At ~16-17Mpc from us, the Virgo cluster is a formidable source of information to study cluster formation and galaxy evolution in rich environments. Several observationally-driven formation scenarios arose within the past decade to explain the properties of galaxies that entered the cluster recently and the nature of the last significant merger that the cluster underwent. Confirming these scenarios requires extremely faithful numerical counterparts of the cluster. This paper presents the first CLONE, Constrained LOcal and Nesting Environment, simulation of the Virgo cluster within a ~15Mpc radius sphere. This cosmological hydrodynamical simulation, with feedback from supernovae and active galactic nuclei, with a ~3x10^7Msun dark matter particle mass and a minimum cell size of 350pc in the zoom region, reproduces Virgo within its large scale environment unlike a random cluster simulation. Overall the distribution of the simulated galaxy population matches the observed one including M87. The simulated cluster formation reveals exquisite agreements with observationally-driven scenarios: within the last Gigayear, about 300 small galaxies (M*>10^7Msun) entered the cluster, most of them within the last 500Myr. The last significant merger event occurred about 2 Gigayears ago: a group with a tenth of the mass of todays cluster entered from the far side as viewed from the Milky Way. This excellent numerical replica of Virgo will permit studying different galaxy type evolution (jellyfish, backsplash, etc.) as well as feedback phenomena in the cluster core via unbiased comparisons between simulated and observed galaxies and hot gas phase profiles to understand this great physics laboratory.
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