Modeling the Future of Gaia Neutron Star–Main-sequence Binaries: From Eccentric Orbits to Millisecond Pulsar–White Dwarfs

Abstract We use MESA to model the future evolution of the 21 Gaia neutron star (NS)–main-sequence binaries (orbital period P orb ∼ 200–1000 days, eccentricity e ≳ 0.2) under two prescriptions: eccentric mass-transfer and enforced efficient circularization before the initiation of mass-transfer. All systems terminate as NS–white dwarfs (WDs), albeit different mass-transfer modes yield sharply divergent properties. Under eccentric mass-transfer, binaries are driven to higher eccentricities (final e ≳ 0.6 mostly) and P orb ∼ 1000–4000 days. Mass-transfer episodes in eccentric orbits are brief (≲10 6 yr), transfer only a few ×10 −2 M ⊙ , and produce only mildly recycled pulsars (spin-period P spin ∼ 100 ms) with low-mass helium WDs. Artificially circularized mass-transfer produces shorter final orbital periods of P orb ∼ 200–2000 days and allows mass-transfer to occur for ∼10 7 yr, so that the NSs accrete ∼0.1 M ⊙ , yielding fully recycled millisecond pulsars (MSPs) with P spin ∼ few–30 ms, including nine systems with carbon–oxygen WDs. Enabling super-Eddington accretion up to 100× the canonical limit makes even eccentric channels efficiently produce MSPs. Incorporating an adaptive, field-dependent magnetic-field-decay timescale, our models reproduce the observed Gyr-long radio lifetimes of MSPs. Independent of the mass-transfer treatment, the descendants of these Gaia systems do not resemble the bulk of the known Galactic MSP–WD binaries, which are nearly circular with P orb ≲ 100 days. The observed MSP–WDs are likely produced by systems with more massive companions that undergo unstable mass-transfer and NS in a common-envelope phase—an evolutionary channel that is not relevant for the Gaia binaries.