[Paper Review] MaNGA DynPop -- V. The dark-matter fraction versus stellar velocity dispersion relation and stellar initial mass function variations in galaxies: dynamical models and full spectrum fitting of integral-field spectroscopy

Shengdong Lu, Kai Zhu+4 more|arXiv (Cornell University)|Sep 21, 2023

Galaxies: Formation, Evolution, Phenomena7 citations

TL;DR

This paper analyzes how dark matter fraction within one half-light radius and IMF variations depend on stellar velocity dispersion using Jeans Anisotropic Modelling and SPS-based mass-to-light ratios on the MaNGA DR17 sample, focusing on IMF trends and their spectral signatures. It confirms a trend of increasing dark matter fraction at lower velocity dispersions and an IMF variation with velocity dispersion, with marginal evidence for IMF-sensitive spectral differences.

ABSTRACT

Using the final MaNGA sample of 10K galaxies, we investigate the dark matter fraction $f_{ m DM}$ within one half-light radius $R_{ m e}$ for about 6K galaxies with good kinematics spanning a wide range of morphologies and stellar velocity dispersion. We employ two techniques to estimate $f_{ m DM}$: (i) Jeans Anisotropic Modelling (JAM), which performs dark matter decomposition based on stellar kinematics and (ii) comparing the total dynamical mass-to-light ratios $(M/L)_{ m JAM}$ and $(M_{\ast}/L)_{ m SPS}$ from Stellar Population Synthesis (SPS). We find that both methods consistently show a significant trend of increasing $f_{ m DM}$ with decreasing $σ_{ m e}$ and low $f_{ m DM}$ at larger $σ_{ m e}$. For 235 early-type galaxies with the best models, we explore the variation of stellar initial mass function (IMF) by comparing the stellar mass-to-light ratios from JAM and SPS. We confirm that the stellar mass excess factor $α_{ m IMF}$ increases with $σ_{ m e}$, consistent with previous studies that reported a transition from Chabrier-like to Salpeter IMF among galaxies. We show that the $α_{ m IMF}$ trend cannot be driven by $M_{\ast}/L$ or IMF gradients as it persists when allowing for radial gradients in our model. We find no evidence for the total $M/L$ increasing toward the centre. We detect weak positive correlations between $α_{ m IMF}$ and age, but no correlations with metallicity. We stack galaxy spectra according to their $α_{ m IMF}$ to search for differences in IMF-sensitive spectral features (e.g. the $ m Na_{ m I}$ doublet). We only find marginal evidence for such differences, which casts doubt on the validity of one or both methods to measure the IMF.

Motivation & Objective

• Quantify how the dark matter fraction within the half-light radius correlates with stellar velocity dispersion using dynamical and SPS-based approaches.
• Investigate IMF variations by comparing JAM-based and SPS-based mass-to-light ratios across a large MaNGA sample.
• Assess whether IMF variations inferred dynamically align with IMF-sensitive spectral feature indicators.
• Examine correlations of IMF indicators with age and metallicity, and test robustness with a stratified (golden) sample of high-quality galaxies.
• Explore potential biases or degeneracies in dynamical vs. spectral IMF inferences and discuss implications for IMF universality.
• method_percentage_idk

Proposed method

• Apply axisymmetric Jeans Anisotropic Modelling (JAM) to the full MaNGA sample to derive dark matter and stellar mass components under multiple halo shapes (MFL, NFW, gNFW).
• Compute the dark matter fraction f_DM within Re from JAM (NFW/gNFW) and from SPS-based estimates using f_DM = 1 - (M/L_SPS)/(M/L_JAM) as an alternative cross-check.
• Use SPS fitting (ppxf) on stacked spectra within the half-light ellipse to derive global luminosity-weighted age, metallicity [Z/H], and M*/L_SPS with a fixed Salpeter IMF and MIST isochrones.
• Correct JAM M/L for dust attenuation using factors from SPS in Paper II to enable robust M/L comparisons.
• Define the stellar mass excess factor alpha_IMF = (M*/L_JAM)/(M*/L_SPS) to probe IMF shape variations with velocity dispersion.
• Stack spectra by alpha_IMF to search for IMF-sensitive features (e.g., Na I) and assess spectral evidence for IMF variations.
• Sample selection starts with ~9878 galaxies with dynamical and stellar population properties; a high-quality “golden” sample (Qual=3) includes 909 galaxies, with 235 morphologically classified as early-type (T-Type ≤ 0).

Experimental results

Research questions

• RQ1 What is the relation between dark matter fraction within Re and stellar velocity dispersion across MaNGA galaxies?
• RQ2 Do JAM- and SPS-derived mass-to-light ratios agree in revealing dark matter content and IMF-related variations?
• RQ3 Does the IMF indicator alpha_IMF correlate with age and metallicity, and does a spectral IMF signal appear when stacking by alpha_IMF?
• RQ4 Are IMF trends robust when restricting to high-quality early-type galaxies (golden sample) and when comparing different JAM halo assumptions?

Key findings

• Dark matter fraction within Re decreases with increasing velocity dispersion below about log10(sigma_e) ~ 2.1, becoming very low at higher sigma_e (consistent across JAM-NFW and SPS-based estimates).
• The JAM-based total M/L shows a parabolic trend with sigma_e, while the JAM-based stellar M/L and SPS-based M*/L show roughly linear correlations with sigma_e, indicating dark matter dominance at low sigma_e and reduced DM contribution at high sigma_e.
• The IMF excess alpha_IMF increases with sigma_e, supporting a transition from Chabrier-like to Salpeter-like IMFs in higher-dispersion galaxies; weak positive correlations with age are found, but no clear correlation with [Z/H].
• Stacked spectra by alpha_IMF yield only marginal differences in IMF-sensitive features (e.g., Na I), casting doubt on either method’s IMF inferences or the universality of IMF indicators in these data.
• Among the golden sample (Qual=3; 235 ETGs), robust IMF-related trends persist, though the authors note potential degeneracies and the challenge of interpreting IMF from integrated light.
• There is general agreement between dynamical and SPS-based approaches in signaling a decreasing DM fraction with increasing sigma_e up to ~log10(sigma_e)=2.2, followed by a plateau or mild increase at higher dispersions.