We investigate quasar outflows at $z geq 6$ by performing zoom-in cosmological hydrodynamical simulations. By employing the SPH code GADGET-3, we zoom in the $2 R_{200}$ region around a $2 times 10^{12} M_{odot}$ halo at $z = 6$, inside a $(500 ~ {rm Mpc})^3$ comoving volume. We compare the results of our AGN runs with a control simulation in which only stellar/SN feedback is considered. Seeding $10^5 M_{odot}$ BHs at the centers of $10^{9} M_{odot}$ halos, we find the following results. BHs accrete gas at the Eddington rate over $z = 9 - 6$. At $z = 6$, our most-massive BH has grown to $M_{rm BH} = 4 times 10^9 M_{odot}$. Fast ($v_{r} > 1000$ km/s), powerful ($dot{M}_{rm out} sim 2000 M_{odot}$/yr) outflows of shock-heated low-density gas form at $z sim 7$, and propagate up to hundreds kpc. Star-formation is quenched over $z = 8 - 6$, and the total SFR (SFR surface density near the galaxy center) is reduced by a factor of $5$ ($1000$). We analyse the relative contribution of multiple physical process: (i) disrupting cosmic filamentary cold gas inflows, (ii) reducing central gas density, (iii) ejecting gas outside the galaxy; and find that AGN feedback has the following effects at $z = 6$. The inflowing gas mass fraction is reduced by $sim 12 %$, the high-density gas fraction is lowered by $sim 13 %$, and $sim 20 %$ of the gas outflows at a speed larger than the escape velocity ($500$ km/s). We conclude that quasar-host galaxies at $z geq 6$ are accreting non-negligible amount of cosmic gas, nevertheless AGN feedback quenches their star formation dominantly by powerful outflows ejecting gas out of the host galaxy halo.
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