[Paper Review] Chemical abundances and gas content in disk galaxies: correlations with the $λ$ spin parameter

Bernardo Cervantes Sodi, X. Hernández|ArXiv.org|Feb 25, 2008

Galaxies: Formation, Evolution, Phenomena3 references3 citations

TL;DR

This paper proposes the spin parameter $\lambda$ as a fundamental, objective physical measure for classifying disk galaxies, demonstrating that lower $\lambda$ values correlate with higher metallicities and lower gas fractions, while higher $\lambda$ values correlate with lower metallicities and higher gas mass fractions. Using a simple dynamical model, the authors derive $\lambda$ from observed luminosities and rotation velocities, revealing strong quantitative correlations that surpass traditional Hubble-type classifications.

ABSTRACT

By using a very simple and general model to describe the dynamics of disk galaxies, we estimate the $λ$ spin parameter for a sample of observed galaxies and present a study in which we show that several important physical properties are intrinsically related to the dynamics of the systems. Although correlations between average metallicity with magnitude or Hubble type are evident, we obtain equally strong correlations with the spin parameter, where galaxies with low $λ$ values present higher abundances and galaxies with high $λ$ values are poor in metals. Also, the gas content of the galaxies correlates with $λ$, with high $λ$ systems showing higher gas mass fractions than low $λ$ galaxies, highlighting the important role this parameter plays in the structure of disk galaxies and the proposal of $λ$ as a robust and objective physical measure of galactic morphology.

Motivation & Objective

• To identify a physically grounded, objective parameter to replace subjective Hubble-type classification in disk galaxies.
• To investigate how the spin parameter $\lambda$ correlates with observable galactic properties such as metallicity and gas content.
• To test whether $\lambda$ can serve as a fundamental parameter linking galactic dynamics to chemical and structural properties.
• To provide empirical, quantitative relations between $\lambda$ and key galactic observables for use in numerical galaxy formation models.
• To demonstrate that $\lambda$ offers a more robust and objective classification framework than traditional morphological types, especially for large survey data.

Proposed method

• A simple dynamical model is used to estimate the spin parameter $\lambda$ from observed blue luminosity $L_B$ and rotational velocity $V_{\text{max}}$, using the formula $\lambda \propto V_{\text{max}}^2 / (L_B^{1/2})$.
• The model assumes a constant mass-to-light ratio $k = 1.5$, consistent with prior studies on gas-rich galaxies.
• Chemical abundances (metallicity) and gas mass fractions are derived from the Pilyavets et al. (2006) sample (PVC), enabling direct comparison with $\lambda$.
• Statistical fitting is performed to derive empirical relations between $\log(\mu)$ (gas fraction) and $\log(\lambda)$, yielding a linear fit with correlation coefficient $r = 0.562$.
• The method avoids subjective visual classification by relying solely on measurable dynamical and photometric parameters.
• The analysis includes confidence intervals for fitted parameters and quantifies scatter (0.167 dex) in the observed correlations.

Experimental results

Research questions

• RQ1 How does the spin parameter $\lambda$ correlate with the metallicity of disk galaxies?
• RQ2 What is the relationship between $\lambda$ and the gas mass fraction in disk galaxies?
• RQ3 Can $\lambda$ serve as a more objective and quantitative alternative to Hubble-type classification?
• RQ4 How do abundance gradients and star formation timescales relate to $\lambda$ in low-mass disk galaxies?
• RQ5 To what extent does $\lambda$ explain variations in galactic structure, such as disk thickness and bulge-to-disk ratio?

Key findings

• Galaxies with low $\lambda$ values exhibit higher metallicities, while those with high $\lambda$ values are metal-poor, confirming theoretical expectations.
• A significant correlation is found between $\lambda$ and gas mass fraction, with high-$\lambda$ systems showing higher gas fractions than low-$\lambda$ systems.
• The empirical relation $\log(\mu) = 0.384 \log(\lambda) + 0.082$ (with $r = 0.562$) quantifies the inverse correlation between $\lambda$ and metallicity.
• The correlation between $\lambda$ and metallicity is stronger than with Hubble type or luminosity, and is more objective and quantitative.
• Low-$\lambda$ systems show steeper abundance gradients, indicating more pronounced radial metallicity variations.
• The results are consistent with independent findings from Berta et al. (2008), who confirm the $\lambda$-star formation rate correlation in SDSS galaxies.