AI 中文总结
该研究提出旋涡星系的动力学-测光相空间框架，结合136个SPARC晚型星系数据揭示光与引力的局域耦合，确定暗物质主导的起始过渡半径。
AI 中文摘要
盘星系中发光物质分布与局域引力场的相互作用，蕴含着超出全局标度关系所捕获的物理信息。我们引入由运动学变量$X(R)=V(R)/R$和测光变量$Y(R)=\text{d}\text{ln}I/\text{d}\text{ln}R$定义的“动力学-测光相空间”，将每个银心半径$R$处的局域引力标度与对数面亮度梯度直接逐点对应。$X=V/R=\text{ω}$表示圆周运动的角频率，可探测局域平均质量密度；$Y$则表征恒星光分布的径向陡度。重子主导的内盘具有大的负$Y$值，而暗物质主导的外区趋近于$Y\rightarrow0$。这种双区行为由光滑的S型关系$Y=[a\text{ln}X+b]/(1+\text{exp}[k(X-X_{\text{trans}})])$描述，在重子区简化为对数耦合关系$Y=a\text{ln}X+b$。我们将该框架应用于SPARC数据库中的136个晚型星系，其倾角范围为$20^\text{o}$至$89^\text{o}$，距离为1至130 Mpc，恒星质量跨越5个数量级。决定系数的中位数为$R^2=0.930$，统计验证包含8项独立测试及5折交叉验证。过渡参数$X_{\text{trans}}$标识暗物质主导的起始点，对应样本的中位数过渡半径$R_{\text{trans}}=5.40$ kpc。
英文摘要
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 $X=V/R=ω$ 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.
Journal refPublished in Monthly Notices of the Royal Astronomical Society, Volume 550, Issue 3, August 2026,stag1270
