Evolution of the relation between the mass accretion rate and the stellar and disk mass from brown dwarfs to stars

The time evolution of the dependence of the mass accretion rate with the stellar mass and the disk mass represents a fundamental way to understand the evolution of protoplanetary disks and the formation of planets. In this work, we present observations with X-shooter of 26 Class II very low-mass stars (< 0.2 M-circle dot) and brown dwarfs in the Ophiuchus, Chamaeleon-I, and Upper Scorpius star-forming regions. These new observations extend the measurement of the mass accretion rate down to spectral type (SpT) M9 (similar to 0.02 M-circle dot) in Ophiuchus and Chamaeleon-I and add 11 very-low-mass stars to the sample of objects previously studied with broadband spectroscopy in Upper Scorpius. We obtained the spectral type and extinction, as well as the physical parameters of the sources. We used the intensity of various emission lines in the spectra of these sources to derive the accretion luminosity and mass accretion rates for the entire sample. Combining these new observations with data from the literature, we compare relations between accretion and stellar and disk properties of four different star-forming regions with different ages: Ophiuchus (similar to 1 Myr), Lupus (similar to 2 Myr), Chamaeleon-I (similar to 3 Myr), and Upper Scorpius (5-12 Myr). We find the slopes of the accretion relationships (L-* - L-acc, M-* - (M) ovet dot(acc)) to steepen in the 1-3 Myr age range (i.e., between Ophiuchus, Lupus, and Chamaeleon-I) and that both relationships may be better described with a single power law. We find that previous claims for a double power-law behavior of the M-* - (M) ovet dot(acc) relationship may have been triggered by the use of a different SpT-T-eff scale. We also find the relationship between the protoplanetary disk mass and the mass accretion rate of the stellar population to steepen with time down to the age of Upper Scorpius. Overall, we observe hints of a faster evolution into low accretion rates of low-mass stars and brown dwarfs. At the same time, we also find that brown dwarfs present higher M-disk/(M) ovet dot(acc) ratios (i.e., longer accretion depletion timescales) than stars in Ophiuchus, Lupus, and Cha-I. This apparently contradictory result may imply that the evolution of protoplanetary disks around brown dwarfs may be different than what is seen in the stellar regime.