Reionisation and the cross-correlation between the CMB and the 21-cm line fluctuations

Hiroyuki Tashiro

IAS, ORSAY

43rd Rencontres de Moriond La Thuile, Italy

N. Aghanim (IAS, Orsay)M. Langer (IAS, Orsay)M. Douspis (IAS, Orsay)S. Zaroubi (Uuiv. of Groningen)

Based on arXiv:0802.3893

In the collaboration with

Reionisation : When does reionisation start?How does reionisation proceed?

Introduction

We know only two observational constraints

Gunn-Peterson effect : absorption of the from the high redshift quasars

CMB anisotropies : Thomson scattering of CMB photons by electrons during reionisation

Redshifted 21 cm line fluctuations one of most promising probing methods for reionisation

Optical depth (WMAP 5 year data)

Neutral hydrogen fraction

To obtain new constraints

(Fan et al, 2006)

The 21 cm cross correlations with CMB polarisation from the reionisation epoch

21 cm transitions of HIAbsorb 21 cm line from CMB

Emit 21 cm line to CMB

Produce fluctuations of CMB brightness temperature

Line emission : redshifted by the cosmological expansion

Multi frequency observations allow us to obtain redshift slices of Universe

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In this talk,

Observation projects : LOFAR, MWA, SKA

CMB Doppler effect Alvarez et al. (2006)

Kinematic Sunyaev-Zeldvich effect

The cross-correlation with CMB temperatures

Salvaterra et al. (2005)

21 cm lines fluctuations

Linear expression of the fluctuations (during the reionisation epoch)

In order to obtain the cross correlations, we need expression for spherical harmonics coefficients,

The 21 cm line fluctuations depends on and

Expanded on the spherical harmonics

E-mode polarisation

Thomson scattering + quadrupole in CMB temperature anisotropies

produce the CMB polarisation

Primordial density fluctuations E-mode polarisation

E-mode polarisation depends on initial gravitational potential

Expression for the spherical harmonics

Source term :

Quadrupole

The angular power spectrum of the cross-correlation

: specified by the cosmological model (

: specified by the reionisation model

From of E-mode polarisation and 21 cm lines,we can obtain the cross-correlation

)

Toy model of reionisation

• Ionised fraction is related to the ratio of ionising photons per hydrogen

•ionising photons comes from collapsed objects ( T_vir > 10^4 )

To obtain , we make two assumptions

Cross power spectrum

Alvarez et al. (2006)

: Transfer function of matter : average bias

Evolution of average ionised fraction

: reionisation epoch

: reionisation duration

>

Angular power spectrum of the cross-correlation

If reionisation has the long duration,quadrupole components during reionisation are superposed.

damping of the oscillations on small scales

•Spectrum shape reflects the quadrupole of CMB

1-st peak position

The angular separation scale of the quadrupole component

• The duration of reionisation induces

The longer it lasts, the more oscillations are damped.

Angular power spectrum of the cross-correlation

The dependence on the reionisation epoch

The evolution of first peak

Multi frequency observations

E-mode polarisation : electron density

21 cm fluctuation : HI density

The shapes of power spectrum does not strongly depend on the reionisation epoch

is the redshift, when

If

,the amplitude reaches to maximum

Angular power spectrum of the cross-correlation

Double reionisation model

The number of peaks in the first peak evolution is

the number of crossings of the 0.5 level of the ionised fraction

Summary

The cross-correlation between 21 cm lines and E-mode polarisation

• Shape of the power spectrum : the quadrupole component of CMB temperature anisotropies

The first peak position gives the scale of the quadrupole

21 cm lines : neutral hydrogenE-mode polarisation : the optical depth

• Damping on small scales : signature of the duration of reionisation

The detection or no detection of the signal gives constraints on the duration

• first peak evolution : the signal reaches its maximum when x_e=0.5

We can follow the redshift evolution of ionisation fraction

For details, see arXiv:0802.3893

21 cm lines fluctuations

HI 21 cm transitionsAbsorb 21 cm lines from CMB

Emit 21 cm lines to CMB

Produce the fluctuations of CMB brightness temperature !

The cosmological redshift : 21 line is redshiftd

Liner expression of the fluctuations (during the reionisation epoch)

Observing the 21/(1+z) lines, we obtain the redshift slice of Universe !

First peak evolution of the power spectrum