Scientific Foundation

The Science Behind StellarGen

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.

25+ scientific papers
CODATA 2018 constants
IAU 2015 solar values
500+ physics constants

Stellar Evolution Models

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.

MIST — MESA Isochrones & Stellar Tracks

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

BHAC15 — Baraffe et al. 2015

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

Spectral Classification

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

Bolometric luminosity
L = 4π σ R² T⁴

Compact Object Remnants

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

Initial Mass Function

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 – 0.075log-normalBrown dwarfs
0.075 – 0.501.30M dwarfs
0.50 – 1.002.30K & G dwarfs
1.00 – 1502.30F, A, B, O stars
1.00 – 300top-heavyPop III only

Binary & Multiple Star Systems

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

Single
One star. No companion.
Binary
Two stars orbiting a common barycentre.
Triple
Inner pair + distant third companion.
Quadruple
Two binary pairs orbiting each other.

Orbital Stability Zones

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.

S-type (circumstellar) critical semi-major axis

Holman & Wiegert 1999 — S-type
acrit = abin × (0.464 − 0.380μ − 0.631e + 0.586μe + 0.150e² − 0.198μe²)

P-type (circumbinary) critical semi-major axis

Holman & Wiegert 1999 — P-type
acrit = abin × (1.60 + 5.10e + 4.12μ − 2.22e² − 4.27μe − 5.09μ² + 4.61μ²e²)

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

Habitable Zone Calculation

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.

BoundaryDefinitionFlux 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

Rotation, Gyrochronology & XUV Output

Stellar rotation evolves with age through magnetic braking. StellarGen models this via a Rossby-number formalism: the Rossby number Ro = Protc (rotation period divided by convective turnover time) governs the transition between saturated and unsaturated activity regimes.

X-ray activity law
Lx/Lbol = (Lx/Lbol)sat × (Ro/Rosat)−β    [β ≈ 2.6, Rosat ≈ 0.10]

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.

Planetary Occurrence Rates

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.

Rocky
0.5 – 1.6 R⊕
Most common type.
≥1 per star on average.
Super-Earth
1.6 – 4 R⊕
Abundant around
FGK and M dwarfs.
Neptune-like
4 – 8 R⊕
Gas/ice envelope.
Common at long periods.
Gas Giant
8 – 24 R⊕
Rare. Occurrence scales
steeply with host [Fe/H].
Ice Giant
4 – 8 R⊕
Methane-rich.
Common at wide orbits.

Occurrence rates modulated by host star type, metallicity and binary suppression. Mean-motion resonances checked following Fabrycky et al. (2014). Kepler Fabrycky+2014

Physical Constants

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.

ConstantValueSource
Gravitational constant G6.67430×10⁻¹¹ m³·kg⁻¹·s⁻²CODATA 2018
Speed of light c2.99792458×10⁸ m/sCODATA 2018
Stefan–Boltzmann σ5.670374419×10⁻⁸ W·m⁻²·K⁻⁴CODATA 2018
Boltzmann constant kB1.380649×10⁻²³ J/KCODATA 2018
Solar mass M☉1.98847×10³⁰ kgmeasured (G-dependent)
Solar radius R☉6.957×10⁸ mIAU 2015
Solar luminosity L☉3.828×10²⁶ WIAU 2015
Solar Teff5772 KIAU 2015
Solar metallicity Z☉0.0134Asplund+2009
Age of the Universe13.8 GyrPlanck 2018

Deterministic Seed-Based Generation

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.

Deterministic float in [0, 1)
hash_to_float(seed, label) = BLAKE2b(seed ‖ label) mod 2⁵³ / 2⁵³

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.

Scientific References

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