Dark Energy Survey Year 3 results: Optimizing the lens sample in a combined galaxy clustering and galaxy-galaxy lensing analysis

We investigate potential gains in cosmological constraints from the combination of galaxy clustering and galaxy-galaxy lensing by optimizing the lens galaxy sample selection using information from Dark Energy Survey (DES) Year 3 data and assuming the DES Year 1 Metacalibration sample for the sources. We explore easily reproducible selections based on magnitude cuts in $i$-band as a function of (photometric) redshift, $z_{\rm phot}$, and benchmark the potential gains against those using the well established redMaGiC sample. We focus on the balance between density and photometric redshift accuracy, while marginalizing over a realistic set of cosmological and systematic parameters. Our optimal selection, the MagLim sample, satisfies $i < 4 \, z_{\rm phot} + 18$ and has $\sim 30\%$ wider redshift distributions but $\sim 3.5$ times more galaxies than redMaGiC. Assuming a wCDM model and equivalent scale cuts to mitigate nonlinear effects, this leads to $40\%$ increase in the figure of merit for the pair combinations of $\Omega_m$, $w$, and $\sigma_8$, and gains of $16\%$ in $\sigma_8$, $10\%$ in $\Omega_m$, and $12\%$ in $w$. Similarly, in LCDM we find an improvement of $19\%$ and $27\%$ on $\sigma_8$ and $\Omega_m$, respectively. We also explore flux-limited samples with a flat magnitude cut finding that the optimal selection, $i < 22.2$, has $\sim 7$ times more galaxies and $\sim 20\%$ wider redshift distributions compared to MagLim, but slightly worse constraints. We show that our results are robust with respect to the assumed galaxy bias and photometric redshift uncertainties with only moderate further gains from increased number of tomographic bins or the inclusion of bin cross-correlations, except in the case of the flux-limited sample, for which these gains are more significant.