Galaxies That Build, Merge and Keep Their Stars (v8.6)

The BPT law

BPT Part 3.14 (Wells and Galaxies) gives every heart a galaxy, its stars and gas the ones its well holds, a satellite well's stars its host's; the Disk Turn Rate sets how a disk turns, Ω_d = √(Δ_v/2)·H_f/(√2·λ⟲), fastest for the disks that formed earliest; and the Eddington Ratio of a Well makes a heart feeding near its limit a quasar. The author, 14 November 2026: "it still needs a ton of work on galaxies building and their movement and the stars movement around them."

The established physics

• Galaxies assemble hierarchically. Small galaxies form first and merge into larger ones; the number of luminous galaxies rises as they form, and the massive ones grow by mergers (White & Rees 1978; Lacey & Cole 1993). A merger turns disks into spheroids: the late universe's massive galaxies are ellipticals and lenticulars, its forming ones spirals (Toomre & Toomre 1972; Barnes & Hernquist 1992).
• Galaxies grow in size. At a fixed stellar mass a galaxy's radius grows about as the scale factor, (1 + z)^−1 for disks and faster for spheroids (van der Wel et al. 2014).
• A minor merger's stars spread through the host in a few of its dynamical times, as streams and shells (Toomre & Toomre 1972; Johnston et al. 2008).
• Quasars have an era. Their number peaks near z ≈ 2, about a third of the present scale factor, at the peak of star formation, and falls after; dimmer active nuclei (Seyferts) dominate later (Richards et al. 2006; Madau & Dickinson 2014). About one quasar in ten is radio-loud, with jets (Kellermann et al. 1989; Ivezić et al. 2002).

The game's math

The galaxies are read as before (Parts 6.1 to 6.5, app.js updateGalaxies, every four Pulses); 8.6 changes how they are drawn (scene3d.js).

• Each galaxy keeps its own stars (setGalaxies() scene3d.js:559). Each galaxy is a record kept by its well's id: its stars, its drawn centre, its drawn reach, its arms' angle, its type. A reading gives each galaxy its count of points (its share of the galaxies' share of the points the device draws, Part 6.8). The record adds the points it gained, each born fading in over 1.2 s (galPoint() scene3d.js:594, the same layout and light rules as Part 6.8), and lets go the ones it lost, the newest first, fading out over 1.2 s. Its stars are never redrawn at fresh places, so a reading changes the picture by what the galaxy gained or lost, not as a new picture.
• A change of type is gradual (scene3d.js:574). When a reading gives a galaxy a new type (a spiral quenched to a lenticular, a merger's spheroid), about 35 % of its stars are let go and replaced by stars of the new type, at each reading until the type stands.
• A galaxy grows under its stars (scene3d.js:751). A star keeps its distance as a share u of its galaxy's reach; the reach drawn is the reading's R (Part 6.5) times 0.4 + 0.6·a^0.8 (a the scale factor, expansionA), gliding to it with a time constant of 0.8 s. Small after the big bang, its full drawn size at the final well.
• A galaxy whose well has merged falls into its host (scene3d.js:580). A galaxy missing from a reading falls into the nearest galaxy within two of their reaches together: its centre glides to the host's with a time constant of 0.9 s, its stars draw in to 0.3 of their distance and fade over 3 s; with no host near, it fades where it stands. The host's new stars fade in as its count rises.
• The centre glides with a time constant of 0.25 s to its well's drawn place, across the torus's seam by the short way.
• The turning (scene3d.js:749). Each star turns on its own orbit, Ω(ρ) as in Part 6.6, and the arms with their pattern. A galaxy's turning is slowed by one factor so that at its scale length it turns at most once in three seconds of the screen: a young disk turns tens of times a flip by the Disk Turn Rate, and held only to the frames' Nyquist limit (Part 6.6) an early galaxy strobed. All its stars slow together, so its inner stars still lap its outer ones.
• The streams (placeStreams() scene3d.js:723) fall to the galaxy as drawn, its glided centre and its grown reach.
• Quasars (scene3d.js:1728). Every well feeding at a tenth of its Eddington rate or more blazes with its glow; one in ten, by a hash of its well's id, the radio-loud, stands two jets out of the skin.
• Quiet hearts (scene3d.js:1711). A heart feeding below a hundredth of its Eddington rate is drawn as a black point of 0.011 of the torus's span in a galaxy and 0.008 alone, half the 0.022 and 0.016 of a feeding one; Well #1 (0.03) and the Ascendant Wells (0.026) keep their marks. A quiet black hole is seen by the stars round it (Part 8.5).

The method, in plain steps:

each reading (every 4 Pulses):
    for each galaxy read: keep its record; add the points it gained (fading in), let go the ones it lost (fading out)
        a new type: let go about a third of its points and draw new ones of the type
    each galaxy not read: it falls into the nearest galaxy within two reaches, or fades where it is
each drawn frame:
    each galaxy's centre glides to its well; its reach glides to R · (0.4 + 0.6 · a^0.8)
    its arms turn, and each star on its own orbit, all slowed by one factor to at most a turn in 3 s
    each star is placed at its share of the reach, its size by its fade

What one run showed

The run of 14 November 2026 (Part 9.11), at level 202: five galaxies after the big bang, all starbursts; 106 by a quarter of the final size; 156 by half; 219 at the final well; spirals the most numerous through the middle of the life, lenticulars, dwarf spheroidals and the first ellipticals rising at its close; up to 27 galaxies at a time falling into their hosts. Quasars: 5 just after the big bang, 64 to 82 between about 0.3 and 0.47 of the final size, then 9 to 24 to the end, the Seyferts rising from 0 to 64 at half the size and about 20 after.

Fixed numbers