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

Abstract: 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 ($\bar{T}_d$), width, and skewness of the temperature PDF affects the recovery of the dust mass, IR luminosity, and dust emissivity index $\beta_d$ 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 $\bar{T}_d <$ 40 K, as seen in some high-redshift quasars and/or evolved galaxies. IR luminosities are generally recovered within the $1\sigma$ uncertainty (< 0.3 dex), except at $\bar{T}_d >$ 80 K, where the peak shifts well beyond ALMA's wavelength coverage. The inferred dust emissivity index is consistently shallower than the input one ($\beta_d$=2) due to the effect of multi-temperature dust, suggesting that a steep $\beta_d$ 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.