The crosscorrelation between CMB and 21 cm fluctuations

The cross-correlation between CMB and 21 -cm fluctuations during the epoch of reionization Hiroyuki Tashiro (IAS, Paris-sud Univ. ) In the collaboration with N. Aghanim M. Langer M. Douspis S. Zaroubi V. Jelic (IAS, Paris-sud Univ. ) (Uuiv. of Groningen) Based on ar. Xiv: 0908. 1632

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

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

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

21 cm fluctuations 21 cm transition : hyper fine structure of neutral hydrogen 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

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

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

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 ).

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

$Toy model of reionisation Evolution of average ionised fraction : reionisation epoch : reionisation$

Toy model of reionisation Evolution of average ionised fraction : reionisation epoch : reionisation duration To obtain 　, we make two main assumptions • ionising photons comes from collapsed objects ( T_vir>> 10^4 ) • Ionised fraction is related to the ratio of ionising photons per hydrogen Cross power spectrum Alvarez et al. (2006) : growth rate of matter power spectrum : average bias : 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.

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

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 H. T et al. 2008 • Spectrum shape reflects the quadrupole of CMB 1 -st peak position The angular separation scale of the quadrupole component • The duration of reionisation induces damping of the oscillations on small scales If reionisation has the long duration, quadrupole components during reionisation are superposed. The longer it lasts, the more oscillations are damped.

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

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

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

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

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

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. Long duration causes the suppression on the small scales, but CMB noise (primordial E-mode component) is large on theses scales

21 cm line - CMB E-mode cross-correlation Tashiro et al. 2009 SN ratio is not sensitive to the duration of the reionisation

Summary • We investigated the detectability of the 21 cm-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 21 cm-Emode cross-correlation is insensitive to the reionization duration.