DRUMS Theory · Galaxy Sizes in DRUMS

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Superfluid Halo Concept

In DRUMS, galaxies are embedded within a coherent superfluid medium. The effective galaxy size is determined by the spatial extent over which the baryonic matter remains coupled to the superfluid flow.

\[ \Psi(\mathbf{x},t) = \sqrt{\rho(\mathbf{x},t)} \, e^{i\theta(\mathbf{x},t)} \]

Phase coherence defines the radius \(R_g\).

Effective Radius from Phase Coupling

The superfluid exerts an acceleration on baryonic matter:

\[ a_s(r) = \frac{\hbar}{m} \frac{d}{dr} |\nabla \theta(r)| \]

The galaxy edge is defined where \(a_s(r) = a_{\text{min}}\).

Mass-Size Relation

The integrated baryonic mass within the radius is:

\[ M_b(R_g) = 4\pi \int_0^{R_g} \rho_b(r) r^2 dr \]

Superfluid coupling implies that larger mass leads to larger \(R_g\).

Energy Equilibrium Constraint

Galactic size is limited by the energy balance between gravitational potential and superfluid coupling:

\[ \frac{G M_b(R_g) m_*}{R_g} \sim m_* a_s(R_g) R_g \]

Solving for \(R_g\):

\[ R_g \sim \frac{G M_b(R_g)}{a_s(R_g)} \]

Vortex and Coherence Limit

Quantized vortices limit the maximum coherent region size:

\[ \oint \mathbf{v}_s \cdot d\mathbf{l} = n \frac{h}{m} \quad \Rightarrow \quad n_{\text{max}} \sim \frac{2\pi R_g v_s}{h/m} \]

Beyond this scale, phase coherence is lost and baryonic matter decouples.

Predictive Scaling

DRUMS predicts a scaling between galaxy mass and size that is consistent with observations:

\[ R_g \propto \frac{M_b^{1/2}}{a_0^{1/2}} \]

where \(a_0\) is a fundamental acceleration scale of the superfluid.

Final Interpretation: Galaxies as Coherent Superfluid Structures

Within DRUMS, galaxy sizes are fully explained as:

Set by the spatial extent of superfluid phase coherence — the region over which the superfluid maintains a single-valued phase.
Determined by a threshold acceleration — where the superfluid's coupling to baryonic matter drops below a critical value.
Stabilized by vortex quantization — the maximum coherent region is limited by the formation of quantized vortices in the superfluid.
Scaling naturally with baryonic mass — the observed mass-size relation emerges directly from superfluid dynamics.

In this reading, the size of a galaxy is not a random outcome of hierarchical merging, nor is it set by dark matter halo properties. It is a direct measurement of the superfluid's coherence length in that region of space. Galaxies are not embedded in dark matter halos — they are coherent superfluid structures whose radii are determined by the fundamental coherence properties of the UFluid and its coupling to baryonic matter.

This interpretation explains the observed uniformity of the galaxy mass-size relation across a wide range of masses and environments. The same superfluid coherence that gives rise to emergent gravity and the cosmic web also sets the scales of individual galaxies. Every galaxy is a frozen record of the superfluid's coherence length at the time of its formation.