Every system StellarGen produces is the result of a deterministic pipeline rooted in peer-reviewed astrophysics — from initial mass sampling through stellar evolution, orbital mechanics, and planetary demographics. No hand-tuned tables. No arbitrary rolls. Real physics, from first principles.
Rather than polynomial approximations, StellarGen interpolates directly from two peer-reviewed stellar evolution track grids — one covering the full mass range, one optimized for cool, low-mass objects where standard models diverge.
The MIST grid (Choi et al. 2016; Dotter 2016) provides evolutionary tracks computed with the MESA stellar code across masses from 0.1 to 300 M☉. StellarGen uses log-interpolation in both mass and age to extract Teff, luminosity, radius and evolutionary phase at any point in a star's life, from pre-main-sequence through white dwarf cooling. Choi+2016
For masses below ~1.4 M☉ — where magnetic activity, convection, and molecular opacities require special treatment — the BHAC15 grid (Baraffe et al. 2015) is used. This model correctly handles the transition from stellar to sub-stellar regimes and covers brown dwarfs down to 0.01 M☉. Baraffe+2015
Effective temperatures are mapped to MK spectral types using the Pecaut & Mamajek (2013, 2022 update) calibration for B through M dwarfs, and Martins, Schaerer & Hiller (2005) for O-type dwarfs. Pecaut+2013 Martins+2005
Stellar evolutionary endpoints follow mass thresholds calibrated to observations. White dwarf photometry uses Bergeron (1995) and Holberg & Bergeron (2006) BCV corrections. Neutron star magnetic field distributions are drawn from Manchester et al. (2005) ATNF catalogue statistics, with magnetar upper limits following Kaspi & Beloborodov (2017). Manchester+2005 Kaspi+2017
The probability of forming a star of a given mass follows the Kroupa (2001) broken power-law IMF — the standard reference for field star populations. Sub-stellar objects follow the Chabrier (2003) log-normal regime. For primordial Pop III stars, the IMF is top-heavy following Hosokawa et al. (2011) and Hirano et al. (2014). Brown dwarf fractions scale with galactic population following Thies & Kroupa (2007). Kroupa+2001 Chabrier+2003
| Mass range (M☉) | Power-law index α | Stellar type |
|---|---|---|
| 0.013 – 0.075 | log-normal | Brown dwarfs |
| 0.075 – 0.50 | 1.30 | M dwarfs |
| 0.50 – 1.00 | 2.30 | K & G dwarfs |
| 1.00 – 150 | 2.30 | F, A, B, O stars |
| 1.00 – 300 | top-heavy | Pop III only |
Most stars in the galaxy are not isolated. StellarGen generates single, binary, triple and quadruple systems — multiplicity fractions are anchored to observational surveys and depend on primary mass. Duchêne+2013 Tokovinin+2018
In multi-star systems, not all orbits are dynamically stable. StellarGen uses the Holman & Wiegert (1999) critical semi-major axis formulae — the standard analytic result from N-body integrations of hierarchical binary systems.
Here μ = m₂/(m₁+m₂) is the binary mass ratio normalized to [0, 0.5], and e is the binary eccentricity. Eccentricity is clamped to 0.8 — the empirical validity limit of the Holman & Wiegert fits.
Circumbinary disk cavity radii follow the Artymowicz & Lubow (1994) prescription: Rcav = abin × (1.7 + 3.0e), which sets the inner truncation radius for P-type planet formation. Holman+1999 Artymowicz+1994
The habitable zone is defined as the circumstellar region where liquid water can exist on a planet's surface under appropriate atmospheric conditions. StellarGen implements the Kopparapu et al. (2013) polynomial flux model — the current community standard.
| Boundary | Definition | Flux limit |
|---|---|---|
| Inner (optimistic) | Recent Venus | ~1.78 S☉ |
| Inner (conservative) | Runaway greenhouse | ~1.11 S☉ |
| Outer (conservative) | Maximum greenhouse | ~0.36 S☉ |
| Outer (optimistic) | Early Mars | ~0.32 S☉ |
The flux limits are modeled as polynomial functions of Teff, valid for stellar temperatures between 2600 K and 7200 K (M to F dwarfs). For binary systems, StellarGen computes a combined barycentric luminosity before applying the HZ model, and verifies that the resulting zone falls within the dynamical stability region. Kopparapu+2013
Stellar rotation evolves with age through magnetic braking. StellarGen models this via a Rossby-number formalism: the Rossby number Ro = Prot/τc (rotation period divided by convective turnover time) governs the transition between saturated and unsaturated activity regimes.
XUV irradiation drives atmospheric escape on planets. Tidal locking — when a companion's gravity synchronizes a star's rotation with its orbital period — is detected when the tidal synchronization timescale falls below the system age. Locked components have Prot = Porb, which typically pushes them into the saturated X-ray regime.
Planet formation statistics come from the Kepler mission transit survey — the largest homogeneous planet census to date — supplemented by radial velocity surveys. Occurrence rates are functions of stellar host type, orbital period, and planet radius.
Occurrence rates modulated by host star type, metallicity and binary suppression. Mean-motion resonances checked following Fabrycky et al. (2014). Kepler Fabrycky+2014
StellarGen uses over 1 000 physical constants and calibrated parameters across its models — from fundamental CODATA values to empirical distribution coefficients from stellar surveys. The table below shows a representative sample of the foundational constants. Every single value is taken from authoritative international standards or peer-reviewed papers — no rounded or approximate values.
| Constant | Value | Source |
|---|---|---|
| Gravitational constant G | 6.67430×10⁻¹¹ m³·kg⁻¹·s⁻² | CODATA 2018 |
| Speed of light c | 2.99792458×10⁸ m/s | CODATA 2018 |
| Stefan–Boltzmann σ | 5.670374419×10⁻⁸ W·m⁻²·K⁻⁴ | CODATA 2018 |
| Boltzmann constant kB | 1.380649×10⁻²³ J/K | CODATA 2018 |
| Solar mass M☉ | 1.98847×10³⁰ kg | measured (G-dependent) |
| Solar radius R☉ | 6.957×10⁸ m | IAU 2015 |
| Solar luminosity L☉ | 3.828×10²⁶ W | IAU 2015 |
| Solar Teff | 5772 K | IAU 2015 |
| Solar metallicity Z☉ | 0.0134 | Asplund+2009 |
| Age of the Universe | 13.8 Gyr | Planck 2018 |
StellarGen's randomness is entirely deterministic and cross-platform reproducible. All random draws flow through a single hash-based RNG using BLAKE2b — a cryptographic hash function — instead of pseudo-random number generators, which can differ across platforms and Python versions.
Each physical quantity is produced by a unique (seed, label) pair. Changing any label changes the result for that quantity only — all other quantities derived from the same seed remain unchanged. Seeds are 63-bit integers, giving 9.2 × 10¹⁸ unique system combinations.
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