  The population of cool carbon (C) stars located far from the galactic plane
is probably made of debris of small galaxies such as the Sagittarius dwarf
spheroidal galaxy (Sgr), which are disrupted by the gravitational field of the
Galaxy. We aim to know this population better through spectroscopy, 2MASS
photometric colours, and variability data. When possible, we compared the halo
results to C star populations in the Fornax dwarf spheroidal galaxy, Sgr, and
the solar neighbourhood. We first present a few new discoveries of C stars in
the halo and in Fornax. The number of spectra of halo C stars is now 125. Forty
percent show Halpha in emission. The narrow location in the JHK diagram of the
halo C stars is found to differ from that of similar C stars in the above
galaxies. The light curves of the Catalina and LINEAR variability databases
were exploited to derive the pulsation periods of 66 halo C stars. A few
supplementary periods were obtained with the TAROT telescopes. We confirm that
the period distribution of the halo strongly resembles that of Fornax, and we
found that is it very different from the C stars in the solar neighbourhood.
There is a larger proportion of short period Mira/SRa variables in the halo
than in Sgr, but the survey for C stars in this dwarf galaxy is not complete,
and the study of their variability needs to be continued to investigate the
link between Sgr and the cool halo C stars.
