Search for pulsations at high radio frequencies from accreting millisecond X-ray pulsars in quiescence

Context. It is commonly believed that millisecond radio pulsars have been spun up by transfer of matter and angular momentum from a low-mass companion during an X-ray active mass transfer phase. A subclass of low-mass X-ray binaries is that of the accreting millisecond X-ray pulsars, transient systems that show periods of X-ray quiescence during which radio emission could switch on. Aims: The aim of this work is to search for millisecond pulsations from three accreting millisecond X-ray pulsars, XTE J1751-305, XTE J1814-338, and SAX J1808.4-3658, observed during their quiescent X-ray phases at high radio frequencies (5 div 8 GHz) in order to overcome the problem of the free-free absorption due to the matter engulfing the system. A positive result would provide definite proof of the recycling model, providing the direct link between the progenitors and their evolutionary products. Methods: The data analysis methodology has been chosen on the basis of the precise knowledge of orbital and spin parameters from X-ray observations. It is subdivided in three steps: we corrected the time series for the effects of (I) the dispersion due to interstellar medium and (II) of the orbital motions, and finally (III) folded modulo the spin period to increase the signal-to-noise ratio. Results: No radio signal with spin and orbital characteristics matching those of the X-ray sources has been found in our search, down to very low flux density upper limits. Conclusions: We analysed several mechanisms that could have prevented the detection of the signal, concluding that the low luminosity of the sources and the geometric factor are the most likely reasons for this negative result.