Realistic Multi-temperature Dust: How Well Can We Constrain the Dust Properties of High-redshift Galaxies?

Determining the dust properties of high-redshift galaxies from their far-infrared continuum emission is challenging due to limited multi-frequency data. As a result, the dust spectral energy distribution (SED) is often modeled as a single-temperature modified blackbody. We assess the accuracy of the single-temperature approximation by constructing realistic dust SEDs using a physically motivated prescription where the dust temperature probability distribution function (PDF) is described by a skewed normal distribution. This approach captures the complexity of the mass-weighted and luminosity-weighted temperature PDFs of simulated galaxies and quasars, and yields far-infrared SEDs that match high-redshift observations. We explore how varying the mean temperature (T̄d), width, and skewness of the temperature PDF affects the recovery of the dust mass, IR luminosity, and dust emissivity index βd at z=7. Fitting the dust SEDs with a single-temperature approximation, we find that dust masses are generally well-recovered, although they may be underestimated by up to 0.6 dex for broad temperature distributions with a low T̄d < 40 K, as seen in some high-redshift quasars and/or evolved galaxies. IR luminosities are generally recovered within the 1σ uncertainty (< 0.3 dex), except at T̄d > 80 K, where the peak shifts well beyond ALMA's wavelength coverage. The inferred dust emissivity index is consistently shallower than the input one (βd=2) due to the effect of multi-temperature dust, suggesting that a steep βd may probe dust composition and grain size variations. With larger galaxy samples and well-sampled dust SEDs, systematic errors from multi-temperature dust may dominate over fitting uncertainties and should thus be considered.