# Fragment mass and the circularization radius

### \(6.48\,M_\odot\) on \(0.4\,\mathrm{pc}\) · rim angular momentum circularizes at \(644\,\mathrm{AU}\)

**Date:** 2026-10-08
**Status:** **RECORD** · public page `/cosmology/filament-line` · no ledger row · no promote
**Parent:** measey.com `documents/a_geom_ft_stellar_condensation_cascade_chunk1.md`

> **The critical line \(\lambda_{\mathrm{crit}}=16.20\,M_\odot\,\mathrm{pc^{-1}}\) on the four-diameter spacing \(0.4\,\mathrm{pc}\) holds \(6.48\,M_\odot\). One solar mass is \(0.154\) of that fragment. The sonic rim specific angular momentum \(j=2.879\times 10^{17}\,\mathrm{m^{2}\,s^{-1}}\), kept through the collapse, circularizes at \(644\,\mathrm{AU}\) about \(6.48\,M_\odot\). The Carrington equator retains \(4.82\times 10^{-6}\) of that rim value. The step from \(644\,\mathrm{AU}\) to a stellar radius is the unpaid shedding. Interior fusion stays held.**

The sheet spacing \(4\pi r_0=0.628\,\mathrm{pc}\) holds \(10.17\,M_\odot\) on the same line. The rim value is the specific angular momentum at \(r_0=0.05\,\mathrm{pc}\) with \(v=c_s\), the quantity already scored. About one solar mass the same \(j\) circularizes at \(4.17\times 10^{3}\,\mathrm{AU}\). Placed on the solar radius it is a speed \(4.14\times 10^{5}\,\mathrm{km\,s^{-1}}\). The Kepler speed at \(R_\odot\) for one solar mass is \(437\,\mathrm{km\,s^{-1}}\). The Carrington equator is \(1.994\,\mathrm{km\,s^{-1}}\).

The path ends at these condensation quantities. It does not name the channel that removes the specific angular momentum between \(644\,\mathrm{AU}\) and \(R_\odot\), and it does not assign the remaining \(5.48\,M_\odot\) of the fragment. Interior fusion stays held. The live line stays §0bn1188. No chip. No promote.

Figure: `public/figures/filament-line/fig2_circularization.png`.