Cosmology with the 6dF Galaxy Survey UCT/ICRAR/APERTIF workshop, - - PowerPoint PPT Presentation

The 6dF survey Correlation function 6dfGS → WALLABY

Cosmology with the 6dF Galaxy Survey

UCT/ICRAR/APERTIF workshop, South Africa, May 2010 Florian Beutler

PhD supervisors: Peter Quinn, Lister Staveley-Smith Chris Blake, Heath Jones

04.05.2010 International Centre for Radio Astronomy Research

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 1

The 6dF survey Correlation function 6dfGS → WALLABY

Outline

Program for the next 20min. The 6dF Galaxy Survey.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 2

The 6dF survey Correlation function 6dfGS → WALLABY

Outline

Program for the next 20min. The 6dF Galaxy Survey. The two point correlation function.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 2

The 6dF survey Correlation function 6dfGS → WALLABY

Outline

Program for the next 20min. The 6dF Galaxy Survey. The two point correlation function. Redshift space distortions.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 2

The 6dF survey Correlation function 6dfGS → WALLABY

Outline

Program for the next 20min. The 6dF Galaxy Survey. The two point correlation function. Redshift space distortions. Estimate of Ωm.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 2

The 6dF survey Correlation function 6dfGS → WALLABY

Outline

Program for the next 20min. The 6dF Galaxy Survey. The two point correlation function. Redshift space distortions. Estimate of Ωm. Testing General Relativity.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 2

The 6dF survey Correlation function 6dfGS → WALLABY

Outline

Program for the next 20min. The 6dF Galaxy Survey. The two point correlation function. Redshift space distortions. Estimate of Ωm. Testing General Relativity. Predictions for WALLABY using 6dFGS.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 2

The 6dF survey Correlation function 6dfGS → WALLABY

What is 6dFGS?

Spectroscopic survey of southern sky (17,000 deg2). Primary sample from 2MASS with Ktot < 12.75; also secondary samples with H < 13.0, J < 13.75, r < 15.6, b < 16.75. Median redshift 0.05 (≈ 150 Mpc). Effective volume ≈ 2x107h−3Mpc3. 125.000 redshifts (137.000 spectra).

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 3

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

The correlation function

What is a correlation function? dP = n2(1 + ξ(r12))dV1dV2 → A correlation function measures the degree of (galaxy) clustering on different scales.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 4

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

The correlation function

What is a correlation function? dP = n2(1 + ξ(r12))dV1dV2 → A correlation function measures the degree of (galaxy) clustering on different scales. How do we measure that?

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 4

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

The correlation function

What is a correlation function? dP = n2(1 + ξ(r12))dV1dV2 → A correlation function measures the degree of (galaxy) clustering on different scales. How do we measure that?

1 Create a mock catalogue: Random distribution of galaxies without any

clustering.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 4

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

Two point correlation function

What is a correlation function? dP = n2(1 + ξ(r12))dV1dV2 A correlation function measures the degree of clustering on different scales. How do we measure that?

1 Create a mock catalogue: Random distribution of galaxies without any

clustering.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 7

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

Two point correlation function

What is a correlation function? dP = n2(1 + ξ(r12))dV1dV2 A correlation function measures the degree of clustering on different scales. How do we measure that?

1 Create a mock catalogue: Random distribution of galaxies without any

clustering.

2 Measure the distance between all galaxy pairs in your survey.

→ DD(s) and RR(s)

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 7

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

Two point correlation function

What is a correlation function? dP = n2(1 + ξ(r12))dV1dV2 A correlation function measures the degree of clustering on different scales. How do we measure that?

1 Create a mock catalogue: Random distribution of galaxies without any

clustering.

2 Measure the distance between all galaxy pairs in your survey.

→ DD(s) and RR(s)

3 The correlation function can be calculated via

ξ(s) = DD(s) RR(s) − 1 (In my analysis I used the Landy & Salay estimator)

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 7

6dF correlation function

Mpc]

• 1

s [h

• 1

10 1 10 (s) ξ

• 2

10

• 1

10 1 10

2

10

6dF 2D correlation function

Redshift space distortions

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

6dF 2D correlation function

Why is that interesting?

• 1. All redshift space distortions originate from gravitational interaction.

With more mass in the Universe we expect more distortions.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 11

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

6dF 2D correlation function

Why is that interesting?

• 1. All redshift space distortions originate from gravitational interaction.

With more mass in the Universe we expect more distortions. → We can measure the total mass in the Universe Ωm.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 11

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

6dF 2D correlation function

Why is that interesting?

• 1. All redshift space distortions originate from gravitational interaction.

With more mass in the Universe we expect more distortions. → We can measure the total mass in the Universe Ωm.

• 2. With a known Ωm General Relativity predicts how much distortion we

have to expect.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 11

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

6dF 2D correlation function

Why is that interesting?

• 1. All redshift space distortions originate from gravitational interaction.

With more mass in the Universe we expect more distortions. → We can measure the total mass in the Universe Ωm.

• 2. With a known Ωm General Relativity predicts how much distortion we

have to expect. → We can test General Relativity and alternative theories (DGP).

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 11

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

6dF 2D correlation function

Why is that interesting?

• 1. All redshift space distortions originate from gravitational interaction.

With more mass in the Universe we expect more distortions. → We can measure the total mass in the Universe Ωm.

• 2. With a known Ωm General Relativity predicts how much distortion we

have to expect. → We can test General Relativity and alternative theories (DGP). f (z) = βb = Ωγ

m(z)

⇒ Ωm = 0.33 ± 0.054 f = growth rate, b ≈ 1.22, Ωm = ρm

ρ0

Theoretical predictions for γ: ΛCDM: γ = 0.55 DGP: γ = 0.69

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 11

6dF 2D correlation function

Mpc]

• 1

[h

p

r

• 30
• 20
• 10

10 20 30 Mpc]

• 1

[h π

• 30
• 20
• 10

10 20 30

• 1

10 1 10

Model free parameters: β, σv, r0, γ

6dF 2D correlation function

β = 0.44 ± 0.04, σv = 586 ± 51, r0 = 6.01 ± 0.09, γ = 1.75 ± 0.03

6dF 2D correlation function

β = 0.44 ± 0.04, σv = 586 ± 51, r0 = 6.01 ± 0.09, γ = 1.75 ± 0.03

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

6dF 2D correlation function

Why is that interesting?

• 1. All redshift space distortions originate from gravitational interaction.

With more mass in the Universe we expect more distortions. → We can measure the total mass in the Universe Ωm.

• 2. With a known Ωm General Relativity predicts how much distortion we

have to expect. → We can test General Relativity and alternative theories (DGP). f (z) = βb = Ωγ

m(z)

⇒ Ωm = 0.33 ± 0.054 f = growth rate, b ≈ 1.22, Ωm = ρm

ρ0

Theoretical predictions for γ: ΛCDM: γ = 0.55 DGP: γ = 0.69

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 15

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

6dF 2D correlation function

Why is that interesting?

• 1. All redshift space distortions originate from gravitational interaction.

With more mass in the Universe we expect more distortions. → We can measure the total mass in the Universe Ωm.

• 2. With a known Ωm General Relativity predicts how much distortion we

have to expect. → We can test General Relativity and alternative theories (DGP). f (z) = βb = Ωγ

m(z)

⇒ Ωm = 0.33 ± 0.054 f = growth rate, b ≈ 1.22, Ωm = ρm

ρ0

Theoretical predictions for γ: ΛCDM: γ = 0.55 DGP: γ = 0.69

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 16

The 6dF survey Correlation function 6dfGS → WALLABY Redshift space distortions

6dF 2D correlation function

Why is that interesting?

• 1. All redshift space distortions originate from gravitational interaction.

With more mass in the Universe we expect more distortions. → We can measure the total mass in the Universe Ωm.

• 2. With a known Ωm General Relativity predicts how much distortion we

have to expect. → We can test General Relativity and alternative theories (DGP). f (z) = βb = Ωγ

m(z)

⇒ Ωm = 0.33 ± 0.054 f = growth rate, b ≈ 1.22, Ωm = ρm

ρ0

Theoretical predictions for γ: ΛCDM: γ = 0.55 DGP: γ = 0.69

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 17

Testing general relativity

redshift z 0.2 0.4 0.6 0.8 1 (z)

8

σ f(z) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 = 0.27)

m

Ω = 0.8,

8

σ CDM ( Λ = 0.27)

m

Ω = 0.62,

8

σ DGP (

ΛCDM : γ = 0.51 ± 0.1 (predicted γ = 0.55) DGP : γ = 0.31 ± 0.1 (predicted γ = 0.69)

Testing general relativity

redshift z 0.2 0.4 0.6 0.8 1 (z)

8

σ f(z) 0.2 0.3 0.4 0.5 0.6 0.7 0.8

2dF SDSS+LRG VVDS WiggleZ

= 0.27)

m

Ω = 0.8,

8

σ CDM ( Λ = 0.27)

m

Ω = 0.62,

8

σ DGP (

ΛCDM : γ = 0.51 ± 0.1 (predicted γ = 0.55) DGP : γ = 0.31 ± 0.1 (predicted γ = 0.69)

Testing general relativity

redshift z 0.2 0.4 0.6 0.8 1 (z)

8

σ f(z) 0.2 0.3 0.4 0.5 0.6 0.7 0.8

2dF SDSS+LRG VVDS WiggleZ 6dF

= 0.27)

m

Ω = 0.8,

8

σ CDM ( Λ = 0.27)

m

Ω = 0.62,

8

σ DGP (

Testing general relativity

redshift z 0.2 0.4 0.6 0.8 1 (z)

8

σ f(z) 0.2 0.3 0.4 0.5 0.6 0.7 0.8

2dF SDSS+LRG VVDS WiggleZ 6dF

= 0.27)

m

Ω = 0.8,

8

σ CDM ( Λ = 0.27)

m

Ω = 0.62,

8

σ DGP (

ΛCDM : γ = 0.51 ± 0.1 (predicted γ = 0.55) DGP : γ = 0.31 ± 0.1 (predicted γ = 0.69)

The 6dF survey Correlation function 6dfGS → WALLABY BAO signal

What can we learn about WALLABY using 6dFGS?

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 21

Compare 6dfGS with WALLABY

z 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 z = 0.001) ∆ number ( 1000 2000 3000 4000 5000 6000 7000 8000 9000

WALLABY 6dFGS

The 6dF survey Correlation function 6dfGS → WALLABY BAO signal

Correlation function error

Jack-knife and Poisson error: σjk(s) =

• (N − 1)

N

N

• k=1

(ξk(s) − ξ(s))2 σPoisson(s) = 1 + ξ(s)

• DD(s)

with the mean value of ξ ξ(s) =

N

• k=1

ξk(s)/N

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 23

Correlation function error

Mpc]

• 1

s [h

• 1

10 1 10

2

10 )

ii

(= C

i

σ

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1 10

jack-knife error Poisson error

BAO peak in the correlation function

Mpc]

• 1

s [h 20 40 60 80 100 120 140 160 180 (s) ξ

• 0.02
• 0.01

0.01 0.02 0.03 0.04 0.05

The 6dF survey Correlation function 6dfGS → WALLABY BAO signal

Conclusion

Gravitational evolution introduces distortion in the redshift space correlation function (redshift-space distortions). Redshift space distortions allow an estimate of Ωm. Redshift space distortions allow to test theories of gravity. Since 6dF and WALLABY are both cosmic variance limited at large scales the BAO detections will have a comparable S/N.

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 26

The 6dF survey Correlation function 6dfGS → WALLABY BAO signal

Conclusion

Gravitational evolution introduces distortion in the redshift space correlation function (redshift-space distortions). Redshift space distortions allow an estimate of Ωm. Redshift space distortions allow to test theories of gravity. Since 6dF and WALLABY are both cosmic variance limited at large scales the BAO detections will have a comparable S/N.

Thank you

Florian Beutler Cosmology with the 6dF Galaxy Survey 04.05.2010 26