Photometric determination of the mass accretion rates of pre-main
  sequence stars. II. NGC346 in the Small Magellanic Cloud
  [Abridged] We have studied the properties of the stellar populations in the
field of the NGC346 cluster in the Small Magellanic Cloud, using a novel
self-consistent method that allows us to reliably identify pre-main sequence
(PMS) objects actively undergoing mass accretion, regardless of their age. The
method does not require spectroscopy and combines broad-band V and I photometry
with narrow-band Halpha imaging to identify all stars with excess Halpha
emission and derive the accretion luminosity Lacc and mass accretion rate Macc
for all of them. The application of this method to existing HST/ACS photometry
of the NGC346 field has allowed us to identify and study 680 bona-fide PMS
stars with masses from ~0.4 to ~4 Msolar and ages in the range from ~1 to ~30
Myr. This is the first study to reveal that, besides a young population of PMS
stars (~ 1 Myr old), in this field there is also an older population of PMS
objects with a median age of ~20 Myr. We provide for all of them accurate
physical parameters. We study the evolution of the mass accretion rate as a
function of stellar parameters and find that logMacc ~ -0.6 Log t + Log m + c,
where t is the age of the star, m its mass and c a quantity that is higher at
lower metallicity. The high mass accretion rates that we find suggest that a
considerable fraction of the stellar mass is accreted during the PMS phase and
that PMS evolutionary models that do not account for this effect will
systematically underestimate the true age when compared with the observations.
