We aim to study the main properties of a volume-limited unbiased sample of well characterized semi-regular variables (SRs) in order to clarify important issues that need to be further explained, such as the formation of axially symmetric planetary nebulae (PNe) from spherical circumstellar envelopes (CSEs) that takes place during the mass loss process along the AGB phase. We present new high S/N IRAM 30m observations of the ^12^CO J=2-1, ^12^CO J=1-0, and ^13^CO J=1-0 lines, in a volume-limited sample of SRs for which the Hipparcos distances are between 100-500 pc and declinations above -25{deg}. We analyzed the data by characterizing the main properties of the CSEs. The ^12^CO J=2-1 data have been used to study the profiles, while the ^12^CO J=1-0 data have been used to estimate mass-loss rates for the complete sample. Moreover, the ^12^CO J=2-1 line has been used to determine the possible structures responsible for such profiles. We have classified the sources into four groups according to the different profiles and final gas expansion velocities. Type 1 and 2 profiles are broad and narrow symmetric lines, respectively. Type 1 profiles, furthermore, are more related to standard spherically symmetric envelopes already studied. Type 3 profiles, on the contrary, are strange profiles with very pronounced asymmetries. Type 4 profiles, finally, are those which show two different components: a narrow line profile superimposed on a broad pedestal component. We find that for sources which show this kind of profile, with two different components, the variation amplitude is very low, what means that these SRs do not have a well developed inner envelope differentiated from the outer one. Interestingly, we report a moderate correlation between mass-loss rates and ^12^CO J=1-0/^12^CO J=2-1 line intensity ratios for O-rich SRs, suggesting a different behaviour between C- and O-rich SRs. By using SHAPE+shapemol, we find a unified simple model based on an oblate spheroid, placed in different orientations, that may explain all the ^12^CO profiles in the sample, indicating that the gas expansion is, in general, predominantly equatorial. Moreover, in order to explain the type 4 profiles, we define an extra component which may somehow be a biconical structure or similar according to the structures already found in this kind of sources. Type 1 and 2 profiles, curiously, may also be explained by standard spherically symmetric envelopes, but often requiring anomalously low velocities. Type 3 and 4 profiles, however, need axial symmetry to be explained. We conclude that most circumstellar shells around SRs show axial, strongly non-spherical symmetry. More interferometric observations are needed in order to make firm conclusions about mass-loss processes and possible morphologies of SRs.

Cone search capability for table J/A+A/629/A94/table1 (Main properties of the observed SRs)