  Determining the mechanisms that drive the evolution of protoplanetary disks
is a necessary step to understand how planets form. Here we measured the mass
accretion rate for young stellar objects at age >5 Myr, a critical test for the
current models of disk evolution. We present the analysis of the spectra of 36
targets in the ~5-10 Myr old Upper Scorpius region for which disk masses were
measured with ALMA. We find that the mass accretion rates in this sample of old
but still survived disks are similarly high as those of the younger (<3 Myr
old) star-forming regions of Lupus and Cha I, when considering the dependence
on stellar and disk mass. In particular, several disks show high mass accretion
rates >10^-9 Msun/yr while having low disk masses. Furthermore, the median
values of the measured mass accretion rates in the disk mass ranges where our
sample is complete at a level ~60-80% are compatible in these three regions. At
the same time, the spread of mass accretion rates at any given disk mass is
still >0.9 dex even at age>5 Myr. These results are in contrast with simple
models of viscous evolution, which would predict that the values of the mass
accretion rate diminish with time, and a tighter correlation with disk mass at
age>5 Myr. Similarly, simple models of internal photoevaporation cannot
reproduce the observed mass accretion rates, while external photoevaporation
might explain the low disk masses and high accretion rates. A partial possible
solution to the discrepancy with the viscous models is that the gas-to-dust
ratio of the disks at >5 Myr is significantly different and higher than the
canonical 100, as suggested by some dust and gas disk evolution models. The
results shown here require the presence of several inter-playing processes,
such as detailed dust evolution, external photoevaporation and possibly MHD
winds, to explain the secular evolution of protoplanetary disks.
