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

TL;DR

This study forwards the evolution of 21 Gaia-identified NS–MS binaries using MESA, incorporating eccentric mass transfer and pulsar spin evolution to predict their endpoints as NS–WD binaries. By comparing eccentric and circularized MT prescriptions, the authors find that eccentric mass transfer yields He WDs with wide, highly eccentric orbits and mild pulsar recycling, while circular MT can produce CO WDs and fully recycled MSPs in wider parameter regimes. The results show distinct final orbital and WD-type distributions between channels and reveal that these Gaia progenitors are unlikely to dominate the Galactic MSP–WD population, implying additional channels such as common-envelope evolution and unstable MT are important. The work connects forward-modelled MSP properties (spin, magnetic field, and orbital parameters) to the observed MSP–WD population, highlighting the need for multiple evolutionary pathways to reproduce the full Galactic distribution and acknowledging observational biases in detecting wide, eccentric systems.

Abstract

We model the evolution of 21 Gaia neutron star (NS)-main-sequence binaries (orbital period $P_{\mathrm{orb}}\sim200$--$1000$ days, eccentricity $e\gtrsim0.2$) using binary evolution with \texttt{MESA}. We examine eccentric mass transfer and models assuming prior circularization. All systems end as NS-white dwarf (WD) binaries, but transfer modes yield distinct outcomes. Under eccentric transfer, binaries are driven to higher $e$, forming orbits with $e\gtrsim0.6$ and $P_{\rm orb}\sim1000$-$4000$ days. Periastron bursts are brief ($\lesssim10^6$ yr), transfer only a few $\times10^{-2}$ M$_\odot$, and produce mildly recycled pulsars ($P_{\mathrm{spin}}\gtrsim50$ ms) with low-mass He WDs. Artificially circularized transfer gives $P_{\rm orb}\sim200$-$2000$ days, lasts $\sim10^7$ yr, and allows NSs to accrete $\sim0.1$ M$_\odot$, forming fully recycled MSPs ($P_{\mathrm{spin}}\sim$ few-30 ms) with CO WDs. Allowing super-Eddington accretion up to $100\times$ the canonical rate makes even eccentric systems efficient MSP producers, though torque coupling remains uncertain. Using an adaptive, field-dependent magnetic-field decay timescale, we find MSPs stay radio-active over Gyr spans. Gaia systems undergoing stable mass transfer remain wide and fail to match the Galactic MSP-WD population, where most, nearly circular systems have $P_{\rm orb}\lesssim100$ days. Binaries with different mass ratios and initial configurations -- likely leading to unstable mass transfer -- are needed to reproduce the observed MSP-WD distribution.

Figures (10)

• Figure 1: Time evolution of key binary and stellar properties for binary ID 0 (left column) and binary ID 5 (right column). We compare four mass-transfer scenarios: Eddington-limited circular (cir–Ed, pink), Eddington-limited eccentric (e–Ed, blue), conservative super-Eddington eccentric (e–SpEdcn, purple), and eccentric with $100\times$ Eddington rate (e–SpEd100, green). Panels from top to bottom show: (a) orbital eccentricity $e$; (b) $\log_{10}(P_{\rm orb}/{\rm d})$; (c) orbital separation at periastron $r_\mathrm{p}$; (d) companion radius $\log_{10}(R_1/R_\odot)$; (e) masses of the companion $M_1$ (solid) and neutron star $M_2$ (dash–dotted); (f) mass-transfer rate $\log_{10}(\dot M/M_\odot,{\rm yr}^{-1})$; and (g) helium (solid) and carbon (dashed) core masses. Time is measured relative to Roche-lobe overflow, $t - t_{\rm RLOF}$. Eccentric models produce short-lived, strongly peaked mass-transfer episodes that consistently form helium WDs, while extended transfer in cir–Ed may occasionally yield carbon–oxygen WDs (e.g., binary ID 5), for our Gaia NS binaries. These binary-evolution outcomes directly feed into our pulsar modelling (Section \ref{['sec:pulsar']}), where the mass-transfer histories determine the subsequent spin-up and magnetic-field burial of the NS.
• Figure 2: Time evolution of the angular‐momentum loss rate, $\log_{10}|\dot J|$, as a function of time since Roche‐lobe overflow, $t - t_{\rm RLOF}$. Top row shows eccentric runs e-–Ed for binary models 0 (left) and 5 (right); bottom row shows the corresponding circular runs cir-–Ed. In each panel the solid black curve is the total $|\dot J|$, while the patterned coloured lines denote the individual loss channels: mass loss (ml, orange dotted), magnetic braking (mb, magenta dashed), spin–orbit coupling (ls, cyan dash‐dotted), and gravitational radiation (gr, purple dash‐dot‐dot), as indicated in the legend. The orbital evolution is dominated by mass exchange and tides (at RLOF) while magnetic braking and gravitational radiation are subdominant.
• Figure 3: Evolution of orbital period $P_\mathrm{orb}$ versus eccentricity $e$ for 21 Gaia NS binaries, starting from their observed values (square markers). We compare models with Eddington‐limited mass transfer (dashed curves, star markers, e-Ed) and fully conservative super‐Eddington mass transfer (dot–dashed curves, triangle markers, e-SpEdcn). Black‐edged squares denote systems that begin with $e \leq 0.4$, where the assumption of delta-function mass loss at periastron Sepinsky2007b is less certain. In all cases, the systems expand and become more eccentric; however, the e-SpEdcn models show weaker expansion and end with slightly lower eccentricities.
• Figure 4: Comparison of initial (square) and final orbital periods: cir-Ed (circle), e-Ed (star), e-SpEdcn (triangle). Coloured squares mark the initial (observed) periods; colours are consistent per 21 individual systems. The solid black guide is $P_\mathrm{orb,1}=P_\mathrm{orb,f}$ (no net change). Dotted gray guides are $P_\mathrm{orb,1}=0.5\times P_\mathrm{orb,f}$ and $P_\mathrm{orb,1}=3\times P_\mathrm{orb,f}$ (indicating a factor-of-two decrease and a threefold increase, respectively). Most final orbits of the binaries increases after full evolution (stable mass transfer and formation of the WD), but four systems in cir-Ed end with periods shorter than their initial values. These binaries expand during stable mass transfer but not enough to recover the orbital period lost during enforced circularization at RLOF.
• Figure 5: Companion mass $M_1$ across 21 Gaia NS binary calculations. Squares denote observed (initial) donor masses; stars, triangles, and circles show the final masses from eccentric Eddington-limited (e-Ed), fully conservative super-Eddington (e-SpEdcn), and circularized Eddington-limited at RLOF (cir-Ed) models, respectively. Shaded vertical bands indicate the metallicity grid ($Z/Z_\odot$). Horizontal dashed lines mark nominal upper mass boundaries for He, CO, and ONe WDs. Although a few eccentric cases (IDs 15–16) lie marginally above the He–CO transition line, their final profiles and central abundances confirm helium‐core compositions. These global mass cutoffs can bias WD-type inference for near-threshold systems, so we instead rely on core-mass fractions and full stellar profiles, which reveal that eccentric-transfer remnants are consistently He WDs, while only wide circularized systems cross into the CO regime