[Paper Review] Far-infrared to millimeter astrophysical dust emission I: A model based on physical properties of amorphous solids

C. Mény, V. D. Gromov+4 more|ArXiv.org|Jan 9, 2007

Astrophysics and Star Formation Studies60 references100 citations

TL;DR

This paper proposes a novel model for far-infrared to millimeter dust emission based on the disordered internal structure of amorphous dust grains, incorporating effects from disordered charge distributions and localized two-level systems (TLS). The model predicts broad, temperature-dependent spectral features that vary with grain internal structure, offering new pathways to identify dust composition from observed emission shapes.

ABSTRACT

We propose a new description of astronomical dust emission in the spectral region from the Far-Infrared to millimeter wavelengths. Unlike previous classical models, this description explicitly incorporates the effect of the disordered internal structure of amorphous dust grains. The model is based on results from solid state physics, used to interpret laboratory data. The model takes into account the effect of absorption by Disordered Charge Distribution, as well as the effect of absorption by localized Two Level Systems. We review constraints on the various free parameters of the model from theory and laboratory experimental data. We show that, for realistic values of the free parameters, the shape of the emission spectrum will exhibit very broad structures which shape will change with the temperature of dust grains in a non trivial way. The spectral shape also depends upon the parameters describing the internal structure of the grains. This opens new perspectives as to identifying the nature of astronomical dust from the observed shape of the FIR/mm emission spectrum. A companion paper will provide an explicit comparison of the model with astronomical data.

Motivation & Objective

• To develop a physically grounded model for dust emission in the far-infrared to millimeter range that accounts for the disordered structure of amorphous dust grains.
• To address limitations in classical dust models that rely on size distributions and fixed compositions without incorporating intrinsic grain physics.
• To explore how internal disorder—specifically two-level systems (TLS) and disordered charge distributions—affects dust emission spectra.
• To provide a framework for interpreting observed spectral shapes in terms of physical grain properties, enabling dust composition identification.
• To lay the groundwork for a companion data comparison paper by establishing theoretical and laboratory constraints on model parameters.

Proposed method

• The model is derived from solid-state physics, specifically the response of disordered materials to electromagnetic radiation.
• It incorporates absorption mechanisms due to disordered charge distributions and localized two-level systems (TLS) in amorphous solids.
• The dielectric response is modeled using a complex susceptibility that includes contributions from tunneling and hopping relaxation processes.
• Key equations include the spectral function for tunneling relaxation, $ F_{\rm phon}(p) $, and the hopping relaxation spectrum derived via integration over barrier height distributions.
• The model uses dimensionless variables and analytical approximations (e.g., piecewise power-law fits to $ F_{\rm phon}(p) $) to compute emissivity across a range of temperatures and frequencies.
• The formalism accounts for temperature-dependent relaxation times and uses Gaussian distributions for barrier heights to model TLS behavior.

Experimental results

Research questions

• RQ1 How do disordered internal structures in amorphous dust grains affect their far-infrared to millimeter emission spectra?
• RQ2 To what extent do two-level systems (TLS) and disordered charge distributions contribute to the observed spectral features in dust emission?
• RQ3 Can the temperature dependence of the spectral shape be explained by intrinsic grain physics rather than just grain size distributions?
• RQ4 How do the parameters describing grain internal structure (e.g., TLS density, barrier height distribution) influence the observed emissivity and spectral index?
• RQ5 Can this model provide a physically consistent explanation for the anticorrelation between dust temperature and spectral index observed in submillimeter data?

Key findings

• The model predicts broad, non-trivial spectral features in the FIR/mm range that vary significantly with dust grain temperature due to the temperature dependence of TLS and charge distribution responses.
• The spectral shape is strongly influenced by parameters describing the internal structure of amorphous grains, such as the distribution of barrier heights and tunneling matrix elements.
• For realistic parameter values derived from laboratory data and solid-state physics, the model produces emissivity spectra that match the broad, featureful shapes seen in astronomical observations.
• The tunneling relaxation spectrum is well-approximated by a function $ F_{\rm phon}(p) $, which is fitted piecewise as $ F_{\rm phon}(p) = F_{\rm phon}(p_i) (p/p_i)^{\beta_{2i}} $, with $ \beta_{2i} $ ranging from -0.03 to -1.00 over $ p $ from 0.001 to 1000.
• The hopping relaxation contribution is derived using a Gaussian distribution of barrier heights and yields a logarithmic dependence on the minimum tunneling splitting, $ \ln(k_{\rm B}T / \Delta_{0}^{\min}) $, with a constant $ C_1 = -0.441 $.
• The model’s emissivity is sensitive to both temperature and grain-specific structural parameters, suggesting that spectral shape can be used to infer dust composition and internal disorder.