AND ASTROPHYSICS The space distribution of HIPPARCOS carbon stars?,??

Abstract. More than 300 galactic carbon-rich stars have been observed by the HIPPARCOS satellite. Parallaxes and proper motions are givenwith an unprecedented accuracy. Carbon stars are however distant giants and there are only 4 stars with a parallax accuracybetter than20 % (26 stars if30%).Direct use of observed data is thus severely hampered by statistical biases.We propose here a model of the distribution of observed parallaxes as deduced from the cumulative distribution of proper motions. A simple P ($) / $−2.35 law for true parallaxes is found to give a good fit to observed parallaxes. Theminimum true par-allax of this magnitude-limited sample amounts to (0.3 0.1) mas. True parallaxes are then generated for statistical purposes. They are found to agreewith the relative photometric angular di-ameter of Knapik&Bergeat (1997) following the theoretical re-lation/0 / $.Diagrams such as Fig. 3b show no distortion even at small parallaxes which suggests they are free of system-atic effects. Finally, the space distribution of the HIPPARCOS carbon stars is discussed. An evaluation of theMalmquist bias is obtained and the local (presumablyunbiased) distributionof car-bon stars is found to beP ($) / $−3.020.09.Aflat subsystem or slab is proposed P ($) / $−3 . It is shown that the HIP-PARCOS sample is reasonably complete for $ 1mas with the possible exception of the faint R0-R2 stars. The Malmquist bias appears also as negligible for the bright N-variables down to $ ’ 0.6mas. No clear correlation with the local arms struc-ture and interstellar extinction could be seen in this magnitude-limited sample of the Sun vicinity. The space density of carbon stars is estimated to range from 40 to 70 stars kpc−3 which is in good agreement with previous estimates of Fuenmayor (1981)