Temporally and Spatially Extended Star Formation in the Brightest Cluster Galaxy of MACS\,J0329.7$-$0211 at $z=0.45$: Implications for Stellar Growth

Abstract: Brightest cluster galaxies (BCGs), particularly those at the centers of cool-core clusters, can exhibit star formation over spatial extents of up to $\gtrsim$100\,kpc at inferred rates of up to $\gtrsim100\rm\,M_\sun\,yr^{-1}$. Is their star formation also extended over time, as might be expected if fuelled by cooling of the surrounding hot intracluster gas -- a residual cooling flow -- as demonstrated hitherto only for the BCG in the Perseus cluster? Here, to infer the formation history of relatively young stars in the BCG of MACS\,J0329.7$-$0211, we fit model single-stellar-populations to the spectral energy distributions (spanning near-UV to near-IR) measured along different sightlines towards its young stellar population. Employing a Markov Chain Monte Carlo method, we show that star formation in this BCG has persisted at a relatively constant rate of $\sim2{\rm\,M_\sun\,yr^{-1}}$ (factors of 10--40 below the rates previously inferred using simpler methods and/or ad hoc assumptions) over the past $\sim$400\,Myr, beyond which any star formation falls below the observational detection threshold. Such persistent star formation from a residual cooling flow can contribute up to $\sim$10\% of the original stellar mass of this BCG if its progenitor was among the most massive red nuggets known at $z\sim$2 having masses of $\sim1\times10^{11}\rm\,M_\sun$, but only a few percent of its overall growth in stellar mass to $\sim8\times10^{11}\rm\,M_\sun$ at $z=0.45$. Although constituting only a minor pathway for the stellar growth of this BCG, persistent star formation from a residual cooling flow can nevertheless contribute significantly to the enormous number of globular clusters found around BCGs in the local Universe.