  This is the second paper of a series devoted to present an updated release of
the BaSTI ( a Bag of Stellar Tracks and Isochrones) stellar model and isochrone
library. Following the publication of the updated solar scaled library, here we
present the library for a $\alpha-$enhanced heavy element distribution. These
new alpha-enhanced models account for all improvements and updates in the
reference solar metal distribution and physics inputs, as in the new solar
scaled library. The models cover a mass range between 0.1 and $15~M_{\odot}$,
18 metallicities between [Fe/H]=-3.20 and +0.06 with [alpha/Fe]=+0.4 , and a
helium to metal enrichment ratio Delta{Y}\Delta{Z}=1.31. For each metallicity,
He-enhanced stellar models are also provided. The isochrones cover (typically)
an age range between 20Myr and 14.5Gyr, including consistently the pre-main
sequence phase. Asteroseismic properties of the theoretical models have also
been calculated. Models and isochrones have been compared with results from
independent calculations, with the previous BaSTI release, and also with
selected observations, to test the accuracy/reliability of these new
calculations. All stellar evolution tracks, asteroseismic properties and
isochrones are made publicly available at http://basti-iac.oa-teramo.inaf.it
