Regime 3 — Galaxies Aren’t a Mystery to Solve First
They’re a Structure to Express Correctly
For decades, the baryonic Tully–Fisher relation (BTFR) has been one of the most famous facts in galaxy dynamics.
If you know a galaxy’s baryonic mass, you can predict its rotation velocity with surprising accuracy — and vice versa.
Most people treat this as a curiosity, or a diagnostic tool, or a battleground for dark matter vs. modified gravity.
But there’s a deeper point hiding in plain sight:
The very existence of the BTFR means the galaxy population forms a closed algebraic system using only local observables.
That’s a much bigger deal than it sounds.
The Usual View: BTFR as a Phenomenon
Ask most astronomers what the BTFR is “for,” and you’ll hear things like:
testing halo models
constraining feedback
checking MOND
measuring slopes and scatter
In other words, the BTFR is treated as something to explain.
But that framing skips over the most important structural fact:
The BTFR exists at all — and it exists without tuning.
The Overlooked Fact: Population-Level Closure
Take the SPARC galaxy sample.
Apply strict analysis-level constraints:
no halo fitting
no cosmological scale-setting
no environment-dependent corrections
no curve-by-curve adjustments
only locally measured observables (mass, velocity, radius)
Under those locks, something remarkable happens:
The entire galaxy population still collapses onto a single, low-scatter algebraic relation.
That’s not a model prediction.
That’s not a theoretical assumption.
That’s not a fit with free parameters introduced at the population level.
It’s a structural property of the data.
Galaxies “agree with each other” without any additional global scaffolding.
Why This Is So Surprising
Galaxies are messy.
Different masses, sizes, surface brightnesses, gas fractions, star-formation histories, environments.
If you asked a theorist what should happen when you strip away all global assumptions and all per-galaxy tuning, they’d probably say:
“The population will fall apart.”
But it doesn’t.
Instead:
A single algebraic closure relation survives across the entire population.
That outcome is not guaranteed by any theory — and it is rarely emphasized.
Closure Before Interpretation
This is the key insight:
Galaxies don’t need to be explained first.
They need to be expressed correctly first.
When you express them under strict local-only constraints, they reveal a coherent structure.
The BTFR isn’t just a correlation.
It’s a demonstration that:
Galactic kinematics are representable as a closed system using only what galaxies locally show.
Interpretation — dark matter, modified gravity, feedback — comes after that.