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Dust physics properties
The absorption and scattering properties of dust are crucial elements to know in order to build a dust model. The efficiencies Qabs and Qsca carry the information of dust grains. They both depend on the incident wavelength and grain composition, size, and to some extent, tempera-ture. Efficiencies can be either measured in laboratories, using synthetic dust grains or samples, or calculated, by solving Maxwell’s equations of the propagation of electromagnetic waves through a system. There are different approaches to determine these efficiencies numerically, and different regimes.
Under an electric field E = E0 e−iω t , with ω the response frequency, we note the response of a solid material, ε , as an imaginary number:
where ε1 and ε2 are its real and imaginary parts, respectively. We also define λ = 2π c/ω , where c is the speed of light. In case of polarized grains, the applied electric field generates a dipole moment:
where α is the electric polarizability of the grain. It is an intrinsic property of matter and pro-vides insight into the nature of the material. Analytic solutions to this problem are known for the whole family of ellipsoidal grains. Here, we will only write the equations for a particular case: spheres. Under that assumption, we can distinguish two regimes to determine the absorption and scattering cross sections.
In the case where a ≫ λ , the grain fully blocks the photons, and we have:
If a ≪ λ , we call this regime the Rayleigh limit or the electric dipole limit. In this case, thecelectric field appears uniform to the small grains, and the cross sections are:
And we can link this to the response ε (Equation 2.8):
with V , the volume of grain material. We can note that, for very small grains, and still in the case where a ≪ λ , as V → 0, Cabs ≫ Csca: absorption prevails over scattering.
In the same regime, at long wavelengths (λ → ∞ or ω → 0), we can write:
At long wavelengths, material with high σ0 will be a poor absorber as Cabs → 0. Figure 2.3 shows an example of the extinction efficiencies for two types of grains, illustrating the λ −2 be-haviour. A very common example of this phenomenon is our daily blue sky, due to the Rayleigh scattering at long wavelengths of sunlight by the particles in the atmosphere.
If the grain size is comparable to the wavelength, the previous solutions are not valid, and the resolution of the Maxwell’s equations is not the same. The Mie theory, introduced by G. Mie and P. Debye around 1908, offers new solutions to this particular case. Then, the response of the grain will depend on the ratio a/λ and its refractive index. As the incident electric wave travels through the grain, the phase shift occurring after a distance a within the grain is an important parameter to estimate the absorption and scattering cross sections of the grain.
We should also notice the importance of the spherical material assumption on the previous development. This is a strong simplification that could have important consequences when confronted with observations. The discrete dipole approximation (DDA; Purcell & Pennypacker 1973) is an approach to avoid considering dust particles as spheroids. It is, however, very complex, and requires numerical calculations. The spheres approach is much faster, and is used by most of the models to this day.
Measurements of dust extinction
Empirically, variations of the extinction with wavelength can be summarized with an extinction curve. Cardelli et al. (1989) showed that the averaged extinction curves measured in the Milky Way could be parameterized simply with The indices B and V refer to the bands at 0.44 and 0.55 µ m, respectively; the reddening E (B − V ) is the difference between the extinctions in these two bands. The same authors showed that the ratio Aλ /Aλref can be completely parameterized by seven parameters, and if RV is known, it can be parameterized by a one-parameter function.
Figure 2.4 shows average extinction curves in the MW with varying RV) from Fitzpatrick (1999). A particular discrepancy between these curves can be noticed: the bump around 4.5 µ m−1 (∼ 217 nm). It is a well known feature of dust extinction, far from being well understood, conveniently called the 2175 Å feature. Its position seems invariant but significant width variations have been observed (Beitia-Antero & Gómez de Castro 2017). Moreover, it appears absent in some lines of sight. If current evidence points towards a transition in graphite or small aromatic hydrocarbons, its origin remains uncertain.
The Diffuse Interstellar Bands
The terms diffuse interstellar bands, or DIBs, refer to a series of extinction features, weak and broad. Their width indicates that they are not atomic absorption lines but rather emerge from large molecules. To this day, about 400 DIBs have been compiled, from 3900 Å to the NIR (Hobbs et al. 2009). It is important to admit that until very recently, none of these lines were ever assigned to a molecule. Figure 2.5 shows a compilation of several DIBs on the spectrum.
This cage-like molecule, composed of 60 carbon atoms and noted C60, resembles a football. In the late 80s, after a serendipitous discovery of C60 presence in space, its positively ionized ion was predicted to be a DIB carrier by Kroto & Jura (1992). Around 1995, two bands are strongly suspected to be due to C+60. In 2015, a team conclusively identifies C+60 as the carrier of two DIBs, at 9577.4 and 9632.6 Å, thanks to an extremely low temperature experiment, that allows the observations of molecules under 6 K (Campbell et al. 2015).
Dust emission
After absorbing the incident light in the UV and optical, dust grains re-emit this energy in the infrared (from mid-infrared to sub-millimetric wavelengths). This emission also depends on the dust grain size and composition, and the shape and intensity of the incident interstellar radiation field, its strength and hardness (see Section 1.3).
Thermal equilibrium
A grain large enough in a radiation field will absorb enough photons to be subject to a constant input of energy, and will re-emit that energy at the same rate. In that particular state, the grain is in equilibrium with the heating rate1. The absorbed energy, Eabs, is:
where nd is the number density of grains, and Jλ is the mean intensity of the interstellar radiation field. and we have energetic equality between emission and absorption, leading to:
where c is the speed of light, h is the Planck constant, and kB is the Boltzmann constant.
The grain emission however, is not a perfect blackbody, and is often referred to as a modified blackbody. The modification lies in the emissivity of the dust grains. The surface brightness, Sλ , from a grain is:
where τλ is the dust optical depth; nd is the number of grains, or dust column density; Σd is the dust surface density; ρ the grain density; md is the dust grain mass; and κλ is grain absorption cross section per unit mass, characterizing the power of a dust grain to absorb/emit, at a given wavelength.
Table of contents :
I General Introduction
1 Enter the void
1.1 Watching a galaxy
1.2 The Interstellar Medium
1.3 The Interstellar Radiation Field
2 Interstellar Dust
2.1 Discovery, history and context
2.2 Dust extinction
2.2.1 Some definitions
2.2.2 Dust physics properties
2.2.3 Measurements of dust extinction
2.2.4 The Diffuse Interstellar Bands
2.3 Dust emission
2.3.1 Thermal equilibrium
2.3.2 Stochastic heating
2.3.3 Aromatic-rich (cyclic) carbonaceous
2.4 Elemental abundances and dust composition
2.5 Grain sizes
2.6 Dust grain models
2.6.1 Draine & Li (2007)
2.6.2 Compiègne et al. (2011)
2.6.3 THEMIS
2.6.4 Calibration
2.7 Observations and Instruments
II Modeling dust emission in the Magellanic Clouds
3 Fitting the IR emission in nearby galaxies
3.1 Context of this study
3.2 Studying nearby galaxies
4 The Magellanic Clouds: close neighbors
4.1 Description of the Clouds
4.2 Interest of the MCs
4.3 Data used in this study
5 Tools and computation
5.1 DustEM
5.2 DustBFF
5.3 Model (re-)calibration
6 Model comparison
6.1 Using a single ISRF
6.2 Using multiple ISRFs
6.3 Varying the small grain size distribution
7 Dust properties inferred from modeling
7.1 Parameter spatial variations
7.2 Silicate grains abundance
7.3 Dust masses and gas-to-dust ratios
8 Exploring the impact of inferred dust properties
8.1 Grain formation/destruction
8.2 Extinction curves
8.3 Other variations in dust models
8.3.1 Change in carbon size distribution
8.3.2 Allowing smaller silicate grains
8.3.3 On the recalibration
8.4 Impact of the ISRF shape
8.5 Using Draine & Li (2007)
9 Conclusions and perspectives on dust in the Magellanic Clouds
III Systematics in Dust Modeling
10 Using radiative transfer in dust studies
10.1 The Radiative Transfer method
10.2 The Radiative Transfer Equation
10.3 Finding a way to solve
10.3.1 3D Discretization
10.3.2 Make the photons move
10.3.3 Monte Carlo solution
11 The DIRTYGrid
11.1 DIRTYGrid description
11.2 Public distribution
12 Methodology
12.1 The fitted: SEDs from the DIRTYGrid
12.2 The fitter: full dust model
12.2.1 Draine & Li (2007)
12.2.2 THEMIS
12.2.3 Model Calibration
12.3 Fitting technique
13 Fitting results
13.1 Using an identical model
13.1.1 Quality of the fits
13.1.2 Recovering dust masses
13.1.3 Finding the PAH Fraction
13.1.4 Investigating the parameter ranges
13.2 Using a different dust composition
13.3 More DIRTYGrid variations
13.3.1 Continuous vs Burst Star formation
13.3.2 Clumpy vs Homogeneous dust distribution
14 Dust RT: conclusions and perspectives
IV General Conclusion & Perspectives
