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

Combined with CMB

Sanchez et al 2006

Combined with CMB

2hbb 2hdmdm

Sanchez et al 2006

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

2dF Random Catalogue

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

)/exp( bc

g zzzdz

dn

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 Random Catalogue

SDSS Random Catalogue

Real and random redshift slices ?????

2dFGRS and SDSS comparison

2dFGRS and SDSS comparison

2dF SDSS overlap

2dF SDSS overlap

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

Differing window functions

Good match at high 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

• All galaxies

• Blue Galaxies

• Red galaxies

• 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

2dF and SDSS P(k)

Red galaxies

“Deconvolved”

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

Non-linearity, scale dependent bias and redshift space distortions

Angulo et al 2007

Non-linearity, scale dependent bias and redshift space distortions

Tegmark et al

2006

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

Parameter Parameter ConstraintsConstraints

Red galaxies Red galaxies onlyonly

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.

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