A unified solution to the low-mass X-ray binary diversity puzzle: saturated magnetic braking coupled with irradiation-driven winds.

The standard magnetic braking (MB) model has long failed to explain key properties of low-mass X-ray binaries (LMXBs) - including their accretion rates, the formation of ultracompact binaries, and orbital expansion - casting doubt on binary evolution and gravitational-wave progenitor predictions. Phenomenological modifications exist, but a unified, physically grounded mechanism has been missing. Here we show that the overlooked coupling between magnetic saturation and irradiation-driven winds (IDW) provides this missing framework. Accretion-powered irradiation enhances the donor wind, which in turn amplifies MB exactly where needed. Our Saturated MB + IDW (SMB + IDW) model simultaneously resolves three outstanding discrepancies with no fine-tuning: (1) it reproduces the full observed distribution of accretion rates across persistent and transient LMXBs; (2) it naturally explains ultracompact X-ray binary formation; and (3) it quantitatively matches the orbital period distribution of descendant millisecond pulsar (MSP) binaries - a critical independent test failed by all previous models. Critically, the SMB + IDW model transforms MB from an externally imposed condition into a self-consistently regulated process tied to the accretion history. By unifying LMXB evolution to MSPs in a single physical picture, our work resolves the long-standing diversity puzzle and establishes a physics-based foundation for next-generation population synthesis, gravitational-wave progenitor predictions, and compact binary interpretation across cosmic time.