A giant Ly$\alpha$ nebula in the core of an X-ray cluster at $z=1.99$: implications for early energy injection

We present the discovery of a giant >= 100 kpc Ly alpha nebula detected in the core of the X-ray emitting cluster CL J1449 +0856 at z = 1.99 through Keck/LRIS narrow-band imaging. This detection extends the known relation between Lya nebulae and overdense regions of the universe to the dense core of a 5-7 x 10(13) M-circle dot cluster. The most plausible candidates to power the nebula are two Chandra-detected AGN host cluster members, while cooling from the X-ray phase and cosmological cold flows are disfavored primarily because of the high Ly alpha to X-ray luminosity ratio (L-Ly alpha/L-X approximate to 0.3, greater than or similar to 10-1000 times. higher than in local cool-core clusters) and by current modeling. Given the physical conditions of the Ly alpha-emitting gas and the possible interplay with the X-ray phase, we argue that the Ly alpha nebula would be short-lived (less than or similar to 10 Myr) if not continuously replenished with cold gas at a rate of greater than or similar to 1000 M-circle dot yr(-1). We investigate the possibility that cluster galaxies supply the required gas through outflows and we show that their total mass outflow rate matches the replenishment necessary to sustain the nebula. This scenario directly implies the extraction of energy from galaxies and its deposition in the surrounding intracluster medium (ICM), as required to explain the thermodynamic properties of local clusters. We estimate an energy injection of the order of approximate to 2 keV per particle in the ICM over a 2 Gyr interval. In our baseline calculation, AGNs provide up to 85% of the injected energy and two-thirds. of the mass, while the rest is supplied by supernovae-driven winds.