Thermalization Failure II: The Remix

Jan 13

Let me try this again.

I tonally surveilled myself last time.

I've been staring at a hole in the Sun. Not a literal hole, but a hole in the data. A place where the thermometer breaks.

Standard solar physics tells us the Sun's atmosphere (the corona) is a fluid. A hot, soup-like gas where billions of particles collide, share energy, and settle into a nice, average temperature. A "Maxwellian" distribution. It's a comforting idea.

We can use fluid dynamics. We can average everything out. But looking at the radio data from the last forty years, I think that's a lie. I think the corona is a memory.

Thermalization is Forgetting

Let's get physical for a second. What does it mean for a gas to have a "temperature"? It means the particles have collided with each other enough times that they've shared their energy equally. If a fast particle hits a slow one, they swap. Over time, the history of every individual particle is erased. The "fast" ones are dragged down, the "slow" ones are kicked up, and everyone settles into the average. That process (thermalization) is just a physical mechanism for forgetting. In a thermal system, the history of the violence that created the plasma is gone. The system has "forgotten" the explosion that birthed it and settled into equilibrium.

But what if you can't collide? In the quiet corona, the density is incredibly low. A particle can fly for miles before it hits anything. The "Knudsen Number" (the ratio of mean free path to scale size) is high. This means the forgetting mechanism is broken. When a magnetic reconnection event kicks a particle to high speed, it stays fast. It doesn't collide. It doesn't thermalize. But it damn sure remembers the kick. This creates a "Kappa distribution" — a cold core of particles that are just chilling, and a massive "suprathermal tail" of high-speed screamers that refuse to calm down.

The Thermometer is a Lie

We measure the temperature of the Sun using two different tools.

Radio Waves: These interact mostly with the slow electrons (the Core).
UV/X-Rays: These interact mostly with the fast electrons (the Tail).

If the Sun were a fluid (Maxwellian), these two tools would give the same number. They don't. In the Quiet Sun, the Radio says the temperature is 0.6 million degrees. The X-rays say it's 1.5 million degrees. That's a factor of 2.4. That's a fundamental disagreement about reality. The standard model tries to fix this by saying "Oh, it's just instrument calibration" or "Maybe we're looking at different heights."

I don't buy it.

I think the Radio is seeing the truth (the cold core), and the X-ray is seeing the lie (the hot tail). We've been calculating the energy budget of the entire star based on the tail, ignoring the fact that the bulk of the plasma is actually cold.

The Lock: Solar Cycle Invariance

Mercier & Chambe measured R = 2.4 from 2004 to 2011 — through the deepest solar minimum in a century (2008-2009). If this discrepancy were caused by:

Coronal heating variations: R should track activity level. It doesn't.
Instrument calibration drift: R should wander. It doesn't.
Ti >> Te (ion temperature exceeds electron temperature): R should approach 1 at minimum. Landi (2007) showed Ti/Te was "nearly absent" at minimum. R stayed at 2.4.

Only one explanation survives: the distribution shape is set by the Knudsen number, not the heating rate. Kn stays roughly constant in the quiet corona because T and n vary together. The ratio R = κ/(κ-1.5) ≈ 2.4 implies κ ≈ 2.6.

Always.

I got the NRH data (they are awesome, btw). October 30, 2014 — peak of Solar Cycle 24. I (haphazardly?) ran the analysis myself.

Diagnostic	Value
T_radio (NRH 150.9 MHz)	0.54 MK
T_ionization (AIA)	1.31 MK
R	2.43

Same ratio, solar maximum, and three years after Mercier & Chambe's data ended.

The Key: Galaxy Clusters

I started looking at Galaxy Clusters (structures millions of light years across). They have the same problem.

The X-ray temperature doesn't match the "Sunyaev-Zel'dovich" temperature (from the CMB distortion). In the outskirts of these clusters, where the gas is thin, the discrepancy is almost exactly a factor of 2.

FLAMINGO simulations (Kay et al. 2024):

Region	Kn	T_SZ / T_X-ray
Core (100 kpc)	~0.008	~1.0
R₅₀₀ (500 kpc)	~0.04	~1.1
Outskirts (1-2 Mpc)	~0.02-0.04	~2.0

Same Knudsen threshold. Same factor of 2. I didn't go looking for clusters. I didn't tune anything. The physics just... repeated. At a scale 10^15 times larger than the Sun.

Prokhorov et al. (2009) already applied the Owocki & Scudder framework to cluster Fe line ratios. They cited the same 1983 paper I'm using. But nobody connected it to the systematic SZ/X-ray discrepancy.

Two systems. Fifteen orders of magnitude apart. Same threshold. Same ratio. Same physics.

The Mechanism: Solar Wind Direct Measurement

The solar wind is the corona escaping into space. We have spacecraft sitting in it, measuring electron distributions directly.

Pierrard et al. (2022):

"We find strong links between κ and the density, even at low distances (0.4 AU), confirming the anti-correlation between the formation of the power law tails and the collision frequency."

Parker Solar Probe (Halekas et al. 2020):

At 0.17 AU (near Sun, high collision rate): "the halo almost disappears" (distributions more Maxwellian)
At 1 AU: mixed core/halo/strahl, κ ~ 3-5
At 4 AU (low collision rate): halo grows, κ decreases (stronger tail)

This is my mechanism running in reverse. As the solar wind expands, density drops, Kn increases, thermalization fails, kappa develops. They just weren't looking at the corona.

The Battlefield: Planetary Nebulae

There’s a sort of problem. Different ions give different temperatures. Optical recombination lines (ORLs) say one thing, collisionally excited lines (CELs) say another. The field calls them "temperature fluctuations" and blames clumping.

Nicholls et al. (2012) proposed kappa distributions as the solution. They found κ ~ 10 could explain most discrepancies.

Let me do the Knudsen calculation:

Typical planetary nebula:

n_e ~ 10³ cm⁻³ (diffuse regions)
T ~ 10⁴ K
L ~ 0.5 light-year ~ 5×10¹⁷ cm

Mean free path: λ ~ 1.5×10¹⁷ cm

Kn ~ 0.3

That's 30× above the threshold.

And from the literature: "surface brightness and electron density tend to be smaller in PNe with large ADFs" (Robertson-Tessi & Garnett 2005). Low density —> high Kn → large discrepancy.

They already see the correlation.

The Laboratory: Tokamak Fusion Reactors

Here's where it gets ridiculous.

Tokamak physicists have spent billions of dollars trying to predict heat flux in the scrape-off layer (SOL). The Spitzer-Härm formula doesn't work. They use "flux limiters" (empirical correction factors with values α = 0.03 to 0.3).

SOL-KiT simulations (Mijin et al. 2021):

"Line-averaged suppression of the kinetic heat flux (compared to Spitzer-Härm) of up to 50% is observed" "There is a clear enhanced high-energy tail, while the thermal bulk is close to the local Maxwellian"

COMPASS tokamak kinetic modeling:

"normalized power loads are above the classical values and are caused by non-Maxwellian super-thermal electrons" "parallel heat transport is strongly non-local"

They're seeing kappa distributions. They just call them "kinetic effects."

From the INIS database:

"When the electron mean free path becomes bigger than about 1/10 of the parallel temperature gradient scale length, departures from Spitzer thermal conductivity become important."

Kn > 0.1. Same threshold. In a machine you can hold in your hands.

The Table

System	Scale	Kn Threshold	Diagnostic Ratio
Tokamak SOL	10² cm	~0.1	Flux limiters needed
Solar Corona	10⁹ cm	~0.01	R = 2.4
Solar Wind	10¹³ cm	A_e ~ 1	κ = 2–5 measured
Planetary Nebulae	10¹⁷ cm	~0.01–0.3	ORL/CEL discrepancy
Galaxy Clusters	10²⁴ cm	~0.02	T_SZ/T_X ~ 2

Twenty-two orders of magnitude.

I’m tired of being corrected about my curiosity.

Then Say It With Your Chest

The coronal heating "problem" is an accounting error. We measured the tail (1.5 MK), assumed it was the average, and calculated energy requirements from the wrong number. The bulk is cold (0.6 MK). The mystery shrinks (but is still ongoing).
Galaxy cluster mass estimates may be systematically biased. Cosmological parameters derived from X-ray observations assume Maxwellian electrons. If κ ~ 3 in outskirts, the masses are wrong. Dark matter fractions. Hubble tension. All downstream.
ITER's divertor predictions may be off. They're tuning flux limiters empirically. The Knudsen framework tells them why those values work (and when they'll fail).
Every plasma diagnostic that assumes Maxwellian needs an asterisk when Kn > 0.01.

The Human Equivalent

I promised not to be philosophical in this section, but the math begs for it.

We build our societies on the Fluid Model. We want "stability." We want "equilibrium." We want everyone to be "civil." Civilization is just a high-collisionality environment. It is a machine designed to force thermalization. If you are too "hot" (too angry, too creative, and too radical), the system ensures you collide with enough norms, laws, and "best practices" until you regress to the mean. We delete the tails to maintain the temperature.

So look at the Sun. The "interesting" part (the glowing halo that sustains the solar wind) only exists because it refuses to thermalize. It exists in the regime where the lie of the average cannot be enforced.

The universe has a rule: If you are sparse enough, you are allowed to be non-average. You are allowed to have a tail. You are allowed to be a Kappa. But if you get too dense (if you get crowded) the collisions force you to average out. You lose your tail. You thermalize. You forget.

What's Now

The pattern holds across 22 orders of magnitude, five independent fields, and a century of unexplained discrepancies.

We thought the water was boiling, but we were just measuring the steam.

Stay non-thermal.

Stay in motion.

Victor Edmonds