Radio pulsars around intermediate-mass black holes in superstellar clusters

We study accretion in binaries hosting an intermediate-mass black hole (IMBH) of similar to 1000 M-circle dot, and a donor star more massive than 15 M-circle dot. These systems experience an active X-ray phase characterized by luminosities varying over a wide interval, from < 10(36) erg s(-1) up to a few 10(40) erg s(-1) typical of the ultraluminous X-ray sources (ULXs). Roche lobe overflow on the zero-age main sequence and donor masses above 20 M(circle dot)can maintain a long-lived accretion phase at the level required to feed a ULX source. In wide systems, wind transfer rates are magnified by the focusing action of the IMBH yielding wind luminosities greater than or similar to 10(38) erg s(-1). These high-mass IMBH binaries can be identified as progenitors of IMBH-radio pulsar (PSR) binaries. We find that the formation of an IMBH-PSR binary does not necessarily require the transit through a ULX phase, but that a ULX can highlight a system that will evolve into an IMBH-PSR, if the mass of the donor star is constrained to lie within 15-30 M-circle dot. We show that binary evolution delivers the pre-exploding helium core in an orbit such that after explosion, the neutron star has a very high probability to remain bound to the IMBH, at distances of 1-10 au. The detection of an IMBH-PSR binary in the Milky Way has suffered, so far, from the same small number of statistics limit affecting the population of ULXs in our Galaxy. Ongoing deeper surveys or next-generation radio telescopes such as the Square Kilometre Array will have an improved chance to unveil such intriguing systems. The timing analysis of a pulsar orbiting around an IMBH would weigh the black hole in the still uncharted interval of mass around 1000 M-circle dot.