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A relation between the mass accretion rate onto the central young star and the mass of the surrounding protoplanetary disk has long been theoretically predicted and observationally sought. For the first time, we have accurately and homogeneously determined the photospheric parameters, mass accretion rate, and disk mass for an essentially complete sample of young stars with disks in the Lupus clouds. Our work combines the results of surveys conducted with VLT/X-Shooter and ALMA. With this dataset we are able to test a basic prediction of viscous accretion theory, the existence of a linear relation between the mass accretion rate onto the central star and the total disk mass. We find a correlation between the mass accretion rate and the disk dust mass, with a ratio that is roughly consistent with the expected viscous timescale when assuming an interstellar medium (ISM) gas-to-dust ratio. This confirms that mass accretion rates are related to the properties of the outer disk. We find no correlation between mass accretion rates and the disk mass measured by CO isotopologues emission lines, possibly owing to the small number of measured disk gas masses. This suggests that the mm-sized dust mass better traces the total disk mass and that masses derived from CO may be underestimated, at least in some cases., C.F.M. gratefully acknowledges an ESA Research Fellowship. G.R. is supported by the DISCSIM project, grant agreement 341137 funded by the European Research Council under ERC-2013-ADG. A.N. would like to acknowledge funding from Science Foundation Ireland (Grant 13/ERC/I2907). Leiden is supported by the European Union A-ERC grant 291141 CHEMPLAN, by the Netherlands Research School for Astronomy (NOVA), and by grant 614.001.352 from the Netherlands Organization for Scientific Research (NWO). JPW and MA were supported by NSF and NASA grants AST-1208911 and NNX15AC92G., This is the final version of the article. It first appeared from EDP Sciences via http://dx.doi.org/10.1051/0004-6361/201628549

We present the first high-resolution sub-mm survey of both dust and gas for a large population of protoplanetary disks. Characterizing fundamental properties of protoplanetary disks on a statistical level is critical to understanding how disks evolve into the diverse exoplanet population. We use ALMA to survey 89 protoplanetary disks around stars with $M_{\ast}>0.1~M_{\odot}$ in the young (1--3~Myr), nearby (150--200~pc) Lupus complex. Our observations cover the 890~$\mu$m continuum and the $^{13}$CO and C$^{18}$O 3--2 lines. We use the sub-mm continuum to constrain $M_{\rm dust}$ to a few Martian masses (0.2--0.4~$M_{\oplus}$) and the CO isotopologue lines to constrain $M_{\rm gas}$ to roughly a Jupiter mass (assuming ISM-like $\rm {[CO]/[H_2]}$ abundance). Of 89 sources, we detect 62 in continuum, 36 in $^{13}$CO, and 11 in C$^{18}$O at $>3\sigma$ significance. Stacking individually undetected sources limits their average dust mass to $\lesssim6$ Lunar masses (0.03~$M_{\oplus}$), indicating rapid evolution once disk clearing begins. We find a positive correlation between $M_{\rm dust}$ and $M_{\ast}$, and present the first evidence for a positive correlation between $M_{\rm gas}$ and $M_{\ast}$, which may explain the dependence of giant planet frequency on host star mass. The mean dust mass in Lupus is 3$\times$ higher than in Upper Sco, while the dust mass distributions in Lupus and Taurus are statistically indistinguishable. Most detected disks have $M_{\rm gas}\lesssim1~M_{\rm Jup}$ and gas-to-dust ratios $