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Description
We report a $\sim5.8\sigma$ detection of the kinetic Sunyaev–Zel’dovich (kSZ) effect in Fourier space, by combining the DESI galaxy clusters and the Planck data. We use the density-weighted pairwise kSZ power spectrum as the summary statistic, and the detailed procedure of the measurement is presented in this paper. Selected by a varying lower mass threshold $M_{\rm th}$, the galaxy cluster 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 $\sim10^{13}-10^{14}{\rm M}_\odot/h$ and the heaviest $\tilde{M}\sim10^{14} {\rm M}_\odot/h$ 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 $\tilde{M}=1.75\times10^{13}{\rm M}_\odot/h$ cluster sample at the median redshift $\tilde{z}=0.64$ has the highest kSZ detection ${\rm S/N}=5.8$. By fitting $\bar{\tau}$s from various samples against their $\tilde{M}$s, we obtain a linear $\log\bar{\tau}-\log \tilde{M}$ relation: $\log\bar{\tau} = \gamma(\log \tilde{M}-14)+\log\alpha$, in which $\gamma=0.95\pm0.08$. We also vary the aperture photometric filter radius and measure the $\bar{\tau}$ profiles of cluster samples, whose constraints on the baryon distribution within and around dark matter halos will be discussed in a companion paper.