Cosmology

EstablishedDirect evaluation of the area law, the adiabat, and the Alfvén speed at the printed base. The 10 G mean is not retuned.

Open Coronal Hole

The open field has no throat. A factor-of-ten adiabat lands at 0.323 MK. The banked channel is a footpoint shake, an ion handoff, and the outward mirror.

Last updated: 8 October 2026

Reading this entry

The open coronal hole page evaluates an untuned 10 G base whose area widens outward, then uses a γ = 5/3 adiabat and an isothermal Parker wind to fix the cool-hole temperature and the speed at Earth. The public channel for that hole is a footpoint shake, an ion handoff, and the outward mirror.

What this is used for

The corona page cites these hole numbers when the two regions are kept distinct. The factor-of-ten landing at 0.323 MK, the Alfvén speed 6897 km s⁻¹, and the 0.8 MK wind at 419 km s⁻¹ are the figures it uses, and the 1 km s⁻¹ driver stays the footpoint shake.

Walk through

Flux conservation gives A ∝ r^s when B ∝ r^{−s}, so from 10 G a full sphere yields 21.6 nT at 1 AU for s = 2 and 0.101 nT for s = 3. On a γ = 5/3 adiabat, 0.1^{2/3} = 0.215 takes 1.5 MK to 0.323 MK, while 0.8–1.0 MK is a density ratio 0.39–0.54. At n_p = 10⁷ cm⁻³ and 10 G the Alfvén speed is 6897 km s⁻¹, and along a field line b̂·(j×B) = 0, so the mirror is the surviving gyrotropic term. With c_s = √(2kT/m_p), the 0.8 MK wind has critical radius 7.22 R and reaches 419 km s⁻¹ at 1 AU for s = 2, s = 3 reaches 526 km s⁻¹, and the 2.0 MK row reaches 752 km s⁻¹.

This page is the open-hole account. The closed-loop package at is a different region, on the coronal-heating page. The base field here stays . The driver stays.

Flux conservation gives when . For the area grows outward. There is no throat. From over a full sphere, gives at , and gives .

and a factor-of-ten density drop. The band – is a density ratio –.

Left: temperature versus density ratio on a gamma 5/3 adiabat, with the factor-of-ten point at 0.323 MK below the 0.8 to 1.0 MK band. Right: Alfvén speed at 10 G, with the printed density far above the 750 to 800 km/s band. — At the Alfvén speed is . A four-percent mass addition in alpha particles lowers it to .

Along a field line, . The magnetic-pressure gradient is cancelled by tension. The mirror force is the surviving gyrotropic term, and it is the banked mirror.

Temperature	Critical radius	Speed at 1 AU
0.8 MK	7.22 R	419 km/s
1.0 MK	5.78 R	485 km/s
1.5 MK	3.85 R	628 km/s
2.0 MK	2.89 R	752 km/s

The isothermal Parker integral uses . Along the field the parallel Lorentz force is zero, so the base does not enter the speed. At the solution reaches at , from a base speed of . The solution reaches . A bulk speed of at turns sonic at and supplies no speed at Earth. The figure stays the footpoint shake.

Speed against radius for the isothermal wind at 0.8 MK. The s=2 curve ends at 419 km/s and the s=3 curve at 526 km/s. Both sit below the 750 to 800 km/s band. — The – band is the row of the same integral, . That row is not the hole.

The hole is the cool row. The public sentence for that hole is the banked channel: a footpoint shake, an ion-circle handoff, and the outward mirror. Electrons in that account stay near . A fast-stream Alfvén speed at Earth, for and with the banked helium factor, is .

Integrity

The area law, the adiabat, the cancellation along the field, the printed Alfvén speed, and the isothermal terminal speeds are direct evaluations. The wind bank stays the current-first channel. The mean and the driver are not retuned. This page charters no ledger row and does not promote.

Source Documents

The working note for this page. It charters no ledger row and does not promote.

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