Modelling the Future of Gaia Neutron Star-Main Sequence Binaries: From Eccentric Orbits to Millisecond Pulsar-White Dwarf

We model the future evolution of 21 Gaia neutron-star–main-sequence binaries (Porb ≈200–1000 d, e ≳0.2) with MESA, comparing eccentric mass transfer to models that assume rapid circularization. All systems end as NS–WDs, but outcomes diverge. With eccentric transfer, binaries are driven to higher e (most end with e ≳0.6, Porb ≈1000–4000 d). Periastron-triggered bursts are brief (≲10^6 yr), move only a few ×10^−2 M⊙, and yield mildly recycled pulsars (Pspin ≳50 ms) with low-mass He WDs. If we enforce circularized transfer, final periods are shorter (≈200–2000 d), mass transfer lasts ≈10^7 yr, NSs accrete ≈0.1 M⊙, and fully recycled MSPs form (Pspin ≈few–30 ms), including nine systems with CO WDs. Allowing super-Eddington accretion up to 100× the canonical limit makes even eccentric channels efficient recyclers, though torques there are uncertain. Introducing an adaptive, field-dependent magnetic-field decay timescale, we find MSPs remain radio-alive for Gyr. Yet Gaia systems that undergo stable mass transfer stay at long periods and do not match the largely circular Galactic MSP–WD population (Porb ≲100 d). Producing the bulk of observed MSP–WDs likely requires binaries with different mass ratios and initial orbits that undergo unstable mass transfer.