Separating the kinetic Sunyaev-Zel'dovich effect from primary cosmic microwave \nbackground fluctuations

In the present work, we propose a new method aiming at extracting the kinetic Sunyaev-Zel'dovich (KSZ) temperature fluctuations embedded in the primary anisotropies of the cosmic microwave background (CMB). We base our study on simulated maps without noise and we consider very simple and minimal assumptions. Our method essentially takes benefit from the spatial correlation between KSZ and the Compton parameter distribution associated with the thermal Sunyaev-Zel'dovich (TSZ) effect of the galaxy clusters; the latter can be obtained by means of multi-frequency based component separation techniques. We reconstruct the KSZ signal by interpolating the CMB fluctuations without making any hypothesis other than that the CMB fluctuations are Gaussian distributed. We present two ways of estimating the KSZ fluctuations, after the interpolation step. In the first, we use a blind technique based on canonical Principal Component Analysis, while the second uses a minimisation criterion based on the fact that KSZ dominates at small angular scales and that it follows a non-Gaussian distribution. Using the correlation between the input and reconstructed KSZ map we show that the latter can be reconstructed in a very satisfactory manner (average correlation coefficient between 0.62 and 0.90), furthermore both the retrieved KSZ power spectrum and temperature fluctuation distribution are in quite good agreement with the original signal. The ratio between the input and reconstructed power spectrum is indeed very close to one up to a multipole in the best case. The method presented here can be considered as a promising starting point to identify in CMB observations the temperature fluctuation associated with the KSZ effect.