We present the first ab initio cosmological simulations of a CR7-like object which approximately reproduce the observed line widths and strengths. In our model, CR7 is powered by a massive ($3.23 times 10^7$ $M_odot$) black hole (BH) the accretion rate of which varies between $simeq$ 0.25 and $simeq$ 0.9 times the Eddington rate on timescales as short as 10$^3$ yr. Our model takes into account multi-dimensional effects, X-ray feedback, secondary ionizations and primordial chemistry. We estimate Ly-$alpha$ line widths by post-processing simulation output with Monte Carlo radiative transfer and calculate emissivity contributions from radiative recombination and collisional excitation. We find the luminosities in the Lyman-$alpha$ and He II 1640 angstrom lines to be $5.0times10^{44}$ and $2.4times10^{43}$ erg s$^{-1}$, respectively, in agreement with the observed values of $>$ $8.3times10^{43}$ and $2.0times10^{43}$ erg s$^{-1}$. We also find that the black hole heats the halo and renders it unable to produce stars as required to keep the halo metal free. These results demonstrate the viability of the BH hypothesis for CR7 in a cosmological context. Assuming the BH mass and accretion rate that we find, we estimate the synchrotron luminosity of CR7 to be $P simeq 10^{40} - 10^{41}$ erg s$^{-1}$, which is sufficiently luminous to be observed in $mu$Jy observations and would discriminate this scenario from one where the luminosity is driven by Population III stars.
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