POSYDON: Binary Population Synthesis Framework

• POSYDON is a modular, general-purpose framework that uses detailed MESA stellar evolution grids to simulate binary systems with self-consistent micro and macrophysics.
• It employs a modular Python structure with kNN classification and Delaunay interpolation, accurately evolving both stars and their mutual orbit throughout their lifecycle.
• Applications include modeling gravitational-wave progenitors, X-ray binaries, and supernova companions, with advanced treatments for mass transfer, common envelope evolution, and tidal interactions.

POSYDON is a modular, general-purpose binary population synthesis framework that integrates grids of detailed single and binary stellar evolution models computed with the MESA code. Unlike “rapid” population synthesis methods reliant on analytic fits or simplified recipes, POSYDON evolves both stellar components and their mutual orbit self-consistently, capturing both the microphysics (e.g., mass-transfer rates, chemical profiles, internal core sizes) and macrophysics (e.g., tides, angular momentum transport, common envelope evolution). Its architecture employs Python classes encapsulating system history and interfaces machine learning methodologies to interpolate and classify evolutionary outcomes. The code is designed to support realistic modeling of massive binary populations with applications ranging from gravitational-wave progenitors to the demographics of X-ray binaries and supernova companions.

1. Architecture and Methodological Foundations

POSYDON builds upon extensive grids of one-dimensional stellar and binary evolution models generated with MESA, which provides robust solutions to the equations governing stellar structure. The framework pre-calculates evolutionary tracks for hydrogen-rich and helium-rich stars over mass ranges typically spanning 0.5–300 M☉ (hydrogen-rich), as well as tracks for detached and interacting binary systems. Model outputs are downsampled using an interpolation error-driven criterion and are systematically tagged with derived properties like envelope binding energy, core mass, or chemical abundance profiles.

POSYDON uses a modular Python implementation. Binary systems are represented as composite objects, most commonly as a BinaryStar class aggregating two SingleStar instances and retaining the history of key parameters (mass, radius, spin, orbital elements) throughout their evolution. Evolution is constructed as stepwise progression through phases including zero-age main sequence (ZAMS), Roche-lobe overflow (RLO), common envelope (CE), and eventual core collapse.

When a system’s initial condition falls between pre-computed grid points, a two-stage pipeline is used: first, the evolutionary “channel” (stable MT, unstable MT, etc.) is identified via a k-nearest neighbors (kNN) classifier, then barycentric interpolation is performed within a multidimensional Delaunay simplex.

2. Physical Processes and Prescriptions

The POSYDON framework self-consistently incorporates a broad suite of physical processes, including:

• Mass Transfer: Roche-lobe protocols are context dependent; main-sequence donors use a “contact” scheme, while giants employ the Kolb prescription. Stability of the mass-transfer process is assessed using thresholds (such as mass-loss rates ≳0.1 M☉ yr⁻¹ or L₂ overflow).
• Angular Momentum Evolution: Stellar spin evolution is governed by internal transport, winds, and binary torques:

$$\dot{\Omega} = \frac{2}{3} \frac{R^2\Omega}{I}\dot{M} - \frac{\Omega}{I}\dot{I}$$

where $R$, $I$, and $\Omega$ denote stellar radius, moment of inertia, and angular velocity, respectively.

• Tidal Effects: Tidal dissipation is modeled for both radiative ($(k/T)_{\rm rad}$) and convective ($(k/T)_{\rm conv}$) envelopes:

$$\left(\frac{k}{T}\right)_\mathrm{rad} = \sqrt{\frac{GMR^2}{a^5}(1+q)^{5/6}E_2}$$

$$\left(\frac{k}{T}\right)_\mathrm{conv} = \frac{2}{21} \frac{f_{\rm conv}}\tau_{\rm conv} \frac{M_{\rm conv}}{M}$$

where $E_2$ is the tidal coefficient, $f_{\rm conv}$ a numerical factor, and $\tau_{\rm conv}$ the convective turnover time. Tidal effects enforce spin-orbit coupling and circularization.

Additional mechanisms include stellar wind mass loss (enhanced near critical rotation), magnetic braking for low-mass stars, and gravitational-wave emission acting on the binary orbit.

3. Grids, Machine Learning, and Interpolation

POSYDON’s core functionality hinges on high-resolution grids of MESA stellar and binary models. For each grid:

• Single-star tracks span key evolutionary phases (ZAMS, core collapse, WD formation), for both H-rich and He-rich stars.
• Binary grids consider initial detached binaries, binaries with a compact companion at RLO, and He-rich star binaries paired with compact objects.

Each grid is post-processed to:

• Downsample the tracks while preserving interpolation accuracy,
• Extract physics quantities (envelope binding energy, core mass, chemical abundance profiles),
• Tag systems with their evolutionary state.

To interpolate between sparse grid points, POSYDON uses:

• kNN for evolutionary channel classification,
• Delaunay triangulation for interpolating physical and system properties in multidimensional parameter space (primary/secondary masses, period, metallicity, rotation, etc.).

This ML-driven approach allows population synthesis over large parameter spaces with the fidelity of detailed MESA modeling and computational tractability.

4. Evolutionary Phases Not Covered by Grids

For phases not represented in MESA grids, POSYDON computes the evolution on-the-fly:

• Detached Eccentric Evolution: Post-supernova eccentric binaries evolve via coupled ODEs for separation, eccentricity, and spin:

  $$\dot{a} = \dot{a}_{\rm wind} + \dot{a}_{\rm tides,1} + \dot{a}_{\rm tides,2} + \dot{a}_{\rm GR}$$

  $$\dot{e} = \dot{e}_{\rm tides,1} + \dot{e}_{\rm tides,2} + \dot{e}_{\rm GR}$$

  The non-degenerate star in such a binary is “matched” to its nearest single-star MESA track.

• Common Envelope Evolution: Dynamically unstable MT triggers a CE phase (flagged by mass-loss, envelope expansion, or RLO instability criteria). CE outcomes rely on the α–λ energy prescription:

  $$\alpha_{\rm CE}\left( \frac{GM_{\rm acc}M_{\rm core}}{2a_{\rm post,CE}} - \frac{GM_{\rm tot}M_{\rm acc}}{2a_{\rm pre,CE}} \right) = \frac{GM_{\rm env}M_{\rm core}}{\lambda_{\rm CE} R}$$

  Envelope binding energy and λ are derived “on-the-fly” from detailed profiles.

• Core Collapse and Supernova: At end-of-life, compact object formation employs prescriptions incorporating fallback, neutrino mass-loss, and natal kicks (Maxwellian distributions for kicks) to set post-SN masses, spins, and orbital changes.

5. Target Binary System Scope

The principal target of POSYDON v1.0 is interacting binary systems with massive primaries (>7 M☉) at solar metallicity ($Z \simeq 0.0142$). These are specifically chosen for relevance to neutron star and black hole formation and gravitational-wave progenitor science. The framework addresses only binary (or higher-order) systems where binary interactions decisively alter evolutionary outcomes via mass transfer, CE evolution, and tidal coupling. Initial parameter distributions (mass, period, rotation) can be aligned to observed statistics or theoretical sample design.

Future expansions are planned to extend the coverage to lower-mass stars, wider metallicity regimes, and more diverse formation channels.

6. Integration and Applications

POSYDON’s methodology, combining detailed stellar evolution grids with algorithmic classification and interpolation, enables synthetic population models for:

• Compact object mergers (GW sources, DNSs, BH-NSs, BBHs),
• X-ray binary formation and demographic studies,
• Supernova progenitor and companion statistics,
• Orbital period, eccentricity, mass and spin evolution statistics,
• Tidal and angular momentum transport effects on binary outcomes.

This structure provides a self-consistent predictive platform to interpret observed populations (e.g., with gravitational-wave sources or high-mass X-ray binaries), connect them to physical model uncertainties (common envelope efficiency, supernova kick physics, mass transfer stability), and guide observational constraints.

Conclusion

POSYDON constitutes a next-generation population synthesis framework, integrating detailed stellar and binary physics through modular, ML-enabled simulation architecture. The code enables the statistically robust modeling of massive binary populations by self-consistently evolving structure and interactions, executing physically motivated treatment of mass transfer, tidal dissipation, and CE evolution, and interpolating outcomes over high-dimensional parameter grids. While version 1.0 is tailored for massive binaries at solar metallicity, the approach establishes a foundation for broad studies of compact object formation channels and high-energy transients, bridging rigorous stellar physics with population synthesis and observational interpretation.