Detection of pairwise kinetic Sunyaev-Zel'dovich effect with DESI galaxy groups and Planck in Fourier space

We report a $\sim5.2\sigma$ detection of the kinetic Sunyaev-Zel'dovich (kSZ) effect in Fourier space, by combining the DESI galaxy groups and the Planck data. We use the density-weighted pairwise kSZ power spectrum as the summary statistic, and the detailed procedure of its measurement is presented in this paper. Meanwhile, we analyze the redshift space group density power spectrum to constrain its bias parameters and photo-z uncertainties. These best-fitted parameters are substituted to a nonlinear kSZ model, and we fit the measured kSZ power spectrum with this model to constrain the group optical depth $\bar{\tau}$. Selected by a varying lower mass threshold $M_{\rm th}$, the galaxy group catalogs with different median masses ($\tilde{M}$) are constructed from the DR9 data of the DESI Legacy Imaging Surveys. $\tilde{M}$ spans a wide range of $\sim10^{13}-10^{14}M_\odot/h$ and the heaviest $\tilde{M}\sim10^{14} M_\odot/h$ is larger than those of most other kSZ detections. When the aperture photometric filter radius $\theta_{\rm AP}$ is set to be $4.2$ arcmin, the $\tilde{M}=1.75\times10^{13}M_\odot/h$ group sample at the median redshift $\tilde{z}=0.64$ has the highest kSZ detection ${\rm S/N}=5.2$. By fitting $\bar{\tau}$s from various samples against their $\tilde{M}$s, we obtain a linear $\log\bar{\tau}-\log \tilde{M}$ relation: $\log\bar{\tau} = \gamma(\log \tilde{M}-14)+\log\beta$, in which $\gamma=0.55\pm0.1$. We also vary the aperture photometric filter radius and measure the $\bar{\tau}$ profiles of group samples, whose constraints on the baryon distribution within and around dark matter halos will be discussed in a companion paper.