1

Landau Damping of Baryonic Structure Formation in the

Post Reionization Epoch

Feng-Yin Chang

Arxiv:1006.5777

Leung Center for

Cosmology and Particle Astrophysics (LeCosPA) ,

National Taiwan University

COSMO/CosPA 2010 , Tokyo

2

Reionization

6ionz

plasma neutral gas plasma

KTion4102~

( from WMAP7)2.15.10

from QSO spectrum Becker,et al (2001)

Larson, et al (2010)

Bolton, et al (2010)

3

Previous Studies• Effects of reionization on intergalactic medium (IGM) an

d low-mass galaxies were studied by many researches.

• In 1986, Rees and Ikeuchi independently pointed out the increasing of gas temperature during reionization could suppress the formation of small galaxies with mass less then Jeans mass.

• Gnedin (2000) proposed the filtering scale as the characteristic scale for the baryonic fluctuation, instead of Jeans scale, for linear and nonlinear regimes.

• Chen and Lai (2007) first consider the plasma collective effects on the baryonic structure formation, but their calculation is incomplete.

P,Chen& KC La,i PRL(2007)

Gnedin, ApJ (2000)

Rees, MNRAS (1986) Ikeuchi AP&SS(2986)

4

Why Plasma Effects?

GyrHckmD ~/][10~ 02

110~ 181730

DD nN 110~ 17 p

Three Plasma Criteria:

Plasma collective effects:

plasma wave, Landau damping, instabilities….

5

Plasma Waves

i

eeii

M

kTkTV

eeBee Tke 222 3 thp kv

6

Linear Fluid Equations

)(42

)(42

22

2

bkbdkdbksbkbk

bkbdkddkdk

ffGca

kH

ffGH

p

Bs m

Tkc

3

5

3/5

2

p

Bs

ie

m

Tkc

~3

5~

3/5,1

2

ionized gases plasma

JJ kk /~

13.1/~

For2,24.0 HeZY

mean molecular weight

7

Landau Damping

be TT

F.Chen

4.0~r

i

0.4 of one oscillation period the ion acoustic wave would be Landau-damped to e-fold of its initial amplitude.

The nonlinear empirical formula

8

Solution of Baryon Fluctuation

ionJionion a

a

k

k

,~, 10

TTb

1,0 db ffFor simplicity,

2

4/2

4/1

4/5

1

1)24/1,(

QQ

dk

bk AA

2ln)4/(

1

1),()24/1,(

iq

dk

bk be ri

damping

where

,124,241 22 qQoscillation part

ln

4cosln

4sin5

),( 4/5 qq

qbi

2

2

22

2

1 12

5,

12

5

Q

QA

Q

QA

:~Jk const.

Gc

ak

sJ 4~~

9

a

Jf a

a

ak

da

ak 0

2/1

22

'1

)(

'31

)/exp( 22fkk

Results

)/exp( 22fkk

Ionized gas

ionized gas

plasma w LD

plasma w/o LD

For ,7ionz

Gnedin &Hui, MNRAS(1998)

The suppression of modes with intermediate and high k due to Landau damping gives rise to a correction of kf

F.Y.Chang, P.Chen, ArXiv:,1006.5777

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Modified Filtering Scale

2ln1.0

1

1),(ln

1~

~

iq

f

J bek

k

),~/exp(),(/ 22

fdkbk kk

]2,8.0[

F.Y.Chang, P.Chen, ArXiv:,1006.5777

.~~/

~constkk JF

11

Jf kk /~

)~/exp( 22

fkk

ionized gas

plasma

Results

3

3

~//

~

~3

4~

FFFF

F

F

kkMM

ak

M

)(a

)(b The two characteristic wavenumbers for plasma and ionized gas deviate larger in high redshift.

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Landau Damping on Early Evolution

4/5

max)(

iondk

bk

a

ak

The small-scale baryon acoustic oscillations in early post-reionization epoch

can help distinguish the models

plasma

ionized gas

13

Recent measurements

We are hereTegmark et. al, 2002

sunF

F

MM

hMpcOk10

1

10~

,)1(~

KT 410~

We seek for a cosmological survey for small-scale structure formation.

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Summary• The plasma collective effects on baryonic structu

re formation in the post-reionization is considered.

• Two major plasma influences: sound speed and Landau damping.

• The ion acoustic modes were rapidly smoothed out due to the Landau damping.

• The Landau damped spectrum should be characterized by a modified filtering scale.

• Measurement of small-scale baryonic oscillation is essential to learn the nature of the cosmic structure formation.