  To investigate the asymptotic giant branch (AGB) population in the Galactic
halo, we search for pulsating AGB stars at a heliocentric distance over 50kpc.
Our research is based on the Catalina Southern Survey (CSS) catalogue of
variables, comprising 1286 long-period variables (LPVs) with declination less
than -20deg. We first focus on the 77 stars in the cap abs(b)>30deg for which
spectral M-type or C-type classification can be derived from Hamburg-ESO
objective prism spectra. Most of these are oxygen-rich (M-type) and very few
are carbon rich. The periods are in the range 100-500 days, and CSS amplitudes
are up to 3 mag. In this small sample, no halo AGB star is fainter than
Ks0=12.5. This may be due to the scarcity of AGBs in the outer halo, or
insufficient instrumental depth. Leaving aside spectral information, we then
searched for even fainter pulsators (Ks>12.5) in the entire CSS catalogue. Gaia
astrometry makes it possible to identify some contaminants. Our final result is
the identification of ten candidate distant LPVs. If these ten stars obey the
fundamental mode K-band period luminosity relation used for Miras and
small-amplitude Miras, their distances are between 50 and 120kpc from the Sun.
In a diagram showing distance versus Gaia tangential velocity, these ten stars
have positions similar to those of other objects in the halo, such as globular
clusters and dwarf galaxies. We also detect some underluminous AGBs that
deserve further study. A detailed catalogue of the 77 high-latitude M or C
stars will be made available at the CDS.
