Starbursting Brightest Cluster Galaxy: a Herschel view of the massive
  cluster MACS J1931.8-2634
  We investigate the dust-obscured star formation properties of the massive,
X-ray selected galaxy cluster MACS J1931.8-2634 at $z$=0.352. Using
far-infrared (FIR) imaging in the range 100-500$\mu$m obtained with the
\textit{Herschel} telescope, we extract 31 sources (2$\sigma$) within $r\sim$1
Mpc from the brightest cluster galaxy (BCG). Among these sources we identify
six cluster members for which we perform an analysis of their spectral energy
distributions (SEDs). We measure total infrared luminosity (L$_{IR}$), star
formation rate (SFR) and dust temperature. The BCG, with
L$_{IR}$=1.4$\times$10$^{12}$L$_\odot$ is an Ultra Luminous Infrared Galaxy and
hosts a type II AGN. We decompose its FIR SED into AGN and starburst components
and find equal contributions from AGN and starburst. We also recompute the SFR
of the BCG finding SFR=150$\pm$15 M$_\odot$yr$^{-1}$. We search for an isobaric
cooling flow in the cool core using {\sl Chandra} X-ray data, and find no
evidence for gas colder than 1.8 keV in the inner 30 kpc, for an upper limit to
the istantaneous mass-deposition rate of 58 M$_\odot$yr$^{-1}$ at 95 % c.l.
This value is $3\times$ lower than the SFR in the BCG, suggesting that the
on-going SF episode lasts longer than the ICM cooling events.
