Stellar populations of galaxies in the ALHAMBRA survey up to $z \sim 1$.
  II. Stellar content of quiescent galaxies within the dust-corrected stellar
  mass$-$colour and the $UVJ$ colour$-$colour diagrams
  Our aim is to determine the distribution of stellar population parameters
(extinction, age, metallicity, and star formation rate) of quiescent galaxies
within the rest-frame stellar mass$-$colour and $UVJ$ colour$-$colour diagrams
corrected for extinction up to $z\sim1$. These novel diagrams reduce the
contamination in samples of quiescent galaxies owing to dust-reddened galaxies,
and they provide useful constraints on stellar population parameters. We set
constraints on the stellar population parameters of quiescent galaxies
combining the ALHAMBRA multi-filter photo-spectra with our SED-fitting code
MUFFIT, making use of composite stellar population models. The extinction
obtained by MUFFIT allowed us to remove dusty star-forming (DSF) galaxies from
the sample of red $UVJ$ galaxies. The distributions of stellar population
parameters across these rest-frame diagrams are revealed after the dust
correction and are fitted by the LOESS method to reduce uncertainty effects.
Quiescent galaxy samples defined via classical $UVJ$ diagrams are typically
contaminated by a $\sim20$% fraction of DSF galaxies. A significant part of the
galaxies in the green valley are actually obscured star-forming galaxies
($\sim30-65$%). Consequently, the transition of galaxies from the blue cloud to
the red sequence, and hence the related mechanisms for quenching, seems to be
much more efficient and faster than previously reported. The rest-frame stellar
mass$-$colour and $UVJ$ colour$-$colour diagrams are useful for constraining
the age, metallicity, extinction, and star formation rate of quiescent galaxies
by only their redshift, rest-frame colours, and/or stellar mass. Dust
correction plays an important role in understanding how quiescent galaxies are
distributed in these diagrams and is key to performing a pure selection of
quiescent galaxies via intrinsic colours.
