The ASAS-SN Catalog of Variable Stars IX: The Spectroscopic Properties of Galactic Variable Stars

The All-Sky Automated Survey for Supernovae (ASAS-SN) provides long baseline (${\sim}4$ yrs) $V-$band light curves for sources brighter than V$\lesssim17$ mag across the whole sky. We produced V-band light curves for a total of ${\sim}61.5$ million sources and systematically searched these sources for variability. We identified ${\sim} 426,000$ variables, including ${\sim} 219,000$ new discoveries. Most (${\sim}74\%$) of our discoveries are in the Southern hemisphere. Here we use spectroscopic information from LAMOST, GALAH, RAVE, and APOGEE to study the physical and chemical properties of these variables. We find that metal-poor eclipsing binaries have orbital periods that are shorter than metal-rich systems at fixed temperature. We identified rotational variables on the main-sequence, red giant branch and the red clump. A substantial fraction (${\gtrsim}80\%$) of the rotating giants have large $v_{\rm rot}$ or large NUV excesses also indicative of fast rotation. The rotational variables have unusual abundances suggestive of analysis problems. Semi-regular variables tend to be lower metallicity ($\rm [Fe/H]{\sim}-0.5$) than most giant stars. We find that the APOGEE DR16 temperatures of oxygen-rich semi-regular variables are strongly correlated with the $W_{RP}-W_{JK}$ color index for $\rm T_{eff}\lesssim3800$ K. Using abundance measurements from APOGEE DR16, we find evidence for Mg, O and N enrichment in the semi-regular variables. We find that the Aluminum abundances of the semi-regular variables are strongly correlated with the pulsation period, where the variables with $\rm P\gtrsim 60$ days are significantly depleted in Al.