random from the
r=17.77 sampler=17.77 sample2.2.Keep/reject according to apparent Keep/reject according to apparent
magnitude limit mapmagnitude limit map
Power Spectrum Estimation
g
gg
k
2
of TransformFourier theis where
)(
kkP
• 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)
Adopted Colour and Luminosity dependent bias relations
13.0
)(13.015.0J
gr
rggb
F
Convert SDSS magnitudes to 2dF Convert SDSS magnitudes to 2dF bands and then apply simple k-bands and then apply simple k-correction from Cole et al 2005correction from Cole et al 2005
Split at restframe colour of 1.07 and adopt the bias relations:Split at restframe colour of 1.07 and adopt the bias relations:
blue)/15.085.0(9.0
red)/15.085.0(3.1
*
*
LLb
LLb
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)
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
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
Very similar P(k) from Tegmark et al (2006)
Parameter Parameter ConstraintsConstraints
Direct Direct comparison comparison ofof2dFGRS and2dFGRS andSDSS SDSS
Tegmark et al 2004Tegmark et al 2004
Parameter Parameter ConstraintsConstraints
Direct Direct comparison comparison ofof2dFGRS and2dFGRS andSDSS SDSS
But SDSS But SDSS are red and are red and 2dF blue 2dF blue selectedselected
• 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 2005Cole et al 2005
Evolution of the mass power spectrum
z=0
z=1
z=2z=3z=4z=5
lineargrowth
non-linearevolution
z=0
z=1
z=2z=3z=4z=5
large scale poweris lost as fluctuationsmove to smaller scales
Model P(k)
Red Red galaxies galaxies are more are more strongly strongly clustered clustered and have a and have a larger larger value of Q.value of Q.
Our Our assumed assumed linear bias linear bias matches matches the the amplitude amplitude around around k=0.1 k=0.1 h/Mpch/Mpc
Conclusions I
• 2dFGRS and SDSS DR5 galaxy power spectra differ in shape at the 2 to 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.