ner_tags: O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: could introduce spurious velocities along the line of sight. In order to test this methodology, we use the GALAXY mock catalogue, in two different scenarios. The first scenario is an ideal one, with no mask or selection function: we apply the three approaches on a box populated with our mock catalogue, and compare the recovered radial velocities with the real ones provided by the catalogue. When performing this comparison, we evaluate a 3D grid for the original galaxy radial velocity by assigning to each cell the radial velocity of the galaxy falling nearest to the cell centre, that is, we adopt a nearest particle (NP) method. For different radial bins of the wavevector, we evaluate the correlation coefficient () computed from the cross-power spectrum between the recovered and the original radial velocity fields and their respective auto-spectra: In this expression, stands for , that is, the radially averaged power spectrum of the line of sight velocity modes. The superscripts stand for “original” and “recovered” components, respectively, and the asterisk denotes the complex conjugate operation. Fig. 3 Correlation coefficient of the recovered line-of-sight velocities with the actual ones in our GALAXY mock catalogue. Solid, dotted, and dashed lines refer to the LINEAR, LOG-LINEAR, and LOG-2LPT approaches, respectively. The red lines consider the ideal scenario without any sky mask or selection function, while the black ones are for the same sky mask and selection function present in the real CGC. In Fig. 3 the red lines display the correlation coefficients for the ideal scenario. Solid, dotted, and dashed lines refer to the LINEAR, LOG-LINEAR, and LOG-2LPT approaches, respectively. On large scales (low modes), the three approaches provide correlation coefficients that are very close to unity, while they seem to lose information on small scales in the same way. We note that a direct comparison to the results of K12 is not possible, since, in our case, we do not use the full dark matter particle catalogue, but only a central halo one. After the real mask and selection function obtained from the CGC is applied to the GALAXY mock catalogue, then the recovery of the peculiar velocities from the three adopted approaches worsens considerably. The black lines in Fig. 3 display, in general, much lower correlation levels than the red ones. The LINEAR approach seems to be the one that retains most information on the largest scales, and it out-performs the LOG-LINEAR and the LOG-2LPT methods on all scales. We hence expect the LINEAR approach to be more sensitive to the kSZ effect than the other two methods, particularly on the largest scales. Once the velocity inversion from the CGC density contrast has been performed, we compute the spatial correlation function between the recovered velocities and the kSZ temperature anisotropies, where is estimated as in Eq. ( 4 ), and the ensemble average is obtained after running through all galaxy pairs lying a