We present the analysis , based on spectra collected at the Large Binocular Telescope , of the stellar populations in seven spheroidal galaxies in the cluster XLSSJ0223 at z \sim 1.22 .
The aim is to constrain the epoch of their formation and their star formation history .
Using absorption line strenghts and full spectral fitting , we derive for the stellar populations of the seven spheroids a median age < Age > =2.4 \pm 0.6 Gyr , corresponding to a median formation redshift < z _ { f } > \sim 2.6 _ { -0.5 } ^ { +0.7 } ( lookback time = 11 _ { -1.0 } ^ { +0.6 } Gyr ) .
We find a significant scatter in age , showing that massive spheroids , at least in our targeted cluster , are not coeval .
The median metallicity is [ Z/H ] =0.09 \pm 0.16 , as for early-types in clusters at 0 < z < 0.9 .
This lack of evolution of [ Z/H ] over the range 0 < z < 1.3 , corresponding to the last 9 billions years , suggests that no significant additional star formation and chemical enrichment are required for cluster spheroids to reach the present-day population .
We do not detect significant correlation between age and velocity dispersion \sigma _ { e } , or dynamical mass M _ { dyn } , or effective stellar mass density \Sigma _ { e } .
On the contrary , the metallicity [ Z/H ] of the seven spheroids is correlated to their dynamical mass M _ { dyn } , according to a relation similar to the one for local spheroids .
[ Z/H ] is also anticorrelated to stellar mass density \Sigma _ { e } because of the anticorrelation between M _ { dyn } and \Sigma _ { e } .
Therefore , the basic trends observed in the local universe were already established at z \sim 1.3 , i.e .
more massive spheroids are more metal rich , have lower stellar mass density and tend to be older than lower-mass galaxies .