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We study the evolution of close binary systems in order to account for theexistence of the recently observed binary system containing the most massivemillisecond pulsar ever detected, PSR J0740+6620, and its ultra-cool heliumwhite dwarf companion. In order to find a progenitor for this object we computethe evolution of several binary systems composed by a neutron star and a normaldonor star employing our stellar code. We assume conservative mass transfer. Wealso explore the effects of irradiation feedback on the system. We find thatirradiated models also provide adequate models for the millisecond pulsar andits companion, so both irradiated and non irradiated systems are goodprogenitors for PSR J0740+6620. Finally, we obtain a binary system that evolvesand accounts for the observational data of the system composed by PSRJ0740+6620 (i.e. orbital period, mass, effective temperature and inferredmetallicity of the companion, and mass of the neutron star) in a time scalesmaller than the age of the Universe. In order to reach an effectivetemperature as low as observed, the donor star should have an helium envelopeas demanded by observations.

Binary evolution leading to the formation of the very massive neutron star in the J0740+6620 binary system