  Aims: We investigated the X-ray emission from young stars and brown dwarfs in
the sigma Orionis cluster (tau~3 Ma, d~385 pc) and its relation to mass,
presence of circumstellar discs, and separation to the cluster centre by taking
advantage of the superb spatial resolution of the Chandra X-ray Observatory.
Methods: We used public HRC-I/Chandra data from a 97.6 ks pointing towards the
cluster centre and complemented them with X-ray data from IPC/Einstein,
HRI/ROSAT, EPIC/XMM-Newton, and ACIS-S/Chandra together with optical and
infrared photometry and spectroscopy from the literature and public catalogues.
On our HRC-I/Chandra data, we measured count rates, estimated X-ray fluxes, and
searched for short-term variability. We also looked for long-term variability
by comparing with previous X-ray observations. Results: Among the 107 detected
X-ray sources, there were 70 cluster stars with known signposts of youth, two
young brown dwarfs, 12 cluster member candidates, four field dwarfs, and two
galaxies with optical-infrared counterpart. The remaining sources had
extragalactic nature. Based on a robust Poisson-chi^2 analysis, nine cluster
stars displayed flares or rotational modulation during the HRC-I observations,
while other eight stars and one brown dwarf showed long-term X-ray flux
variations. We constructed a cluster X-ray luminosity function from O9.5 (~18
Msol) to M6.5 (~0.06 Msol). We found: a tendency of early-type stars in
multiple systems or with spectroscopic peculiarities to display X-ray emission,
that the two detected brown dwarfs and the least-massive star are among the
sigma Orionis objects with the highest L_X/L_J ratios, and that a large
fraction of known classical T Tauri stars in the cluster are absent in this and
other X-ray surveys. We concluded that dozens X-ray sigma Orionis stars and
brown dwarfs are still to be detected [abridged].
