Star formation activity in a young galaxy cluster at z=0.866
  The galaxy cluster RXJ1257$+$4738 at $z=0.866$ is one of the highest redshift
clusters with a richness of multi-wavelength data, and thus a good target to
study the star formation-density relation at early epochs. Using a sample of
spectroscopically-confirmed cluster members, we derive the star formation rates
of our galaxies using two methods, (I) the relation between SFR and total
infrared luminosity extrapolated from the observed \textit{Spitzer} MIPS
24$\mu$m imaging data, and (II) spectral energy distribution (SED) fitting
using the MAGPHYS code, including eight different bands.
  We show that, for this cluster, the SFR-density relation is very weak and
seems to be dominated by the two central galaxies and the SFR presents a mild
dependence on stellar mass, with more massive galaxies having higher SFR.
However, the specific SFR (SSFR) decreases with stellar mass, meaning that more
massive galaxies are forming less stars per unit of mass, and thus suggesting
that the increase in star-forming members is driven by cluster assembly and
infall.
  If the environment is somehow driving the SF, one would expect a relation
between the SSFR and the cluster centric distance, but that is not the case. A
possible scenario to explain this lack of correlation is the contamination by
infalling galaxies in the inner part of the cluster which may be on their
initial pass through the cluster center. As these galaxies have higher SFRs for
their stellar mass, they enhance the mean SSFR in the center of the cluster.
