Generation III Bern Model Overview

• Generation III Bern Model is a comprehensive end-to-end planetary formation and evolution framework that integrates multi-embryo accretion, migration, gas dynamics, and long-term thermodynamic processes.
• The model couples N-body interactions and detailed disc physics with forward modeling of transit and radial-velocity observations to simulate and statistically validate exoplanet survey data.
• It successfully reproduces trends like the radius valley and metallicity correlations while highlighting challenges such as excess planet counts and discrepancies in orbital eccentricities and periods.

Searching arXiv for papers on the Generation III Bern Model and related NGPPS studies. The Generation III Bern model is a combined global end-to-end planetary formation and evolution model within the New Generation Planetary Population Synthesis (NGPPS) framework. Built on the core accretion paradigm, it follows planetary systems from a protoplanetary gas and planetesimal disc through concurrent multi-embryo growth, gas accretion, migration, collisions, and full N-body interactions, and then into Gigayear evolution including cooling, contraction, atmospheric escape, bloating, Roche-lobe overflow, and stellar tides. Its stated purpose is to predict not only masses and orbital distances but also radii, luminosities, magnitudes, evaporation rates, compositions, and long-term orbital evolution across a broad mass and separation range, and to do so in a form suitable for direct statistical comparison with exoplanet surveys (Emsenhuber et al., 2020). In later NGPPS studies, the same framework is used to generate synthetic ensembles of planetary systems and to compare them with Kepler-like transit samples and the HARPS/Coralie radial-velocity survey after applying explicit observational selection effects (Mishra et al., 2021, Emsenhuber et al., 11 Sep 2025).

1. Genealogy within the Bern population-synthesis program

The Generation III Bern model is presented as the first Bern framework that unifies multi-planet formation and long-term post-formation evolution in a single coupled architecture. Earlier Bern generations treated only subsets of that problem: Generation I addressed single-planet formation up to disc dispersal; Generation Ib extended to long-term thermodynamic evolution but remained essentially single-planet; Generation II introduced multiple embryos and N-body interactions but only during the formation phase; Generation III combines these strands into one end-to-end model (Emsenhuber et al., 2020).

Bern generation	Scope	Limitation relative to Generation III
Generation I	Single-planet formation up to disc dispersal	No long-term evolution; no concurrent multi-planet N-body formation
Generation Ib	Long-term thermodynamic evolution	Still essentially single-planet
Generation II	Multiple embryos and N-body interactions during formation	No full post-formation evolution
Generation III	Multi-planet formation plus long-term evolution	Integrates both in one framework

This generational framing is important because the defining novelty of Generation III is not a single physical prescription, but the coupling of previously separate components. The model is explicitly described as bringing together N-body interactions among many concurrently forming embryos and full post-formation evolution including cooling, contraction, atmospheric escape, bloating, Roche-lobe overflow, and tidal decay (Emsenhuber et al., 2020). A plausible implication is that the model’s identity lies as much in systems integration as in any individual submodule.

2. Physical architecture and governing components

The model is organized as a chain of coupled submodules for stellar evolution, gas-disc evolution, planetesimal-disc evolution, planetary internal structure, accretion, migration, N-body dynamics, and long-term evolution (Emsenhuber et al., 2020). The gas disc is treated as a 1D axisymmetric viscous disc with $\alpha$-viscosity, internal and external photoevaporation, irradiation, and vertical thermal structure; later NGPPS studies summarize the adopted turbulence parameter as fixed to

$\alpha = 2\times 10^{-3},$

chosen to reproduce observed disc mass-accretion relations (Emsenhuber et al., 11 Sep 2025). The 2020 global-model paper gives the viscous diffusion equation in the form

$$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$

and emphasizes that disc thermodynamics includes both viscous heating and stellar irradiation (Emsenhuber et al., 2020).

Solid growth proceeds through planetesimal accretion in the oligarchic regime. Planetesimals are treated as a surface-density field with dynamical state variables $e$ and $i$, rather than as individual bodies, and their evolution includes gas drag and stirring by embryos and other planetesimals (Emsenhuber et al., 2020). In the nominal Generation III setup described in the original NGPPS paper, the planetesimal radius is fixed to $300\,\mathrm{m}$, a simplification later identified as consequential when confronting RV data (Emsenhuber et al., 2020, Emsenhuber et al., 11 Sep 2025). The model tracks planetary internal structure through 1D hydrostatic equations and treats planets as having an “onion-like” structure with iron core, silicate mantle, water-ice layer, and H/He envelope; a later improvement noted in the metallicity study is that core composition is tracked self-consistently using the disc compositional model, so the iron/silicate ratio can evolve through planetesimal accretion and giant impacts (Chen et al., 14 Jul 2025).

Gas accretion is split into an attached, planet-limited phase and a detached, disc-limited phase. The papers consistently identify the transition to runaway gas accretion with core masses of order $\sim 10\,M_\oplus$, after which accretion becomes limited by disc supply (Mishra et al., 2021, Emsenhuber et al., 11 Sep 2025). Migration is included in both Type I and Type II regimes, with transition after the Crida et al. criterion in later NGPPS descriptions; multi-planet interactions are handled with the Mercury N-body package, allowing scattering, resonances, collisions, and dynamical instabilities (Emsenhuber et al., 11 Sep 2025, Chen et al., 14 Jul 2025). Long-term evolution then extends to $10\,\mathrm{Gyr}$, including cooling and contraction, atmospheric escape, and tidal migration, which is why Generation III can be used not only for masses and periods but also for radius-distribution and radius-valley analyses (Emsenhuber et al., 2020, Chen et al., 14 Jul 2025).

3. Population-synthesis workflow and initial conditions

The Generation III Bern model is used not merely to simulate individual systems, but to perform population synthesis by Monte Carlo sampling of initial disc and embryo properties. In the NGPPS architecture papers, the synthesis starts from a gas disc, a planetesimal disc, and multiple embryos already inserted into the disc; a representative setup places embryos of mass $10^{-2}\,M_\oplus$ randomly in logarithmic orbital distance between the inner edge and $40\,\mathrm{au}$, with no two embryos within $\alpha = 2\times 10^{-3},$0 Hill radii (Emsenhuber et al., 2020). The metallicity study states that the synthesis starts from a disk state after collapse in the Class I stage, with $\alpha = 2\times 10^{-3},$1 embryos already inserted, each with mass $\alpha = 2\times 10^{-3},$2, randomly placed in logarithmic orbital distance (Chen et al., 14 Jul 2025). In the “peas in a pod” study, embryo locations are described as distributed approximately uniformly in $\alpha = 2\times 10^{-3},$3 between the disk inner edge and $\alpha = 2\times 10^{-3},$4, with spacing by at least $\alpha = 2\times 10^{-3},$5 after runaway growth (Mishra et al., 2021).

The disk properties varied across synthetic systems include gas disk mass, disk size, disk inner edge, disk lifetime or photoevaporation rate, and metallicity or dust-to-gas ratio (Mishra et al., 2021, Chen et al., 14 Jul 2025). The metallicity prescription is given explicitly as

$\alpha = 2\times 10^{-3},$6

with the solar dust-to-gas ratio taken as $\alpha = 2\times 10^{-3},$7 (Chen et al., 14 Jul 2025). This makes host-star metallicity a direct control variable for the initial solid reservoir, and therefore for core-growth timescales, gas-accretion onset, migration history, and dynamical excitation.

Different NGPPS studies use related but distinct synthetic ensembles. The “peas in a pod” analysis simulates $\alpha = 2\times 10^{-3},$8 planetary systems for each of three nominal embryo counts—$\alpha = 2\times 10^{-3},$9, $$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$0, and $$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$1 embryos per disk—and focuses mainly on the $$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$2-embryo population; it also removes “failed embryos” below $$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$3 from most architectural analyses (Mishra et al., 2021). The HARPS/Coralie comparison focuses mainly on the nominal population NG76, with $$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$4 embryos per disc and a $$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$5 formation stage, and on NG76longshot, which extends the formation and N-body stage to $$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$6 to test later dynamical instabilities (Emsenhuber et al., 11 Sep 2025). Synthetic systems are then evolved individually to $$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$7, although specific observational comparisons may evaluate them at $$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$8 or use survey-specific age cuts (Emsenhuber et al., 11 Sep 2025, Chen et al., 14 Jul 2025).

4. Forward modeling of observations and survey confrontation

A central feature of the Generation III Bern model in practice is that its output is not compared to observations “raw.” Instead, the synthetic populations are passed through explicit observational filters. For transit surveys, the NGPPS VI paper introduces KOBE, “Kepler Observes Bern Exoplanets,” as a forward model that takes the intrinsic Bern populations and simulates what a Kepler-like survey would detect (Mishra et al., 2021). KOBE operates in three sequential layers: kobeshadows/ for transit geometry, kobetransits/ for transit detectability and Kepler signal-to-noise using the FGK-star CDPP distribution, and kobevetter/ for Robovetter completeness and reliability. A planet becomes a periodic threshold crossing event if it has at least two transits and $$\frac{\partial \Sigma_g}{\partial t} = \frac{1}{r}\frac{\partial}{\partial r} \left[ 3r^{1/2}\frac{\partial}{\partial r} \left(r^{1/2}\nu\Sigma_g\right) \right] - \text{photoevaporation} - \text{planet accretion}, \qquad \nu = \alpha c_s H,$$9, following Weiss et al. in using a minimum of two transits rather than three (Mishra et al., 2021). The final output is the KOBE catalogue, from which the authors define KOBE multi-planetary systems (KMPS) for direct comparison with the California-Kepler Survey multi-planet sample.

For radial-velocity data, the HARPS/Coralie study applies an analogous biasing procedure to the synthetic populations. The observed reference is the combined HARPS + Coralie volume-limited sample of $e$0 FGK stars within $e$1, containing $e$2 planets/candidates around $e$3 systems and a mean multiplicity

$e$4

For each Monte Carlo realization, $e$5 synthetic systems are drawn, a random line of sight is assigned, $e$6 is computed, and each planet receives a detection probability from the survey completeness map in $e$7 and period; planets in regions with detection probability below $e$8 are treated as undetected (Emsenhuber et al., 11 Sep 2025). Statistical comparison then uses a two-sided Kolmogorov-Smirnov test for one-dimensional distributions, a 2D KS test for mass-period comparisons, and $e$9 biased realizations of the synthetic population to estimate confidence intervals (Emsenhuber et al., 11 Sep 2025).

These forward models are not merely technical wrappers. They are structurally important because they allow three-way comparisons among the underlying Bern population, the biased synthetic detections, and real surveys. This makes it possible to distinguish intrinsic formation signatures from the distortions introduced by transit geometry, completeness, vetting, RV sensitivity, and inclination effects (Mishra et al., 2021, Emsenhuber et al., 11 Sep 2025).

5. Emergent architectures, demographic regularities, and metallicity systematics

One of the most studied outputs of the Generation III Bern model is the emergence of within-system architectural regularities. In the KOBE analysis of “peas in a pod,” adjacent planets in the same synthetic system exhibit strong size similarity and mass similarity. In the KOBE-observed multi-planet sample, the size correlation is reported as Pearson $i$0, while the underlying Bern population already shows $i$1; about $i$2 of adjacent pairs are size-ordered in KMPS, whereas only about $i$3 are ordered in the underlying population (Mishra et al., 2021). The model interpretation is that size similarity is largely derivative of mass similarity, because the KMPS planets display strong mass-radius monotonicity with a Spearman coefficient of about $i$4 (Mishra et al., 2021). The same study argues that mass similarity is primordial, arising from oligarchic growth and broadly uniform early accretion, whereas spacing and packing are not primordial but are strengthened later by orbital migration, resonance capture, mergers, ejections, and other dynamical interactions (Mishra et al., 2021).

The spacing and packing results are particularly revealing about the model’s internal dynamics. For spacing similarity, measured through

$i$5

the underlying Bern population shows a stronger correlation, about $i$6, than the KOBE-observed population, about $i$7, while the CKS sample is reported at about $i$8 (Mishra et al., 2021). Packing correlations show the same pattern: for KMPS, size-based packing gives $i$9 and mass-based packing $300\,\mathrm{m}$0, whereas the underlying population gives about $300\,\mathrm{m}$1 and $300\,\mathrm{m}$2, respectively (Mishra et al., 2021). The stated interpretation is that transit selection tends to dilute, rather than generate, these correlations. Systems with larger lost-planet fractions, used as a proxy for dynamical activity, show stronger spacing and packing correlations, especially in the $300\,\mathrm{m}$3- and $300\,\mathrm{m}$4-embryo populations (Mishra et al., 2021).

The metallicity study extends this demographic program by analyzing how Generation III populations depend on $300\,\mathrm{m}$5. Using biased synthetic samples, it finds positive metallicity correlations for hot, warm, and cold Jupiters with $300\,\mathrm{m}$6 in the occurrence-law parameterization

$300\,\mathrm{m}$7

and weaker but still positive correlations for Neptune-size planets, with $300\,\mathrm{m}$8 for hot Neptunes, $300\,\mathrm{m}$9 for warm Neptunes, and $\sim 10\,M_\oplus$0 for cold Neptunes (Chen et al., 14 Jul 2025). For small Kepler-like planets of $\sim 10\,M_\oplus$1–$\sim 10\,M_\oplus$2, the occurrence rate, system fraction, and multiplicity increase with metallicity up to $\sim 10\,M_\oplus$3 and then decrease at higher metallicity, while sub-Earths exhibit a strong anti-correlation with metallicity (Chen et al., 14 Jul 2025).

A major success claimed for the Generation III Bern model is the reproduction of radius-valley morphology and its metallicity dependence. The metallicity paper adopts the standard solar-mass valley boundaries

$\sim 10\,M_\oplus$4

and reports that the radius valley becomes deeper and more prominent with increasing $\sim 10\,M_\oplus$5, the super-Earth/sub-Neptune ratio changes accordingly, and the mean radius above the valley increases with metallicity, while the lower-side mean radius remains essentially constant (Chen et al., 14 Jul 2025). The quantitative fits

$\sim 10\,M_\oplus$6

$\sim 10\,M_\oplus$7

$\sim 10\,M_\oplus$8

$\sim 10\,M_\oplus$9

$10\,\mathrm{Gyr}$0

are reported to be in quantitative agreement with the LAMOST-Gaia-Kepler analysis of Chen et al. (2022) (Chen et al., 14 Jul 2025).

6. Empirical performance, tensions, and current limitations

When confronted quantitatively with RV data, the Generation III Bern model reproduces several broad observed features but also shows systematic mismatches. The HARPS/Coralie comparison states that the nominal population reproduces two main groups in the mass-distance plane—close-in sub-Neptunes and distant giants—a bimodal mass function with a relative desert between Neptune and Saturn masses, mean multiplicity close to the observed value, a broadly correct metallicity trend, a broadly similar period-ratio distribution, and an eccentricity distribution that at least qualitatively resembles the survey sample (Emsenhuber et al., 11 Sep 2025). The same paper, however, is unusually explicit that the nominal synthetic population has too many planets by about $10\,\mathrm{Gyr}$1, a desert that is too deep by about $10\,\mathrm{Gyr}$2, a relative excess of giant planets by about $10\,\mathrm{Gyr}$3, eccentricities that are on average too low by a factor of about two, with median $10\,\mathrm{Gyr}$4 versus $10\,\mathrm{Gyr}$5, and a metallicity effect that is too weak; the synthetic planets are also overall too close to the star compared with the HARPS sample (Emsenhuber et al., 11 Sep 2025).

Several discrepancies are highlighted as structurally important. The nominal population predicts $10\,\mathrm{Gyr}$6 detectable planets compared with $10\,\mathrm{Gyr}$7 observed, but with mean multiplicity $10\,\mathrm{Gyr}$8, close to the observed $10\,\mathrm{Gyr}$9, implying that the excess lies mainly in the number of systems with detectable planets rather than in extreme over-multiplicity (Emsenhuber et al., 11 Sep 2025). The giant-planet peak is too massive, near $10^{-2}\,M_\oplus$0 instead of the observed $10^{-2}\,M_\oplus$1, which the paper interprets as evidence that envelope masses and detached-phase disc-limited gas accretion are overestimated (Emsenhuber et al., 11 Sep 2025). Sub-Neptunes are too light and too close to the star, with observed systems typically at $10^{-2}\,M_\oplus$2–$10^{-2}\,M_\oplus$3 days while synthetic ones are more often at $10^{-2}\,M_\oplus$4–$10^{-2}\,M_\oplus$5 days (Emsenhuber et al., 11 Sep 2025). The nominal synthetic population contains no hot Jupiters, even though the survey should contain about $10^{-2}\,M_\oplus$6–$10^{-2}\,M_\oplus$7 of them given an occurrence rate of about $10^{-2}\,M_\oplus$8–$10^{-2}\,M_\oplus$9 in $40\,\mathrm{au}$0 stars (Emsenhuber et al., 11 Sep 2025).

Parameter retuning improves some observables but does not remove the underlying tension. The optimized NG192 population increases the planetesimal radius from $40\,\mathrm{au}$1 to $40\,\mathrm{au}$2, reduces both Type I and Type II migration to $40\,\mathrm{au}$3 of the nominal rate, and changes the maximum gas accretion rate from the minimum of Bondi and local reservoir rate to the minimum of Bondi rate and the radial gas flow through the disc (Emsenhuber et al., 11 Sep 2025). This yields $40\,\mathrm{au}$4 planets in $40\,\mathrm{au}$5 systems with mean multiplicity $40\,\mathrm{au}$6, and the KS mass-function distance becomes $40\,\mathrm{au}$7, just below the threshold $40\,\mathrm{au}$8 (Emsenhuber et al., 11 Sep 2025). Yet the model still fails in joint mass-period space, with $40\,\mathrm{au}$9 in the 2D KS test, and the planets remain too close in (Emsenhuber et al., 11 Sep 2025). The paper therefore concludes that simple parameter adjustments are insufficient, and that physical processes appear to be missing.

The metallicity study reaches a closely related conclusion from a different angle. Although it reports that the Generation III Bern model successfully reproduces many observed metallicity correlations, it also states that the predicted dependences of orbital eccentricity and period on $\alpha = 2\times 10^{-3},$00 are significantly weaker than observed (Chen et al., 14 Jul 2025). For instance, the model finds a metallicity difference between planets with $\alpha = 2\times 10^{-3},$01 d and $\alpha = 2\times 10^{-3},$02 d of

$\alpha = 2\times 10^{-3},$03

whereas the observational difference is described as around $\alpha = 2\times 10^{-3},$04 dex (Chen et al., 14 Jul 2025). The stated missing ingredients include the absence of a metallicity dependence of the disk inner edge, the absence of post-disc high-eccentricity migration, and the fact that only the first $\alpha = 2\times 10^{-3},$05 of planetary interactions are modeled, so long-term secular chaos and late dynamical delivery are not captured (Chen et al., 14 Jul 2025). Across both survey-comparison papers, the emerging interpretation is consistent: the Generation III Bern model captures the core physics of formation and early evolution in a physically rich and statistically useful way, but remains incomplete for processes that set the dynamical temperature of planetary systems over Gyr timescales and for channels that produce wider initial architectures, slower detached-phase gas accretion, stronger eccentricity excitation, and late-arriving close-in giants (Emsenhuber et al., 11 Sep 2025, Chen et al., 14 Jul 2025).