Star system generation

Every star system in Pax Abyssi other than the Solar System is generated. A deterministic pipeline takes a real star's row from the star catalogue and builds its planets, moons, rings and asteroid belts from published planet occurrence rates, templates of how real systems are arranged, and physics engines for each kind of world. Feed it the same star and it builds the same system, every time. We generate systems this way because the surveys have told us, star type by star type, how often planets form and how their orbits are arranged, and a generator built on those numbers produces skies of planets a real astronomer would recognise. This page follows one system through the seven stages and says, at each, what is observation, what is model and what is our own design. The pipeline is IN THE GAME: its output is what a pilot flies through.

1. The star

Everything starts from the star. Its catalogue row supplies a spectral type, brightness and distance; the sim derives the rest. Effective temperature comes from spectroscopy where a measurement exists, otherwise from the star's colour through a blackbody relation ^[1] or from its spectral type through a standard table of dwarf stars ^[2]; mass, luminosity, metallicity and age follow from measured values where the catalogue has them and from standard relations where it does not. Double and multiple stars get companions whose separations and mass ratios are drawn from the measured statistics of binary stars ^{[3] [4]}.

Two derived quantities shape everything downstream. The first is the star's temperature zones. A planet with no atmosphere, reflecting nothing and spreading its heat evenly, settles at the equilibrium temperature

$$T_\mathrm{eq} = 278\ \mathrm{K}\,(1 - A)^{1/4}\left(\frac{L}{L_\odot}\right)^{1/4}\left(\frac{a}{1\ \mathrm{AU}}\right)^{-1/2},$$

where $A$ is the planet's albedo, $L$ the star's luminosity and $a$ the orbital distance; the sim rounds the constant to 279 K. Setting $T_\mathrm{eq}$ fixed and solving for $a$ shows that any temperature boundary moves outward as $\sqrt{L}$. A star 100 times brighter than the Sun has its zones 10 times farther out. The second is the set of snow lines, the distances beyond which ices condense: the sim puts water's at $2.7\sqrt{L}$ AU, following the classic value of 2.7 AU for the young Sun ^[5], and places snow lines for carbon dioxide, ammonia, methane, carbon monoxide and nitrogen farther out on the same scaling.

The sim's six zones, in AU, are

These are generation labels. The science of where liquid water is possible is on Habitable zone.

2. Planets or none

Next the sim decides whether the star has planets at all, with a single probability built from the measured occurrence rates: a base value read off the star's spectral subtype (0.89 for a Sun-like G2 dwarf, 0.96 for M dwarfs, falling steeply for hot stars), multiplied by factors for a close companion star, low metallicity, an old population, an evolved star and extreme youth. The derivation and the survey results behind it are on Planet occurrence. A star with catalogued exoplanets always has planets.

3. The template

A star with planets draws one of 24 planetary system archetypes, templates such as a compact chain of rocky planets, a Sol-like system split at the snow line, or a hot Jupiter with distant companions. The draw is weighted by spectral class, so red dwarfs mostly get compact systems and hot stars mostly get wide or debris-rich ones, then adjusted for the star's metallicity, age, companions, Galactic population and activity. A companion star removes templates whose orbits it would not allow, using the stability limits of Holman and Wiegert ^[6]. The templates carry what the surveys found about how real systems are arranged, including the fingerprints of migration: hot Jupiters, compact resonant chains and wide, cold giants.

4. The blueprint

The template lays out a list of orbital slots, each an orbital distance, by its own spacing rule: resonant period ratios for chains, a near-constant distance ratio for geometric systems, and so on. Each slot is labelled with its zone and filled by drawing a planet type from that template's table for that zone, so a cool-zone slot in a Sol-like template is likely to hold a giant and a torch-zone slot a barren rock or a lava world.

Two further steps adjust the draw. Disc chemistry: the star's composition stands in for the composition of the disc its planets formed from. Where carbon outnumbers oxygen (C/O above 1) carbon planets become five times likelier and silicate worlds less so; an iron-rich disc favours iron planets. Temperature guards: every slot's equilibrium temperature is checked against the type drawn for it. An ice world or subsurface-ocean world above 400 K becomes barren rock, or a lava world above 1,800 K; a volcanic world above 1,200 K and a barren one above 2,000 K become lava worlds.

5. Physics

Each planet then goes to the physics engine for its type, which computes the full property set: mass and radius, surface gravity, atmosphere and pressure, albedo, day and night temperatures, rotation, magnetic field and the rest. An engine can find that the planet it was handed cannot exist as labelled, and send it back with a new type. A greenhouse world that turns out cool enough for water to rain becomes a temperate world; a rocky world whose surface melts becomes a lava world; an ocean that freezes over becomes a subsurface ocean world. Up to five such passes are allowed. Throughout, the engines keep the orbital distance the template gave, so a resonant chain stays resonant. A final pass rerolls look-alikes so that two planets in one system do not wear the same surface.

6. Moons, rings and belts

Moons are added per planet type. Hot giants close to their stars get none, cold gas giants typically get three to eight, and rocky planets zero to three; they are spaced outward from just beyond the planet's Roche limit and kept within a third of its Hill radius (see Natural satellite and Orbit). Giant planets may get rings, placed inside the Roche limit for icy grains, where a moon could not hold together.

Asteroid belts follow the giants. A belt between the star and its innermost giant is placed where that giant's resonances clear and stir the orbits, between its 4:1 and 2:1 mean-motion resonances. Kepler's third law puts those at

$$\frac{a_{4:1}}{a_\mathrm{giant}} = \left(\tfrac{1}{4}\right)^{2/3} = 0.397, \qquad \frac{a_{2:1}}{a_\mathrm{giant}} = \left(\tfrac{1}{2}\right)^{2/3} = 0.630,$$

which for Jupiter at 5.20 AU gives about 2.06 to 3.28 AU, the edges of the real main belt. Outer belts like the Kuiper belt, and Trojan swarms at a planet's leading and trailing Lagrange points, are added with set probabilities (see Asteroid belt).

7. Orbits and time

Each body receives six Keplerian orbital elements, and its position is solved for the game's reference date, 1 January 2538. The whole system is written to a file that the game reads; from then on the game moves every body along its Keplerian ellipse on every simulation tick, in double precision at true scale (see Orbit). Two-body orbits keep every generated system stable and exactly repeatable: the planet you find at a star on one machine is where it is on every other.

Known exoplanet systems

For the 653 catalogue stars with confirmed exoplanets, 928 planets in all in the sim's cross-match with the NASA Exoplanet Archive ^[7], the pipeline keeps the real planets at their measured orbits. Where a planet's radius is unmeasured it is estimated from its mass with the empirical mass-radius relation of Chen and Kipping ^[8], and its type follows from its mass and temperature. The template is chosen to match the known planets, and the sim adds generated planets only in the gaps the surveys could not have seen. A star card in the game keeps the two apart: known planets and generated planets are reported separately.

See also

• Planet occurrence
• Planetary system archetypes
• Star catalogue
• Orbit
• Natural satellite
• Asteroid belt
• Habitable zone
• Planet classification
• Science in Pax Abyssi
• Sol

References

1. 1Ballesteros, F. J. (2012). New insights into black bodies. EPL (Europhysics Letters) 97, 34008. doi:10.1209/0295-5075/97/34008
2. 2Pecaut, M. J. and Mamajek, E. E. (2013). Intrinsic Colors, Temperatures, and Bolometric Corrections of Pre-main-sequence Stars. The Astrophysical Journal Supplement Series 208, 9. doi:10.1088/0067-0049/208/1/9
3. 3Offner, S. S. R. et al. (2023). The Origin and Evolution of Multiple Star Systems. Protostars and Planets VII. arxiv.org/abs/2203.10066
4. 4Moe, M. and Di Stefano, R. (2017). Mind Your Ps and Qs: The Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars. The Astrophysical Journal Supplement Series 230, 15. doi:10.3847/1538-4365/aa6fb6
5. 5Hayashi, C. (1981). Structure of the Solar Nebula, Growth and Decay of Magnetic Fields and Effects of Magnetic and Turbulent Viscosities on the Nebula. Progress of Theoretical Physics Supplement 70, 35-53. doi:10.1143/PTPS.70.35
6. 6Holman, M. J. and Wiegert, P. A. (1999). Long-Term Stability of Planets in Binary Systems. The Astronomical Journal 117, 621-628. doi:10.1086/300695
7. 7NASA Exoplanet Archive. NASA Exoplanet Archive. NASA Exoplanet Science Institute, Caltech/IPAC. exoplanetarchive.ipac.caltech.edu/
8. 8Chen, J. and Kipping, D. (2017). Probabilistic Forecasting of the Masses and Radii of Other Worlds. The Astrophysical Journal 834, 17. doi:10.3847/1538-4357/834/1/17