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 H{alpha} 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 it is 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.

Cone search capability for table J/A+A/562/A24/tablea4 (Halo C stars with periods)

Cone search capability for table J/A+A/562/A24/table2 (TAROT observations of cool carbon stars and obtained periods)

Cone search capability for table J/A+A/562/A24/table5 (Fornax C stars with periods)

Cone search capability for table J/A+A/562/A24/tablea2 (Objects in the direction of Fornax that are not carbon stars)

Cone search capability for table J/A+A/562/A24/table1 (Observed carbon stars in the halo and in the dwarf galaxies Carina and Fornax)