A CO,2-1 line survey is performed toward a sample of 58 high Galactic latitude post-AGB (pAGB) stars. To complement the observations, a compilation of literature CO,2-1 line data of known pAGB stars is done. After combining the datasets, CO,2-1 line data are available for 133 pAGB stars (about 34 per cent of known pAGB stars) among which 44 are detections. The CO line strengths are compared with infrared dust emission for these pAGB stars by defining a ratio between the integrated CO,2-1 line flux and {it IRAS} 25,mu flux density (CO-IR ratio). The relationship between the CO-IR ratio and the {it IRAS} color C23 (defined with the 25 and 60,mu flux densities) is called here the CO-IR diagram. The pAGB objects are found to be located between AGB stars and planetary nebulae (PNe), and segregate into three distinctive groups (I, II and III) on the CO-IR diagram. By analyzing their various properties such as chemical types, spectral types, binarity, circumstellar envelope expansion velocities, and pAGB sub-types on the CO-IR diagram, it is argued that the group-I objects are mainly intermediate mass C-rich pAGB stars in early pAGB stage (almost all of the considered carbon rich `21,mu stars belong to this group); the group-II objects are massive or intermediate mass pAGB stars which already follow the profound trend of PNe; and the group-III objects are mainly low mass binary pAGB stars with very weak CO,2-1 line emission (almost all of the considered RV,Tau variables belong to this group). The CO-IR diagram is proven to be a powerful tool to investigate the co-evolution of circumstellar gas and dust during the short pAGB stage of stellar evolution.
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