<figure><img src="image_538.png" /></figure>

**At low signal-to-noise (Fig. V.21.c),** the inferred values of $q_{\text{PAH}}$ (green stars) are now almost similar for every source. We are in the case where the uncertainty on each individual source is so large that we can not recover their individual values. We can however give their most likely value, based on the distribution of the sample. This type of result has to be interpreted in a Bayesian way, to be consistent (i.e. performing tests on the MCMC). The fact that the inferred values of $q_{\text{PAH}}$ all collapsed on a single point does not mean we would deduce that the points all have the same value. If we were performing some tests, we would realize that they are uncorrelated: if we were randomly drawing parameter values from the posterior, they would be scattered with a distribution similar to the true values. In a sense, we obtain here a result similar to stacking the sources, but in a smarter way, as some parameters are better constrained than others. For instance, in Fig. V.21.c, we see that we have only access to $\langle q_{\text{PAH}} \rangle$ (y-axis), but we resolve the $\langle U \rangle$ of individual sources (x-axis).

<figure><img src="image_539.png" /></figure>

HB methods are useful when the parameter uncertainty of some sources is comparable to or larger than the scatter of this property over the whole sample.

<figure><img src="image_540.png" /></figure>

**FIGURE V.21 – Demonstration of the effect of the prior in a HB model.** The red dots in the different panels represent three simulations of 1000 sources, with similar physical properties, similar calibration uncertainties, but different signal-to-noise ratios (S/N). Each simulation has been fitted with our HB code (Galliano, 2018). We represent the marginalized posterior of the PAH mass fraction, $q_{\text{PAH}}$, and mean starlight intensity, $\langle U \rangle$ (cf. Sect. III.1.2.2). Licensed under CC BY-SA 4.0.

**Holistic prior.** From a statistical point of view, it is always preferable to treat all the variables we are interested in as if they were drawn from the same multivariate distribution, however complex it might be. Stein (1956) showed that the usual estimator of the mean ($\Sigma_i X_i / N$) of a multivariate normal variable is inadmissible (for more than two variables), that is we could always find a more accurate one. In other words, if we were interested in analyzing together several variables, not necessarily correlated, such as the dust and stellar masses, it would always be more suitable to use estimators that combine all of them. This is known as *Stein's paradox*. Although Stein (1956)'s approach was frequentist, this is a general conclusion. From a Bayesian point of view, it means that we should put all the variables we are interested in analyzing, even if they are not SED model parameters, in the prior. In addition, if these external variables happen to be correlated with some SED model parameters, they will help refining their estimates. This is illustrated in Fig. V.22. We show in both panels a simulation

<figure><img src="image_541.png" /></figure>
<figure><img src="image_542.png" /></figure>

of the correlation between the dust mass, which is a SED model parameter, and the gas, which is not. When performing a regular HB fit, and plotting the correlation as a function of M<sub>gas</sub>, we obtain the correlation in Fig. V.22.a. We see that the agreement with the true values breaks off at low mass (also the lowest signal-to-noise). If we now include M<sub>gas</sub> in the prior<sup>16</sup>, we obtain the correlation in Fig. V.22.b. It provides a much better agreement with the true values. This is because adding M<sub>gas</sub> in the prior brought some extra information. The information provided by a non-dusty parameter helped refine the dust SED fit. For instance, imagine that you have no constraints on the dust mass of a source, but you know its gas mass. You could infer its dust mass by taking the mean dustiness of the rest of the sample. This holistic prior does that, in a smarter way, as it accounts for all the correlations in a statistically consistent way.

<figure><img src="image_543.png" /></figure>

The HB approach allows an optimal, holistic treatment of all the quantities of interest, even if they are not related to the dust.

<figure><img src="image_544.png" /></figure>

FIGURE V.22 – *The holistic approach: inclusion of external parameters into the prior.* Both panels represent the same simulation (red dots) of 300 sources, with physical properties typical of star-forming galaxies, including noise and calibration errors (Galliano, 2018). We have added a parameter that is external to our SED model, the gas mass, M<sub>gas</sub>. In panel (a), we show the HB inference of the dust mass as a function of the synthetic observations of the gas mass (cyan error bars). In panel (b), we show the HB inference of the parameters when they are both in the prior (blue ellipses). Licensed under CC BY-SA 4.0.

### V.3.3.3 Other Developments

SED modeling is far from the only possible application of HB methods. We briefly discuss below two other models we have developed.

**Cosmic dust evolution.** The dust evolution model we have discussed in Sect. IV.3 has been fitted to galaxies by Galliano et al. (2021), in a HB way. To be precise, we have used the output of HerBIE,

<figure><img src="image_545.png" /></figure>

<footnote n="16">16. From a technical point of view, *including* an external parameter in the prior, such as M<sub>gas</sub>, can be seen as adding an identity model component: M<sub>gas</sub> = f(M<sub>gas</sub>). Concretely, it means that, at each iteration, we sample M<sub>gas</sub> from its uncertainty distribution, and the distribution of M<sub>gas</sub> and its potential correlations with the other parameters inform the prior.</footnote>
<figure><img src="image_546.png" /></figure>

$M_{\text{dust}}$, $M_{\text{gas}}$, $M_{\star}$, SFR and metallicity, as observables. We then have modeled the SFH-related parameters in a HB way, and have assumed that the dust efficiencies were common to all galaxies (i.e. we inferred one single value for the whole sample). These common parameters were not in the hierarchical prior, because their value is the same for all galaxies. They were however sampled with the other parameters, in a consistent way. We were successful at recovering dust evolution timescales consistent with the MW at Solar metallicity (cf. Sect. IV.3.1.2). One important improvement would be to treat everything within the same HB model: (i) the SED; (ii) the stellar and gas parameters; and (iii) the dust evolution. This is something we plan to achieve in the near future.

**MIR spectral decomposition.** The type of MIR spectral decomposition that we have discussed in Sect. III.2.1.2 could also benefit from the HB approach. Although the model is mostly linear, there are a lot of degeneracies between the uncertainties of adjacent blended bands, such as the 7.6 and 7.8 µm features. In addition, plateaus and weak features are usually poorly constrained and their intensity can considerably bias the fit at low signal-to-noise. Hu et al. (in prep.) have developed such a HB MIR spectral decomposition tool. Its efficiency has been assessed on simulated data, and it is now being applied to M 82. This model will be valuable to analyze the spectra from the JWST.

<figure><img src="image_547.png" /></figure>
<figure><img src="image_548.png" /></figure>
<figure><img src="image_549.png" /></figure>

# Chapter VI

## Conclusion and Prospective

> We look at the present through a rear view mirror. We march backwards into the future.

(Marshall MCLUHAN; McLuhan, 1967)

### Contents

<table><tr><td>VI.1 What Have We Learned About ISD in the Past Decade?</td><td>268</td></tr><tr><td>VI.1.1 About Dust Properties</td><td>268</td></tr><tr><td>Grain opacity.</td><td>268</td></tr><tr><td>Scaling relations.</td><td>268</td></tr><tr><td>Dust properties of low-metallicity systems.</td><td>268</td></tr><tr><td>The Submillimeter excess.</td><td>268</td></tr><tr><td>The AME.</td><td>269</td></tr><tr><td>Stoichiometry and grain structure.</td><td>269</td></tr><tr><td>Dust models.</td><td>269</td></tr><tr><td>Polarization.</td><td>269</td></tr><tr><td>Laboratory data.</td><td>269</td></tr><tr><td>VI.1.2 About Dust Evolution</td><td>269</td></tr><tr><td>Dust sources.</td><td>269</td></tr><tr><td>Evolution of the Aromatic Feature Carriers.</td><td>269</td></tr><tr><td>Thermal sputtering.</td><td>270</td></tr><tr><td>Emissivity Variations in the ISM.</td><td>270</td></tr><tr><td>Distant objects.</td><td>270</td></tr><tr><td>VI.2 What Are the Open Questions for the Next Decade?</td><td>270</td></tr><tr><td>VI.2.1 Extragalactic Dust</td><td>270</td></tr><tr><td>Studies of diffuse dust in nearby galaxies.</td><td>270</td></tr><tr><td>Quiescent low-metallicity galaxies.</td><td>270</td></tr><tr><td>Circumgalactic dust.</td><td>271</td></tr><tr><td>VI.2.2 Dust Evolution Modeling</td><td>271</td></tr><tr><td>Local evolution modeling.</td><td>271</td></tr><tr><td>Cosmic dust evolution models.</td><td>271</td></tr><tr><td>VI.2.3 Dusty Epiphenomena</td><td>271</td></tr><tr><td>Long-wavelength properties.</td><td>271</td></tr><tr><td>DIBs.</td><td>271</td></tr><tr><td>VI.2.4 The Need for a New FIR Observatory</td><td>272</td></tr><tr><td>VI.2.5 The Public Image of Interstellar Dust</td><td>272</td></tr><tr><td>VI.3 Current Future Projects</td><td>272</td></tr></table>

<figure><img src="image_550.png" /></figure>
<table><tr><td>VI.3.1 The Modelosaur Approach</td><td>272</td></tr><tr><td>VI.3.2 Out-of-the-Box Idea Bin</td><td>273</td></tr></table>

# VI.1 What Have We Learned About ISD in the Past Decade?

We have seen in Sect. V.3.1 that ISD studies were particular because of the inherent complexity of the dust make-up and of the low weight of evidence provided by individual observables. This sometimes leads colleagues from other fields to think that our subject is messy and stalling. If we however integrate over a large number of studies, we can delineate some clear breakthroughs. I try the exercise of listing them here<fnref n="1" />. This is of course a subjective account of the progress, biased by my own interests. The observations acquired by Herschel and Planck played an instrumental role in these.

## VI.1.1 About Dust Properties

**Grain opacity.** Herschel and Planck have brought invaluable information about the FIR and submm optical properties of dust grains, in the MW and nearby galaxies (cf. Sect. III.1.3.3). Before that, the commonly-used opacities were a factor of ≈ 2–3 lower, biasing the dust masses one would estimate. We still do not know the exact constitution of interstellar grains and its evolution, but we know relatively well the zero level FIR-submm opacity they should have in the diffuse ISM of the MW and a few nearby galaxies.

**Scaling relations.** The large number of galaxies observed by Herschel and the effort to build homogeneous ancillary data samples have provided consistent estimates of the dust, stellar and gaseous properties for a large number of objects, with spatial resolution in numerous cases (cf. Sects. IV.2 – IV.3). These relations provide snapshots of galaxy evolution at different stages. They are now well sampled over most of the parameter space (metallicity, gas fraction and specific star formation rate). They are the main benchmarks dust evolution models must account for. The most important ones and the information they convey are the following.

* The dustiness-metallicity relation exhibits two distinct regimes of dust production: (i) at very low metallicity, dominated by stardust; and (ii) at high metallicity, dominated by grain growth in the ISM.

* The dustiness-gas-fraction relation links the gas depletion timescale and the evolution probed by the dustiness-metallicity relation.

* Scaling relations linking the dust content to the diffuse X-ray emission are promising tools to constrain grain sputtering timescales.

**Dust properties of low-metallicity systems.** I have emphasized in Sect. IV.3 that low-metallicity systems (i.e. dwarf galaxies) were crucial to constrain dust evolution models, because they sample a different grain production regime than higher metallicity objects. Herschel has provided us with the first FIR SEDs of extremely low-metallicity galaxies that were decisive in understanding the early stages of dust evolution.

**The Submillimeter excess.** Twenty years after its discovery the submm excess is still a mysterious epiphenomenon (cf. Sect. III.2.2.1). In the last years: (i) several studies have hinted that it could be more prominent in diffuse regions of galaxies; and (ii) a new physical process that could explain its origin has been proposed (magnetic grains).

<footnote n="1">1. I have, with many others, contributed to the first 5 items of Sect. VI.1.1 and to the first 4 items of Sect. VI.1.2.</footnote>
**The AME.** The AME has, for the first time, been detected in extragalactic systems (cf. Sect. III.2.2.2). To our humble opinion, the debate about its origin (PAHs or nanosilicates) is closed, in favor of PAHs.

**Stoichiometry and grain structure.** Important progress has been made constraining the grain structure and stoichiometry using X-ray edge absorption. The results are sometimes difficult to understand, such as the high crystalline fraction discussed in Sect. II.2.1.3. The technics are however promising and will revolutionize our understanding of the dust constitution, when ATHENA will be observing.

**Dust models.** A few dust models have been published in the last decade. The THEMIS model (cf. Sect. II.3.2.2) is, in our opinion, the most innovative for the following reasons.

* It is designed as an evolution model. Some fundamental properties of the constitution of the grain mixture (a-C:(H) hydrogenation, size distribution, mantle thickness) can be varied to account for different observables. This way, we have a few physically-grounded parameters to empirically explore the effects of dust evolution. It is an important progress over classic, static models.

* It is laboratory-data based.

* The model can be adapted to account for polarization constraints.

* It is the only recent model accounting for the 3.4 µm aliphatic feature.

* It is one of the only models to be consistent with the revised FIR-submm opacity that I have mentioned earlier.

**Polarization.** Whole-sky submm polarized emission maps have been produced by Planck, at several wavelengths (cf. Sect. II.2.2.2). On top of permitting unprecedented studies of the magnetic field, they provide evidence that the bulk of the large grain emission is homogeneous in size and composition.

**Laboratory data.** Long-wavelength (FIR-submm) measures of a diversity of dust analogues have been produced (cf. Sect. II.2.4.3). They provide the necessary data that, when consistently included in dust models, will help us to: (i) better constrain the evolution of grain mantles; and (ii) characterize more precisely the submm excess.

## VI.1.2 About Dust Evolution

**Dust sources.** Our understanding of the dust production mechanisms has considerably progressed, thanks to Herschel (cf. Sects. IV.2 – IV.3).

**The modeling of scaling relations,** in particular the dustiness-metallicity relation, provides clear evidence that: (i) dust growth in the ISM is the prominent grain production regime around Solar metallicity; and (ii) condensation in SN II ejecta dominates at very low metallicity.

**Observations of individual SNRs** have shown that large amounts of dust could be produced shortly after SN II explosions. It suggests that a large fraction of these freshly-formed grains must be destroyed by the reverse shock.

**Evolution of the Aromatic Feature Carriers.** Before the 2010s, ISO and Spitzer were crucial to understand the variations of the strength of the UIBs (cf. Sect. III.2.1.1). In the 2010s, the detailed modeling of the FIR SED permitted by Herschel, allowed us to understand more finely how the abundance of the grains carrying these features evolves. To our mind, the important points are that: (i) their mass fraction is better correlated with metallicity than with the strength of the ISRF; and (ii) they are spatially associated with molecular clouds.
<figure><img src="image_551.png" /></figure>

**Thermal sputtering.** ETGs, due to the paucity of their ISM, had been poorly studied before Herschel. We have now been able to characterize their dust content. It appears that these environments exhibit a dust deficit due to grain destruction in their permeating coronal gas. They are thus potentially interesting laboratories to constrain sputtering timescales (cf. Sect. IV.2.2.2).

**Emissivity Variations in the ISM.** The good coverage and sensitivity of Herschel and Planck allowed us to better characterize the way the FIR-submm emissivity evolves from the diffuse ISM to dense regions, in the MW and the Magellanic clouds (cf. Sect. IV.2). It is now clear that the increase of emissivity with ISM density, resulting from mantle accretion and grain coagulation, is a universal process.

**Distant objects.** The dust content of numerous galaxies at very high redshifts ($z > 6$) has been constrained, thanks to ALMA. It appears that dust-rich objects existed only a few 100 Myrs after reionization, requiring fast grain build-up. In our opinion, this can be explained with rapid dust growth in the ISM (cf. Sect. IV.3).

# VI.2 What Are the Open Questions for the Next Decade?

I now try to delineate a few open questions that should occupy us during the next decade. The list below is as subjective as Sect. VI.1. This is not everything we *should* do, but rather everything we *will be able* to do, knowing the available observing facilities.

## VI.2.1 Extragalactic Dust

**Studies of diffuse dust in nearby galaxies.** The diffuse ISM of the MW is the only medium used to constrain dust models, because it provides simultaneous information about extinction, emission and elemental depletions (cf. Sect. II.3). The combination of these different constraints is crucial to solve the degeneracies between emissivity and size distribution. This is why dust models are calibrated on these data, and why we do not yet have reliable dust models for the SMC, for instance. Such observations are however available, in a fragmented way, in external systems such as the Magellanic clouds and M 31. An effort should be made to produce an homogeneous data set of similar constraints in a few external galaxies and to build dust models using it. This implies several challenges.

* The extraction of the emission from the diffuse ISM is required to make sure we have homogeneous physical conditions and are not biased by the variation of the FIR opacity. The large beam of Planck renders this task difficult in external galaxies, but can be compensated by using other observations (e.g. Herschel and ground-based submm data).

* Additional observations are probably needed to cover the missing information. Facilities such as the Multi Unit Spectroscopic Explorer (MUSE; Bacon et al., 2010, for abundances) and ALMA (for the submm continuum) provide exceptional data that have not yet been utilized to their full potential in our field.

Having different extragalactic dust models would allow us to: (i) understand how the diffuse dust properties vary as a function of metallicity; and (ii) have a more robust way to study external galaxies, by using models that take into account the effect of cosmic dust evolution on the grain mixture.

**Quiescent low-metallicity galaxies.** I have emphasized several times the crucial role low-metallicity systems play in constraining dust evolution. These objects are however faint and we usually observe those which are actively star-forming. We therefore suffer from a selection effect that hides the nature of low-metallicity quiescent systems. I have given an example of what such systems could bring to our understanding of the evolution of MIR features in Fig. IV.22. The question is in which
<figure><img src="image_552.png" /></figure>

quadrant of this figure they will fall? Obtaining JWST spectra of these objects would probably be a game changer.

**Circumgalactic dust.** Grains present in the immediate vicinity of galaxies, either in the infalling or outflowing gas, are currently poorly known. Yet, infall and outflow might be an important mechanism regulating the dustiness of galaxies. JWST and ALMA observations might be able to characterize circumgalactic grain properties beyond the nearby Universe, because of their resolving power. For local objects, NIKA2 is currently acquiring mm maps of infalls and outflows in nearby galaxies.

### VI.2.2 Dust Evolution Modeling

**Local evolution modeling.** I have emphasized that a dust model such as THEMIS provides a unique framework to model SEDs, taking into account dust evolution. Its current limitation is however that we lack a quantitative link between the evolution parameters (a-C(H) hydrogenation, size distribution and mantle thickness) and the environmental conditions (density and ISRF intensity). This can be achieved by empirically calibrating the tuning parameters of the evolution processes discussed in Sect. IV.2. The goal would be to have a reliable dust model predicting the constitution of the grain mixture as a function of $n_{\text{gas}}$ and $G_0$.

**Cosmic dust evolution models.** The empirical modeling of cosmic dust evolution, that was the center of Sect. IV.3, calls for several improvements that could greatly change our understanding of the matter.

1. If we want to be able to precisely constrain the grain growth and SN II blast-wave destruction timescales, we need the most accurate possible stellar elemental and dust yields. This is an effort asked to the circumstellar community, both modelers and observers.

2. We need to adopt a more consistent approach between the different physical elements involved (dust, gas and stellar emissions and evolutions; cf. Sect. V.3.3.3).

3. When modeling SEDs at scales of several tens of parsecs or larger, we need to properly account for the mixing of physical conditions. This is currently done phenomenologically (cf. Sect. III.1.2.2). Ideally, we should move toward fitting models accounting for the statistical distribution of dust and stars, with a wide range of topologies, accounting for: (i) dust evolution in the ISM, as a function of $n_{\text{gas}}$ and $G_0$, as I have mentioned earlier; and (ii) radiative transfer.

### VI.2.3 Dusty Epiphenomena

**Long-wavelength properties.** The current submm-to-cm ground-based observatories (such as NIKA2, ALMA, etc.) open windows to progress on our understanding of the submm excess (cf. Sect. III.2.2.1) and of the AME (cf. Sect. III.2.2.2). By combining these new observations with archival Spitzer, AKARI and Herschel data, we should be able to systematically test the different possible scenarios. In addition, this analysis should be performed with dust models including state-of-the-art submm-mm laboratory opacities of interstellar grain analogues, in order to provide a reliable baseline.

**DIBs.** DIBs have been extensively observed with Gaia. Since we do not know their nature, unbiased exploration of how their properties vary with all available ISM tracers should be performed, in a big data way.
<figure><img src="image_553.png" /></figure>

VI.2.4 The Need for a New FIR Observatory

I have illustrated all along this manuscript what modeling the IR SED of various regions can bring. In particular, the FIR regime is crucial to properly constrain the peak of the large equilibrium grain emission. This is the only way we can quantify the total dust mass and its excitation conditions. These quantities are necessary to interpret any other observables, such as the strength of the aromatic features, the submm excess, etc. We currently have good archival data for most nearby galaxies. We however lack: (i) continuous MIR-to-FIR spectroscopy to better constrain SED models and study the various solid-state features in emission and absorption; and (ii) deep observations of quiescent low-metallicity systems (cf. Sect. VI.2.1). After the cancellation of SPICA, our community should regroup around a new project.

VI.2.5 The Public Image of Interstellar Dust

On a *public relation* viewpoint, we should think about the way our field is represented.

Among colleagues, there is still a distinction between the ISM (i.e. the MW) and the ISM of other galaxies. This hierarchy between *intragalactic* and *extragalactic* ISM is becoming less and less justified. In addition, *interstellar media* (extragalactic ISM) provide unique constraints on ISM physics, as I have illustrated along this manuscript. The plural is justified, as they are characterized by different heating and cooling mechanisms, different grain formation processes, etc. We should motivate the new generation of astronomers to consider ISMology as a field where, depending on the studied physical process, we can use a galaxy or a Galactic region as a laboratory.

To the outside world, “dust” physics is not very appealing. What we do is important, but we need a better name. The US environmental protection agency defines nanoparticles as having sizes roughly between 1 and 100 nm. This is very close to the range of sizes of interstellar grains (cf. *Sect. II.3.3.1*). We could thus call our object of study *Cosmic NanoParticles* (CNP), when talking to the outside world, and keep talking about *dust* between us.

VI.3 Current Future Projects

I finish by listing the future projects I am currently considering working on. These are motivated by
the challenges I have listed in *Sect. VI.2*.

VI.3.1 The *Modelosaur* Approach

It is more and more becoming a necessity to consistently model the different processes (dust, gas
and stellar physics), in a large Bayesian framework. I plan to progressively include more physical
processes in HerBIE to account for a wider diversity of observables:

1. the modeling of stellar evolution;

2. the consistency between SED modeling, and dust and chemical evolution;

3. the account of local dust evolution and of the systematic uncertainties of the model (depending on the developers of THEMIS);

4. radiative transfer grids of different dust-star topologies;

5. including the constraints from photoionization and photodissociation lines.

A first step will be the project ICED (IAS-CEA Evolution of Dust) that I have put together. It will consist in modeling the spatial distribution of the dust properties in nearby galaxies, to constrain local grain evolution. This will be done with the data from DustPedia, as well as from the NIKA2 guaranteed time project IMEGIN.

<figure><img src="image_554.png" /></figure>
<figure><img src="image_555.png" /></figure>

VI.3.2 Out-of-the-Box Idea Bin

* One way to solve the degeneracy between size distribution and emissivity is to observe a given dust mixture illuminated by a time-varying ISRF. This way, we can see the same grains exposed to two different fields, at two different times. This is possible with the light echo of SNe (e.g. Arendt et al., 2016), but very limited. Nearby Cepheids provide periodic variable sources, that modern observatories give us access to. I am currently working on a feasibility study of the observations of their echo with the JWST and ALMA.

* I currently have an intern working on the feasibility of using *Natural Language Processing* (NLP) methods, in collaboration with IRIS.AI, to tackle the origin of DIBs. NLP is a machine-learning method that, when trained on a large corpus of scientific articles, can be used to find relations between concepts, formulate new research directions, etc. It is aimed at dealing with information overload. The idea of the project is to see if we can automatically find clues in the chemistry and material science literature that could be relevant to DIBs.

* I am planning to use machine-learning to accelerate the interpolation of large model grids in HerBIE. Machine-learning, trained on hydrodynamical simulations, could also be useful to simulate realistic dust-star topologies (accounting for clustering, etc.), for which we would solve the radiative transfer. These grids would be SED model building blocks.

<figure><img src="image_556.png" /></figure>
<figure><img src="image_557.png" /></figure>
<figure><img src="image_558.png" /></figure>

# Appendix A

## List of Acronyms

*Education is what is left after you have forgotten all you have learned.*

(Forgotten author)

## Contents

<table><tr><td>A.1 General Acronyms</td><td>275</td></tr><tr><td>A.2 Telescope and Instrument Acronyms</td><td>277</td></tr><tr><td>A.3 Model and Project Acronyms</td><td>278</td></tr><tr><td>A.4 Denomination of the Main Spectral Windows</td><td>279</td></tr></table>

### A.1 General Acronyms

<table><thead><tr><td>Acronym</td><td>Expression</td></tr></thead><tbody><tr><td>3D</td><td>3-Dimensional</td></tr><tr><td>ACF</td><td>AutoCorrelation Function</td></tr><tr><td>AGB</td><td>Asymptotic Giant Branch stars</td></tr><tr><td>AGN</td><td>Active Galactic Nucleus</td></tr><tr><td>AME</td><td>Anomalous Microwave Emission</td></tr><tr><td>BCD</td><td>Blue Compact Dwarf Galaxies</td></tr><tr><td>BEMBB</td><td>Broken-Emissivity Modified Black Body</td></tr><tr><td>BG</td><td>Big Grain</td></tr><tr><td>BH</td><td>Black Hole</td></tr><tr><td>CCD</td><td>Charge-Coupled Device</td></tr><tr><td>CDF</td><td>Cumulative Distribution Function</td></tr><tr><td>CGS</td><td>Centimetre-Gram-Second</td></tr><tr><td>CIB</td><td>Cosmic Infrared Background</td></tr><tr><td>CMB</td><td>Cosmic Microwave Background</td></tr><tr><td>CNP</td><td>Cosmic NanoParticles</td></tr><tr><td>CNM</td><td>Cold Neutral Medium</td></tr><tr><td>DCD</td><td>Disordered Charge Distribution</td></tr><tr><td>DDA</td><td>Discrete Dipole Approximation</td></tr><tr><td>DGL</td><td>Diffuse Galactic Light</td></tr><tr><td>DGS</td><td>Dwarf Galaxy Sample</td></tr><tr><td>DIB</td><td>Diffuse Interstellar Bands</td></tr><tr><td>DLA</td><td>Damped Lyman-Alpha systems</td></tr></tbody></table>

<figure><img src="image_559.png" /></figure>
<table><thead><tr><td>Acronym</td><td>Expression</td></tr></thead><tbody><tr><td>EMT</td><td>Effective Medium Theory</td></tr><tr><td>ERE</td><td>Extended Red Emission</td></tr><tr><td>ETG</td><td>Early-Type Galaxy</td></tr><tr><td>eVSG</td><td>evaporating Very Small Grains</td></tr><tr><td>FIR</td><td>Far-InfraRed</td></tr><tr><td>FUV</td><td>Far-UltraViolet</td></tr><tr><td>FWHM</td><td>Full Width at Half Maximum</td></tr><tr><td>GEMS</td><td>Glass with Embedded Metals and Sulfides</td></tr><tr><td>GRB</td><td>Gamma-Ray Burst</td></tr><tr><td>HB</td><td>Hierarchical Bayesian</td></tr><tr><td>HDR</td><td>Habilitation à Diriger des Recherches</td></tr><tr><td>HIM</td><td>Hot Ionized Medium</td></tr><tr><td>ICM</td><td>InterClump Medium</td></tr><tr><td>IDP</td><td>Interplanetary Dust Particles</td></tr><tr><td>iid</td><td>independent, identically distributed</td></tr><tr><td>IMF</td><td>Initial Mass Function</td></tr><tr><td>IR</td><td>InfraRed</td></tr><tr><td>ISD</td><td>InterStellar Dust</td></tr><tr><td>ISM</td><td>InterStellar Medium</td></tr><tr><td>ISRF</td><td>InterStellar Radiation Field</td></tr><tr><td>ISS</td><td>International Space Station</td></tr><tr><td>LIRG</td><td>Luminous InfraRed Galaxies</td></tr><tr><td>LMC</td><td>Large Magellanic Cloud</td></tr><tr><td>LIMS</td><td>Low- and Intermediate-Mass Stars</td></tr><tr><td>LTG</td><td>Late-Type Galaxy</td></tr><tr><td>MBB</td><td>Modified Black Body</td></tr><tr><td>MCRT</td><td>Monte-Carlo Radiative Transfer</td></tr><tr><td>MCMC</td><td>Markov Chain Monte-Carlo</td></tr><tr><td>MIR</td><td>Mid-InfraRed</td></tr><tr><td>MKS</td><td>Meter-Kilogram-Second</td></tr><tr><td>MKSA</td><td>Meter-Kilogram-Second-Ampere</td></tr><tr><td>ML</td><td>Machine-Learning</td></tr><tr><td>MLE</td><td>Maximum-Likelihood Estimation</td></tr><tr><td>MS</td><td>Main Sequence</td></tr><tr><td>MW</td><td>Milky Way</td></tr><tr><td>NHST</td><td>Null Hypothesis Significance Test</td></tr><tr><td>NIR</td><td>Near-InfraRed</td></tr><tr><td>NLP</td><td>Natural Language Processing</td></tr><tr><td>NS</td><td>Neutron Star</td></tr><tr><td>NUV</td><td>Near-UltraViolet</td></tr><tr><td>OOP</td><td>Out-Of-Plane</td></tr><tr><td>PAH</td><td>Polycyclic Aromatic Hydrocarbon</td></tr><tr><td>PCA</td><td>Principal Component Analysis</td></tr><tr><td>PDF</td><td>Probability Density Function</td></tr><tr><td>PDR</td><td>PhotoDissociation Regions</td></tr><tr><td>PN</td><td>Planetary Nebula</td></tr><tr><td>ppb</td><td>part per billion</td></tr><tr><td>ppp</td><td>posterior predictive p-value</td></tr><tr><td>QSO</td><td>Quasi-Stellar Object</td></tr><tr><td>RAT</td><td>Radiative Alignment Torques</td></tr></tbody></table>
<figure><img src="image_560.png" /></figure>

<table><caption>TABLE A.1 – List of acronyms used throughout the manuscript.</caption><thead><tr><th>Acronym</th><th>Expression</th></tr></thead><tbody><tr><td>SSC</td><td>Super Star Cluster</td></tr><tr><td>SED</td><td>Spectral Energy Distribution</td></tr><tr><td>SF</td><td>Star Formation</td></tr><tr><td>SFH</td><td>Star Formation History</td></tr><tr><td>SFR</td><td>Star Formation Rate</td></tr><tr><td>SI</td><td>International System of units</td></tr><tr><td>SLED</td><td>Spectral Line Energy Distribution</td></tr><tr><td>SMC</td><td>Small Magellanic Cloud</td></tr><tr><td>SN</td><td>SuperNova</td></tr><tr><td>SN Ia</td><td>Type Ia SuperNova</td></tr><tr><td>SN II</td><td>Type II SuperNova</td></tr><tr><td>SNR</td><td>SuperNova Remnant</td></tr><tr><td>sSFR</td><td>specific Star Formation Rate</td></tr><tr><td>SUE</td><td>Skewed Uncertainty Ellipse</td></tr><tr><td>TIR</td><td>Total InfraRed</td></tr><tr><td>TLS</td><td>Two-Level System</td></tr><tr><td>TPAGB</td><td>Thermally-Pulsing Asymptotic Giant Branch</td></tr><tr><td>TMA</td><td>Too Many Acronyms</td></tr><tr><td>UIB</td><td>Unidentified Infrared Bands</td></tr><tr><td>ULIRG</td><td>UltraLuminous InfraRed Galaxies</td></tr><tr><td>UV</td><td>UltraViolet</td></tr><tr><td>VCD</td><td>Very Cold Dust</td></tr><tr><td>VSG</td><td>Very Small Grain</td></tr><tr><td>YSO</td><td>Young Stellar Object</td></tr><tr><td>WD</td><td>White Dwarf</td></tr><tr><td>WIM</td><td>Warm Ionized Medium</td></tr><tr><td>WNM</td><td>Warm Neutral Medium</td></tr><tr><td>WR</td><td>Wolf Rayet star</td></tr><tr><td>ZAMS</td><td>Zero-Age Main Sequence</td></tr></tbody></table>

## A.2 Telescope and Instrument Acronyms

<table><thead><tr><th>Acronym</th><th>Telescope or Instrument</th></tr></thead><tbody><tr><td>ALMA</td><td>Atacama Large Millimeter/submillimeter Array</td></tr><tr><td>APEX</td><td>Atacama Pathfinder Experiment</td></tr><tr><td>ATHENA</td><td>Advanced Telescope for High Energy Astrophysics</td></tr><tr><td>BLAST</td><td>Balloon-borne Large Aperture Submillimeter Telescope</td></tr><tr><td>COBE</td><td>COsmic Background Explorer</td></tr><tr><td>CSO</td><td>Caltech Submillimeter Observatory</td></tr><tr><td>DIRBE</td><td>Diffuse Infrared Background Experiment</td></tr><tr><td>DMR</td><td>Differential Microwave Radiometer</td></tr><tr><td>FIRAS</td><td>Far-InfraRed Absolute Spectrophotometer</td></tr><tr><td>FIS</td><td>Far-Infrared Surveyor</td></tr><tr><td>FUSE</td><td>Far Ultraviolet Spectroscopic Explorer</td></tr><tr><td>FTS</td><td>Fourier Transform Spectrometer</td></tr><tr><td>HFI</td><td>High Frequency Instrument</td></tr><tr><td>HIFI</td><td>Heterodyne Instrument for the Far-Infrared</td></tr><tr><td>HST</td><td>Hubble Space Telescope</td></tr></tbody></table>

<figure><img src="image_561.png" /></figure>
<table><caption>TABLE A.2 – List of instrumental acronyms used throughout the manuscript.</caption><thead><tr><td>Acronym</td><td>Telescope or Instrument</td></tr></thead><tbody><tr><td>IRAC</td><td>InfraRed Array Camera</td></tr><tr><td>IRAM</td><td>Institut de RadioAstronomie Millimétrique</td></tr><tr><td>IRAS</td><td>InfraRed Astronomical Satellite</td></tr><tr><td>IRC</td><td>InfraRed Camera</td></tr><tr><td>IRS</td><td>InfraRed Spectrograph</td></tr><tr><td>IRTF</td><td>InfraRed Telescope Facility</td></tr><tr><td>ISO</td><td>Infrared Space Observatory</td></tr><tr><td>IUE</td><td>International Ultraviolet Explorer</td></tr><tr><td>JCMT</td><td>James Clerk Maxwell Telescope</td></tr><tr><td>JWST</td><td>James Webb Space Telescope</td></tr><tr><td>KAO</td><td>Kuiper Airborne Observatory</td></tr><tr><td>LFI</td><td>Low Frequency Instrument</td></tr><tr><td>MIPS</td><td>Multiband Imaging Photometer for Spitzer</td></tr><tr><td>MIRI</td><td>Mid-InfraRed Instrument</td></tr><tr><td>MUSE</td><td>Multi Unit Spectroscopic Explorer</td></tr><tr><td>NCT</td><td>Nuclear Compton Telescope</td></tr><tr><td>NIKA2</td><td>New IRAM Kids Arrays</td></tr><tr><td>NIRcam</td><td>Near-InfraRed Camera</td></tr><tr><td>NIRISS</td><td>Near-InfraRed Imager and Slitless Spectrograph</td></tr><tr><td>NIRspec</td><td>Near-InfraRed Spectrograph</td></tr><tr><td>OAO</td><td>Orbiting Astronomical Observatory</td></tr><tr><td>PACS</td><td>Photodetector Array Camera and Spectrometer</td></tr><tr><td>PILOT</td><td>Polarized Instrument for the Long-wavelength Observation of the Tenuous ISM</td></tr><tr><td>PRONAOS</td><td>PROjet National pour l'Observation Submillimétrique</td></tr><tr><td>SOFIA</td><td>Stratospheric Observatory for Infrared Astronomy</td></tr><tr><td>SPICA</td><td>SPace Infrared telescope for Cosmology and Astrophysics</td></tr><tr><td>SPIRE</td><td>Spectral and Photometric Imaging REceiver</td></tr><tr><td>UKIRT</td><td>United Kingdom InfraRed Telescope</td></tr><tr><td>VLT</td><td>Very Large Telescope</td></tr><tr><td>WIRO</td><td>Wyoming InfraRed Observatory</td></tr><tr><td>WISE</td><td>Wide-field Infrared survey Explorer</td></tr><tr><td>WMAP</td><td>Wilkinson Microwave Anisotropy Probe</td></tr></tbody></table>

## A.3 Model and Project Acronyms

<table><caption>TABLE A.3 – List of model acronyms used throughout the manuscript.</caption><thead><tr><td>Acronym</td><td>Model Name</td></tr></thead><tbody><tr><td>DGS</td><td>Dwarf Galaxy Survey</td></tr><tr><td>DustPedia</td><td>A definitive study of dust in the local Universe</td></tr><tr><td>HerBIE</td><td>HiERarchical Bayesian Inference for dust Emission</td></tr><tr><td>HERITAGE</td><td>HERschel Inventory of The Agents of Galaxy Evolution</td></tr><tr><td>SAGE</td><td>Surveying the Agents of Galaxy Evolution</td></tr><tr><td>THEMIS</td><td>The Heterogeneous Evolution Model for Interstellar Solids</td></tr></tbody></table>
<figure><img src="image_562.png" /></figure>

**A.4 Denomination of the Main Spectral Windows**

Table A.4 gives the acronyms and spectral ranges of the most important electromagnetic domains. For each domain, we give the interval in photon wavelength, frequency and energy. There are slight variations of these intervals across the literature. The physical phenomena listed in the right column are indicative of the typical most dominant emission at the scale of a galaxy. Fig. A.1 shows where these different domains fall on the SED of a nearby galaxy.

<figure><img src="image_563.png" /><figcaption>FIGURE A.1 – *Spectral domains represented over the SED of a nearby galaxy.* See Table A.4 for the acronyms. Licensed under CC BY-SA 4.0.</figcaption></figure>
<figure><img src="image_564.png" /></figure>

<table><caption>TABLE A.4 – Denomination of the main spectral windows.</caption><thead><tr><th rowspan="2">Abbreviation</th><th rowspan="2">Name</th><th colspan="2">Spectral range</th><th rowspan="2">Predominant physical origin</th></tr><tr><th>Start</th><th>End</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-weight: bold;">HIGH ENERGIES</td></tr><tr><td>γ</td><td>γ rays</td><td>...</td><td>0.01 nm<br>30 EHz<br>0.12 GeV</td><td>Cosmic rays</td></tr><tr><td>X</td><td>X rays</td><td>0.01 nm<br>30 EHz<br>120 keV</td><td>10 nm<br>0.03 EHz<br>0.12 keV</td><td>Accretion disks & coronal plasmas</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">UV-VISIBLE</td></tr><tr><td>EUV</td><td>Extreme-UV</td><td>10 nm<br>30 PHz<br>120 eV</td><td>124 nm<br>2.4 PHz<br>10 eV</td><td>Massive stars</td></tr><tr><td>FUV</td><td>Far-UltraViolet</td><td>124 nm<br>2.4 PHz<br>10 eV</td><td>200 nm<br>1.5 PHz<br>6.2 eV</td><td>Massive stars</td></tr><tr><td>NUV</td><td>Near-UV</td><td>200 nm<br>1.5 PHz<br>6.2 eV</td><td>380 nm<br>0.8 PHz<br>3.3 eV</td><td>Massive stars</td></tr><tr><td>vis.</td><td>Visible</td><td>0.38 µm<br>0.8 PHz<br>3.3 eV</td><td>0.8 µm<br>0.4 PHz<br>1.5 eV</td><td>Intermediate & low-mass stars</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">COLD UNIVERSE</td></tr><tr><td>NIR</td><td>Near-InfraRed</td><td>0.8 µm<br>400 THz<br>1.5 eV</td><td>5µm<br>60 THz<br>0.25 eV</td><td>Circumstellar material</td></tr><tr><td>MIR</td><td>Mid-InfraRed</td><td>5 µm<br>60 THz<br>250 meV</td><td>40 µm<br>7.5 THz<br>30 meV</td><td>Aromatic features & hot dust</td></tr><tr><td>FIR</td><td>Far-InfraRed</td><td>40 µm<br>7.5 THz<br>30 meV</td><td>200 µm<br>1.5 THz<br>6 meV</td><td>Large ISM grains</td></tr><tr><td>submm</td><td>Submillimeter</td><td>200 µm<br>1.5 THz<br>6 meV</td><td>800 µm<br>0.4 THz<br>1.5 meV</td><td>Cold dust</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">RADIO/MICROWAVE</td></tr><tr><td>mm</td><td>Millimeter</td><td>0.8 mm<br>400 GHz<br>1.5 meV</td><td>5 mm<br>60 GHz<br>0.25 meV</td><td>Cold dust & free-free</td></tr><tr><td>cm</td><td>Centimeter</td><td>0.5 cm<br>60 GHz<br>250 µeV</td><td>6 cm<br>5 GHz<br>20 µeV</td><td>Free-free & synchrotron</td></tr></tbody></table>

<figure><img src="image_565.png" /></figure>
<figure><img src="image_566.png" /></figure>

# Appendix B

## Astronomers and Units

> I hope all Americans will do everything in their power to introduce the French metrical system. (...) I look upon our English system as a wickedly, brain-destroying system of bondage under which we suffer. The reason why we continue to use it, is the imaginary difficulty of making a change.

(William THOMSON, Lord Kelvin; Thomson, 1889)

### Contents

<table><tr><td>B.1 Brief History of Unit Systems</td><td>281</td></tr><tr><td>The necessity to unify disparate measures.</td><td>281</td></tr><tr><td>Measuring the Earth.</td><td>281</td></tr><tr><td>The introduction of the metric system.</td><td>282</td></tr><tr><td>Difficulty of adoption.</td><td>282</td></tr><tr><td>The international system.</td><td>282</td></tr><tr><td>B.2 Working with Units</td><td>282</td></tr></table>

### B.1 Brief History of Unit Systems

**The necessity to unify disparate measures.** During Antiquity and the Middle Age, measures of weight, length and duration were varying from one place to another. The first government in History to try and homogenize measures was under king Henri III, in England. The 1297 version of the *Magna Carta* (originally signed in 1215), expressed the will to define standards for measuring weights and distances. "*Article 25. One measure of Wine shall be through our Realm, and one measure of Ale, and one measure of Corn, that is to say, the Quarter of London; and one breadth of dyed Cloth, Russets, and Haberjects, that is to say, two Yards within the lists. And it shall be of Weights as it is of Measures.*" The rest of the world kept using different yards and pounds, for several centuries.

**Measuring the Earth.** In France, the *Académie royale des sciences* was funded in 1666 by Jean-Baptiste COLBERT, under king Louis XIV, influenced by his secretary for sciences and arts, Charles PERRAULT (Débarbat & Quinn, 2019). In 1667, the royal observatory was created and astronomers were tasked with providing more accurate maps of the realm. Clergyman Jean PICARD performed a series of measures by triangulation, with a unique measuring board, and estimated the size of the Earth (*Mesure de la Terre*, 1671). During the XVIIIth century, several scientific expeditions in Latin America or the North Pole (by La Condamine, Maupertuis, et al.) refined the measurement of the size of the Earth and confirmed its flattening around the poles.

<figure><img src="image_567.png" /></figure>
<figure><img src="image_568.png" /></figure>

**The introduction of the metric system.** It is only during the French revolution (1789–1799) that the metric system was introduced. It was consistent with its time. It was aimed at erasing differences in an abstract way, with new standards independent of the old human references (foot, inch, etc.). One of its important features was that it was a decimal system, simplifying calculations. It can be traced back to the months before the revolution, in 1789. The *cahiers de doléances* (register of grievances) expressed the wish to have unified measures throughout the realm. In 1790, Charles-Maurice DE TALLEYRAND-PÉRIGORD, a bishop elected at the recent national assembly, submitted a memoir to adopt a new system of weights and measures, contributed by Marie-Jean-Antoine CRITAT DE CONDORCET and Joseph-Jérôme LEFRANÇOIS DE LALANDE (Débarbat & Quinn, 2019). In 1792, Jean-Baptiste DELAMBRE and Pierre-François MÉCHAIN were charged with measuring the length of the meridian between Dunkerque and Barcelona (Alder, 2015). The definition of the meter was then 1/10000000 of the distance between the North Pole and the equator. The kilogram was defined as the mass of one cubic decimeter of water.

**Difficulty of adoption.** The metric system was not adopted right away, even in France. It was mocked by Napoléon, although Laplace promoted the advantage of its decimal system to him. For a while, we kept "mesure usuelles", which were a standardization of imperial units. In Germany, around 1830, Carl-Friedrich GAUSS formalized the metric unit system in physics, and proposed to add the seconds to meters and kilograms, leading to the *CGS system* (Centimetre-Gram-Second). During the 1851 World's fair in London, France promoted the metric system to the world. It led to the "*Treaty of the Metre*", signed in Paris in 1875, by seventeen countries adopting the metric system. Great Britain, the Netherlands and Portugal were opposed. England, in particular, felt that adopting the French system would be a political defeat. A diplomatic solution was proposed in adopting the Greenwich meridian, during the 1883 Geodetic Congress: *"The Conference hopes that, if the whole world is agreed upon the unification of longitudes and hours in accepting the Greenwich meridian as the point of departure, Great Britain will find in this fact an additional motive to take on her side new steps in favour of the unification of weights and measures, by joining the Metrical Convention of May 20, 1875"* (The Geodetic Congress, 1883). The Greenwich meridian was finally adopted during the 1884 International Meridian Conference, but England did not adopt the metric system...

**The international system.** Since 1960, the *International System of units* (SI) is the *Meter-Kilogram-Second-Ampere system* (MKSA or MKS). Astronomers are one of the last communities to use CGS units (and the Gaussian system for electrodynamics; Table B.4). The continued use of a mix between imperial units and the CGS system is counterproductive. The most dramatic example is the crash of the 1999 *Mars Climate Observer* probe, because of a conversion mistake between imperial and metric units (*Popular Mechanics*, 2017). Table B.1 gives the correspondence between the MKS and CGS systems, and Tables B.2–B.3 list the fundamental constants in both systems. Table B.4 compares the MKSA and Gaussian systems for electrodynamics.

## B.2 Working with Units

My personal experience in working with units led me to the following advices.

**Adopt specific units for each problem,** so that the quantities one have to deal with are close to unity (in orders of magnitude). This is particularly important to avoid numerical problems. In IS-Mology, the µm is a good wavelength unit, and the cm⁻³ a good density unit, and the pc a good distance unit.

**Deciding which quantity should be logarithmic** must be based on the way the uncertainty on this quantity has been estimated. The conversion between linear and logarithmic quantities indeed is not straightforward. Keeping the same 1σ range is a good practice, but it is not rigorously

<figure><img src="image_569.png" /></figure>
<figure><img src="image_570.png" /></figure>

<table><caption>TABLE B.1 – Unit conversion.</caption><thead><tr><th>Quantity</th><th>International units (MKS)</th><th>Astronomer's units (CGS)</th></tr></thead><tbody><tr><td colspan="3">GENERAL</td></tr><tr><td>Length</td><td>1 m (meter)</td><td>10<sup>2</sup> cm (centimeter)</td></tr><tr><td>Force</td><td>1 N (Newton)</td><td>10<sup>5</sup> dyn (dynes)</td></tr><tr><td>Energy</td><td>1 J (joule)</td><td>10<sup>7</sup> erg</td></tr><tr><td>Power</td><td>1 W (watt)</td><td>10<sup>7</sup> erg/s</td></tr><tr><td>Flux (1 Jansky)</td><td>10<sup>-26</sup> W/m<sup>2</sup>/Hz</td><td>10<sup>-23</sup> erg/s/cm<sup>2</sup>/Hz</td></tr><tr><td colspan="3">ELECTROMAGNETISM</td></tr><tr><td>Charge</td><td>1 C (Coulomb)</td><td>2.99792458 × 10<sup>9</sup> esu (electrostatic unit)</td></tr><tr><td>Current</td><td>1 A (Ampere)</td><td>2.99792458 × 10<sup>9</sup> esu/s</td></tr><tr><td>Electric potential</td><td>1 V (volt)</td><td>1/299.792458 statV (statvolt)</td></tr><tr><td>Electric field</td><td>1 V/m</td><td>1/299.792458 statV/cm</td></tr><tr><td>Magnetic field</td><td>1 T (Tesla)</td><td>10<sup>4</sup> G (Gauss)</td></tr><tr><td>Magnetic flux</td><td>1 Wb (Weber)</td><td>10<sup>8</sup> G.cm<sup>2</sup></td></tr><tr><td>Auxiliary field H</td><td>1 A/m</td><td>4π × 10<sup>-3</sup> Oe (Oersted)</td></tr><tr><td colspan="3">ANGULAR DISTANCE</td></tr><tr><td>1 arcsec</td><td>4.848 × 10<sup>-6</sup> rad</td><td></td></tr><tr><td>1 arcsec at 1 Mpc</td><td>4.848 pc</td><td></td></tr></tbody></table>

equivalent:

$$ \log X \pm \sigma_{\log X} \Leftrightarrow X^{+\left(10^{\sigma_{\log X}} - 1\right)X} \cdot \left(1 - 10^{-\sigma_{\log X}}\right)X \quad (B.1) $$

The underlying probability law is different in both cases. It is preferable to choose a representation of the quantity so that its uncertainty is the closest to a normal law. If we are estimating the uncertainty on a parameter, the dynamical range is important. If a quantity varies by more than one order of magnitude, it is often a good choice to treat the logarithm of this quantity in a Bayesian model. Concerning fluxes, the magnitude system is logarithmic, but it is not a decimal system (it uses a cumbersome 2.5 factor), and it relies on arbitrary zero-point fluxes (cf. Table B.5). The only useful formula concerning magnitudes is to get out of them:

$$ F_v(\lambda_0) = F_{v,0} \times 10^{-0.4m(\lambda_0)}. \quad (B.2) $$

**Perform conversions through the SI**, and avoid CGS units, which are already deprecated outside astronomy. CGS are indeed boomer units, so is the Gaussian unit system in electrodynamics. In terms of computing, it is important to have a reliable conversion module in the different programming languages that one uses, to avoid stupid mistakes.

<figure><img src="image_571.png" /></figure>
<figure><img src="image_572.png" /></figure>

<table><caption>TABLE B.2 – Fundamental constants.</caption><thead><tr><th>Quantity</th><th>International units (MKS)</th><th>Astronomer's units (CGS)</th></tr></thead><tbody><tr><td colspan="3" style="text-align: center; font-weight: bold;">UNIVERSAL</td></tr><tr><td>Light speed, c</td><td>2.999792458 × 10<sup>8</sup> m/s</td><td>2.999792458 × 10<sup>10</sup> cm/s</td></tr><tr><td>Newton constant, G</td><td>6.67428 × 10<sup>-11</sup> m<sup>3</sup>/kg/s<sup>2</sup></td><td>6.67428 × 10<sup>-8</sup> cm<sup>3</sup>/g/s<sup>2</sup></td></tr><tr><td>Planck constant, h</td><td>6.62606896 × 10<sup>-34</sup> J.s</td><td>6.62606896 × 10<sup>-27</sup> erg.s</td></tr><tr><td>ħ = h/2π</td><td>1.054571628 × 10<sup>-34</sup> J.s</td><td>1.054571628 × 10<sup>-27</sup> erg.s</td></tr><tr><td>Magnetic constant, μ<sub>0</sub> = 4π × 10<sup>-7</sup></td><td>1.2566370614 × 10<sup>-6</sup> N/A<sup>2</sup></td><td></td></tr><tr><td>Electric constant, ε<sub>0</sub> = 1/μ<sub>0</sub>c<sup>2</sup></td><td>8.854187817 × 10<sup>-12</sup> F/m</td><td></td></tr><tr><td>Elementary charge, e</td><td>1.602176487 × 10<sup>-19</sup> C</td><td>4.8065295 × 10<sup>-10</sup> esu</td></tr><tr><td colspan="3" style="text-align: center; font-weight: bold;">ATOMIC</td></tr><tr><td>Electron mass, m<sub>e</sub></td><td>9.10938215 × 10<sup>-31</sup> kg</td><td>9.10938215 × 10<sup>-28</sup> g</td></tr><tr><td>m<sub>e</sub>c<sup>2</sup></td><td>8.18710438 × 10<sup>-14</sup> J</td><td>8.18710438 × 10<sup>-7</sup> erg</td></tr><tr><td>m<sub>e</sub>c<sup>2</sup>/e</td><td>0.510998910 MeV</td><td></td></tr><tr><td>Proton mass, m<sub>p</sub></td><td>1.672621637 × 10<sup>-27</sup> kg</td><td>1.672621637 × 10<sup>-24</sup> g</td></tr><tr><td>m<sub>p</sub>c<sup>2</sup></td><td>1.503277359 × 10<sup>-10</sup> J</td><td>1.503277359 × 10<sup>-3</sup> erg</td></tr><tr><td>m<sub>p</sub>c<sup>2</sup>/e</td><td>0.938272013 GeV</td><td></td></tr><tr><td>Rydberg, R<sub>∞</sub> = α<sup>2</sup>m<sub>e</sub>c/2ħ</td><td>10973731.568527 m<sup>-1</sup></td><td>109737.31568527 cm<sup>-1</sup></td></tr><tr><td>R<sub>∞</sub>c</td><td>3.289841960361 × 10<sup>15</sup> Hz</td><td></td></tr><tr><td>R<sub>∞</sub>hc</td><td>2.17987197 × 10<sup>-18</sup> J</td><td>2.17987197 × 10<sup>-11</sup> erg</td></tr><tr><td>R<sub>∞</sub>hc/e</td><td>13.60569193 eV</td><td></td></tr><tr><td colspan="3" style="text-align: center; font-weight: bold;">MACROSCOPIC</td></tr><tr><td>Boltzmann constant, k</td><td>1.3806504 × 10<sup>-23</sup> J/K</td><td>1.3806504 × 10<sup>-16</sup> erg/K</td></tr><tr><td>k/e</td><td>8.617343 × 10<sup>-5</sup> eV/K</td><td></td></tr><tr><td>k/eh</td><td>69.50356 × 10<sup>10</sup> Hz/K</td><td></td></tr><tr><td>Atomic mass unit, m<sub>u</sub> = m(<sup>12</sup>C)/12</td><td>1.660538782 × 10<sup>-27</sup> kg</td><td>1.660538782 × 10<sup>-24</sup> g</td></tr><tr><td>Avogadro number, N<sub>A</sub></td><td>6.02214179 × 10<sup>23</sup> mol<sup>-1</sup></td><td></td></tr><tr><td>Molar gas constant, R = kN<sub>A</sub></td><td>8.314472 J/mol/K</td><td>8.314472 × 10<sup>7</sup> erg/mol/K</td></tr></tbody></table>

<figure><img src="image_573.png" /></figure>
<figure><img src="image_574.png" /></figure>

<table><caption>TABLE B.3 – Astronomical constants.</caption><thead><tr><th>Quantity</th><th>International units (MKS)</th><th>Astronomer's units (CGS)</th></tr></thead><tbody><tr><td colspan="3">GENERAL</td></tr><tr><td>Astronomical unit, a.u. ≡ &lt;☉ - ⊕&gt;</td><td>1.495979 × 10<sup>11</sup> m</td><td>1.495979 × 10<sup>13</sup> cm</td></tr><tr><td>Parsec, pc ≡ 1 a.u./1"</td><td>3.085678 × 10<sup>16</sup> m</td><td>3.085678 × 10<sup>18</sup> cm</td></tr><tr><td colspan="3">SOLAR SYSTEM</td></tr><tr><td>Solar radius, R<sub>☉</sub></td><td>6.9599 × 10<sup>8</sup> m</td><td>6.9599 × 10<sup>10</sup> cm</td></tr><tr><td>Solar mass, M<sub>☉</sub></td><td>1.9889 × 10<sup>30</sup> kg</td><td>1.9889 × 10<sup>33</sup> g</td></tr><tr><td>Solar luminosity, L<sub>☉</sub></td><td>3.846 × 10<sup>26</sup> W</td><td>3.846 × 10<sup>33</sup> erg/s</td></tr><tr><td>Earth radius, R<sub>⊕</sub></td><td>6.378140 × 10<sup>6</sup> m</td><td>6.378140 × 10<sup>8</sup> cm</td></tr><tr><td>Earth mass, M<sub>⊕</sub></td><td>5.974 × 10<sup>24</sup> kg</td><td>5.974 × 10<sup>27</sup> g</td></tr><tr><td colspan="3">GALAXY</td></tr><tr><td>Solar velocity around G.C., Θ<sub>☉</sub></td><td>220 km/s</td><td></td></tr><tr><td>Distance sun-G.C., R<sub>☉</sub></td><td>8.0 kpc</td><td></td></tr><tr><td>Local disk density, ρ<sub>disk</sub></td><td>3 − 12 × 10<sup>−21</sup> kg/m<sup>3</sup></td><td>3 − 12 × 10<sup>−24</sup> g/cm<sup>3</sup></td></tr><tr><td>n<sub>disk</sub></td><td>1 − 5 × 10<sup>6</sup> m<sup>−3</sup></td><td>1 − 5 cm<sup>−3</sup></td></tr><tr><td>Local halo density, ρ<sub>halo</sub></td><td>2 − 13 × 10<sup>−22</sup> kg/m<sup>3</sup></td><td>2 − 13 × 10<sup>−25</sup> g/cm<sup>3</sup></td></tr><tr><td>n<sub>halo</sub></td><td>10 − 60 × 10<sup>4</sup> m<sup>−3</sup></td><td>0.1 − 0.6 cm<sup>−3</sup></td></tr><tr><td colspan="3">COSMOLOGY</td></tr><tr><td>Hubble expansion rate, H<sub>0</sub></td><td>71 km/s/Mpc</td><td></td></tr><tr><td>Critical density, ρ<sub>c</sub> ≡ 3H<sub>0</sub><sup>2</sup>/8πG</td><td>1.399062 × 10<sup>11</sup> M<sub>☉</sub>/Mpc<sup>3</sup></td><td>9.472 × 10<sup>−30</sup> g/cm<sup>3</sup></td></tr><tr><td>Pressureless matter density, Ω<sub>M</sub> ≡ ρ<sub>M</sub>/ρ<sub>c</sub></td><td>0.15 ≲ Ω<sub>M</sub> ≲ 0.45</td><td></td></tr><tr><td>Baryon density, Ω<sub>B</sub> ≡ ρ<sub>B</sub>/ρ<sub>c</sub></td><td>0.019 ≲ Ω<sub>B</sub> ≲ 0.046</td><td></td></tr><tr><td>Cosmological constant, Ω<sub>Λ</sub> ≡ Λ<sub>c</sub><sup>2</sup>/3H<sub>0</sub><sup>2</sup></td><td>0.6 ≲ Ω<sub>Λ</sub> ≲ 0.8</td><td></td></tr></tbody></table>

<figure><img src="image_575.png" /></figure>
<figure><img src="image_576.png" /></figure>

<table><caption>TABLE B.4 – *Classical electrodynamics*.</caption><thead><tr><th>Quantity</th><th>Rationalized MKSA</th><th>Gaussian units</th></tr></thead><tbody><tr><td>Lorentz Force</td><td>→F = q(→E + →v ∧ →B)<br>→dF/→dV = ρ→E + →j ∧ →B</td><td>→F = q(→E + →v/c ∧ →B)<br>→dF/→dV = ρ→E + →j/c ∧ →B</td></tr><tr><td>Dielectric Constant & Permeability</td><td>ε₀ = 10<sup>7</sup> &nbsp;&nbsp;&nbsp;&nbsp; μ₀ = 4π10<sup>-7</sup></td><td>ε₀ = 1 &nbsp;&nbsp;&nbsp;&nbsp; μ₀ = 1</td></tr><tr><td>Displacement & Magnetic Field</td><td>→D = ε→E + →P<br>→H = →B/μ - →M</td><td>→D = ε→E + 4π→P<br>→H = →B/μ - 4π→M</td></tr><tr><td>Maxwell Equations</td><td>→∇.→D = ρ<br>→∇ ∧ →H = →j + ∂→D/∂t<br>→∇ ∧ →E + ∂→B/∂t = →0<br>→∇.→B = 0</td><td>→∇.→D = 4πρ<br>→∇ ∧ →H = (4π/c →j + 1/c ∂→D/∂t)<br>→∇ ∧ →E + 1/c ∂→B/∂t = →0<br>→∇.→B = 0</td></tr><tr><td>Poynting Vector</td><td>→P = →E ∧ →H</td><td>→P = c/4π →E ∧ →H</td></tr><tr><td>Electromagnetic Power</td><td>P = ∬_S →P.d→S</td><td>P = ∬_S →P.d→S</td></tr><tr><td>Energy Density</td><td>U = 1/2 (ε→E<sup>2</sup> + →B<sup>2</sup>/μ)</td><td>U = 1/8π (ε→E<sup>2</sup> + →B<sup>2</sup>/μ)</td></tr></tbody></table>

<figure><img src="image_577.png" /></figure>
<figure><img src="image_578.png" /></figure>

<table><caption>TABLE B.5 – The magnitude system.</caption><thead><tr><th></th><th>Central wavelength, λ<sub>0</sub></th><th>Zero-point flux, F<sub>v,0</sub></th></tr></thead><tbody><tr><td>U</td><td>0.36 μm</td><td>1884 Jy</td></tr><tr><td>B</td><td>0.44 μm</td><td>4646 Jy</td></tr><tr><td>V</td><td>0.55 μm</td><td>3953 Jy</td></tr><tr><td>R</td><td>0.66 μm</td><td>2875 Jy</td></tr><tr><td>I</td><td>0.80 μm</td><td>2241 Jy</td></tr><tr><td>J</td><td>1.25 μm</td><td>1602 Jy</td></tr><tr><td>H</td><td>1.60 μm</td><td>1010 Jy</td></tr><tr><td>K</td><td>2.18 μm</td><td>630 Jy</td></tr><tr><td>L</td><td>3.45 μm</td><td>278 Jy</td></tr><tr><td>M</td><td>4.75 μm</td><td>153 Jy</td></tr><tr><td>N</td><td>10.6 μm</td><td>36.3 Jy</td></tr></tbody></table>

<figure><img src="image_579.png" /></figure>
<figure><img src="image_580.png" /></figure>
<figure><img src="image_581.png" /></figure>

# Appendix C

## Useful Formulae

> There is no royal road to science, and only those who do not dread the fatiguing climb of its steep paths have a chance of gaining its luminous summits.

(Karl MARX; Marx, 1872)

## Contents

<table><tr><td>C.1</td><td>3D Quantities and Volume Integrals</td><td>290</td></tr><tr><td>C.1.1</td><td>Differential Operators</td><td>290</td></tr><tr><td>C.1.1.1</td><td>Gradient</td><td>290</td></tr><tr><td>C.1.1.2</td><td>Laplacian</td><td>291</td></tr><tr><td>C.1.1.3</td><td>Divergence</td><td>291</td></tr><tr><td>C.1.1.4</td><td>Curl</td><td>291</td></tr><tr><td>C.1.2</td><td>Vectorial Analysis</td><td>291</td></tr><tr><td>C.1.3</td><td>Integral Theorems</td><td>292</td></tr><tr><td>C.1.4</td><td>Dust Heating and Cooling: Two Ways of Slicing the Pis</td><td>292</td></tr><tr><td>C.1.4.1</td><td>Solution 1</td><td>293</td></tr><tr><td>C.1.4.2</td><td>Solution 2</td><td>293</td></tr><tr><td>C.2</td><td>Statistics</td><td>293</td></tr><tr><td>C.2.1</td><td>General Formulae</td><td>293</td></tr><tr><td>C.2.1.1</td><td>Moments of a PDF</td><td>293</td></tr><tr><td></td><td>Definitions.</td><td>293</td></tr><tr><td></td><td>Estimators.</td><td>294</td></tr><tr><td>C.2.1.2</td><td>Marginalization</td><td>294</td></tr><tr><td>C.2.1.3</td><td>Variable Change</td><td>294</td></tr><tr><td>C.2.1.4</td><td>Combining Uncertainties</td><td>294</td></tr><tr><td></td><td>Rant about systematics.</td><td>295</td></tr><tr><td>C.2.2</td><td>Useful Probability Distributions</td><td>295</td></tr><tr><td>C.2.2.1</td><td>Binomial Distribution</td><td>295</td></tr><tr><td>C.2.2.2</td><td>Poisson Distribution</td><td>295</td></tr><tr><td>C.2.2.3</td><td>Gaussian Distribution</td><td>295</td></tr><tr><td></td><td>Multivariate form.</td><td>295</td></tr><tr><td></td><td>Error function.</td><td>296</td></tr><tr><td>C.2.2.4</td><td>Student's t Distribution</td><td>296</td></tr><tr><td>C.2.2.5</td><td>Split-Normal Distribution</td><td>296</td></tr><tr><td>C.2.2.6</td><td>Lorentzian Distribution</td><td>296</td></tr><tr><td>C.2.3</td><td>Drawing random variables from an arbitrary distribution</td><td>296</td></tr></table>

<figure><img src="image_582.png" /></figure>
<figure><img src="image_583.png" /></figure>

<table><tbody><tr><td>C.2.3.1</td><td>The Rejection Method</td><td>296</td></tr><tr><td>C.2.3.2</td><td>Inverting the CDF</td><td>297</td></tr><tr><td>C.3</td><td>Trigonometry</td><td>297</td></tr><tr><td>C.3.1</td><td>Transformations</td><td>298</td></tr><tr><td>C.3.1.1</td><td>Rotations</td><td>298</td></tr><tr><td>C.3.1.2</td><td>Relations Between Functions</td><td>298</td></tr><tr><td>C.3.2</td><td>Addition</td><td>298</td></tr><tr><td>C.3.2.1</td><td>Summing Angles</td><td>298</td></tr><tr><td>C.3.2.2</td><td>Inverse Relations</td><td>298</td></tr><tr><td>C.3.3</td><td>Linearization</td><td>298</td></tr><tr><td>C.3.3.1</td><td>Squares and Cubes</td><td>298</td></tr><tr><td>C.3.3.2</td><td>Inverse Relations</td><td>299</td></tr></tbody></table>

This appendix contains various unrelated formulae that I find useful in my daily practice, but that I do not necessarily remember. The problem is that gathering them here suppresses any incentive to memorize them, therefore making it essential to have them written here.

# C.1 3D Quantities and Volume Integrals

## C.1.1 Differential Operators

The three most common coordinate systems are represented in Fig. C.1. In what follows, we express the differential operators in these systems.

<figure><img src="image_584.png" /><figcaption>FIGURE C.1 – Most common coordinate systems. Licensed under CC BY-SA 4.0.</figcaption></figure>

### C.1.1.1 Gradient

**Cartesian:** $\vec{\nabla} U = \frac{\partial U}{\partial x} \hat{x} + \frac{\partial U}{\partial y} \hat{y} + \frac{\partial U}{\partial z} \hat{z}$.

**Cylindrical:** $\vec{\nabla} U = \frac{\partial U}{\partial \rho} \hat{\rho} + \frac{1}{\rho} \frac{\partial U}{\partial \phi} \hat{\phi} + \frac{\partial U}{\partial z} \hat{z}$.

**Spherical:** $\vec{\nabla} U = \frac{\partial U}{\partial r} \hat{r} + \frac{1}{r} \frac{\partial U}{\partial \theta} \hat{\theta} + \frac{1}{r \sin \theta} \frac{\partial U}{\partial \phi} \hat{\phi}$.

<figure><img src="image_585.png" /></figure>
<figure><img src="image_586.png" /></figure>

### C.1.1.2 Laplacian

Cartesian: $\vec{\nabla}^2 U = \frac{\partial^2 U}{\partial x^2} + \frac{\partial^2 U}{\partial y^2} + \frac{\partial^2 U}{\partial z^2}$.

Cylindrical: $\vec{\nabla}^2 U = \frac{1}{\rho} \frac{\partial}{\partial \rho} \left( \rho \frac{\partial U}{\partial \rho} \right) + \frac{1}{\rho^2} \frac{\partial^2 U}{\partial \phi^2} + \frac{\partial^2 U}{\partial z^2}$.

Spherical: $\vec{\nabla}^2 U = \frac{1}{r} \frac{\partial^2}{\partial r^2} (rU) + \frac{1}{r^2 \sin\theta} \frac{\partial}{\partial\theta} \left( \sin\theta \frac{\partial U}{\partial\theta} \right) + \frac{1}{r^2 \sin^2\theta} \frac{\partial^2 U}{\partial\phi^2}$.

### C.1.1.3 Divergence

Cartesian: $\vec{\nabla} \cdot \vec{A} = \frac{\partial A_x}{\partial x} + \frac{\partial A_y}{\partial y} + \frac{\partial A_z}{\partial z}$.

Cylindrical: $\vec{\nabla} \cdot \vec{A} = \frac{1}{\rho} \frac{\partial}{\partial \rho} (\rho A_{\rho}) + \frac{1}{\rho} \frac{\partial A_{\phi}}{\partial \phi} + \frac{\partial A_z}{\partial z}$.

Spherical: $\vec{\nabla} \cdot \vec{A} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 A_r) + \frac{1}{r \sin\theta} \frac{\partial}{\partial\theta} (\sin\theta A_{\theta}) + \frac{1}{r \sin\theta} \frac{\partial A_{\phi}}{\partial\phi}$.

### C.1.1.4 Curl

Cartesian: $\vec{\nabla} \wedge \vec{A} = \left( \frac{\partial A_z}{\partial y} - \frac{\partial A_y}{\partial z} \right) \hat{x} + \left( \frac{\partial A_x}{\partial z} - \frac{\partial A_z}{\partial x} \right) \hat{y} + \left( \frac{\partial A_y}{\partial x} - \frac{\partial A_x}{\partial y} \right) \hat{z}$.

Cylindrical: $\vec{\nabla} \wedge \vec{A} = \left( \frac{1}{\rho} \frac{\partial A_z}{\partial \rho} - \frac{\partial A_{\phi}}{\partial z} \right) \hat{\rho} + \left( \frac{\partial A_{\rho}}{\partial z} - \frac{\partial A_z}{\partial \rho} \right) \hat{\phi} + \frac{1}{\rho} \left( \frac{\partial \rho A_{\phi}}{\partial \rho} - \frac{\partial A_{\rho}}{\partial \phi} \right) \hat{z}$.

Spherical: $\vec{\nabla} \wedge \vec{A} = \frac{1}{r \sin\theta} \left( \frac{\partial \sin\theta A_{\phi}}{\partial\theta} - \frac{\partial A_{\theta}}{\partial\phi} \right) \hat{r} + \frac{1}{r \sin\theta} \left( \frac{\partial A_r}{\partial\phi} - \sin\theta \frac{\partial r A_{\phi}}{\partial r} \right) \hat{\theta} + \frac{1}{r} \left( \frac{\partial r A_{\theta}}{\partial r} - \frac{\partial A_r}{\partial\theta} \right) \hat{\phi}$.

## C.1.2 Vectorial Analysis

$$ \vec{A} \cdot (\vec{B} \wedge \vec{C}) = \vec{B} \cdot (\vec{C} \wedge \vec{A}) = \vec{C} \cdot (\vec{A} \wedge \vec{B}) \quad (C.1) $$

$$ \vec{A} \wedge (\vec{B} \wedge \vec{C}) = (\vec{A} \cdot \vec{C}) \vec{B} - (\vec{A} \cdot \vec{B}) \vec{C} \quad (C.2) $$

$$ (\vec{A} \wedge \vec{B}) \cdot (\vec{C} \wedge \vec{D}) = (\vec{A} \cdot \vec{C})(\vec{B} \cdot \vec{D}) - (\vec{A} \cdot \vec{D})(\vec{B} \cdot \vec{C}) \quad (C.3) $$

$$ \vec{\nabla} \wedge \vec{\nabla} \psi = \vec{0} \quad (C.4) $$

$$ \vec{\nabla} \cdot (\vec{\nabla} \wedge \vec{A}) = 0 \quad (C.5) $$

$$ \vec{\nabla} \wedge (\vec{\nabla} \wedge \vec{A}) = \vec{\nabla} (\vec{\nabla} \cdot \vec{A}) - \vec{\nabla}^2 \vec{A} \quad (C.6) $$

$$ \vec{\nabla} \cdot (\psi \vec{A}) = \vec{A} \cdot \vec{\nabla} \psi + \psi \vec{\nabla} \cdot \vec{A} \quad (C.7) $$

$$ \vec{\nabla} \wedge (\psi \vec{A}) = \vec{\nabla} \psi \wedge \vec{A} + \psi \vec{\nabla} \wedge \vec{A} \quad (C.8) $$

$$ \vec{\nabla} (\vec{A} \cdot \vec{B}) = (\vec{A} \cdot \vec{\nabla}) \vec{B} + (\vec{B} \cdot \vec{\nabla}) \vec{A} + \vec{A} \wedge (\vec{\nabla} \wedge \vec{B}) + \vec{B} \wedge (\vec{\nabla} \wedge \vec{A}) \quad (C.9) $$

$$ \vec{\nabla} \cdot (\vec{A} \wedge \vec{B}) = \vec{B} \cdot (\vec{\nabla} \wedge \vec{A}) - \vec{A} \cdot (\vec{\nabla} \wedge \vec{B}) \quad (C.10) $$

$$ \vec{\nabla} \wedge (\vec{A} \wedge \vec{B}) = \vec{A} (\vec{\nabla} \cdot \vec{B}) - \vec{B} (\vec{\nabla} \cdot \vec{A}) + (\vec{B} \cdot \vec{\nabla}) \vec{A} - (\vec{A} \cdot \vec{\nabla}) \vec{B} \quad (C.11) $$

<figure><img src="image_587.png" /></figure>
<figure><img src="image_588.png" /></figure>

### C.1.3 Integral Theorems

$$ \iiint_V \vec{\nabla} \cdot \vec{A} \, dV = \oint \vec{A} \cdot d\vec{S} \qquad (C.12) $$

$$ \iiint_V \vec{\nabla} \psi \, dV = \oint \psi \, d\vec{S} \qquad (C.13) $$

$$ \iiint_V \vec{\nabla} \wedge \vec{A} \, dV = -\oint \vec{A} \wedge d\vec{S} \qquad (C.14) $$

$$ \iiint_V (\phi \vec{\nabla}^2 \psi + \vec{\nabla} \phi \cdot \vec{\nabla} \psi) \, dV = \oint \phi \vec{\nabla} \psi \cdot d\vec{S} \qquad (C.15) $$

$$ \iiint_V (\phi \vec{\nabla}^2 \psi - \psi \vec{\nabla}^2 \phi) \, dV = \oint (\phi \vec{\nabla} \psi - \psi \vec{\nabla} \phi) \cdot d\vec{S} \qquad (C.16) $$

$$ \iint_S (\vec{\nabla} \wedge \vec{A}) \cdot d\vec{S} = \oint_C \vec{A} \cdot d\vec{l} \qquad (C.17) $$

$$ \iint_S \vec{\nabla} \psi \wedge d\vec{S} = -\oint_C \psi d\vec{l} \qquad (C.18) $$

### C.1.4 Dust Heating and Cooling: Two Ways of Slicing the Pis

One of the most elementary equations for a grain is the relation between its absorption efficiency and the power it absorbs or emits, given in Eq. (I.78) and Eq. (I.79). Yet, it often causes problems to newcomers, who, by trying to visualize the rays, get the numerical factor in the integrand ($4\pi^2 a^2$) wrong. I have seen several improper values: $16\pi^2 a^2$, $4\pi a^2$, etc. The solution is of course to explicitly write the integral, which I do below. I also provide two alternative visual solutions to count the factor the right way.

<figure><img src="image_589.png" /><figcaption>FIGURE C.2 – Two ways of slicing the $\pi s$. This figure represents the two possible orders to integrate the power absorbed by a grain. For the emitted power, the direction of the arrows is simply reversed. Licensed under CC BY-SA 4.0.</figcaption></figure>

The power absorbed by a spherical grain of radius $a$, exposed to an isotropic ISRF with mean intensity $J_v$, $P_{abs}$, can be expressed as:

$$ dP_{abs}(a, \theta, \phi) = \left( \int_{0}^{\infty} Q_{abs}(a, v) J_{v}(v) dv \right) dA d\Omega, \qquad (C.19) $$

where $dA$ and $d\Omega = d\cos\theta d\phi$ are the grain surface and solid angle elements. $\Omega$ indicates the direction of the incident rays. The possible orders of the integrals over these two elements is illustrated in Fig. C.2.

<figure><img src="image_590.png" /></figure>
### C.1.4.1 Solution 1

The case represented in Fig. C.2.a corresponds to the case where we first integrate over dA. Thus, parallel rays with a given direction $(\theta, \phi)$ intercept the grain on a surface $\pi a^2$:

$$dP_{\text{abs}}(a, \theta, \phi) = \pi a^2 \left( \int_{0}^{\infty} Q_{\text{abs}}(a, v) J_{v}(v) dv \right) d\Omega. \qquad (C.20)$$

Then, we need to integrate over all the possible ray directions:

$$P_{\text{abs}}(a) = \pi a^2 \left( \int_{0}^{\infty} Q_{\text{abs}}(a, v) J_{v}(v) dv \right) \iint_{\text{sphere}} d\Omega \qquad (C.21)$$

$$= \int_{0}^{\infty} 4\pi^2 a^2 Q_{\text{abs}}(a, v) J_{v}(v) dv. \qquad (C.22)$$

### C.1.4.2 Solution 2

The case represented in Fig. C.2.b corresponds to the case where we first integrate the flux over the ray directions, on an incident surface:

$$dP_{\text{abs}}(a) = \left( \int_{0}^{\infty} Q_{\text{abs}}(a, v) J_{v}(v) dv \right) \int_{0}^{1} \cos\theta d\cos\theta \int_{0}^{2\pi} d\phi \qquad (C.23)$$

$$= \pi \left( \int_{0}^{\infty} Q_{\text{abs}}(a, v) J_{v}(v) dv \right). \qquad (C.24)$$

There is only a $\pi$ factor here, as we integrate the flux on a surface element, somewhere on the grain. The rest of the grain shields this surface from the radiation coming from the other hemisphere. In addition, this integration is weighted by the inclination of the rays on the surface (this is the classical flux formula). We thus have the flux received by a surface element of the grain, from all possible ray directions. We now simply need to integrate over the whole grain surface: $4\pi a^2$:

$$P_{\text{abs}}(a) = \int_{0}^{\infty} 4\pi^2 a^2 Q_{\text{abs}}(a, v) J_{v}(v) dv. \qquad (C.25)$$

## C.2 Statistics

### C.2.1 General Formulae

#### C.2.1.1 Moments of a PDF

**Definitions.** If we have a joint PDF, $p(x, y)$, of two variables, X and Y, the first moments are the following.

**Normalization:** $1 = \iint_{-\infty}^{\infty} p(x, y) dx dy$.

**Mean:** $\langle X \rangle = \iint_{-\infty}^{\infty} xp(x, y) dx dy$.

**Variance:** $V(X) = \iint_{-\infty}^{\infty} [x - \langle X \rangle]^2 p(x, y) dx dy$.

**Skewness:** $\gamma_1(X) = \iint_{-\infty}^{\infty} \left[ \frac{x - \langle X \rangle}{\sigma(X)} \right]^3 p(x, y) dx dy$.

**Covariance:** $V(X, Y) = \iint_{-\infty}^{\infty} [x - \langle X \rangle] \times [y - \langle Y \rangle] p(x, y) dx dy$.

**Standard-deviation:** $\sigma(X) = \sqrt{V(X)}$.

**Correlation coefficient:** $\rho(X) = V(X, Y)/\sigma(X)\sigma(Y)$.
<figure><img src="image_591.png" /></figure>

**Estimators.** The most commonly used non-robust estimators are the following.

**Mean:** $\langle X \rangle \approx \frac{1}{N} \sum_{i=1}^{N} x_i \left( \pm \frac{\sigma}{\sqrt{N}} \right)$.

**Standard-deviation:** $\sigma(X) \approx \sqrt{\frac{1}{N-1} \sum_{i=1}^{N} (x_i - \langle X \rangle)^2} \left( \pm \frac{\sigma}{\sqrt{2(N-1)}} \right)$.

**Skewness:** $\gamma_1(X) \approx \frac{N}{(N-1)(N-2)} \sum_{i=1}^{N} \left( \frac{x_i - \langle X \rangle}{\sigma(X)} \right)^3$.

**Correlation coefficient:** $\rho(X, Y) \approx \frac{1}{N-1} \sum_{i=1}^{N} \left( \frac{x_i - \langle X \rangle}{\sigma(X)} \right) \left( \frac{y_i - \langle Y \rangle}{\sigma(Y)} \right)$.

### C.2.1.2 Marginalization

Marginalizing over a parameter, $\theta$:

$$p(y) = \int_{-\infty}^{\infty} p(\theta) p(y|\theta) d\theta. \qquad (C.26)$$

Comparing two data sets, $y$ and $\tilde{y}$:

$$p(\tilde{y}|y) = \int_{-\infty}^{\infty} p(\tilde{y}|\theta) p(\theta|y) d\theta. \qquad (C.27)$$

### C.2.1.3 Variable Change

If we have two sets of random variables, $\vec{u}$ and $\vec{v}$, such that $\vec{v} = f(\vec{u})$, then the relation between their PDF is:

$$p_v(\vec{v}) = |\mathcal{J}| \times p_u(f^{-1}(\vec{v})), \qquad (C.28)$$

where the Jacobian of the transformation is:

$$\mathcal{J}_{i,j} \equiv \frac{\partial u_i}{\partial v_j}. \qquad (C.29)$$

### C.2.1.4 Combining Uncertainties

If we have a set of random variables, $\vec{x}$, the uncertainty of an arbitrary function of these parameters, $f(\vec{x})$, is given by:

$$\sigma^2(f(\vec{x})) = (\vec{\nabla} f(\vec{x}))^T \nabla f(\vec{x}), \qquad (C.30)$$

where $\nabla$ is the covariance matrix of the variable set. In the 2D case, posing $\vec{x} = (a, b)$, we have:

$$\vec{\nabla} f = \begin{pmatrix} \frac{\partial f}{\partial a} \\ \frac{\partial f}{\partial b} \end{pmatrix} \quad \& \quad \mathcal{V} = \begin{pmatrix} \sigma_a^2 & \rho \sigma_a \sigma_b \\ \rho \sigma_a \sigma_b & \sigma_b^2 \end{pmatrix}, \qquad (C.31)$$

and Eq. (C.30) gives the usual expression:

$$\sigma^2_{f(\vec{x})} = \left(\frac{\partial f}{\partial a}\right)^2 \sigma_a^2 + \left(\frac{\partial f}{\partial b}\right)^2 \sigma_b^2 + 2 \left(\frac{\partial f}{\partial a}\right) \left(\frac{\partial f}{\partial b}\right) \rho \sigma_a \sigma_b. \qquad (C.32)$$

Similarly, the covariance of two functions of the parameter set, $f(\vec{x})$ and $g(\vec{x})$, is:

$$V(f(\vec{x}), g(\vec{x})) = (\vec{\nabla} f(\vec{x}))^T \nabla g(\vec{x}). \qquad (C.33)$$

<figure><img src="image_592.png" /></figure>
**Rant about systematics.** There is a long-lasting laboratorian legend that “systematics must be non-quadratically summed”. This is true in some cases and false in others. Everything depends on what we are talking about.

1. If we are measuring a flux, F, with noise, $\sigma_{noise}$, and calibration uncertainty (systematics), $\sigma_{cal}$, the total uncertainty on the flux will be, according to Eq. (C.32): $\sigma_{tot} = \sqrt{\sigma_{noise}^2 + \sigma_{cal}^2}$. This is because $\rho = 0$. The fluctuations of the detector's signal at the time of the observation do not have anything to do with the error the instrument's team made by deriving the calibration factor.

2. Now, if we are summing the flux in two pixels with same flux and noise levels, we will get, using Eq. (C.32): $\sigma_{tot} = \sqrt{2\sigma_{noise}^2 + 4\sigma_{cal}^2}$, because the calibration factors of the pixels were correlated. The total calibration uncertainty is this time linearly summed: $\sigma_{cal tot} = 2\sigma_{cal}$, because $\rho = 1$ (the error due to the calibration uncertainty is the same for both pixels).

3. If we are now summing two systematics, such as the calibration and the background subtraction uncertainties, $\sigma_{cal}$ and $\sigma_{back}$, we will sum them quadratically: $\sigma_{syst} = \sqrt{\sigma_{cal}^2 + \sigma_{back}^2}$. This is because the error the instrument's team made deriving the calibration factor is independent of the error we have made by selecting a region in one of the corners of our map, assuming it was free of galaxy emission.

## C.2.2 Useful Probability Distributions

### C.2.2.1 Binomial Distribution

Discrete probability distribution to get $r$ successes out of $n$ tries, each one having a probability $p$:

$$P_{\text{binomial}}(r|p, n) \equiv C_r^n p^r (1-p)^{n-r} = \frac{n!}{r!(n-r)!} p^r (1-p)^{n-r}, \quad (C.34)$$

with $\langle r \rangle = np$ and $\sigma(r) = \sqrt{np(1-p)}$.

### C.2.2.2 Poisson Distribution

Discrete probability distribution to get $r$ events per unit time knowing the mean expected number, $\lambda$, of such events per unit time:

$$P_{\text{Poisson}}(r|\lambda) \equiv \frac{e^{-\lambda}\lambda^r}{r!}, \quad (C.35)$$

with $\langle r \rangle = \lambda$ and $\sigma(r) = \sqrt{\lambda}$. The superposition of two Poissonian events ($\lambda_a, \lambda_b$) is also Poissonian with mean $\lambda = \lambda_a + \lambda_b$. It is the limit of the binomial distribution to large numbers:

$$P_{\text{Poisson}}(r|\lambda) = \lim_{n \to \infty} P_{\text{binomial}}\left(r \middle| \frac{\lambda}{n}, n\right). \quad (C.36)$$

### C.2.2.3 Gaussian Distribution

$$P_{\text{Gauss}}(x|\mu, \sigma) \equiv \frac{1}{\sqrt{2\pi}\sigma} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right), \quad (C.37)$$

with $\langle x \rangle = \mu$, $\sigma(x) = \sigma$ and all superior moments equal to 0. It is the limit of a Poisson distribution when $\lambda \gg 1$: $P_{\text{Poisson}}(r|\lambda) = \lim_{\lambda \gg 1} P_{\text{Gauss}}(r|\lambda, \sqrt{\lambda})$.

**Multivariate form.** A multivariate normal law of mean $\vec{\mu}$ and covariance matrix $\mathcal{V}$ is defined as:

$$P_{\text{Gauss}}(\vec{x} | \vec{\mu}, \mathcal{V}) \equiv \frac{1}{(2\pi)^{n/2} \sqrt{|\mathcal{V}|}} \exp\left(-\frac{1}{2} (\vec{x} - \vec{\mu})^\mathrm{T} \mathcal{V}^{-1} (\vec{x} - \vec{\mu})\right). \quad (C.38)$$
**Error function.** Noting $\Phi(x)$ the CDF of a reduced normal law, the error function is defined such that:

$$ \Phi(x) = \frac{1}{2} \left( 1 + \operatorname{erf}\left(\frac{x}{\sqrt{2}}\right) \right). \qquad (C.39) $$

It is thus:

$$ \operatorname{erf}(x) \equiv \frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-t^2} dt = 2\Phi(x\sqrt{2}) - 1. \qquad (C.40) $$

### C.2.2.4 Student's t Distribution

It is defined as:

$$ P_{\text{Student}}(x|f) \equiv \frac{1}{\sqrt{f\pi}} \frac{\Gamma\left(\frac{f+1}{2}\right)}{\Gamma\left(\frac{f}{2}\right)} \left(1 + \frac{x^2}{f}\right)^{-\frac{f+1}{2}}, \qquad (C.41) $$

with $f > 0$ being the degree of freedom. Its mean is 0 and its standard-deviation, for $f > 2$, is $\sigma = \sqrt{f/(f-2)}$.

### C.2.2.5 Split-Normal Distribution

It is, to my mind, the most convenient asymmetric distribution:

$$ P_{\text{split-norm}}(x|\mu, \lambda, \tau) \equiv \sqrt{\frac{2}{\pi}} \frac{1}{\lambda(1+\tau)} \times \begin{cases} \exp\left(-\frac{1}{2}\left(\frac{x-\mu}{\lambda}\right)^2\right) & \text{if } x \le \mu \\ \exp\left(-\frac{1}{2}\left(\frac{x-\mu}{\lambda\tau}\right)^2\right) & \text{if } x > \mu. \end{cases} \qquad (C.42) $$

Posing:

$$ b = \frac{\pi - 2}{\pi} (\tau - 1)^2 + \tau, \qquad (C.43) $$

the first moments are:

$$ \langle X \rangle = \mu + \sqrt{\frac{2}{\pi}}\lambda(\tau - 1) \qquad (C.44) $$

$$ \sigma(X) = \sqrt{b\lambda} \qquad (C.45) $$

$$ \gamma_1(X) = b^{-3/2} \sqrt{\frac{2}{\pi}} (\tau - 1) \times \left[ \left( \frac{4}{\pi} - 1 \right) (\tau - 1)^2 + \tau \right]. \qquad (C.46) $$

### C.2.2.6 Lorentzian Distribution

$$ P_{\text{Lorentz}}(x|\mu, \gamma) \equiv \frac{2}{\pi\gamma} \frac{1}{1 + \left(\frac{x-\mu}{\gamma/2}\right)^2}. \qquad (C.47) $$

Its mean is $\mu$, its FWHM is $\gamma$, but its standard-deviation is not defined.

## C.2.3 Drawing random variables from an arbitrary distribution

### C.2.3.1 The Rejection Method

The rejection method is a widely used technique to draw a random variable, $x'$, from an arbitrary PDF, $f(x)$. It requires the ability to easily draw a random variable, $x_1$, from a proposal distribution, $g(x)$, such that $g(x) \ge f(x) \forall x$. In case $f(x)$ is finite over $[x_{\min}, x_{\max}]$, we can take:

$$ g(x) = \begin{cases} \max(f) & \text{for } x_{\min} \le x \le x_{\max} \\ 0 & \text{elsewhere.} \end{cases} \qquad (C.48) $$
The algorithm is the following.

1. Draw a random variable $x_1$ from $g(x)$.

2. Draw a uniform random variable between 0 and 1, $\Theta_1$.

3. If $\Theta_1 < f(x_1)/g(x_1)$, then $x' = x_1$ is accepted. Otherwise, if $\Theta_1 \ge f(x_1)/g(x_1)$, this draw is rejected, and we need to go back to the first step.

The closer $g(x)$ is from $f(x)$, the lower the rejection rate will be, and the faster the method will be. It is illustrated in Fig. C.3.a.

<figure><img src="image_593.png" /><figcaption>FIGURE C.3 – Methods for drawing random numbers from arbitrary distributions. Panel (a) represents the rejection method applied to the distribution in blue, with the proposal in red. We have represented a first rejected draw and a second accepted one. Panel (b) represents the CDF method applied to the distribution in panel (a). Licensed under CC BY-SA 4.0.</figcaption></figure>

### C.2.3.2 Inverting the CDF

A general Monte-Carlo technique to draw a random variable, $x'$, from an arbitrary PDF, $f(x)$, consists in drawing a uniform random variable between 0 and 1, $\Theta$, and inverting the Cumulative Distribution Function (CDF) of $f(x)$:

$$F(x) = \int_{-\infty}^{x} f(y) \, dy. \qquad (C.49)$$

The desired random variable is then simply:

$$x' = F^{-1}(\Theta). \qquad (C.50)$$

It is illustrated in Fig. C.3.b.

## C.3 Trigonometry

$$\cos a = \cos b \qquad \Leftrightarrow \qquad a = b [2\pi] \lor a = -b [2\pi] \qquad (C.51)$$

$$\sin a = \sin b \qquad \Leftrightarrow \qquad a = b [2\pi] \lor a = \pi - b [2\pi] \qquad (C.52)$$

$$\tan a = \tan b \qquad \Leftrightarrow \qquad a = b [2\pi] \qquad (C.53)$$
<figure><img src="image_594.png" /></figure>

## C.3.1 Transformations

### C.3.1.1 Rotations

$$ \cos(\frac{\pi}{2} + x) = -\sin x $$

$$ \cos(\frac{\pi}{2} - x) = \sin x $$

$$ \cos(\pi - x) = -\cos x $$

$$ \cos(\pi + x) = -\cos x $$

$$ \cos(-x) = \cos x $$

$$ \sin(\frac{\pi}{2} + x) = \cos x \qquad (C.54) $$

$$ \sin(\frac{\pi}{2} - x) = \cos x \qquad (C.55) $$

$$ \sin(\pi - x) = \sin x \qquad (C.56) $$

$$ \sin(\pi + x) = -\sin x \qquad (C.57) $$

$$ \sin(-x) = -\sin x \qquad (C.58) $$

### C.3.1.2 Relations Between Functions

$$ \cos^2 x + \sin^2 x = 1 $$

$$ 1 + \tan^2 x = \frac{1}{\cos^2 x} \qquad (C.59) $$

$$ \cos(2x) = \frac{1 - \tan^2 x}{1 + \tan^2 x} $$

$$ \sin(2x) = \frac{2 \tan x}{1 + \tan^2 x} $$

$$ \tan(2x) = \frac{2 \tan x}{1 - \tan^2 x} \qquad (C.60) $$

## C.3.2 Addition

### C.3.2.1 Summing Angles

$$ \cos(a - b) = \cos a \cos b + \sin a \sin b $$

$$ \sin(a - b) = \sin a \cos b - \cos a \sin b $$

$$ \tan(a - b) = \frac{\tan a - \tan b}{1 + \tan a \tan b} $$

$$ \cos(a + b) = \cos a \cos b - \sin a \sin b $$

$$ \sin(a + b) = \sin a \cos b + \cos a \sin b $$

$$ \tan(a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b} \qquad (C.63) $$

### C.3.2.2 Inverse Relations

$$ \cos a \cos b = \frac{1}{2}[\cos(a-b) + \cos(a+b)] \qquad (C.64) $$

$$ \cos a \sin b = \frac{1}{2}[\sin(a+b) - \sin(a-b)] \qquad (C.65) $$

$$ \sin a \sin b = \frac{1}{2}[\cos(a-b) - \cos(a+b)] \qquad (C.66) $$

$$ \cos a + \cos b = 2 \cos \left( \frac{a+b}{2} \right) \cos \left( \frac{a-b}{2} \right) $$

$$ \cos a - \cos b = -2 \sin \left( \frac{a+b}{2} \right) \sin \left( \frac{a-b}{2} \right) \qquad (C.67) $$

$$ \sin a + \sin b = 2 \sin \left( \frac{a+b}{2} \right) \cos \left( \frac{a-b}{2} \right) $$

$$ \sin a - \sin b = 2 \sin \left( \frac{a-b}{2} \right) \cos \left( \frac{a+b}{2} \right) \qquad (C.68) $$

## C.3.3 Linearization

### C.3.3.1 Squares and Cubes

$$ \cos^2 x = \frac{1 + \cos(2x)}{2} $$

$$ \sin^2 x = \frac{1 - \cos(2x)}{2} $$

$$ \tan^2 x = \frac{1 - \cos(2x)}{1 + \cos(2x)} \qquad (C.69) $$

$$ \cos^3 x = \frac{\cos(3x) + 3 \cos x}{4} $$

$$ \sin^3 x = \frac{-\sin(3x) + 3 \sin x}{4} $$

$$ \tan^3 x = \frac{-\sin(3x) + 3 \sin x}{\cos(3x) + 3 \cos x} \qquad (C.70) $$

<figure><img src="image_595.png" /></figure>
<figure><img src="image_596.png" /></figure>

### C.3.3.2 Inverse Relations

$$ \cos(2x) = \cos^2 x - \sin^2 x = 2\cos^2 x - 1 = 1 - 2\sin^2 x \quad (C.71) $$

$$ \sin(2x) = 2 \sin x \cdot \cos x \qquad \tan(2x) = \frac{2 \tan x}{1 - \tan^2 x} \quad (C.72) $$

$$ \cos(3x) = 4 \cos^3 x - 3 \cos x \sin(3x) = 3 \sin x - 4 \sin^3 x \qquad \tan(3x) = \frac{3 \tan x - \tan^3 x}{1 - 3 \tan^2 x} \quad (C.73) $$

<figure><img src="image_597.png" /></figure>
<figure><img src="image_598.png" /></figure>
<figure><img src="image_599.png" /></figure>

# Acknowledgements

*Bien faire et laisser dire.*

(devise d'Étienne François SALLÉ DE CHOU)

<figure><img src="image_600.png" /></figure>

FIGURE D. 1 – *Nerdy allegory of my collaboration network.* Large collaborations are sources of funding and of Gigabytes of data. They subsequently trigger transitions between levels in laboratories. Collaborators usually become more bound to their academic institution with time. We also notice some charge exchange and a few individuals becoming free electrons in the private sector. Licensed under CC BY-SA 4.0.

I am particularly grateful to the colleagues who have accepted to participate in my HDR committee and to read this whole manuscript: Véronique BUAT, Vassilis CHARMANDARIS, Thomas HENNING, Laurent VERSTRAETE, Stéphane CHARLOT and François-Xavier DÉSERT. I thank them for their comments and the interesting discussions we had. I also thank Hervé DOLE for handling the administrative procedure of this accreditation.

I thank the people who willingly provided me with useful comments, clarifying the text and correcting some errors: Dangning HU, Anthony JONES, Vianney LEBOUTEILLER, Suzanne MADDEN, Marc-Antoine MIVILLE-DESCHÊNES and Takashi ONAKA. I also thank Christine JOBLIN for her insight on the 3.4 µm feature, and Matteo BUGLI for a useful discussion about SNe and collapsars. I thank Anthony JONES and Nathalie YSARD for providing me with their DDA results, plotted in Fig. I.21, and Chia-Yu HU for his sputtering yield polynomial fits used to make Fig. IV.13. I am finally grateful to all the
<figure><img src="image_601.png" /></figure>

people who have granted me the permission to reproduce their figures in this manuscript: Lou AL-LAMANDOLA, Jean-Philippe BERNARD, Robert GENDLER, Peter HOPPE, Tom JARRETT, Andy MATTIODA and Marc-Antoine MIVILLE-DESCHÊNES.

<figure><img src="image_602.png" /></figure>

No dust grains were harmed in the making of this work.

<figure><img src="image_603.png" /></figure>
<figure><img src="image_604.png" /></figure>

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**Titre:** Propriétés et évolution de la poussière interstellaire. Le point de vue des galaxies proches.

**Mots clés :** Milieu interstellaire – Poussière – Astronomie infrarouge – Évolution des galaxies – Science des données.

**Résumé :** La poussière interstellaire est un ingrédient physique clef des galaxies, responsable de l'obscurcissement de la formation stellaire, de la régulation du chauffage et du refroidissement du gaz, et de la croissance de la complexité chimique. Dans ce manuscrit, je donne une large revue des propriétés de la poussière interstellaire et des techniques modernes utilisées pour l'étudier. Je commence avec une introduction générale, présentant les principaux concepts, en physique moléculaire et physique du solide, requis pour comprendre la littérature contemporaine sur le sujet. Je passe en suite en revue les évidences empiriques que nous utilisons de nos jours pour contraindre les modèles à l'état de l'art. S'ensuit une longue discussion sur notre compréhension actuelle des propriétés des grains dans les galaxies proches, avec un

accident sur la modélisation des distributions spectrales d'énergie. Le chapitre suivant présente l'évolution des grains, à toutes les échelles. Je passe en revue les différents processus microphysiques d'évolution et la manière dont ils sont pris en compte dans les modèles d'évolution cosmique des grains. Je donne mon opinion sur l'origine de la poussière interstellaire dans les galaxies en fonction de la métallité. Le dernier chapitre traite de méthodologie. J'y donne une introduction sur la méthode bayésienne et la compare aux techniques fréquentistes. J'y discute les conséquences épistémologiques des deux approches, et montre pourquoi le champ d'étude de la poussière interstellaire requiert un point de vue probabiliste. Je finis le manuscrit par un résumé des avancées majeures obtenues au cours de la dernière décennie et je fais une prospective pour la prochaine.

**Title:** A Nearby Galaxy Perspective on Interstellar Dust Properties and their Evolution.

**Keywords:** Interstellar medium – Dust – Infrared astronomy – Galaxy evolution – Data science.

**Abstract:** Interstellar dust is a key physical ingredient of galaxies, obscuring star formation, regulating the heating and cooling of the gas, and building-up chemical complexity. In this manuscript, I give a wide review of interstellar dust properties and some of the modern techniques used to study it. I start with a general introduction presenting the main concepts, in molecular and solid-state physics, required to understand the contemporary literature on the subject. I then review the empirical evidence we currently use to constrain state-of-the-art dust models. Follows a long discussion about our current understanding of the grain properties of nearby galaxies, with an emphasis on the

results from spectral energy distribution modeling. The following chapter presents dust evolution at all scales. I review the different microphysical evolution processes, and the way they are accounted for in cosmic dust evolution models. I give my take on the origin of interstellar dust in galaxies of different metallicities. The last chapter focusses on methodology. I give an introduction to the Bayesian method and compare it to frequentist techniques. I discuss the epistemological consequences of the two approaches, and show why the field of interstellar dust requires a probabilistic viewpoint. I end the manuscript with a summary of the major breakthroughs achieved in the past decade, and delineate a few prospectives for the next decade.