2005ApJ...624..331H

Observations made with the Heinrich Hertz Telescope of CO millimeter and submillimeter emission toward a sample of 22 proto-planetary nebula (PPN) candidates resulted in detections of 12 sources in the CO J=2-1 line. Of these 12, seven sources were also detected in the J=4-3 line. These 4-3 transitions are the highest yet observed in all but one of these PPNs. Statistical equilibrium/radiative transfer models were calculated for the CO emission in the circumstellar envelopes (CSEs), assuming various power-law density distributions. These models were compared with the intensity and profile shape of the observed spectra. For the region of the CSE probed by CO emission, the density laws must be steeper than inverse squared and are consistent with power laws between ρ∝r^–3 and r^–4. These radial density distributions imply that the mass loss was not constant but increased during the last part of the asymptotic giant branch (AGB) phase. Mass-loss rates at the end of the AGB for the three best-constrained sources are found to be 7.7x10^–5 M_☉/yr (IRAS 22272+5435), 2.3x10^–5 M_☉/yr (IRAS 07134+1005), and 1.3x10^–5 M_☉/yr (IRAS 17436+5003) for the case of ρ∝r^–3. These time-varying mass-loss rates can be integrated to calculate the enclosed envelope masses ejected in the past ∼10,000 yr. The ejected envelope masses close to the star lie in the range 0.02-0.30 M_☉; these values are consistent with theoretical models, which indicate that <20% of the stellar mass loss occurs in the last 10,000 years of the AGB. These results are in contrast to some recent dust studies based on infrared emission, however, in which much higher envelope masses are determined. The density laws, mass-loss rates, and enclosed envelope masses that we derive furnish important constraints for evolutionary models of stars in the late AGB and during the transition to the planetary nebula phase.