Todays galaxies experienced cosmic reionization at different times in different locations. For the first time, reionization ($50%$ ionized) redshifts, $z_R$, at the location of their progenitors are derived from new, fully-coupled radiation-hydrodynamics simulation of galaxy formation and reionization at $z > 6$, matched to N-body simulation to z = 0. Constrained initial conditions were chosen to form the well-known structures of the local universe, including the Local Group and Virgo, in a (91 Mpc)$^3$ volume large enough to model both global and local reionization. Reionization simulation CoDa I-AMR, by CPU-GPU code EMMA, used (2048)$^3$ particles and (2048)$^3$ initial cells, adaptively-refined, while N-body simulation CoDa I-DM2048, by Gadget2, used (2048)$^3$ particles, to find reionization times for all galaxies at z = 0 with masses $M(z=0)ge 10^8 M_odot$. Galaxies with $M(z=0) gtrsim 10^{11} M_odot$ reionized earlier than the universe as a whole, by up to $sim$ 500 Myrs, with significant scatter. For Milky-Way-like galaxies, $z_R$ ranged from 8 to 15. Galaxies with $M(z=0) lesssim 10^{11} M_odot$ typically reionized as late or later than globally-averaged $50%$ reionization at $langle z_Rrangle =7.8$, in neighborhoods where reionization was completed by external radiation. The spread of reionization times within galaxies was sometimes as large as the galaxy-to-galaxy scatter. The Milky Way and M31 reionized earlier than global reionization but later than typical for their mass, neither dominated by external radiation. Their most massive progenitors at $z>6$ had $z_R$ = 9.8 (MW) and 11 (M31), while their total masses had $z_R$ = 8.2 (both).
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