We present high-quality , medium resolution X-shooter/VLT spectra in the range 300-2500 nm for a sample of 12 very low-mass stars in the \sigma Orionis cluster .
The sample includes eight stars with evidence of disks from Spitzer and four without , with masses ranging from 0.08 to 0.3 M _ { \odot } .
The aim of this first paper is to investigate the reliability of the many accretion tracers currently used to measure the mass accretion rate in low-mass , young stars and the accuracy of the correlations between these secondary tracers ( mainly accretion line luminosities ) found in the literature .
We use our spectra to measure the accretion luminosity from the continuum excess emission in the UV and visual ; the derived mass accretion rates range from 10 ^ { -9 } M _ { \odot } yr ^ { -1 } down to 5 \times 10 ^ { -11 } M _ { \odot } yr ^ { -1 } , allowing us to investigate the behavior of the accretion-driven emission lines in very-low mass accretion rate regimes .
We compute the luminosity of ten accretion-driven emission lines , from the UV to the near-IR , all obtained simultaneously .
In general , most of the secondary tracers correlate well with the accretion luminosity derived from the continuum excess emission .
We recompute the relationships between the accretion luminosities and the line luminosities , we confirm the validity of the correlations given in the literature , with the possible exception of H \alpha .
Metallic lines , such as the CaII IR triplet or the Na I line at 589.3 nm , show a larger dispersion .
When looking at individual objects , we find that the Hydrogen recombination lines , from the UV to the near-IR , give good and consistent measurements of L _ { acc } often in better agreement than the uncertainties introduced by the adopted correlations .
The average L _ { acc } derived from several Hydrogen lines , measured simultaneously , have a much reduced error .
This suggests that some of the spread in the literature correlations may be due to the use of non-simultaneous observations of lines and continuum .
Three stars in our sample deviate from this behavior , and we discuss them individually .