The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR16 luminous red galaxy and emission line galaxy samples: cosmic distance and structure growth measurements using multiple tracers in configuration space

We perform a multi-tracer analysis using the complete Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 luminous red galaxy (LRG) and the DR16 emission line galaxy (ELG) samples in the configuration space, and successfully detect a cross correlation between the two samples, and find $f\sigma_8=0.342 \pm 0.085$ ($\sim25$ per cent accuracy) from cross sample alone. We perform a joint measurement of the baryonic acoustic oscillations (BAO) and redshift space distortions (RSD) parameters at a single effective redshift of $z_{\rm eff}= 0.77$, using the auto- and cross-correlation functions of the LRG and ELG samples, and find that $D_M(z_{\rm eff})/r_d = 18.93\pm 0.37, \ D_H(z_{\rm eff})/r_d = 19.65 \pm 0.54$, and $f\sigma_8(z_{\rm eff}) = 0.445 \pm 0.038$, which is consistent with a $\Lambda$CDM model at $68\%$ CL. Compared to the single-tracer analysis on the LRG sample, the Figure of Merit (FoM) of $\alpha_{\perp}, \alpha_{||}$ and $f\sigma_8$ gets improved by a factor of $1.18$ in our multi-tracer analysis, and in particular, the statistical uncertainty of $f\sigma_8$ is reduced by $11.6 \%$.