Cosmology

ModelledThe 1.73 MK figure is the closed-loop package. The open hole is the separate account below.

Solar Coronal Heating

A closed-loop balance at the printed current and voltage is 1.73 MK. An open coronal hole is a different region, with a different temperature and a different speed.

Last updated: 8 October 2026

Reading this entry

Solar coronal heating places a closed-loop Spitzer balance, tagged [M], in which differential rotation drives I ≈ 2.0×10¹² A across V ≈ 10 kV and the equilibrium prints 1.73 MK inside the observed coronal range. The open hole is a second region on the same page, with its own temperature and speed.

What this is used for

The open-hole account uses 1.73 MK, the power P = IV = 2.0×10¹⁶ W, and the density 1.0×10¹⁴ m⁻³ as the closed-loop package. The hole section supplies 0.323 MK, Alfvén speed 6897 km s⁻¹, and Parker speed 419 km s⁻¹.

Walk through

The photosphere is printed at 5772 K and the observed corona as 1.5 to 3.0 MK. Closed-loop inputs I ≈ 2.0×10¹² A and V ≈ 10 kV deposit P = 2.0×10¹⁶ W, and the Spitzer balance is T_corona = (P_Birkeland L_loop / (κ₀ A_channel))^{2/7} = 1.732×10⁶ K = 1.73 MK. The table sets 1.73 MK beside 5,772 K and the range 1.50–3.00 MK, with modelled n_e = 1.0×10¹⁴ m⁻³. The open-hole section uses B₀ = 10 G and n_p = 10⁷ cm⁻³, takes 1.5 MK to 0.323 MK on a γ = 5/3 factor-of-ten drop, and prints an Alfvén speed 6897 km s⁻¹ with a Parker wind of 419 km s⁻¹ at 1 AU for 0.8 MK.

Integrity note (Doctrine v1.0.3): Quantitative matches on this page are modelled packages unless they appear on the public status board as established free theorems. Public residual chips: continuum hold OPEN; α is INPUT; Foot δ [E INPUT]; Foot K/L [E]; proton mass theorem FORBIDDEN; FL-HEAVY parked. Soft packages are not finished UFT certificates.

1. The Coronal Heating Paradox

The surface of the Sun (photosphere) has a temperature of . Standard thermal physics dictates that heat flows from hot to cold regions. However, the solar corona is maintained at an astonishing (MK).

The closed-loop package below is one modelled balance, at one printed current and one printed voltage. An open coronal hole is a different region. Its temperature and its speed are in the next section. The two numbers are not two answers for the same plasma.

2. Current Loop Energy Balance & Spitzer Conductive Equilibrium

These inputs are the closed-loop package. Solar differential rotation is taken to drive polar current loops carrying across , depositing power . Equating Ohmic power input to Spitzer thermal conductive losses along magnetic loop channels:

Spitzer Conductive Equilibrium Temperature Formula

3. Comparison with Solar Data

Region / Parameter	Photosphere Surface	Observed Corona Range	CPT Derived Value	Status
Temperature	5,772 K	1.50 – 3.00 MK	1.73 MK	Modelled [M]
Particle Density $n_e$	~10²³ m⁻³	~10¹⁴ m⁻³	1.0 × 10¹⁴ m⁻³	Modelled [M]
Heat Source	Nuclear Core Fusion	Reconnection / Waves	Birkeland Ohmic Dissipation	Modelled [M]

4. The open hole is a different region

Holes and closed bright structures are different objects. The hole account uses the printed base and , with that field left as it is.

A factor-of-ten density drop on a adiabat takes to . The band – is a density ratio –, not a factor of ten. Along a field line the magnetic-pressure gradient is cancelled by tension. The area of a flux tube has no throat.

At that printed base the Alfvén speed is . An isothermal Parker wind at the hole temperature is at . The public sentence for the hole is the banked channel: a footpoint shake, an ion-circle handoff, and the outward mirror. Electrons in that account stay near . The driver is not retuned. The hole page is the open coronal hole.

STATUS: [M] MODELLED PACKAGE FOR THE CLOSED LOOP

The value belongs to the closed-loop inputs printed above. The open hole carries , , and . This page charters no ledger row and does not promote.

Source Documents

The primary research documents underlying this page. All files are freely viewable and downloadable. They represent the working research as written — including integrity tags, equations, and finding IDs.

Two coronal accounts

Documents open in the CPT Research Library — a formatted viewer for all source research files.