Aims. We performed a detailed membership selection and studied the accretion properties of low-mass stars in the two apparently very similar young (1-10 Myr) clusters sigma Ori and lambda Ori. Methods. We observed 98 and 49 low-mass (0.2-1.0 M_sun) stars in sigma Ori and lambda Ori respectively, using the multi-object optical spectrograph FLAMES at the VLT, with the high-resolution (R=17,000) HR15N grating (6470-6790 AA). We used radial velocities, Li and Halpha to establish cluster membership and Halpha and other optical emission lines to analyze the accretion properties of members. Results. We identified 65 and 45 members of the sigma Ori and lambda Ori clusters, respectively and discovered 16 new candidate binary systems. We also measured rotational broadening for 20 stars and estimated the mass accretion rates in 25 stars of the sigma Ori cluster, finding values between 10^-11 and 10^-7.7 M_sun yr^-1 and in 4 stars of the lambda Ori cluster, finding values between 10^-11 and 10^-10.1 M_sun yr-1. Comparing our results with the infrared photometry obtained by the Spitzer satellite, we find that the fraction of stars with disks and the fraction of active disks is larger in the sigma Ori cluster (52+-9% and 78+-16%) than in lambda Ori (28+-8% and 40+-20%) Conclusions. The different disk and accretion properties of the two clusters could be due either to the effect of the high-mass stars and the supernova explosion in the lambda Ori cluster or to different ages of the cluster populations. Further observations are required to draw a definitive conclusion.
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