The RESOLVE and ECO Gas in Galaxy Groups Initiative: The Group Finder and the Group H I-Halo Mass Relation

We present a four-step group-finding algorithm for the Gas in Galaxy Groups (G3) initiative, a spin-off of the z ~ 0 REsolved Spectroscopy Of a Local VolumE (RESOLVE) and Environmental COntext (ECO) surveys. In preparation for future comparisons to intermediate redshift (e.g., the LADUMA survey), we design the group finder to adapt to incomplete, shallow, or nonuniform data. We use mock catalogs to optimize the group finder's performance. Compared to friends-of-friends (with false-pair splitting), the G3 algorithm offers improved completeness and halo-mass recovery with minimal loss of purity. Combining it with the volume-limited H I census data for RESOLVE and ECO, we examine the H I content of galaxy groups as a function of group halo mass. Group-integrated H I mass M <SUB>H I,grp</SUB> rises monotonically over halo masses M <SUB>halo</SUB> ~ 10<SUP>11</SUP>-10<SUP>14.5</SUP> M <SUB>⊙</SUB>, pivoting in slope at M <SUB>halo</SUB> ~ 10<SUP>11.4</SUP> M <SUB>⊙</SUB>, the gas-richness threshold scale. We present the first measurement of the scatter in this relation, which has a median of ~0.3 dex and is asymmetric toward lower M <SUB>H I,grp</SUB>. We discuss interesting tensions with theoretical predictions and prior measurements of the M <SUB>H I,grp</SUB>-M <SUB>halo</SUB> relation. In an appendix, we release RESOLVE DR4 and ECO DR3, including updates to survey redshifts, photometry, and group catalogs, as well as a major expansion of the ECO H I inventory with value-added data products.