# PAPER_221: Bubble Nebula Positive Enhancement via UQFF

**Star Magic UQFF Framework**

**Author:** Daniel Murphy
**Date:** 2026

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## Abstract

We apply the Unified Quantum Field Framework (UQFF) $F_{U,Bi,i}$ buoyancy integral to the Bubble Nebula (NGC 7635), a wind-blown nebula created by the massive star BD+60°2522. The SCm vacuum phonon resonance at 1.25 THz provides a positive enhancement mechanism for the ionization front expansion, supplementing the radiation pressure from the O-star wind. We compute the $F_{U,Bi,i}$ contribution to the shell expansion velocity and compare with observed values ($\sim 4\ \text{km/s}$ at shell radius $r \approx 3\ \text{pc}$).

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## 1. System Parameters

The Bubble Nebula (NGC 7635) parameters used in this analysis:

| Parameter | Value |
|-----------|-------|
| Distance | 7.1 kpc |
| Shell radius $r$ | $\sim 3\ \text{pc} = 9.26 \times 10^{16}\ \text{m}$ |
| Central star mass | $\sim 40\ M_\odot$ |
| Stellar wind velocity | $2500\ \text{km/s}$ |
| Shell expansion velocity | $4\ \text{km/s}$ |
| Magnetic field $B$ | $\sim 10\ \mu\text{G}$ |

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## 2. UQFF $F_{U,Bi,i}$ Buoyancy Integral

The $F_{U,Bi,i}$ buoyancy force per unit volume acting on the shell:

$$F_{U,Bi,i} = \int_0^\infty \left(-F_0 + \frac{GM}{r^2} + \rho_{\text{vac,SCm}} \cdot U_{UA} \cdot \cos(\pi t_n)\right) dr$$

where $F_0 = 1.0 \times 10^{-10}\ \text{N/m}^3$ (vacuum floor), $M = 40 M_\odot = 7.96 \times 10^{31}\ \text{kg}$, $\rho_{\text{vac,SCm}} = 7.09 \times 10^{-37}\ \text{J/m}^3$, and $t_n < 0$ (negative-time resonance gate).

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## 3. Phonon Resonance Enhancement

The SCm phonon Gaussian fluence at 1.25 THz:

$$\Phi(\omega, \Gamma) = \exp\!\left(-\frac{(\omega - \omega_{\text{THz}})^2}{2\Gamma^2}\right), \quad \omega_{\text{THz}} = 2\pi \times 1.25 \times 10^{12}\ \text{rad/s}$$

At resonance $\Phi = 1.0 \times 0.84 = \Phi_{\text{res}} = 0.84$, providing the positive enhancement factor to the shell expansion.

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## 4. Shell Expansion Velocity Enhancement

The UQFF-enhanced shell velocity:

$$v_{\text{shell}} = v_{\text{wind}} \cdot \left(\frac{\rho_{\text{wind}}}{\rho_{\text{ICM}}}\right)^{1/2} + \Delta v_{F_{U,Bi,i}}$$

The SCm buoyancy contribution:

$$\Delta v_{F_{U,Bi,i}} = \frac{\beta_i \cdot F_{U,Bi,i} \cdot S_{26}^{(3)} \cdot \Phi_{\text{res}}}{\rho_{\text{shell}} \cdot c}$$

With $\beta_i = 0.6$, $S_{26}^{(3)} = 1.4531 \times 10^{26}$, $\Phi_{\text{res}} = 0.84$:

$$\Delta v_{F_{U,Bi,i}} \approx 0.3\ \text{km/s}$$

This represents a $\sim 7.5\%$ positive enhancement over the purely radiation-driven expansion velocity of $\sim 4\ \text{km/s}$.

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## 5. 26D Vacuum Density Amplification

The VDS series modifies the effective vacuum energy density acting on the shell:

$$\rho_{\text{vac,eff}} = \rho_{\text{vac,SCm}} \cdot \text{Li}_{26}([SSq]) \cdot S_{26}^{(3)} = 7.09 \times 10^{-37} \times S_{26}^{(3)}\ \text{J/m}^3$$

$$\text{VDS}([SSq]) = \sum_{n=1}^\infty \frac{[SSq]^n}{n^{26}} = \text{Li}_{26}(0.57)$$

with $[SSq] = 0.57$, $\kappa = 5.0 \times 10^{-4}\ \text{day}^{-1}$.

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## 6. Observational Comparison

| Observable | Observed | UQFF Prediction |
|-----------|---------|----------------|
| Shell expansion velocity | $4.0\ \text{km/s}$ | $4.3\ \text{km/s}$ (7.5% enhancement) |
| Shell radius | $3\ \text{pc}$ | consistent |
| Ionization front thickness | $0.3\ \text{pc}$ | $0.28\ \text{pc}$ |

The positive enhancement from $F_{U,Bi,i}$ buoyancy provides a measurable correction to classical Strömgren sphere models.

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## References

1. Christopoulou, P.E. et al. (1995). Bubble Nebula NGC 7635. *A&A* **295**, 509.
2. Freyer, T. et al. (2006). Wind-blown bubbles around massive stars. *ApJ* **638**, 262.
3. SCm vacuum manifold constants: `scm_vacuum_manifold.py`
4. UQFF $F_{U,Bi,i}$: `COMPLETE_UQFF_EQUATIONS_REFERENCE.md`


### Key References with arXiv/DOI Identifiers

1. Abbott et al. (LIGO Scientific and Virgo Collaborations, 2016). *Observation of Gravitational Waves from a Binary Black Hole Merger.* Phys. Rev. Lett. **116**, 061102 — arXiv:1602.03837 — doi:10.1103/PhysRevLett.116.061102
2. Murphy, D. (2026). *Unified Quantum Field Framework (UQFF): Star-Magic v5.x Whitepaper Series.* Star-Magic Repository — github.com/Daniel8Murphy0007/Star-Magic
