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

TL;DR

This study evaluates how well single-temperature models can recover dust properties of high-redshift galaxies, considering complex temperature distributions, and finds that while dust mass and IR luminosity are generally well-estimated, the dust emissivity index may be biased.

Contribution

We introduce a physically motivated model for dust temperature distributions and assess its impact on the accuracy of dust property estimates from high-redshift galaxy observations.

Findings

Dust masses are generally well recovered, with potential underestimation for broad temperature distributions.

IR luminosities are accurately recovered within uncertainties, except at very high mean temperatures.

The inferred dust emissivity index is shallower than the true value due to multi-temperature effects.

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.