There is provided a mercury-free arc tube for a discharge lamp unit. The mercury-free arc tube includes a plurality of electrodes and a sealed chamber including a metal halide and a starting rare gas enclosed in the sealed chamber. A clearness index value P2·W/ρ is equal to or greater than about 800, where ρ denotes a density (mg/cm3) of the enclosed metal halide, P denotes a pressure (atmospheres) of the enclosed starting rare gas, and W denotes a maximum input power (watts) input to the sealed chamber through the electrodes.