The cold dark matter model predicts galaxies have 100 times more dark matter mass than stars. Nevertheless, recent observations report the existence of dark-matter-deficient galaxies with less dark matter than expected. To solve this problem, we investigate the physical processes of galaxy formation in head-on collisions between gas-containing dark matter subhaloes (DMSHs). Analytical estimation of the collision frequency between DMSHs associated with a massive host halo indicates that collisions frequently occur within one-tenth of the virial radius of the host halo, with a collision time-scale of about $10 \,\mathrm{Myr}$, and the most frequent relative velocity increases with increasing radius. Using analytical models and numerical simulations, we show the bifurcation channel of the formation of dark-matter-dominated and dark-matter-deficient galaxies. In the case of low-velocity collisions, a dark-matter-dominated galaxy is formed by the merging of two DMSHs. In the case of moderate-velocity collisions, the two DMSHs penetrate each other. However, the gas medium collides, and star formation begins as the gas density increases, forming a dwarf galaxy without dark matter at the collision surface. In the case of high-velocity collisions, shock-breakout occurs due to the shock waves generated at the collision surface reaching the gas surface, and no galaxy forms. For example, the simulation demonstrates that a pair of DMSHs with a mass of $10^9\,\mathrm{M_\odot}$ containing gas of 0.1 solar metallicity forms a dark-matter-deficient galaxy with a stellar mass of $10^7\,\mathrm{M_\odot}$ for a relative velocity of $200 \,\mathrm{km\,s^{-1}}$.
The paper was published in the Monthly Notices of the Royal Astronomical Society.