A mercury-free arc tube for a discharge lamp unit including a closed glass bulb and a pair of electrode rods provided in the closed glass bulb so as to be opposite to each other. The closed glass bulb does not contain mercury as in the related art arc tubes, but contains main light emitting metal halide and starting rare gas enclosed in the closed glass bulb. In accordance with necessity, predetermined buffer metal halide in place of mercury may be enclosed to suppress the lowering of the tube voltage to some extent. In addition, the tube current I is increased to make the tube voltage high. The tube current I (unit: A) and the outer diameter d (unit: mm) of each electrode rod are set to have a relationship of 1.0I/d5.0. As a result, though such an increased tube current is used, the electrode temperature is kept in optimum temperature.