Stellar Null Wells

The BPT law

BPT Part 2.9 states the Stellar Null Well Condition, r▣ = 2·G·M▣/c²: "A dead core with M▣ > M_TOV ≈ 2.3 M☉ collapses inside its own horizon r▣." "This is the same horizon, and the same Null Well, as every other in the book; only the road to it is different. A harmonic collapse makes a Null Well from overflowing data at a Nova; a star makes one from matter that has burned through its fuel. Stellar Null Wells are born small, 5 – 50 Suns, and late, a few million years after the first stars. They grow by accretion and by merging, and with nothing left to eat they evaporate." Its Census of Null Wells makes them "the bulk" of the Progeny Count Law's 2^(L/3). BPT Part 6.10 gives the Stellar Null Well Fraction, f▣ = N_well/N⊛ ≈ 1.3–1.8 × 10⁻³ for the Kroupa function, "about one star in six hundred".

BPT Part 3.14 (Proto Wells: Where Wells Will Form) ties them to the sites: away from direct collapse "the gas cools, breaks into stars, and the site waits for them: its well is born when its first heavy star dies and the remnant sinks to its heart"; in the game, "its first stellar well born within its reach sinks to it (drawn at once) and the two merge into its heart". The ruling of 2026-10-29: "we should see the stars go supernova to create the wells".

The established physics

As Part 5.9: Tolman–Oppenheimer–Volkoff limit; Woosley, Heger & Weaver (2002).

The game's math

stepMatterPost() app.js:678–686, for each well reported by stepStars() (Part 5.9):

ids = registerWells([[r, c]], [mass], pulseCounter, starMult)     a new physical well, weight starMult
wellsFromStars += starMult
the well is marked stellar, ownSuns = rem
if a waiting site's halo holds it: fillSite(site, 'remnant', ...)    the site becomes its galaxy's heart
message for the first three

registerWells() app.js:1509 adds weight to wellsStand, the count of real wells the drawn ones stand for. Stellar wells are excluded from galaxies (!w.stellar, app.js:3095) and from quasar feedback (app.js:783). Their growth, mergers and evaporation are documented with the wells in Chapter 3 (Parts 3.5, 3.7 and 3.10).

Worked case: of the 41,700 stars a level-28 universe's law gives, the code's Kroupa sampler makes about 0.086 % of 25 Suns or more (Part 5.5), about 36 stars that end as wells. Their lives are under 0.02 Tempos against a sub-step of 0.125, so each stellar well appears within a sub-step of its star's birth.

In the game

A Stellar Null Well is born in the same moment as its star's supernova flash (Part 5.9). The first three are announced with a banner headed Stellar Null Well: "A star of N Suns has died and its core collapsed into a well of X Suns · born small, it will feed, merge and in the end evaporate", the third adding " · further ones are counted on the HUD" (app.js:684). After that the Stars line's "stellar wells n" counts them, and the HUD's Wells line counts them among all wells (app.js:2142).

Each well's life record says how it was born: "from a dying star of N Suns: a Stellar Null Well of X Suns" (app.js:681). When the remnant falls inside a waiting site, the site's record adds "its well was born by its first dying star, of N Suns: the remnant sank to its heart" (app.js:682, 1448), and from then the site is its galaxy's heart, drawn and tapped as the galaxies of Chapter 6. The scene's list of wells is refreshed at once (app.js:686); which wells are drawn is Chapter 3's.

At the end the Null wells counted box notes "… from dying stars" (app.js:2778) and the Stars born box "… stellar wells" (app.js:2783).

The scale model

Each drawn stellar well stands for starMult real ones; at level 202 each is about 3 × 10¹⁷.

Where the game and the theory differ

• Dying lots undercount their wells. A lot of n stars that ends as wells reports min(n, 4) wells (Part 5.9), each standing for starMult, so wellsStand and wellsFromStars gain min(n, 4)·starMult while the tally S.bh gains n (and the end card's stellar wells show S.bh·starMult). For n > 4 the census of wells and the count of stellar wells disagree by n/4. The mass is right (each reported well carries n/min(n, 4) of the remnants).

Fixed numbers