Cosmology

EstablishedDirect evaluation of the critical line at the named temperature and radius.

Critical Filament

At 10 K, a radius of 0.05 pc fixes the density, the Bennett current, and the two clocks. It does not by itself produce a star.

Last updated: 8 October 2026

Reading this entry

The critical-filament page is the cold-line step of the galaxy-to-star bridge, placed as [M packaging]. At 10 K and μ = 2.37 the sound speed and the Bennett line mass fix the density, the current, and the core-bead mass of a 0.05 pc cylinder by direct arithmetic.

What this is used for

Stellar-types and ionization pages take this filament as the condensation quantities they continue. The fragment mass 6.48 M_☉ on a 0.4 pc spacing, the Bennett current 2.70×10¹³ A, and the circularization radius 644 AU are the handoff, and interior clocks continue on the stellar-types page.

Walk through

An isothermal cylinder at T = 10 K and μ = 2.37 has c_s = 0.1866 km s⁻¹ and λ_crit = 2 c_s²/G = 16.20 M_☉ pc⁻¹, and the Ostriker density at r₀ = 0.05 pc is n_H₂ = 2.98×10⁴ cm⁻³. The Bennett current of that line has R_pg = 1, B(r₀) = 35.0 μG, and I = 2.70×10¹³ A, with a four-diameter fragment spacing of 0.4 pc and a sheet factor 4π r₀ = 0.628 pc. At that density the free-fall time is 1.78×10⁵ yr and the Alfvén time is 1.85×10⁵ yr, and the 0.4 pc spacing holds 6.48 M_☉. The rim value j = 2.879×10¹⁷ m² s⁻¹ circularizes at 644 AU about that fragment, and on the solar radius the same j is 4.14×10⁵ km s⁻¹.

An isothermal cylinder at and mean mass has sound speed . The critical line mass is .

The Bennett current of that critical line has pinch ratio and surface field . The current is . A near-critical cylinder fragments on a spacing of about four diameters, for a diameter of . The sheet factor is .

At the density fixed by

, the free-fall time is

and the Alfvén time is

. The

free-fall is the clock at

The specific angular momentum of a sonic rotation at , set against the Carrington solar equator, is larger by a factor . The retained fraction is . The critical line on the four-diameter spacing holds . One solar mass is of that fragment. The sheet spacing holds . Kept through the collapse, the rim value circularizes at about . Placed on the solar radius the same is a speed . The Kepler speed there, for one solar mass, is .

Three radii on a logarithmic axis: the solar radius, 644 AU, and 0.05 pc. — The conserved rim specific angular momentum meets a circular orbit at . The shedding from there to a stellar radius is unpaid. Interior fusion stays held.

The path ends at these condensation quantities. Placed interior clocks are on the stellar-types page.

Integrity

The density, the Bennett current, the spacing, the two clocks, the fragment mass, and the circularization radius are direct evaluations of the named line. The shedding inward of 644 AU is unpaid. Placed interior clocks are on the stellar-types page. This page charters no ledger row and does not promote.

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