Axionic boson stars in magnetized conducting media

Axions are possible candidates for the dark matter in the present Universe. They have been argued to form axionic boson stars with small masses 10^-14M_--10^-11M_. Since they possess oscillating electric fields in a magnetic field, they dissipate their energies in magnetized conducting media such as white dwarfs or neutron stars. At the same time the oscillating electric fields generate a monochromatic radiation with an energy equal to the mass of the axion. We argue that the effect of the energy dissipation can be seen in old white dwarfs. In particular, we show that colliding with sufficiently cooled white dwarfs, plausible candidates of MACHOs, the axionic boson stars dissipate their energies in the dwarfs and heat up the dwarfs. Consequently the white dwarfs in the halo can emit a detectable amount of thermal radiation with the collision. On the other hand, monochromatic radiation can be seen only during the collision, a period of the dwarf passing the axionic boson star. Assuming that MACHOs are dark white dwarfs, we show that there is a threshold in the luminosity function of the white dwarfs below which the number of white dwarfs in the halo increases discontinuously. The threshold in the luminosity function is expected to be located around 10^-5.5L_--10^-7L_. Its precise value is determined by the mass of the axionic boson stars dominant in the halo.