Quadrupole spectrum, baryonic signature in the 2dF QSO sample

Quadrupole spectrum, baryonic signaturein the 2dF QSO sample

Kazuhiro Yamamoto

(Hiroshima Univ.)

K.Y. ApJ 595 577 (03)K.Y. ApJ 605 620 (04)K.Y., Bassett, Nishioka PRL 94 051301 (05)K.Y., Nakamichi, Kamino, Bassett, Nishioka astro-ph/0505

Collaborator B.A. Bassett, Nishioka, Nakamichi, Kamino

Miller, Nichol & Batsuski 　　　　　　ApJ (2001)

Detection of baryon acoustic oscillation ?

Baryon features in matter power　spectrum

Eisenstein, Hu (1998)Meiksin, White, Peacock (1999) c.f. Sugiyama (1995)

Time evolution effect on the statistical quantities

n(z) mean number density b(z) clustering bias D1(z) growth factor

Theoretical template of P(k)

(KY, Nishioka Suto 1999)

Fitting of the power spectrum of the 2dF QSO sample (K.Y. ApJ, 2002,2004)

The 2QZ sample is publicly available at http://www.2dfquasar.org/

High-z sample, Time evolution effect, Geometric distortion effect

Power spectrum analysis by 2QZ group Hoyle et al. (02), Outram et al. (03)

δ(r

ad)

α（rad）p2p

2p

2p−

75°

5°

Angular map of the 2dF quasars (~20000)

The 2QZ survey covers the two area of 5×75 deg2

19156 QSOs

In my analysis, incorporating the masked region, I used

0.2 < z < 2.2

x (1/H0)

Y (1

/H0)

2.2=z0=z

Map of QSOs in the NGC

The Final catalogue: http://www.2dfquasar.org/

Power Spectrum of the 2dF QSOs

Outram et al.

Our work

ΛCDM model,045.0,28.0 =Ω=Ω Bm

contours of the likelihood function

9.0,7.0,1 8 === σhn

045.0=ΩB

2

22

)(

])()([

kP

kPkP thobs

k D−= Âχ

2/2χ−∝ e

,06.0

,27.0

=Ω=Ω

B

m

Peak values

Consistent with other cosmological observations

Constraint on the density parameters

mΩ

m

BΩ

Ω

Finite baryon fraction model better matches the data!

ΛCDM model

1.0

28.0

=Ω=Ω

B

m as w becomes larger

Theoretical curve depends on w (the equation of state parameter of the dark energy)

the equation of state can be measured if thepower spectrum was determined precisely

Constraint on w from QSO power spectrum

mΩ

Contour of the likelihood function

w

9.0,1,7.0

05.0

8 ====Ω

σnhB fixed

The constraint on w isnot very tight.

The shot-noise contribution, the mean number density n=10-6/[h-1Mpc]3

The usefulness of the method when the power spectrum is measured precisely

Redshift-space distortion Independent information Linear Distortion linear velocity field, Bias Finger of God effect random velocity, non-lin. Geometric distortion cosmological expansion (Alcock-Paczynski effect)

Quadrupole spectrum P2(k)

The KAOS/WFMOS promises the precise measurement of P(k)

Concern about Nonlinear effects on the power spectrum Clustering bias can be uncertain factor

‡‡‡=

=,2,0

)(cos)()cos,(l

ll LkPkP θθ

Obs. line of sightθ

)(0 kP )(2 kP

)(4 kP

　　 monopole spectrum quadrupole spectrum

Linear theory

Non-linear model

On small scales, the non-linear effects is important for l ≧２Higher multipoles l≧４ will not be measured even by KAOS

Theoretical prediction for P0 and P2, assuming KAOS like sample around Z~１

(0.5<Z<1.5, n=10-4 h3Mpc-3 , 103deg2)

(KY、Bassett, Nishioka 2005)

Clustering Bias parameterization

ν,,, 110 pbb

Cosmology

marginalize

˜˜¯

ˆÁÁË

Ê˙˚

˘ÍÎ

È+˜

ˆÁÁË

Ê −+= −

ν

11

11

0

1.0

)(1

)(

11),(

1

hMpc

kzDb

zD

bkzb

p

mw Ω,

Feasibility to determine w, focusing on The scale dependence of the bias The nonlinear effects

Fisher matrix analysis wD

Theoretical modeling of P0(k) and P2(k)

(1-sigma error)

1 sigma error of w as function of the baryon density

Linear Nonlinear

Constraint on w is significantly improved by combining P0 and P2 in the case of no baryon density

P0

P2

P0+P2 P0+P2

P0

P2

ΩBΩB

Δｗ Δｗ

P2 is useful in breaking degeneracy between bias and dark energy

Measurement of the quandrupole spectrum in the 2dF QSO sample

K.Y., Nakamichi, Kamino,Bassett, Nishioka (2005)

)(

)(

0

2

kP

kP)(0 kP

Chi2 for P0 and P2 as a function of bias

P0

P2

P0 and P2 give constraints on the bias b0 independently

2

22

)(

])()([

kP

kPkP thobs

k D−= Âχ

Bias parameter

Conclusions

1. The 2dF QSO power spectrum P0(k) better matches the finite baryon fraction model, and the baryon oscillation might be detected.

2. We measured P2(k) in the 2dF QSO sample

3. P2(k) will be measured in the KAOS with high precision

4. P2(k) is sensitive to the nonlinear effects

5. P2(k) becomes useful in the small baryon fraction model This means the importance of the Alcock-Paczynski effect in the region where the baryon oscillation is not distinct