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The phenomenological study of evolving galaxy populations has shown that star forming galaxies can be quenched by two distinct processes: mass quenching and environment quenching (Peng et al. 2010). To explore the mass quenching process in local galaxies, we study the massive central disk galaxies with stellar mass above the Schechter characteristic mass. In Zhang et al. (2019), we showed that during the quenching of the massive central disk galaxies as their star formation rate (SFR) decreases, their molecular gas mass and star formation efficiency drop rapidly, but their HI gas mass remains surprisingly constant. To identify the underlying physical mechanisms, in this work we analyze the change during quenching of various structure parameters, bar frequency, and active galactic nucleus (AGN) activity. We find three closely related facts. On average, as SFR decreases in these galaxies: (1) they become progressively more compact, indicated by their significantly increasing concentration index, bulge-to-total mass ratio, and central velocity dispersion, which are mainly driven by the growth and compaction of their bulge component; (2) the frequency of barred galaxies increases dramatically, and at a given concentration index the barred galaxies have a significantly higher quiescent fraction than unbarred galaxies, implying that the galactic bar may play an important role in mass quenching; and (3) the "AGN" frequency increases dramatically from 10% on the main sequence to almost 100% for the most quiescent galaxies, which is mainly driven by the sharp increase of LINERs. These observational results lead to a self-consistent picture of how mass quenching operates., Comment: 20 pages, 11 figures. Published in ApJ