We analyse FIR dust continuum measurements for 14 galaxies (redshift z ≈ 7) in the ALMA Reionization Era Bright Emission Line Survey (REBELS) Large Program to derive their physical properties. Our model uses three input data, i.e. (a) the UV spectral slope, β, (b) the observed UV continuum flux at 1500 Å, F1500, (c) the observed continuum flux at ≈ 158 μ, F158, and considers Milky Way (MW) and SMC extinction curves, along with different dust geometries. We find that REBELS galaxies have 28-90.5 per cent of their star formation obscured; the total (UV+IR) star formation rates are in the range 31.5 <SFR(/M⊙yr-1) < 129.5. The sample-averaged dust mass and temperature are (1.3± 1.1)× 10-7 M⊙ and 52 ± 11 K, respectively. However, in some galaxies dust is particularly abundant (REBELS-14, M'd ≈ 3.4 × 10-7 M⊙), or hot (REBELS-18, T'd ≈ 67 K). The dust distribution is compact (<0.3 kpc for 70 per cent of the galaxies). The inferred dust yield per supernova is 0.1 ≤ yd/M⊙≤ 3.3, with 70 per cent of the galaxies requiring yd < 0.25 M⊙. Three galaxies (REBELS-12, 14, 39) require yd > 1 M⊙, which is likely inconsistent with pure SN production, and might require dust growth via accretion of heavy elements from the interstellar medium. With the SFR predicted by the model and a MW extinction curve, REBELS galaxies detected in [C ii] nicely follow the local LCII-SFR relation, and are approximately located on the Kennicutt-Schmidt relation. The sample-averaged gas depletion time is 0.11yP-2 Gyr, where yP is the ratio of the gas-to-stellar distribution radius. For some systems, a solution simultaneously matching the observed (β, F1500, F158) values cannot be found. This occurs when the index Im = (F158/F1500)/(β - βint), where βint is the intrinsic UV slope, exceeds Im∗ ≈ 1120 for an MW curve. For these objects, we argue that the FIR and UV emitting regions are not co-spatial, questioning the use of the IRX-β relation.
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