Conversion of Dark matter axions to photons in magnetospheres of neutron stars

We propose a new method to detect observational appearance of Dark Matter axions. The method utilizes observations of neutron stars (NSs) in radio. It is based on the conversion of axions to photons in strong magnetic fields of NSs (Primakoff effect). Whether the conversion takes place, the radio spectrum of the object would have a very distinctive feature -- a narrow spike at a frequency corresponding to the rest mass of the axion. For example, if the coupling constant of the photon-axion interaction is $M=10^{10}$ GeV, the density of Dark Matter axions is $\rho=10^{-24} {\rm g cm^{-3}}$, and the axion mass is $5 {\rm \mu eV}$, then a flux from a strongly magnetized ($10^{14}$ G) NS at the distance 300 pc from the Sun is expected to be about few tenths of mJy at the frequency $\approx 1200$ MHz in the bandwidth $\approx 3$ MHz. Close-by X-ray dim isolated neutron stars are proposed as good candidates to look for such radio emission.