  Understanding how galaxies quench their star formation is crucial for studies
of galaxy evolution. Quenching is related to the cold gas decrease. In the
first paper we showed that the dust removal timescale in early-type galaxies
(ETGs) is about 2.5 Gyr. Here we present carbon monoxide (CO) and 21 cm
hydrogen (H I) line observations of these galaxies and measure the timescale of
removal of the cold interstellar medium (ISM). We find that all the cold ISM
components (dust, molecular and atomic gas) decline at similar rates. This
allows us to rule out a wide range of potential ISM removal mechanisms
(including starburst-driven outflows, astration, a decline in the number of
asymptotic giant branch stars), and artificial effects like stellar mass-age
correlation, environmental influence, mergers, and selection bias, leaving
ionization by evolved low-mass stars and ionization/outflows by supernovae Type
Ia or active galactic nuclei as viable mechanisms. We also provide evidence for
an internal origin of the detected ISM. Moreover, we find that the quenching of
star formation in these galaxies cannot be explained by a reduction in gas
amount alone, because the star formation rates (SFRs) decrease faster (on a
timescale of about 1.8 Gyr) than the amount of cold gas. Furthermore, the star
formation efficiency of the ETGs (SFE = SFR/MH2) is lower than that of
star-forming galaxies, whereas their gas mass fractions (fH2 = MH2/M*) are
normal. This may be explained by the stabilization of gas against
fragmentation, for example due to morphological quenching, turbulence, or
magnetic fields.
