Binary Population Synthesis Predictions

• Binary population synthesis predictions are statistical forecasts that map initial binary parameters to observable outcomes in stellar evolution.
• They utilize a range of modeling techniques—from rapid parametric codes to detailed stellar-structure grids—to simulate processes like mass transfer, common envelope evolution, and supernova events.
• These predictions help quantify formation rates and properties of compact objects, supernova progenitors, and other astrophysical transients under varying physical assumptions.

Binary population-synthesis predictions provide statistical forecasts for the properties, rates, and evolutionary pathways of binary star systems and their resultant astrophysical transients based on first-principles or calibrated models of stellar and binary evolution. Binary population synthesis (BPS) leverages large ensembles of synthetic binaries, evolved using physically motivated prescriptions for key processes (mass transfer, common envelope evolution, angular momentum loss, supernovae, etc.), to map initial parameter distributions to expected observable populations such as accreting systems, double-degenerate binaries, compact mergers, supernova progenitors, and their companions.

1. Methodologies and Model Frameworks

BPS codes exist in a diversity of forms, ranging from rapid parametric 'fitting formulae' codes (e.g., BSE, binary_c, ComBinE, COSMIC) to next-generation frameworks built on dense grids of detailed stellar-structure calculations (e.g., POSYDON). These codes begin with initial distributions reflecting observationally motivated primary masses, mass ratios, orbital periods, and eccentricities (e.g., Chabrier, Kroupa, or Salpeter IMFs, flat or power-law q-distributions, log-normal period distributions), and simulate full binary evolution from the zero-age main sequence (ZAMS) through phases such as:

• Roche-lobe overflow (parameterized via Eggleton’s approximation for the lobe radius)
• Dynamically unstable mass transfer triggering common envelope (CE) evolution
• Wind mass loss and, potentially, accretion (e.g., Bondi–Hoyle or wind RLOF)
• Tidal interactions influencing orbital circularization and synchronization
• Core collapse (with prescriptions for supernova types, explosion energies, remnant masses, and natal kicks)
• Gravitational-wave-driven orbital decay for compact binaries

Implementation may use precomputed grids (e.g., MESA-based tracks in POSYDON), machine-learning classifiers, and advanced interpolation schemes to achieve rapid predictions with high fidelity to underlying stellar physics (Andrews et al., 4 Nov 2024, Fragos et al., 2022, Breivik et al., 2019, Han et al., 2020).

Recent advances (e.g., POSYDON v2) expand coverage to a cosmological metallicity range and include treatments of single stars, mergers, and reverse-mass transfer, enabling modeling of the full diversity of high-mass binaries and their remnants (Andrews et al., 4 Nov 2024).

2. Influential Physical Parameters and Their Uncertainties

BPS predictions are subject to major uncertainties arising from:

• Mass Transfer Stability: The criteria (often defined as a critical mass ratio q₍crit₎, or via the relative adiabatic responses ζ_L and ζ_ad) for whether transfer is stable or triggers a CE phase. Prescription choices can dramatically alter predicted populations of post-interaction binaries (Toonen et al., 2013, Clausen et al., 2011, Han et al., 2020).
• Common Envelope Evolution: Encapsulated in the α–λ energy formalism, where α₍CE₎ is the efficiency with which orbital energy unbinds the envelope, and λ parameterizes the envelope binding energy. The treatment of λ (e.g., using internal, thermal, recombination energy, or not) and α₍CE₎ both affect survivability of close binaries and population outcomes. Efficient envelope ejection (large λ or α₍CE₎) favors survival and produces longer post-CE periods (Ablimit et al., 2017, Clausen et al., 2011, Toonen et al., 2013).
• Remnant Mass and Kick Physics: Prescriptions for remnant masses (whether sharp or probabilistic, accounting for fallback and stochasticity) and natal kicks have a large effect on the survival and properties of binaries through supernovae. Probabilistic schemes allow for populations of low-mass black holes in the ‘mass gap’ and more realistic distributions of double neutron star parameters (Mandel et al., 2020).
• Mass Transfer Efficiency: The fraction β or fₐcc of transferred mass accreted by the companion is a critical but poorly constrained parameter. Physically motivated, rotationally limited accretion schemes often yield very low mean efficiencies (~4–7% for SESN companions near solar metallicity), while artificially conservative mass transfer is disfavored by companion statistics (Zapartas et al., 18 Aug 2025, Schürmann et al., 31 Mar 2025). In massive binaries, a mass-dependent transfer efficiency is necessary to reproduce observed Be/X-ray and WR/O binaries (Schürmann et al., 31 Mar 2025).
• Metallicity Effects: The strength of stellar winds (and hence pre-supernova mass loss) scales strongly with metallicity, affecting core masses, remnant-mass distributions, and merger rates. Lower metallicity environments produce higher-mass black holes and elevate merger rates of double compact objects (Ablimit et al., 2017, Lamberts et al., 2018, Andrews et al., 4 Nov 2024).

3. Population Predictions, Observational Benchmarks, and Diagnostics

BPS models are used to predict:

• The birthrates and number distributions of compact binaries (WD+MS, DWD, NS binaries, BH binaries) and their period and mass distributions (Toonen et al., 2013, Breivik et al., 2019, Lamberts et al., 2018)
• The rates, delay-time distributions, and dominant channels for luminous transients: Type Ia/Ib/c/II SNe, gamma-ray bursts (GRBs), and gravitational-wave (GW) source mergers (Clausen et al., 2011, Chrimes et al., 2019, Fragos et al., 2022)
• Elemental yields and chemical enrichment patterns (C, N, O, s-process elements) for various binary fractions and dredge-up calibrations (Osborn et al., 2 Dec 2024)
• The companion demographics and luminosities for SN progenitors, offering tests via direct imaging (e.g., HST detection/non-detection of SESN companions) (Zapartas et al., 18 Aug 2025)
• The expected GW foreground and resolvable populations for LISA and design sensitivities for ground-based detectors (Breivik et al., 2019, Stevenson et al., 2015, Lamberts et al., 2018)

Comparison to observation constrains key physics. For hot subdwarfs, for example, the period distribution of sdB + F-dwarf binaries is especially diagnostic for distinguishing between stable RLOF and CE formation channels (Clausen et al., 2011). The relative frequencies of Be/X-ray binaries, WR binaries, and predicted OB+BH systems in the SMC require mass-transfer efficiency to vary with accretor mass (Schürmann et al., 31 Mar 2025).

In the context of SESNe, companion luminosity demographics from HST imaging match models only if mass accretion efficiency is low and if most massive Wolf–Rayet stars fail to explode (i.e., “failed SN” hypothesis). The population synthesis likelihood framework formalizes this test, utilizing cumulative probability distributions for companion luminosity and rigorous statistical comparison (joint log-likelihoods, Bayes factors) to discriminate between physical models (Zapartas et al., 18 Aug 2025).

4. Case Studies and Specific Findings

Significant results from selected domains include:

• Hot Subdwarfs: The parameterization of helium ignition, choice of λ, and α₍CE₎ strongly control the sdB binary population morphology. Only by targeting the period distribution of sdB + early F dwarf systems can one robustly break parameter degeneracies in mass transfer physics (Clausen et al., 2011).
• Extreme Horizontal Branch Stars and UV Upturn: Including the 2HeWD merger channel in BPS modes naturally produces extreme horizontal branch (EHB) stars as major contributors to the UV upturn in old stellar populations, matching CMD and SED features in NGC 6791 and ETGs (Hernández-Pérez et al., 2013).
• Double Compact Object Mergers: The merger rates, chirp mass distribution, and spatial demographics of black hole and neutron star binaries depend sensitively on metallicity, kick physics, and CE treatment. In Milky Way-type galaxies, BBHs are predominantly produced at low metallicity and reside in the halo and stellar streams (Lamberts et al., 2018).
• Chemical Enrichment: Binary evolution systematically reduces the yields of C and s-process elements compared to single-star yields (by ~20–25% at binary fraction 0.7), and reproduces the observed abundance patterns in Ba stars, with a rare class of massive Ba stars predicted by the models (Osborn et al., 2 Dec 2024).
• SESN Companion Demographics: Population synthesis models predict 80–90% of Type Ib/c SESNe and 60–85% of Type IIb SESNe should retain a rapidly rotating MS companion at explosion, broadly consistent with HST imaging constraints. The observed luminosity distribution disfavors conservative mass transfer and supports hybrid scenarios where only modest mass gain induces successful explosions for less massive, partially stripped progenitors, while massive WR stars often collapse to black holes without a SN display. The likelihood framework for SESN populations is sensitive to companion detection depth and is a benchmark for future survey calibration (Zapartas et al., 18 Aug 2025).

5. Code Comparisons, Consensus, and Discrepancies

Detailed comparison of multiple BPS codes (binary_c, Brussels, SeBa, StarTrack) under matched assumptions reveals that residual discrepancies are rooted in differences in adopted physical prescriptions (e.g., mass transfer, wind AM loss, CE treatment), not in numerical implementation. For WD and DWD channels, concordance is high, provided initial distributions and stability criteria are harmonized (Toonen et al., 2013). Areas requiring further constraint, with substantial downstream population impact, include:

• Single star evolutionary tracks (initial-final mass relations, wind prescriptions)
• Stability criteria for mass transfer (how q₍crit₎ and ζ parameters are chosen)
• CE evolution parameters (choice of energy formalism, value and treatment of λ and α₍CE₎)
• Prescriptions for wind angular momentum loss and natal kick velocity scaling

Assumptions are particularly critical for the prediction of rare but astrophysically informative systems—e.g., high-mass BH mergers, massive Ba stars, or the properties of the most rapidly rotating companions in SESNe (Toonen et al., 2013, Osborn et al., 2 Dec 2024, Schürmann et al., 31 Mar 2025, Zapartas et al., 18 Aug 2025).

6. Future Prospects and Directions

BPS remains a rapidly developing field. Upcoming directions include:

• Expansion of codes such as POSYDON to cosmological metallicity ranges, improved modeling of single-star components, stellar mergers, and reverse-mass transfer, and robust post-processing pipelines for rate calculation across cosmic volume and redshift (Andrews et al., 4 Nov 2024).
• Enhanced integration with large stellar survey data (e.g., Gaia, LAMOST, Kepler, TESS) for improved initial distributions and constraints on uncertain physical parameters (Han et al., 2020).
• Development of probabilistic frameworks and differentiable BPS codes to efficiently explore and infer population parameters directly from GW and electromagnetic survey catalogs, as in backward population synthesis pipelines (Wong et al., 2022).
• Simultaneous use of multi-messenger diagnostics (gravitational-wave, electromagnetic, and chemical enrichment) to break degeneracies in binary evolution physics.
• Systematic observational searches targeting populations robustly predicted by models (e.g., OB+black hole binaries in low-metallicity galaxies (Schürmann et al., 31 Mar 2025), subdwarf–neutron star binaries with high radial velocity semi-amplitudes (Wu et al., 2019), or faint SESN companions in nearby transients (Zapartas et al., 18 Aug 2025)).

Overall, the interplay of increasingly detailed binary evolution modeling, physically calibrated parameterizations, and rigorous statistical confrontation with data is yielding rapidly multiplying insights across the diverse landscape of binary star populations and associated astrophysical transients.