Radio-quiet neutron star 1E 1207.4-5209: a possible strong Gravitational-wave source

There are four puzzles on 1E 1207.4-5209: (1) the characteristic age of the pulsar is much higher than the estimated age of the supernova remnant; (2) the magnetic field inferred from spin-down is significantly different from the value obtained from the cyclotron absorption lines; (3) the spinning down of the pulsar is non-monotonic; (4) the magnitude of the frequency's first derivative varies significantly and its sign is also variable. The third puzzle can be explained by a wide binary system, with orbital period from 0.2 to 6 yr. This letter proposes that all four puzzles can be explained naturally by an ultra-compact binary with orbital period of between 0.5 and 3.3 min. With the shortest orbital period and a close distance of 2 kpc, the characteristic amplitude of gravitational waves is $h\sim3\times10^{-21}$. It would be an excellent source of gravitational-wave detectors such as the Laser Interferometer Space Antenna.