Aims: We investigated in detail nine sources in the direction of the young sigma Orionis cluster, which is considered a unique site for studying stellar and substellar formation. The nine sources were selected because of some peculiar properties, such as extremely red infrared colours or too strong Halpha emission for their blue optical colours. Methods: We took high-quality, low-resolution spectroscopy (R ~ 500) of the nine targets with ALFOSC at the Nordic Optical Telescope. We also re-analyzed [24]-band photometry from MIPS/Spitzer and compiled the best photometry available at the ViJHKs passbands and the four IRAC/Spitzer channels for constructing accurate spectral energy distributions covering from 0.55 to 24 mum. Results: The nine targets were classified into: one Herbig Ae/Be star with a scatterer edge-on disc, two G-type stars, one X-ray flaring, early-M, young star with chromospheric Halpha emission, one very low-mass, accreting, young spectroscopic binary, two young objects at the brown dwarf boundary with the characteristics of classical T Tauri stars, and two emission-line galaxies, one undergoing star formation, and another one whose spectral energy distribution is dominated by an active galactic nucleus. Besides, we discover three infrared sources associated to overdensities in a cold cloud in the cluster centre. Conclusions: Low-resolution spectroscopy and spectral energy distributions are a vital tool for measuring the physical properties and the evolution of young stars and candidates in the sigma Orionis cluster.

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