GRB host galaxies with strong H2 absorption: CO-dark molecular gas at the peak of cosmic star formation

We present a pilot search of CO emission in three H-2-absorbing, long-duration gamma-ray burst (GRB) host galaxies at z similar to 2-3. We used the Atacama Large Millimeter/submillimeter Array (ALMA) to target the CO(3 - 2) emission line and report non-detections for all three hosts. These are used to place limits on the host molecular gas masses, assuming a metallicity-dependent CO-to-H-2 conversion factor (alpha(CO)). We find, M-mo(l) < 3.5 x 10(10) M-circle dot (GRB 080607), M-mo(l) < 4.7 x 10(11) M-circle dot (GRB 120815A), and M-mo(l) < 8.9 x 10(11) M-circle dot (GRB 181020A). The high limits on the molecular gas mass for the latter two cases arc a consequence of their low stellar masses M-* (M-* less than or similar to 10(8) M-circle dot) and low gas-phase metallicities (Z similar to 0.03 Z(circle dot)). The limit on the M-mo(l)/M-* ratio derived for GRB 080607, however, is consistent with the average population of star-forming galaxies at similar redshifts and stellar masses. We discuss the broader implications for a metallicity-dependent CO-to-H2 conversion factor and demonstrate that the canonical Galactic alpha(CO) will severely underestimate the actual molecular gas mass for all galaxies at z > 1 with M-* < 10(10) M-circle dot. To better quantify this we develop a simple approach to estimate the relevant alpha(CO) factor based only on the redshift and stellar mass of individual galaxies. The elevated conversion factors will make these galaxies appear CO-'dark' and difficult to detect in emission, as is the case for the majority of GRB hosts. GRB spectroscopy thus offers a complementary approach to identify low-metallicity, star-forming galaxies with abundant molecular gas reservoirs at high redshifts that are otherwise missed by current ALMA surveys.