  We present a study of the large-scale spatial distribution of 6482 RASS X-ray
sources in approximately 5000 deg^2 in the direction of Orion. We examine the
astrophysical properties of a sub-sample of ~100 optical counterparts, using
optical spectroscopy. This sub-sample is used to investigate the space density
of the RASS young star candidates by comparing X-ray number counts with
Galactic model predictions. We characterize the observed sub-sample in terms of
spectral type, lithium content, radial and rotational velocities, as well as
iron abundance. A population synthesis model is then applied to analyze the
stellar content of the RASS in the studied area. We find that stars associated
with the Orion star-forming region do show a high lithium content. A population
of late-type stars with lithium equivalent widths larger than Pleiades stars of
the same spectral type (hence younger than ~70-100 Myr) is found widely spread
over the studied area. Two new young stellar aggregates, namely "X-ray Clump
0534+22" (age~2-10 Myr) and "X-ray Clump 0430-08" (age~2-20 Myr), are also
identified. The spectroscopic follow-up and comparison with Galactic model
predictions reveal that the X-ray selected stellar population in the direction
of Orion is characterized by three distinct components, namely the clustered,
the young dispersed, and the widespread field populations. The clustered
population is mainly associated with regions of recent or ongoing star
formation and correlates spatially with molecular clouds. The dispersed young
population follows a broad lane apparently coinciding spatially with the Gould
Belt, while the widespread population consists primarily of active field stars
older than 100 Myr. We expect the "bi-dimensional" picture emerging from this
study to grow in depth as soon as the distance and the kinematics of the
studied sources will become available from the future Gaia mission.
