High plasma cut-off frequency blocks the radio emission from accreting millisecond X-ray pulsar SAX J1808.4-3658

SAX J1808.4-3658 is the first discovered transient accreting millisecond X-ray pulsar (AMXP) with a spin frequency of 401 Hz. It has been proposed that its radio pulses should be detected during the low state of X-ray emission, however there is no any successful evidence for its occurring a radio pulsar state with the sensitive radio telescopes. In this paper, we present a calculation of the plasma cut-off oscillation frequency of the accreting plasma above the magnetosphere of SAX J1808.4-3658, and obtain a limiting value of about ∼ 5.9 GHz, corresponding to the lowest X-ray luminosity, which is higher than the favorite “search window” (e.g. 1.4 GHz) of radio pulsar surveys. Moreover, after comparing the pressure of the dipole electromagnetic radiation with that of the accreting matter, we find that the transformational condition from the accretion-powered to rotational-powered pulsar state implies a critical X-ray luminosity of 4.57×10^33 ^-1 . We propose the observational suggestion for searching the radio pulsar state of SAX J1808.4-3658 is that the radio astronomers should use the telescope with high frequency receivers to search the transition from AMXP to radio MSP during the low X-ray luminosity phase (e.g. quiescence).