أين تنتهي النجوم ويبدأ غير المرئي سريع

الملخص الأصلي

كما كتبه المؤلفون، بالإنجليزية arXiv:2608.11264v1

The interplay between luminous matter distribution and the local gravitational field within disc galaxies encodes physical information beyond that captured by global scaling relations. We introduce a \emph{dynamical--photometric phase space} defined by the kinematic variable $$X(R)=V(R)/R$$ and the photometric variable $$Y(R)=\mathrm{d}\ln I/\mathrm{d}\ln R$$, placing the local gravitational scale and the logarithmic surface brightness gradient into direct pointwise correspondence at each galactocentric radius $$R$$. The quantity $$X=V/R=\omega$$ represents the angular frequency of circular motion and acts as a probe of the local mean mass density, while $$Y$$ measures the radial steepness of the stellar light distribution. The baryon-dominated inner disc is characterized by large negative $$Y$$, whereas the dark-matter-dominated outer region approaches $$Y\rightarrow0$$. This two-regime behaviour is described by the smooth sigmoid relation $$Y=[a\ln X+b]/(1+\exp[k(X-X_{\rm trans})])$$, which reduces to the logarithmic coupling $$Y=a\ln X+b$$ in the baryonic zone. We apply this framework to 136 late-type galaxies from the SPARC database, spanning inclinations $$20^{\circ}$$--$$89^{\circ}$$, distances $$1$$--$$130$$\,Mpc, and five decades in stellar mass. The median coefficient of determination is $$R^{2}=0.930$$. Statistical validation includes eight independent tests together with 5-fold cross-validation. The transition parameter $$X_{\rm trans}$$ identifies the onset of dark-matter dominance, corresponding to a median transition radius $$R_{\rm trans}=5.40$$\,kpc across the sample.