1. 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

2. 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)

3. The 21 cm cross correlations with CMB polarisation from the reionisation epoch 21 cm transitions of HI Absorb 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 { 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)

4. 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

5. 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

6. 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 )

7. 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 >

8. 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.

9. 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

10. 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

11. 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 hydrogen E-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:0802.3893arXiv:0802.3893

12. 21 cm lines fluctuations HI 21 cm transitions Absorb 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 !

14. First peak evolution of the power spectrum