  Star formation in galaxies at the center of cooling-flow galaxy clusters is
an important phenomenon in the context of formation and evolution of massive
galaxies in the Universe. Yet, star formation rates (SFRs) in such systems
continue to be elusive. We use our Bayesian-motivated spectral energy
distribution (SED)-fitting code, BAYESCOOL, to estimate the plausible SFR
values in the brightest cluster galaxy of a massive, X-ray luminous galaxy
cluster, Phoenix. Previous studies of Phoenix have resulted in the highest
measurement of SFR for any galaxy, with the estimates reaching up to 1000 solar
masses/yr. However, a very small number of models have been considered in those
studies. BAYESCOOL allows us to probe a large parameter space. We consider two
models for star formation history, instantaneous bursts and continuous star
formation, a wide range of ages for the old and the young stellar population,
along with other discrete parameters, such as the initial mass function,
metallicities, internal extinction and extinction law. We find that in the
absence of any prior except that the maximum cooling rate < 3000 solar
masses/yr, the SFR lies in the range (2230-2890) solar masses/yr. If we impose
an observational prior on the internal extinction, E(B-V) < 0.6, the best-fit
SFR lies in (454-494) solar masses/yr, and we consider this as the most
probable range of SFR values for Phoenix. The SFR dependence on the extinction
is a reflection of the standard age-extinction degeneracy, which can be
overcome by using a prior on one of the two quantities in question.
