The cross-correlation between CMB and 21-cm fluctuations during the epoch of reionization Hiroyuki Tashiro N. Aghanim (IAS, Paris-sud Univ.) M. Langer (IAS, Paris-sud Univ.) M. Douspis (IAS, Paris-sud Univ.) S. Zaroubi (Uuiv. of Groningen) V. Jelic (Uuiv. of Groningen) In the collaboration with Based on arXiv: (IAS, Paris-sud Univ.)

Out Line 1, signal from the epoch of reionization 21 cm fluctuations CMB temperature fluctuations CMB polarization 2, 21 cm-CMB cross-correlation 3, detectability of the 21cm-CMB cross-correlation 4, summary 21 cm – CMB temperature cross-correlation 21 cm – CMB polarization cross-correlation

Stars, galaxies, galaxy clusters Density fluctuations Reionisation : a significant milestone in the history of the structure formation Epoch of Reionization Question of the reionization : When and how did reionization occur ? What source caused reionization?

Stars, galaxies, galaxy clusters Density fluctuations Reionisation : a significant milestone in the history of the structure formation Epoch of Reionization High-z galaxies etc… CMB temperature anisotropies, polarization Ly-alpha, 21 cm fluctuations Methods for probing reionization

Stars, galaxies, galaxy clusters Density fluctuations Reionisation : a significant milestone in the history of the structure formation Epoch of Reionization High-z galaxies etc… CMB temperature anisotropies, polarization Ly-alpha, 21 cm fluctuations Methods for probing reionization

21cm transition : hyper fine structure of neutral hydrogen 21 cm fluctuations Line emission : Neutral hydrogen at z 21 cm fluctuations : sensitive to the neutral hydrogen

21 cm lines fluctuations The brightness temperature of the 21 cm lines (during the reionization epoch) The 21 cm line fluctuations depend on the fluctuations of the ionized fraction and the baryon density, and

Doppler effect velocity the temperature anisotropies during the reionisation CMB temperature anisotropy during reionisation Gravitational potential Free electron CMB photon redshifted (blueshifted) CMB ： optical depth of Thomson scattering,

E-mode polarisation Thomson scattering + quadrupole in CMB temperature anisotropies produce the CMB polarisation E-mode polarisation depends on initial gravitational potential Expression of E-mode polarisation Source term : QuadrupoleTransfer function of CMB temp. quadrupole

Cross-correlation between 21 cm lines and CMB 21 cm lines : neutral hydrogen CMB anisotropy during reionisation Temperature anisotropy : Doppler effect Ionized fraction, density fluctuations Polarisation anisotropy : Thomson scattering Ionized fraction, quadrupole component of CMB temp. They are different direct and complementary probes of reionisation The cross-correlations will provide even more information than their respective auto-correlations We focus on the cross-correlation in the linear order ( large scales ).

: specified by the cosmological model : specified by the reionisation model Angular power spectrum of cross-correlation 21cm line CMB Alvarez et al. (2006) Continuity eq. 21 cm line - CMB temp. cross-correlation : growth rate of baryon power spectrum

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 main assumptions Cross power spectrum Alvarez et al. (2006) : growth rate of matter power spectrum: average bias Evolution of average ionised fraction : reionisation epoch : reionisation duration > : minimum mass of sources

Angular power spectrum of the cross-correlation Spectrum shape reflects baryon density fluctuations The amplitude depends on the duration of reionisation The longer the reionisation lasts, the lower the amplitude becomes.

CMB temp. : electron density 21 cm fluctuation : HI density Angular power spectrum of the cross-correlation Alvarez et al. (2006) z_re=15 z_re=12 is the redshift, when If, the amplitude reaches to maximum The evolution of the peak amplitude Multi frequency 21cm observations

The angular power spectrum of the cross-correlation Angular power spectrum of the cross-correlation between 21 cm fluctuations and E-mode polarisation

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. H.T et al. 2008

Angular power spectrum of the cross-correlation The evolution of first peak Multi frequency observations E-mode polarisation : electron density 21 cm fluctuation : HI density is the redshift, when If, the amplitude reaches to maximum H.T et al. 2008

LOFAR: Netherlands SKA: ??? MWA: Australia Ongoing 21cm projects Detectability of the cross-correlation CMB observation Planck

Signal to Noise ratio analysis We neglect the foreground noise noise power spectrum of 21 cm fluctuations noise power spectrum of CMB anisotropy Primordial CMB + Noise power spectrum of Planck Observablity of the cross-correlation signal Experimental noise dominates

21 cm line - CMB temp. cross-correlation Signal to Noise ratio analysis

(Bowman et al. 2006) (Jelic et al. 2006) ( Experimental noise power spectrum of 21 cm fluctuations 21 cm line - CMB temp. cross-correlation

Signal to Noise ratio analysis

21 cm line - CMB E-mode cross-correlation SN ratio is not sensitive to the duration of the reionisation

21 cm line - CMB E-mode cross-correlation Noise : “super SKA” The 21-cm and E-mode cross-correlation signal with the estimated errors. z_obs=10, z_ re=10. but CMB noise (primordial E-mode component) is large on theses scales Long duration causes the suppression on the small scales,

21 cm line - CMB E-mode cross-correlation Tashiro et al SN ratio is not sensitive to the duration of the reionisation

Summary We investigated the detectability of the 21cm-CMB cross-correlation by the signal-to-noise analysis. The 21 cm-CMB temp. cross-correlation is sensitive to the reionization duration. Therefore the SN ratio depends on the reionization duration. If the reionisation process is instantaneous, LOFAR can detect the cross-correlation signal between CMB temp. and 21 cm fluctuations with S/N=1. The detection of the 21 cm-Emode cross-correlation is difficult. The noise from the primordial E-mode polarization is dominant on small scales. Therefore, the 21cm-Emode cross-correlation is insensitive to the reionization duration.