Investigating the Correlation between Dark Matter Content, Ages and Mass-to-Light Ratios in Spiral Galaxies

TL;DR

This study investigates how galactic age relates to dark matter content in spiral galaxies by fitting rotation curves with a three-component model (Hernquist bulge, exponential disk, and NFW halo) across a 16-galaxy sample. It identifies dark-matter-dominated regions beyond the NFW scale radius and estimates DM mass, halo density, and I-band M/L using the Tully–Fisher relation, with ages drawn from stellar population studies. The analysis reveals strong positive correlations between age and DM mass ($r \approx 0.91$) and density ($r \approx 0.91$), as well as a notable age–M/L link ($r \approx 0.78$), all robust to outliers. These findings align with assembly-bias and smooth-accretion predictions from cosmological simulations, supporting a picture in which older galaxies have assembled more massive and denser halos and exhibit enhanced dark-matter dominance relative to their luminosity.

Abstract

We present an empirical investigation into the relationship between galactic age and dark matter content across a sample of 16 nearby, well-resolved spiral galaxies. Using raw rotation curve data from IOA Tokyo's publicly available repository, we model each galaxy's mass distribution via a three-component decomposition (Hernquist bulge, exponential disk, and a Navarro-Frenk-White (NFW) dark matter halo) fit using Monte Carlo simulations. The onset of dark matter dominance was identified using the NFW scale radius, beyond which we computed the total enclosed mass via Keplerian dynamics. I-band luminosities for these regions were estimated using a calibrated Tully-Fisher relation, yielding precise mass-to-light (M/L) ratios. We further calculated dark matter mass and density using NFW profile equations, and galaxy ages were retrieved through an extensive literature survey of stellar population studies. Our analysis reveals strong positive correlations between galactic age and both dark matter mass (Pearson $r \approx 0.91$; Spearman $ρ\approx 0.93$) and density (Pearson $r \approx 0.91$; Spearman $ρ\approx 0.91$), as well as M/L ratios, suggesting a robust link between evolutionary history and dark matter build-up. These findings are in quantitative agreement with predictions from large-scale cosmological simulations that incorporate assembly bias and smooth accretion-dominated growth, reinforcing the view that older galaxies, having formed earlier in high-density peaks, have accumulated significantly more dark matter over cosmic time. Our results offer observational evidence for time-dependent dark matter assembly and establish galactic age as a meaningful tracer of halo evolution.

Figures (7)

• Figure 1: Decomposed rotation curves for the sample of 16 spiral galaxies. The black points with error bars represent the observed raw rotation velocities derived from combined CO, HI, and optical observations.
• Figure 2: Identification of Dark Matter dominated regions. The vertical line marks the NFW scale radius ($r_s$) for each galaxy. The region to the right ($r \ge r_s$) is defined as the dark matter-dominated envelope. The total enclosed mass ($M_{enc}$) and I-band luminosity were calculated specifically within this outer radial domain to minimize baryonic contamination.
• Figure 3: Correlation between Dark Matter Mass ($M_{DM}$) and Galactic Age. The scatter plot shows a strong positive correlation (Pearson $r \approx 0.91$) between the age of the stellar population and the mass of the dark matter halo. The solid line represents the linear best fit. This trend supports the "smooth accretion" scenario, suggesting that older galaxies have had more cosmic time to accumulate diffuse dark matter.
• Figure 4: Correlation between Dark Matter Density ($\rho_{DM}$) and Galactic Age. The data reveals that older galaxies possess significantly denser dark matter halos (Pearson $r \approx 0.91$). This result is quantitatively consistent with cosmological "assembly bias" simulations, which predict that early-forming halos are more concentrated than those forming later.
• Figure 5: Dark Matter Mass ($M_{DM}$) vs. Mass-to-Light Ratio ($(M/L)_I$). The positive correlation (Pearson $r \approx 0.85$) indicates that galaxies with more massive halos are increasingly dark matter-dominated relative to their optical luminosity.