tokens: where We find that the pairwise kSZ dipole, ξ kSZ, l = 1 , is negative in linear theory. This means that gravitational attraction predicts a slight tendency of any pair of galaxies to be moving towards rather than away from each other at large scales, where we follow the convention that if two galaxies are moving towards each other, their contribution to the pairwise velocity is negative. The linear Kaiser effect from RSDs increases the amplitude of the pairwise kSZ dipole by ∼ 20 per cent for both LOWZ and CMASS at linear regimes. On the other hand, at non-linear small scales RSDs displace galaxies away from each other, and thus, in redshift space the sign of ξ kSZ, l = 1 changes around 10 h −1 Mpc ( k ≃ 0.2 h Mpc −1 ) from negative to positive (Okumura et al. 2014 ; Sugiyama et al. 2016 ; Sugiyama et al. 2017 ). This small-scale effect of RSDs is analogous to the Finger-of-God (FoG) effect but is not the same, because we have shown that this change in sign of ξ kSZ, l = 1 appears even in the Zel'dovich approximation that does not form haloes (Sugiyama et al. 2016 ). Therefore, it could be considered that the change in sign of ξ kSZ, l = 1 is caused by non-linear velocity dispersion effects, part of which is the FoG effect. The latest kSZ measurement using the high-resolution ACT data (De Bernardis et al. 2017 ) clearly shows the expected change in sign of the pairwise velocity at ∼10 h −1 Mpc. Fig. 2 shows the theoretical predictions of the pairwise kSZ dipole and octopole in linear theory (equations 37 and 39 ) for the LOWZ sample ( f σ 8 = 0.392 and b σ 8 = 1.283), where we use the best-fitting value of the optical depth, τ E = 3.95 × 10 −5 , estimated from our kSZ measurement (Section 7.2 ). Since this figure shows the linear theory results that we use in our analysis, the change in sign of ξ kSZ, l = 1 around ∼10 h −1 Mpc does not occur unlike non-linear theories (Okumura et al. 2014 ; Sugiyama et al. 2016 ). As the shape of the pairwise kSZ power spectrum is proportional to P lin ( k )/ k , the amplitude increases at large scales. As the data improves, we will be able to investigate the pairwise kSZ signal at larger scales than ∼200 h −1 Mpc (e.g. De Bernardis et al. 2017 , fig. 3). While the data should show a baryon acoustic peak around ∼100 h −1 Mpc in the linear theory prediction of ξ kSZ, l = 1 (see blue line in the right-hand panel of Fig. 2 ), the peak is significantly broadened by non-linear effects (Sugiyama et al. 2016 ). The octopole, which is generated from the RSD effect and is free of the linear bias, is about 10 times smaller than the dipole. In future kSZ measurements such as Advanced ACTPol and CMB-S4, we will want to measure all of the multipoles up to the octopole. This full measurement will constrain cosmological parameters, especially for the linear growth rate f σ 8 and the Hubble expansion parameter H (Sugiyama et al. 2017 ). However, the data used in this work is too noisy to detect the octopole; therefore, we do
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