A Dynamical-Photometric Phase Space for Spiral Galaxies: Probing the Local Coupling Between Light and Gravity

Abstract

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 $Y\to 0$. This two-regime behaviour is described by the smooth sigmoid relation $Y=[a\ln X+b]/(1+\exp [k(X-X_{\mathrm{trans}})])$, 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 $X_{\mathrm{trans}}$ identifies the onset of dark-matter dominance, corresponding to a median transition radius $R_{\mathrm{trans}}=5.40$\,kpc across the sample.

References in corpus (28)

• A Universal Density Profile from Hierarchical Clustering
• Rotation Curves of Spiral Galaxies
• Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions
• The Baryonic Tully-Fisher Relation
• The Core-Cusp Problem
• SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves
• The Radial Acceleration Relation in Rotationally Supported Galaxies
• One Law To Rule Them All: The Radial Acceleration Relation of Galaxies
• The structure of galactic disks: Studying late-type spiral galaxies using SDSS
• NON-AXISYMMETRIC STRUCTURES IN THE STELLAR DISKS OF GALAXIES
• The small scatter of the baryonic Tully-Fisher relation
• Imfit: A Fast, Flexible New Program for Astronomical Image Fitting
• Reconstructing the stellar mass distributions of galaxies using S4G IRAC 3.6 and 4.5 micron images: II. The conversion from light to mass
• The PdBI Arcsecond Whirlpool Survey (PAWS): Environmental Dependence of Giant Molecular Cloud Properties in M51
• The Spitzer Survey of Stellar Structure in Galaxies (S${}^4$G): Precise Stellar Mass Distributions from Automated Dust Correction at 3.6 microns
• The PdBI Arcsecond Whirlpool Survey (PAWS). I. A Cloud-Scale/Multi-Wavelength View of the Interstellar Medium in a Grand-Design Spiral Galaxy
• Color--Mass-to-Light Ratio Relations for Disk Galaxies
• The Mass Discrepancy-Acceleration Relation: Disk Mass and the Dark Matter Distribution
• The Outer Disks of Early-Type Galaxies. I. Surface-Brightness Profiles of Barred Galaxies
• The baryonic Tully-Fisher relation for different velocity definitions and implications for galaxy angular momentum
• Testing Feedback-Modified Dark Matter Haloes with Galaxy Rotation Curves: Estimation of Halo Parameters and Consistency with $\Lambda$CDM
• A comprehensive catalog of dark matter halo models for SPARC galaxies
• The Relation between Stellar and Dynamical Surface Densities in the Central Regions of Disk Galaxies
• The rapid onset of stellar bars in the baryon-dominated centers of disk galaxies
• The SOPHIE search for northern extrasolar planets. XIV. A temperate ($T_{\mathrm{eq}}\sim 300$ K) super-earth around the nearby star Gliese 411
• The radial acceleration relation in galaxy clusters
• Stellar Accelerations and the Galactic Gravitational Field
• On the possible common origin of M16 and M17