Nucleosynthesis in AGB stars traced by oxygen isotopic ratios: I. Determining the stellar initial mass by means of the ¹⁷O/¹⁸O ratio

Aims. We seek to investigate the ¹⁷O/¹⁸O ratio for a sample of AGB stars containing M-, S-, and C-type stars. These ratios are evaluated in relation to fundamental stellar evolution parameters: the stellar initial mass and pulsation period. Methods. Circumstellar ¹³C¹⁶O, ¹²C¹⁷O, and ¹²C¹⁸O line observations were obtained for a sample of nine stars with various single-dish long-wavelength facilities. Line intensity ratios are shown to relate directly to the surface ¹⁷O/¹⁸O abundance ratio. Results. Stellar evolution models predict the ¹⁷O/¹⁸O ratio to be a sensitive function of initial mass and to remain constant throughout the entire TP-AGB phase for stars initially less massive than 5 M_Ȯ. This makes the measured ratio a probe of the initial stellar mass. Conclusions. Observed ¹⁷O/¹⁸O ratios are found to be well in the range predicted by stellar evolution models that do not consider convective overshooting. From this, accurate initial mass estimates are calculated for seven sources. For the remaining two sources, there are two mass solutions, although there is a larger probability that the low-mass solution is correct. Finally, we present hints at a possible separation between M/S- and C-type stars when comparing the ¹⁷O/¹⁸O ratio to the stellar pulsation period.