Cosmology and Initial Mass Function Assumptions. Throughout this paper we assume a simplified cosmology of ΩM=0.3, ΩΛ=0.7, and H0= 70 km s−1 Mpc−1, when calculating physical parameters. Such values are commonly assumed to make literature comparisons easier, as the precise measured values evolve over time. We adopt the Chabrier 31 initial mass function throughout, correcting literature values where appropriate.
Hubble and Spitzer Space Telescope Observations. The full details of the data reduction of the REQUIEM Hubble Space Telescope (HST) and Spitzer Space Telescope data are found in the REQUIEM methodology paper 32. All targets have a minimum of 5 (up to 16) HST and 2 Spitzer/IRAC filters, covering λrest~1000Å to ~1μm. In addition to ground-based spectroscopic campaigns 3, HST/WFC3 G141 grism spectroscopy exists for five out of the six targets, excluding MRG-M1423.
Star-formation Rate and Stellar Mass Estimates. Star formation rates and stellar mass estimates are derived from a joint analysis of photometry and ground-based spectroscopy, modeling the rest-frame ultraviolet to near-infrared spectral energy distribution 8,10. These papers adopt the Calzetti 33 dust attenuation curve and parameterized star formation histories when fitting the stellar continuum with stellar population synthesis models. Both exponentially decaying8 and similar star formation histories that allow linear growth before the exponential decay10 yield consistent stellar mass and star-formation rate estimates and are generally well-suited to describe quiescent galaxies 34. The procedures to fit the data to stellar population models marginalize over the redshift, velocity dispersion, age, metallicity, dust attenuation, and the emission line parameters, including an analysis of systematic uncertainties introduced by the model assumptions.
Lens Model Assumptions. The full details of the lens models for all strong lensed sources presented herein can be found in the original discovery papers 7-10. The magnification factor was used to correct the stellar masses and star-formation rates. However, because the dust and molecular gas fractions and the specific star-formation rates, the main focus of this paper, are relative quantities, they are independent of the details of the lens models.
Reduction of ALMA Data. ALMA 1.3mm continuum observations were carried out in programs 2018.1.00276.S and 2019.1.0027.S. The observations were designed to reach limits on fH2~1%; due to the range in redshift and lensing magnification within the sample, the observations reach 1σ depths of 9-56μJy. The correlator was configured for standard Band 6 continuum observations, with 7.5GHz total usable bandwidth. The data were reduced using the standard ALMA pipeline and imaged with natural weighting to maximize sensitivity. The observations were designed to avoid spatially resolving the target sources to the extent possible, and reach spatial resolutions ~1.0-1.5 arcseconds. We also created lower-resolution images of each source with a uv taper and found no evidence for extended emission in any source. Flux densities for the two detected sources were measured from the peak pixel values in the images. For the remaining undetected sources, we place upper limits on the 1.3mm emission using the image root-mean-square values.
For the four undetected REQUIEM-ALMA galaxies, each non-detection map is divided by the magnification and the individual maps' demagnified root-mean-square defines the weight when averaging to generate a weighted stack. This methodology is similar to others in the literature for unresolved sources 35, with our sample having roughly similar beam sizes that span 1.4-1.6 x 1.1-1.2 arcseconds. The same weights are used to calculate the average stellar mass and consequently the limit in fdust= Mdust/M★ for the stack. The resulting deep 3σ limit in the dust continuum from the undetected REQUIEM-ALMA sources is 0.81μJy at an average redshift of z=2.59. For an average stellar mass of log10(M★/M⊙) of 10.52, this corresponds to fdust of 2.6x10-5.
Molecular Gas Mass Estimates. By probing the Rayleigh-Jeans tail at λrest>250μm, the dust continuum can be used as a proxy for the mass of the molecular interstellar medium, MH2. We estimate dust mass, Mdust, from a modified blackbody fit 36, assuming a dust temperature of 25K, a dust emissivity index, β, of 1.8, and a dust mass opacity coefficient, κ345GHz of 0.0484 m2/kg 37. By assuming a molecular gas to dust mass ratio, δ, of 100 37, we can thereby infer MH2 from Mdust. In principle Mdust could trace both neutral and molecular hydrogen, and quiescent galaxies at z~0 are known to harbor non-negligible neutral gas reservoirs 38. Local studies show that the neutral hydrogen contribution varies widely 19, 39. While we assume that all of the hydrogen gas is in the molecular form, a significant contribution from neutral hydrogen to our dust detection would only serve to strengthen our conclusion. For comparison, we also calculate MH2 explicitly following an empirical calibration 17, finding an offset of 0.1 dex lower in MH2, yielding even lower inferred molecular gas fractions.
An alternative viable explanation of the null detections is that δ increases dramatically for a significant fraction of early quiescent galaxies. There exists theoretical 40 and observational 41 evidence that in certain circumstances thermal sputtering by hot electrons could in principle efficiently destroy dust in dead galaxies. CO observations are required to rule out extreme molecular gas to dust ratios that would be necessary to reconcile our observations with higher, more typical values of fH2. While CO observations of quiescent galaxies at z>1.5 are scant, such ratios are difficult to justify, as they imply that CO should be detectable 42. At least in the case of our two detections, such exotic ratios are already ruled out by strong CO upper limits 43.
We adopt a dust temperature of 25K, which corresponds to a luminosity-weighted temperature of roughly 30K. However, the cold interstellar medium of local quiescent galaxies is generally colder, with luminosity-weighted dust temperatures observed to be 23.9±0.8K (with a range from 17K to 32K) 44. While adopting significantly colder dust templates would increase our estimates of molecular gas fraction 45, our upper limits would still leave room for tension. Moreover, star formation in quiescent galaxies at high redshift is generally less suppressed in comparison to local dead galaxies, and as such the expected dust temperature of the cold interstellar medium remains unclear.
Literature Comparisons. We include two additional quiescent targets at similar high redshifts of z>1.5 with upper limits from dust continuum measurements 14 and CO measurements 15., as well as results from stacking dust continuum 12. For the dust continuum measurements, all data is recalibrated using the same set of assumptions applied herein. We further assemble measurements of 183 star-forming galaxies at 1.5<z<3.0 from the literature, tracing molecular gas via dust continuum 14, 17, 46, 47 and CO 48-55, comprising the contours presented in Figure 3.
Methods References. (see References 31-55)