The HII region W3 is one of the most outstanding regions of high-mass star formation. Based on a new analysis of the $^{12}$CO($J$ = 2-1) data obtained at 38$$ resolution, we have found that each of the two active regions of high-mass star formation, W3 Main and W3(OH), is associated with two clouds of different velocities separated by 3-4 km s$^{-1}$, having cloud mass of 2000-4000 $M_odot$ in each. In the two regions we have found typical signatures of a cloud-cloud collision, i.e.,the complementary distribution with/without a displacement between the two clouds and/or a V-shape in the position-velocity diagram. We frame a hypothesis that a cloud-cloud collision triggered the high-mass star formation in the two regions. The collision in W3 Main involves a small cloud of $sim$5 pc in diameter which collided with a large cloud of 10 pc $times$ 20 pc. The collision in W3 Main compressed the gas in the direction of the collision path toward the west over a timescale of $sim$1 Myr, where the dense gas W3 core associated with ten O stars are formed. The collision also produced a cavity in the large cloud having a size similar to the small cloud. The collision in W3(OH) has a younger timescale of $sim$0.5 Myr and the forming-star candidates are heavily embedded in the clouds. The results reinforce the idea that a cloud-cloud collision is an essential process in high-mass star formation by rapidly creating the initial condition of 1 g cm$^{-2}$ in the natal gas.
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