Quasar 2175 \AA$ $ dust absorbers II: Correlation analysis and relationship with other absorption line systems

We present the cold neutral content (H I and C I gas) of 13 quasar 2175 \AA$$ dust absorbers (2DAs) at $z$ = 1.6 - 2.5 to investigate the correlation between the presence of the UV extinction bump with other physical characteristics. These 2DAs were initially selected from the Sloan Digital Sky Surveys I - III and followed up with the Keck-II telescope and the Multiple Mirror Telescope as detailed in our Paper I. We perform a correlation analysis between metallicity, redshift, depletion level, velocity width, and explore relationships between 2DAs and other absorption line systems. The 2DAs on average have higher metallicity, higher depletion levels, and larger velocity widths than Damped Lyman-$\alpha$ absorbers (DLAs) or subDLAs. The correlation between [Zn/H] and [Fe/Zn] or [Zn/H] and log$\Delta$V$_{90}$ can be used as alternative stellar mass estimators based on the well-established mass-metallicity relation. The estimated stellar masses of the 2DAs in this sample are in the range of $\sim$ 10$^9$ to $\sim$2 $\times$ 10$^{11}$ $M_{\odot}$ with a median value of $\sim$2 $\times$ 10$^{10}$ $M_{\odot}$. The relationship with other quasar absorption line systems can be described as (1) 2DAs are a subset of Mg II and Fe II absorbers, (2) 2DAs are preferentially metal-strong DLAs/subDLAs, (3) More importantly, all of the 2DAs show C I detections with logN(C I) $>$ 14.0 cm$^{-2}$, (4) 2DAs can be used as molecular gas tracers. Their host galaxies are likely to be chemically enriched, evolved, massive (more massive than typical DLA/subDLA galaxies), and presumably star-forming galaxies.