A galaxy-independent radial variable reveals universal Dark-matter profiles

TL;DR

The paper addresses the lack of a universal dark-matter (DM) halo profile by introducing a galaxy-independent scaling that normalizes galactic radii across SPARC galaxies. By defining $r = r_0 r_{\mathrm{sc}}$ with $r_0$ set by $g_{\mathrm{bar}}(r_0) = 2\times 10^{-12}\,\mathrm{m\,s^{-2}}$ and $r_{\mathrm{sc}} = \sqrt{\frac{2\times 10^{-12}}{g_{\mathrm{bar}}}}$, the authors aggregate 2693 rotation-curve measurements into a single universal radial domain. They find that DM effects start around $r_{\mathrm{sc}} \approx 0.1$, DM mass grows linearly with radius, and the derived DM density follows $\rho_{\mathrm{DM}} \propto r_{\mathrm{sc}}^{-2}$, consistent with an isothermal-like outer halo and a nearly constant unified rotation velocity for larger $r_{\mathrm{sc}}$. These results, not evident in galaxy-by-galaxy fits, provide a model-independent benchmark that constrains standard profiles like NFW and Burkert and place meaningful constraints on the nature of DM particles by implying a dynamically relaxed, gravity-dominated outer halo across SPARC galaxies.

Abstract

Standard parametric halo models fail to provide a universal description of the dark-matter (DM) distribution in SPARC galaxies, motivating a non-parametric approach to identify common DM properties across systems of different sizes and masses. Assuming that in the DM-dominated regime the baryonic mass enters only through a global scale, we define a galaxy-independent radial variable $r_{\mathrm{sc}}$ by factorizing the physical radius as $r = r_0\, r_{\mathrm{sc}}$, where $r_0$ is determined by the condition $g_\mathrm{bar}(r_0) = 2 \times 10^{-12}\,\mathrm{m/s^2}$. Using all 2693 rotation-curve measurements from 153 SPARC galaxies, we derive unified radial distributions of observed acceleration, circular velocity, and DM mass. The combined data reveal: \newline - the onset of DM effects at $r_{\mathrm{sc}} \approx 0.1$, \newline - with DM dominating the baryonic contribution for $r_{\mathrm{sc}} \gtrsim 0.2$. \newline - a linear growth of DM mass with radius, \newline $ m_{\mathrm{DM}}/M_{\mathrm{bar}} = (6.9 \pm 0.2)\, r_{\mathrm{sc}} - (0.30 \pm 0.04)$, \newline - a density profile $ρ\propto r_{\mathrm{sc}}^{-2}$ indicative of an isothermal-like halo, \newline - and a nearly constant unified rotation velocity for $r_{\mathrm{sc}} > 0.2$. These empirical relations are not apparent in galaxy-by-galaxy rotation-curve fits. They suggest that SPARC galaxies share a common outer-halo structure, providing a model-independent benchmark for evaluating theoretical profiles such as NFW and Burkert and offering new constraints on the nature of dark matter.

Figures (4)

• Figure 1: a: Distribution of $g_{\mathrm{obs}}$ values (red dots) and the binned averages (black thick points). Also shown are average values of the $g_{\mathrm{bar}}$ bins (black points/line). b: Distribution of $g_{\mathrm{obs}}$ averages (black thick points) and the fit of Eq. \ref{['equ:fit']} (red). Average values of $g_{\mathrm{bar}}$ are shown as black points and dashed line.
• Figure 2: Unified velocities $v_{\mathrm{u}}$ as a function of $r_{\mathrm{sc}}$ (thick black points). Gray points and blue line show the transformed values from the linear mass fit (Eq. \ref{['equ:medfit']}). Black points and line show the velocities expected from baryonic mass alone.
• Figure 3: a: Observations of DM mass ratios (red dots) and binned averages (thick black points). b: Binned averages (thick black points) and fits from Eq. \ref{['equ:fit']} (red) and Eq. \ref{['equ:medfit']} (blue).
• Figure 4: DM density $\rho_{\mathrm{DM}}$ in shell volumes (thick black points), and $\rho_{\mathrm{DM}} = (k/4\pi) r_{eff}^{-2}$(red points and line).