Estimations of dark matter fractions for ETGs using the broken-power-law model and machine learning techniques

ABSTRACT Using gravitational lensing data combined with machine learning techniques, we probe the dark matter fractions within 77 early-type galaxies (ETGs) up to redshifts of $z \approx 0.7$. Our analysis leverages data from the strong-lensing surveys BOSS Emission-Line Lens Survey and Sloan Lens ACS Survey. Guided by the broken-power-law (BPL) model and the Fundamental Plane, we estimate total galaxy masses within the visible radius. Central to our approach is a two-layer ensemble of machine-learning models designed to infer the stellar mass-to-light ($M/L$) ratio from minimal observed data. Our methodology bolsters predictive accuracy and addresses prevalent machine learning challenges, notably overfitting and hyperparameter sensitivity. To further enhance reliability, we adopt bootstrapping techniques for error estimation in the $M/L$ ratio, providing a rigorous method to quantify uncertainties. With average stellar masses of $5.08 \times 10^{10}\, \mathrm{M}_\odot$, we find that all of the galaxies studied exhibit a dark matter fraction $\ge 70{{\ \rm per\ cent}}$, with a mean value of $87.57{{\ \rm per\ cent}} \pm 1.11{{\ \rm per\ cent}}$. A notable trend is the positive correlation between the dark matter fraction and dark matter mass. Further, clear correlations link dark matter fractions to galaxy size and luminosity. These insights underscore the role of gravitational lensing as an indispensable tool in probing dark matter and galactic structure. Our research merges advanced machine-learning techniques with rigorous astrophysical analysis, offering a scalable, image-independent method for estimating dark matter content across the full radii of lensing galaxies.