  We study the effect of the instantaneous gas expulsion on star clusters
wherein the residual gas has a density profile shallower than that of the
embedded cluster. This is expected if star formation proceeds with a given SFE
per free-fall time in a centrally-concentrated molecular clump. We perform
direct N-body simulations whose initial conditions are generated by the program
"mkhalo" "falcON" adapted for our models. Our model clusters initially have a
Plummer profile and are in virial equilibrium with the gravitational potential
of the cluster-forming clump. The residual gas contribution is computed based
on the model of Parmentier&Pfalzner(2013). Our simulations include mass loss by
stellar evolution and the tidal field of the Galaxy. We find that a star
cluster with a minimum global SFE of 15% is able to survive instantaneous gas
expulsion and to produce a bound cluster. Its violent relaxation lasts no
longer than 20 Myr, independently of its global SFE and initial stellar mass.
At the end of violent relaxation the bound fractions of surviving clusters with
the same global SFEs are similar regardless of their initial stellar mass.
Their subsequent lifetime in the gravitational field of the Galaxy depends on
their bound stellar masses. We therefore conclude that the critical SFE needed
to produce a bound cluster is 15%, which is twice smaller than earlier
estimates of 33%. Thus we have improved the survival likelihood of young
clusters after instantaneous gas expulsion. Those can now survive instantaneous
gas expulsion with global SFEs as low as those observed for embedded clusters
of Solar Neighbourhood (15-30%). This is the consequence of the star cluster
having a density profile steeper than that of the residual gas. However, in
terms of the effective SFE, measured by the virial ratio of the cluster at gas
expulsion, our results are in agreement with previous studies.
