We include a fully coupled treatment of metal and dust enrichment into the Delphi semi-analytic model of galaxy formation to explain the dust content of 13 Lyman Break Galaxies (LBGs) detected by the Atacama Large millimetre Array (ALMA) REBELS Large Program at z ≃ 7. We find that the galaxy dust mass, Md, is regulated by the combination of SNII dust production, astration, shock destruction, and ejection in outflows; grain growth (with a standard timescale τ0 = 30 Myr) plays a negligible role. The model predicts a dust-to-stellar mass ratio of $\sim 0.07-0.1{{\ \rm per\ cent}}$ and a UV-to-total star formation rate relation such that log(ψUV) = −0.05 [log(ψ)]2 + 0.86 log(ψ) − 0.05 (implying that 55-80 per cent of the star formation is obscured) for REBELS galaxies with stellar mass $M_* = 10^{9-10} \rm M_\odot$. This relation reconciles the intrinsic UV luminosity of LBGs with their observed luminosity function at z = 7. However, 2 out of the 13 systems show dust-to-stellar mass ratios ($\sim 0.94-1.1{{\ \rm per\ cent}}$) that are up to 18 × larger than expected from the fiducial relation. Due to the physical coupling between dust and metal enrichment, even decreasing τ0 to very low values (0.3 Myr) only increases the dust-to-stellar mass ratio by a factor ∼2. Given that grain growth is not a viable explanation for such high observed ratios of the dust-to-stellar mass, we propose alternative solutions.

ALMA observations have revealed the presence of dust in the first generations of galaxies in the Universe. However, the dust temperature Td remains mostly unconstrained due to the few available FIR continuum data at redshift z > 5. This introduces large uncertainties in several properties of high-z galaxies, namely their dust masses, infrared luminosities, and obscured fraction of star formation. Using a new method based on simultaneous [C $\scriptstyle \rm II$] 158μm line and underlying dust continuum measurements, we derive Td in the continuum and [C $\scriptstyle \rm II$] detected z ≈ 7 galaxies in the ALMA Large Project REBELS sample. We find 39 K < Td < 58 K, and dust masses in the narrow range Md = (0.9 − 3.6) × 107M⊙. These results allow us to extend for the first time the reported Td(z) relation into the Epoch of Reionization. We produce a new physical model that explains the increasing Td(z) trend with the decrease of gas depletion time, tdep = Mg/SFR, induced by the higher cosmological accretion rate at early times; this hypothesis yields Td∝(1 + z)0.4. The model also explains the observed Td scatter at a fixed redshift. We find that dust is warmer in obscured sources, as a larger obscuration results in more efficient dust heating. For UV-transparent (obscured) galaxies, Td only depends on the gas column density (metallicity), $T_{\rm d} \propto N_{\rm H}^{1/6}$ (Td∝Z−1/6). REBELS galaxies are on average relatively transparent, with effective gas column densities around NH ≃ (0.03 − 1) × 1021cm−2. We predict that other high-z galaxies (e.g. MACS0416-Y1, A2744-YD4), with estimated Td ≫ 60 K, are significantly obscured, low-metallicity systems. In fact Td is higher in metal-poor systems due to their smaller dust content, which for fixed LIR results in warmer temperatures.

We report ALMA Band 9 continuum observations of the normal, dusty star-forming galaxy A1689-zD1 at z = 7.13, resulting in a ∼4.6 σ detection at 702 GHz. For the first time these observations probe the far-infrared (FIR) spectrum shortward of the emission peak of a galaxy in the Epoch of Reionization (EoR). Together with ancillary data from earlier works, we derive the dust temperature, Td, and mass, Md, of A1689-zD1 using both traditional modified blackbody spectral energy density fitting, and a new method that relies only on the [C ii] 158 μm line and underlying continuum data. The two methods give $T_{\rm d} = (42^{+13}_{-7}, 40^{+13}_{-7}$) K, and $M_{\rm d} = (1.7^{+1.3}_{-0.7}, 2.0^{+1.8}_{-1.0})\, \times {}\, 10^{7} \, M_{\odot }$. Band 9 observations improve the accuracy of the dust temperature (mass) estimate by ∼50 per cent (6 times). The derived temperatures confirm the reported increasing Td-redshift trend between z = 0 and 8; the dust mass is consistent with a supernova origin. Although A1689-zD1 is a normal UV-selected galaxy, our results, implying that ∼85 per cent of its star formation rate is obscured, underline the non-negligible effects of dust in EoR galaxies.

Abstract ALMA observations have revealed the presence of dust in galaxies in the Epoch of Reionization (redshift z > 6). However, the dust temperature, Td, remains unconstrained, and this introduces large uncertainties, particularly in the dust mass determinations. Using an analytical and physically-motivated model, we show that dust in high-z, star-forming giant molecular clouds (GMC), largely dominating the observed far-infrared luminosity, is warmer (Td ≳ 60 K) than locally. This is due to the more compact GMC structure induced by the higher gas pressure and turbulence characterising early galaxies. The compactness also delays GMC dispersal by stellar feedback, thus $\sim 40\%$ of the total UV radiation emitted by newly born stars remains obscured. A higher Td has additional implications: it (a) reduces the tension between local and high-z IRX-β relation, (b) alleviates the problem of the uncomfortably large dust masses deduced from observations of some EoR galaxies.

At redshift z > 5 the far-infrared (FIR) continuum spectra of main-sequence galaxies are sparsely sampled, often with a single data point. The dust temperature Td, SED thus has to be assumed in the FIR continuum fitting. This introduces large uncertainties regarding the derived dust mass (Md), FIR luminosity, and obscured fraction of the star formation rate. These are crucial quantities to quantify the effect of dust obscuration in high-z galaxies. To overcome observations limitations, we introduce a new method that combines dust continuum information with the overlying [C $\scriptstyle \rm II$]158μm line emission. By breaking the Md − Td, SED degeneracy, with our method, we can reliably constrain the dust temperature with a single observation at 158μm. This method can be applied to all ALMA and NOEMA [C $\scriptstyle \rm II$] observations, and exploited in ALMA Large Programs such as ALPINE and REBELS targeting [C $\scriptstyle \rm II$] emitters at high-z. We also provide a physical interpretation of the empirical relation recently found between molecular gas mass and [C $\scriptstyle \rm II$] luminosity. We derive an analogous relation linking the total gas surface density and [C $\scriptstyle \rm II$] surface brightness. By combining the two, we predict the cosmic evolution of the surface density ratio $\Sigma _{\rm H_2} / \Sigma _{\rm gas}$. We find that $\Sigma _{\rm H_2} / \Sigma _{\rm gas}$ slowly increases with redshift, which is compatible with current observations at 0 < z < 4.