Exhausted gas reservoirs drive massive galaxy quenching in the early universe

When the Universe was merely three billion years old, about half of massive galaxies had already formed the bulk of their stars and new star formation plummeted [1]. How galaxies quench at such early times remains a puzzle, as their dark matter halos contain large gas reservoirs [2-4]. This gas should cool eciently, sustaining star formation over long periods [5,6]. Here we present sensitive 1.3mm wavelength observations of cold dust in six quenched galaxies in the redshift range z=1.6 to z=3.2 with stellar masses ranging from 2.5x1010M ⊙ to 5x1011M ⊙ , which are magnied by foreground galaxy clusters. Even with factors of up to 30 in magnication, four of the six galaxies are undetected at this wavelength. We show that these quenched galaxies have extremely little dust at early times, and by proxy very little cold molecular gas. The median dust mass is <0.01% of the stellar mass (molecular gas mass <1%), more than two orders of magnitude less than star-forming galaxies at this epoch [4]. The implication is that most early galaxies shut off star formation because their reservoir of molecular gas was rapidly depleted or removed, and is not being replenished.

). The targets are all strongly lensed, with magni cation factors ranging from a factor of 2.7 (MRG-M1423) to 30 (MRG-M1341). Five out of the six galaxies are classi ed as quiescent due to unusually low star-formation rates that reach down to 0.2 M ⊙ yr -1 , as measured from tting the optical to infrared spectral energy distributions (see Methods). While the most distant target, MRG-M1423, has a more typical star-formation rate of 70 M ⊙ yr -1 over the previous 100 Myr, consistent with normal starforming galaxies at z = 3, its spectrum reveals classic post-starburst signatures that support a picture where it has quenched rapidly within the last 100 Myr 11 . These targets are qualitatively different than existing millimeter/CO data tracing cold interstellar medium phases in that they have order of magnitude lower star-formation rates for their stellar mass [11][12][13][14] , higher redshifts 15,16 , and have uniquely deep ux limits facilitated by strong lensing magni cation.
For the redshift range of our sample, our 1.3mm wavelength observations correspond to 300-500μm restframe on the Rayleigh-Jeans tail of the dust emission, which serves as a robust proxy for the cold molecular gas mass 17 . We clearly detect two of the sources in the dust continuum: MRG-M0138 at 0.27±0.03 mJy and MRG-M2129 at 9.74±0.16 mJy. With percent-level molecular gas fractions, these are the rst direct detections of cold dust in individual quiescent galaxies outside the local universe. In contrast with the extended stellar light pro les, and despite the enhanced resolution from strong lensing magni cation, both sources remain unresolved. This suggests that they have high dust and molecular gas surface densities, as the dust continuum is centrally concentrated and signi cantly less extended than the stellar light (see Figure 1). Such a result has also been found in star-forming galaxies at similar redshifts 18 . The sensitive ALMA dust continuum imaging of the remaining four sources all yield strong upper limits, with the 3σ detection limits ranging from 30-150 μJy before lensing corrections. We estimate the dust mass, M dust , by adopting a modi ed blackbody t and making standard assumptions about dust temperature and emissivity (see Methods).
We show the redshift evolution of the dust fraction, f dust =M dust /M , for our sample of lensed quenched galaxies in Figure 2. By adopting a ratio of the molecular gas mass to dust mass of 100 (see Methods), we estimate M H2 directly from M dust and also show the inferred molecular gas fraction, f H2 = M H2 /M (right axis). Even if we adopt an extremely conservative molecular gas to dust mass ratio that is a factor of ten higher, f H2 is still well below that of normal star-forming galaxies at this epoch 2 . Both of our unambiguously detected galaxies have low molecular gas fractions of 4.6±0.5% and 0.6±0.1%, respectively. Strong upper limits from CO emission for these two targets (A. Man et al. in prep) rule out more exotic molecular gas-to-dust ratios in these particular cases, which would otherwise imply larger cold gas reservoirs. While studies of cold gas in quiescent galaxies in the local Universe are consistent with scaling relations 19 , our observations reveal a population of massive galaxies at z > 1.5 that have molecular gas fractions more than order of magnitude lower than empirical predictions. Our measured f H2 is 0.8±0.4 dex lower on average than scaling relation predictions for the given star-formation rates and stellar mass 2 .
Our program is the rst to measure a broad range of (low) molecular gas masses in massive galaxies with suppressed star-formation rates ( Figure 3). A comprehensive literature search at 1.5<z<3.0 (see Methods) demonstrates that galaxies typically form copious new stars (median log(SFR/M ) = -8.6) and have a bountiful fuel supply, with a median value of f H2 = 51%. By comparison, our galaxies instead form two orders of magnitude fewer new stars (median log(SFR/M ) = -10.7) and have a median upper limit of f H2 < 1%. Until now, such low molecular gas fractions have only been measurable in galaxies in the local universe 19 . Our new measurements con rm that the cold interstellar medium was already rapidly depleted at high redshift in at least some galaxies, not slowly consumed until the present day. Another study has already set the stage at high redshift, nding moderate cold gas reservoirs based on stacking dust continuum measurements in a mass-representative sample, albeit at signi cantly lower resolution 12 . While the cold gas reservoir of MRG-M2129 is consistent with these rst results, all other sources remain in signi cant tension. Our results also contradict the moderate cold gas reservoirs detected in recentlyquenched galaxies at lower redshifts that instead imply reduced star formation e ciency 15 . While in principle, differences in the ages of the stellar populations could explain this discrepancy 20 , our sample includes both recently-quenched (~100-800 Myr) and older passively evolving galaxies (~1.3-1.6 Gyr) 7-10 . The scatter in molecular gas fractions at low star-formation rates suggests a diverse range of evolutionary pathways to quiescence. The emerging picture at the highest redshifts is one where most massive quiescent galaxies either rapidly deplete their cold gas within the rst few billion years of the Big Bang, or eject it into the surrounding intergalactic medium. Quiescent galaxies are spectroscopically con rmed as early as z=4 21 . The existence of these early quiescent galaxies and the rapid and complete exhaustion of gas implied by our data are critical constraints on models of galaxy evolution, which currently struggle to produce realistic quiescent galaxies across redshift 21 . Predictions from cosmological simulations for the molecular gas leftover after star formation ceases span multiple orders of magnitude 22,23 . The essential problem is that high redshift dark matter halos contain enormous gas reservoirs 2-4 that should cool e ciently and maintain steady star formation over long timescales 5,6 . Indeed, many early massive galaxies do just that, having star-formation rates of order 100 M ⊙ yr -1 24 and sizable molecular gas reservoirs 3

. Our new observations
show that the cessation of star formation, when it occurs, is not caused by a sudden ine ciency in the conversion of cold gas to stars but due to the depletion or removal of these reservoirs.
This lack of cold gas appears to be permanent. In the absence of a heating mechanism, the hot gas biding time in the halo of massive galaxies should theoretically cool and fall back onto galaxies within a billion years 25 . Yet, we do not frequently observe rejuvenation in massive galaxies 26 . In light of this, our observations suggest there must be a physical mechanism that effectively blocks the replenishment of the cold gas reservoirs 27 . In the local Universe, centrally driven winds observed in quiescent galaxies are known to clear the gas out of the system, and the central low-level active supermassive black hole has su cient mechanical energy to heat the gas and suppress star formation 28 . Tentative evidence also exists at high redshifts for maintenance mode energy injection from central supermassive black holes 29 . This process may explain why quiescent galaxies are unable to effectively re-accrete cold gas in the subsequent 10 billion years of evolution to the present day, although there are other possibilities 30 . Our new data demonstrate a lack of dust, and by inference cold gas, indicating that such a physical process may have already occurred at signi cantly earlier times.
This study marks the rst detection of the dust continuum of individual massive quiescent galaxies above z=0, with measurements implying low f H2 of a few percent or less. However, the use of the dust continuum as a proxy for the interstellar medium in massive galaxies with star-formation rates must be further investigated. In particular, while securing detections of both CO emission and dust continuum for the same high redshift quiescent galaxy is paramount, such observations are costly with our current generation of telescopes without the help of strong gravitational lensing magni cation. Upcoming upgrades to existing facilities will offer pathways forward, including the wide-area, sensitive measurements enabled by the TolTEC instrument on the Large Millimeter Telescope and the improved spectroscopic capabilities forthcoming for the next generation Very Large Array. In the meantime, this program offers valuable information to constrain the wide range of theoretical predictions. 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 lters, covering λ rest~1 000Å to ~1μm. In addition to ground-based spectroscopic campaigns 3 , HST/WFC3 G141 grism spectroscopy exists for ve out of the six targets, excluding MRG-M1423.

Methods
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 tting the stellar continuum with stellar population synthesis models. Both exponentially decaying 8 and similar star formation histories that allow linear growth before the exponential decay 10 yield consistent stellar mass and star-formation rate estimates and are generally well-suited to describe quiescent galaxies 34 . The procedures to t 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 magni cation factor was used to correct the stellar masses and star-formation rates. However, because the dust and molecular gas fractions and the speci c star-formation rates, the main focus of this paper, are relative quantities, they are independent of the details of the lens models. 56μJy. The correlator was con gured 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 lowerresolution 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 magni cation and the individual maps' demagni ed root-mean-square de nes 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 f dust = M dust /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 log 10 (M /M ⊙ ) of 10.52, this corresponds to f dust of 2.6x10 -5 .
Molecular Gas Mass Estimates. By probing the Rayleigh-Jeans tail at λ rest >250μm, the dust continuum can be used as a proxy for the mass of the molecular interstellar medium, M H2 . We estimate dust mass, M dust , from a modi ed blackbody t 36 , assuming a dust temperature of 25K, a dust emissivity index, β, of 1.8, and a dust mass opacity coe cient, κ 345GHz of 0.0484 m 2 /kg 37 . By assuming a molecular gas to dust mass ratio, δ, of 100 37 , we can thereby infer M H2 from M dust . In principle M dust 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 signi cant contribution from neutral hydrogen to our dust detection would only serve to strengthen our conclusion. For comparison, we also calculate M H2 explicitly following an empirical calibration 17 , nding an offset of 0.1 dex lower in M H2 , yielding even lower inferred molecular gas fractions.
An alternative viable explanation of the null detections is that δ increases dramatically for a signi cant 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 e ciently 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 f H2 . While CO observations of quiescent galaxies at z>1.5 are scant, such ratios are di cult 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 luminosityweighted dust temperatures observed to be 23.9±0.8K (with a range from 17K to 32K) 44 . While adopting signi cantly 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][49][50][51][52][53][54][55] , comprising the contours presented in Figure 3. Author Contributions: KEW proposed and carried out the observations, conducted the analysis in this paper, and authored the majority of the text. CCW performed the weighted stack of the data, helped to create Figure 3, and edited the text in the main body. LM performed the direct analysis of the ALMA ux densities and created the color images in Figure 1. JSS carried out the reduction and direct analysis of the raw ALMA data. MA reduced the HST images. GEM, AP, ST, and FV helped interpret the millimeter data and contributed to the dust and gas mass analysis. DN helped interpret the data in the context of cosmological simulation models. All authors, including RB, GBB, JL, AM, EJN, CP, KS, and PvD, contributed to the overall interpretation of the results and various aspects of the analysis and writing.