Chapter 2
Dust Observables and Models

The present chapter is intended to provide a comprehensive overview of the current state of the field. It discusses both the observables that can be used to constrain dust properties, and the current state-of-the-art models. It bridges the basic physical knowledge of Chap. 1 with their current application.

2.1 A Brief History of Interstellar Dust Studies

(a) First photograph of Orion (1880)	(b) Sir William HERSCHEL	(c) Reenactment

The History of our progressive understanding of ISD is driven by the successive technological innovations that allowed us to shed light on its nature.

Telescopes

allowed deep-sky observations already through the XVIII${}^{\mathrm{th}}$ century (e.g. Wilson, 2007). Charles MESSIER’s catalog of “nebulae” was first established in 1774. The quality and size of mirrors increased through the XIX${}^{\mathrm{th}}$ century, and at the beginning of the XX${}^{\mathrm{th}}$ century, the first meter-class telescopes, with silvered-glass mirrors ¹, were built. The Mount Wilson Observatory was founded in 1904, and its 1.5-m Hale telescope was commissioned in 1908.

Photographic plates

turned astronomical observations into a reproducible empirical science. They required long exposures and reliable tracking of the sky’s apparent rotation. Photography was invented by Nicéphore NIÉPCE in the 1820’s. His associate, Louis DAGUERRE, perfected the technique and commercialized the first daguerreotype ² in 1839. The first attempts to capture images of the sky (the Moon and the Sun), were performed using this invention, in the 1840’s. Emulsion plates were substituted to daguerreotypes, and the first deep-sky picture (the Orion nebula; Fig. 2.1.a) was taken by Henry DRAPER in 1880 (Barker, 1888).

Solid-state physics

was given a strong impulse, after World War II, by the prospective development of electronics (Martin, 2013). The transistor was invented in 1947, at Bell laboratories in New Jersey. This impulse led to the development of technical and conceptual tools for the optical and electronic properties of solids that our field would benefit from.

The introduction of computers

revolutionized all scientific fields. The principle of the computer was laid out in Alan TURING’s seminal 1937 article (Turing, 1937). The first computers were developed during World War II to break the German encryption codes (e.g. McGrayne, 2011). They started to be used in astrophysics during the 1950’s, to compute stellar structures. Before that, some calculations were impossible. For instance, the first dust model of the 1930’s was made of small iron particles (e.g. Schoenberg & Jung, 1937; Greenstein, 1938), in part because Mie computations for small metal spheres were easier on paper than for large dielectrics (van de Hulst, 1986). The first dust radiative transfer numerical computations were performed in the early 1970’s, using iterative methods (Mathis, 1970) and Monte-Carlo methods (Mattila, 1970).

The development of modern detectors

solved the issues of photography: (i) non-linear response; (ii) restricted dynamic range; (iii) low detection efficiency; (iv) reciprocity failure; and (v)  adjacency effects (Boksenberg, 1982). The first Charge-Coupled Device (CCD) was invented in 1969 at Bell laboratories (Amelio et al., 1970). In the IR, photomultipliers and bolometers were developed in the 1930’s, and found important military applications during World War II and later: night vision and guiding rockets (Rogalski, 2012, for an extensive review). The first IR thermal detector had in fact been built 150 years earlier by Sir William HERSCHEL, in 1800. He used a prism to split the Sun light over several thermometers (cf. Fig. 2.1.b; Rogalski, 2012). He found that the highest temperature was beyond the red, that is in the infrared ³ (Fig. 2.1.c).

The possibility to send airborne and space observatories

opened the spectral windows where the atmosphere is opaque (cf. Sect. 2.1.1.1). The interest to send telescopes in space was first advocated for by Lyman SPITZER Jr., in 1946 (Spitzer, 1946). The first successful space telescope was launched in 1968. It was the Orbiting Astronomical Observatory (OAO), operating in the UV (Code et al., 1970). The first airborne observatory was the balloon experiment Stratoscope I, operating in the IR, in 1958.

The next technological innovation that will revolutionize our field is difficult to predict. We can however note that quantum computers should permit ab initio calculations of the properties and evolution of complex molecules and solids, in the near future. If this is true, it should allow us to precisely characterize the dust composition in different environments.

2.1.1 The Challenges of Observing Interstellar Regions

2.1.1.1 Limitations Due to the Atmosphere

The atmosphere of Earth is transparent in only a few spectral windows. The bottom panel of Fig. 2.2 shows its absorbance as a function of wavelength. We see in particular that the UV and FIR ranges are completely opaque, and thus inaccessible from the ground. This is the reason why the first evidences for ISD came from the extinction of starlight in the visible range. The last forty years have seen the development of space and airborne observatories in the UV and IR windows, providing us with a panchromatic view of ISD properties (top panel of Fig. 2.2).

2.1.1.2 Historical Ground-Based Observatories

The meter-class visible telescopes. The first discoveries about ISD were performed in the visible domain, by understanding the extinction toward stars. Robert TRUMPLER’s seminal paper (Trumpler, 1930) was based on observations made at the Lick observatory, near San Jose, as well as Edward BARNARD’s most famous observations (Barnard, 1899, 1919). Such telescopes, all across the world, were the main source of empirical constraints on dust, until the end of the 1970’s.

The first MIR telescopes. Ground-based observations, at high altitude, in dry regions of the globe such as the Mauna Kea, are possible in the MIR (cf. Fig. 2.2). IR astronomy really started in the 1960’s (cf. Walker, 2000, for an historical review). The first IR surveys of the northern and southern skies were performed by Neugebauer & Leighton (1968) and Price (1968), at 2 $\mu m$. A generation of 2-to-3-m MIR telescopes were commissioned at the end of the 1970’s, such as the Wyoming InfraRed Observatory (WIRO; 1977; $\text{⌀}=2.3$ m), the United Kingdom InfraRed Telescope (UKIRT; 1978; $\text{⌀}=3.8$ m) and the InfraRed Telescope Facility (IRTF; 1979; $\text{⌀}=3$ m). Current large telescopes such as Subaru (Mauna Kea; $\text{⌀}=8.2$ m) or the Very Large Telescope (VLT; Paranal; $\text{⌀}=8.2$ m) operate in the visible-to-MIR range.

The submillimeter observatories. On the other side of the FIR atmospheric absorption, the submillimeter domain can be observed from the ground in dry conditions. The first ground-based submillimeter observatories appeared in 1990’s. Among them are: the Caltech Submilleter Observatory (CSO; Mauna Kea; $\text{⌀}=10$ m; 1986-2015), the James Clerk Maxwell Telescope (JCMT; Mauna Kea; $\text{⌀}=15$ m; 1987), the Atacama Pathfinder Experiment (APEX; Atacama desert; $\text{⌀}=12$ m; 2004) and the Atacama Large Millimeter/submillimeter Array (ALMA; Atacama desert; interferometer; 2011).

2.1.1.3 Airborne Observatories

(a) Balloon crash	(b) PILOT	(c) SOFIA

Balloons. Stratospheric balloons can reach altitudes of $\simeq 40$ km, well above most water vapor absorption. They can observe for several days continuously, but landing is hazardous (Fig. 2.3.a). The first IR balloon was launched from Johns Hopkins in 1959, and a balloon sent by the Goddard Institute of Space Sciences mapped the sky at 100 $\mu m$ in 1966 (Walker, 2000). During the past two decades, several balloons provided observations of the dust continuum intensity and polarization in different regions of the sky, including: the Balloon-borne Large Aperture Submillimeter Telescope (BLAST; 1997-2010; $⌀=2$ m;  Pascale et al., 2008); the PROjet National pour l’Observation Submillimétrique (PRONAOS; 1994-1999; $⌀=2$ m;  Serra et al., 2002); the Polarized Instrument for the Long-wavelength Observation of the Tenuous ISM (PILOT; 2015-2017; $⌀=0.73$ m;  Bernard et al., 2016, Fig. 2.3.b).

Airplanes. Airplanes can fly up to $\simeq 15$ km altitude and operate during $\simeq 10$ h. Numerous flights can be scheduled, contrary to balloons, which usually do only a few flights in their whole lifetime. The telescope motion being limited by its orientation perpendicular to the plane (Fig. 2.3.c), the flight path has to be adapted to the observed source. The Kuiper Airborne Observatory (KAO; 1974-1995; $⌀=0.9$ m;  Erickson & Meyer, 2013) was a transport jet plane converted into an observatory. The Stratospheric Observatory for Infrared Astronomy (SOFIA; 2010-; $⌀=2.5$ m;  Young et al., 2012, Fig. 2.3.c) is its current successor. It is a retired Boeing 747, modified to host the telescope.

2.1.1.4 Space Telescopes

IRAS. The InfraRed Astronomical Satellite (IRAS; 1983; $⌀=0.57$ m;  Neugebauer et al., 1984) was the first observatory to perform an all-sky survey at IR wavelengths. It mapped the sky in four broadbands centered at $\lambda =12$, 25, 60 and 100 $\mu m$, with angular resolutions of $0.5^{\prime }-2^{\prime }$. It opened the IR window, which was largely unexplored at the time. It discovered more than $300000$ point sources, many of them being starburst galaxies. These new objects, with deeply embedded star formation at the scale of the whole galaxy, emitting more than $95\%$ of their luminosity in the IR, were unexpected (e.g. Soifer et al., 1987, for a review). The new categories of Luminous InfraRed Galaxies (LIRG) and UltraLuminous InfraRed Galaxies (ULIRG) were created to describe what had been observed. Dusty disks around stars were also discovered (Beichman, 1987). By accessing the cold grain emission, the first reliable dust masses of galaxies and Galactic clouds could be estimated. The IR emission provided a new constraint that shaped modern dust models (Désert et al., 1990). IRAS data are still used nowadays (e.g. Galliano et al., 2021, hereafter G21).

COBE. The COsmic Background Explorer (COBE; 1989-1993; $⌀=0.2$ m;  Boggess et al., 1992) was aimed at mapping the CMB, as its name indicates. However, two of its three instruments were used to map the whole sky in the MIR and FIR, providing the main constraints on the emission of dust models until the Planck mission (Sodroski et al., 1994; Dwek et al., 1997). The third instrument, covering the microwave range was also instrumental in providing the first evidence of spinning grains.

DIRBE

(Diffuse Infrared Background Experiment) was an instrument observing through ten broadbands at: $\lambda =1.25$, 2.2, 3.5, 4.9, 12, 25, 60, 100, 140 and 240 $\mu m$ (Hauser et al., 1998).

FIRAS

(Far-InfraRed Absolute Spectrophotometer) was a low spectral resolution spectro-imager, observing between $\lambda =100$ $\mu m$ and 10 mm (Mather et al., 1999). At long wavelengths, the angular resolution was only $7^{\circ }$.

DMR

(Differential Microwave Radiometer) was mapping the sky in three broadbands centered at $\lambda =3.3$, 5.6 and 9.5 cm (Smoot et al., 1994).

ISO. The Infrared Space Observatory (ISO; 1995-1998; $⌀=0.6$ m;  Kessler et al., 1996) was the first mission to extensively perform spectroscopy over the whole IR range. For that reason, it provided a wealth of data about all spectral features: silicates (Molster & Kemper, 2005), PAHs (Abergel et al., 2005; Sauvage et al., 2005), ices (Dartois et al., 2005). Studies of IR gas lines also took off: molecular (Habart et al., 2005) and ionized (Peeters et al., 2005). Finally, it refined our knowledge, through dust tracers, of star formation at all scales (Nisini et al., 2005; Verma et al., 2005; Elbaz et al., 2005). There were four instruments onboard.

ISOCAM

(Cesarsky et al., 1996a) was a low spectral resolution MIR spectro-imaging camera, in the $\lambda =2.5-17$ $\mu m$ range. It also had twenty broad and narrow bands in the same range.

SWS

(de Graauw et al., 1996) was a medium to high spectral resolution ($R\equiv \lambda ∕\mathit{\Delta \lambda }=1000-35000$) MIR spectrometer in the $\lambda =2.4-45$ $\mu m$ range.

LWS

(Clegg et al., 1996) was a low to medium spectral resolution ($R\simeq 150-9700$) FIR spectrometer, in the $\lambda =43-198$ $\mu m$ range. Combined together, SWS and LWS provided several continuous spectra over the whole IR range ($\lambda =2.4-198$ $\mu m$; e.g.  Peeters et al., 2002b), that have never been equaled.

ISOPHOT

(Lemke et al., 1996) was a photometer observing through several broad and narrow band filters, in the $\lambda =2.5-240$ $\mu m$.

Spitzer. The Spitzer space telescope (cryogenic operation: 2003-2009; $⌀=0.85$ m;  Werner et al., 2004) was the successor of ISO. Its larger mirror size and more modern detectors allowed it to refine our understanding of what ISO discovered, and observe a significantly larger number of targets. Its angular resolution was $40^{\mathit{\prime \prime }}$ at 160 $\mu m$. It had three instruments onboard.

IRAC

(InfraRed Array Camera; Fazio et al., 2004) was performing photometry through four broadbands, centered at $\lambda =3.6$, 4.5, 5.8 and 8.0 $\mu m$.

IRS

(InfraRed Spectrograph; Houck et al., 2004) was a medium and high spectral resolution ($R=90-600$) spectro-imager, observing in the $\lambda =5.3-38$ $\mu m$ range.

MIPS

(Multiband Imaging Photometer for Spitzer;Rieke et al., 2004) was a photometer observing through three broadbands centered at $\lambda =24$, 70 and 160 $\mu m$.

AKARI. The AKARI space telescope (cryogenic phase: 2006-2008; $⌀=0.69$ m;  Murakami et al., 2007) was comparable to Spitzer. One of its advantages was its ability to record spectra down to 2 $\mu m$, while Spitzer/IRS was limited to 5 $\mu m$. AKARI performed an all-sky survey in several MIR to FIR bands. It had two instruments onboard.

IRC

(InfraRed Camera; Onaka et al., 2007) was a MIR camera with numerous broad and narrow bands, as well as a low/mid-spectral resolution spectrometer, observing in the $\lambda =1.8-26.5$ $\mu m$ range.

FIS

(Far-Infrared Surveyor; Kawada et al., 2007) was a FIR photometer observing through four broadbands centered at $\lambda =65$, 90, 140 and 160 $\mu m$. It also had a Fourier Transform Spectrometer (FTS) over the same range.

WISE. The Wide-field Infrared Survey Explorer (WISE; 2009-2011; $⌀=0.4$ m;  Wright et al., 2010) was a MIR all sky surveyor. It mapped the sky through four broad photometric bands centered at $\lambda =3.4$, 4.6, 12 and 22 $\mu m$.

Herschel. The Herschel space observatory (2009-2013; $⌀=3.5$ m;  Pilbratt et al., 2010) was a FIR-submm mission. Its large mirror allowed it to reach subarcminute angular resolution at long wavelength ($36^{\mathit{\prime \prime }}$ at $\lambda =500$ $\mu m$). Combined with Spitzer data at shorter wavelengths, it gives access to the full dust emission and provides the most reliable dust property estimates of galaxies and Galactic regions. Herschel data allowed us to build large databases of galaxy dust properties (e.g. Davies et al., 2017). It also allowed us to better constrain the submillimeter grain opacity (Meixner et al., 2010; Galliano et al., 2011). Among its discoveries, it demonstrated the filamentary nature of star-forming regions (André et al., 2010). It had three instruments onboard.

PACS

(Photodetector Array Camera and Spectrometer;Poglitsch et al., 2010) was an imager observing through three broadbands centered at $\lambda =70$, 100 and 160 $\mu m$. It also had a spectrometer that could target specific FIR lines.

SPIRE

(Spectral and Photometric Imaging REceiver;Griffin et al., 2010) was a photometer observing through three broadbands centered at $\lambda =250$, 350 and 500 $\mu m$. It also had a FTS providing a continuous, medium spectral resolution spectrum over the $\lambda =194-671$ $\mu m$ spectral range.

HIFI

(Heterodyne Instrument for the Far-Infrared;de Graauw et al., 2010) was a very high spectral resolution ($R\simeq 10^7$) spectrometer covering the $\lambda =157-625$ $\mu m$ spectral range. It was designed to accurately measure gas line intensities.

Planck. The Planck space observatory (2009-2013; $⌀=1.5$ m;  Tauber et al., 2010) was a FIR-to-microwave satellite designed to study the cosmological background. It is a successor to COBE. It was launched in the same rocket as Herschel. It performed an all sky survey in all its bands (Fig. 2.4). Planck had a larger beam than Herschel ($5^{\prime }$ at $\lambda =1$ mm), but had an accurate absolute calibration. Its measure of the emission of the diffuse ISM of the MW is now the main constraint on dust models (e.g. Compiègne et al., 2011). Planck could also measure the linear polarization in all its bands. It thus provided unique constraints on the grain properties (e.g. Guillet et al., 2018) and maps of the Galactic magnetic field (e.g. Planck Collaboration et al., 2016b). It had two instruments onboard.

HFI

(High Frequency Instrument; Lamarre et al., 2010) was a photometer/polarizer observing through six broadbands centered at $\lambda =350$, 550, 850, 1380, 2096 and 2997 $\mu m$.

LFI

(Low Frequency Instrument; Mandolesi et al., 2010) was a photometer/polarizer observing through three broadbands centered at $\lambda =4.3$, 6.8 and 10 cm.

The JWST. The James Webb Space Telescope (JWST; 2021-; $⌀=6.5$ m;  McElwain et al., 2020) should be launched a few months after the time this manuscript is being written. Its large segmented mirror, that will unfold in space, will allow us to access sub-arcsec resolution in the MIR. It will have four instruments onboard.

MIRI

(Mid-InfraRed Instrument; $\lambda =5-27$ $\mu m$;Rieke et al., 2015) contains an camera and an imaging spectrometer. It will be the most relevant instrument to ISD studies.

NIRspec

(Near-InfraRed Spectrograph; $\lambda =0.6-5$ $\mu m$;Birkmann et al., 2016) is a NIR spectrometer.

NIRcam

(Near-InfraRed Camera; $\lambda =0.6-5$ $\mu m$;Beichman et al., 2012) is a NIR camera.

NIRISS

(Near-InfraRed Imager and Slitless Spectrograph; $\lambda =0.8-5$$\mu m$;Doyon et al., 2012) will perform NIR imaging and spectroscopy.

UV and X-ray Satellites. The UV spectral shape of the extinction curve is an important constraint on dust models. UV satellite have one advantage over IR instruments: they do not need to be cooled down. IR instruments indeed need a cryostat to limit their proper emission. The lifetime of IR missions is thus the lifetime of their helium supply, typically only a few years, whereas UV telescopes can operate during several decades. The most important UV missions are the following.

IUE

(International Ultraviolet Explorer; 1978-1996; $⌀=0.45$ m;Boggess et al., 1978) was the first important UV mission, expanding our view on dust extinction at $\lambda =115-320$ nm.

HST

(Hubble Space Telescope; 1990-; $⌀=2.4$ m;Burrows et al., 1991) can take spectra in the near-UV range.

FUSE

(Far Ultraviolet Spectroscopic Explorer; 1999-2007; $⌀=1.5$ m;Moos et al., 2000) extended the spectral coverage of IUE at $\lambda =90.5-110.5$ nm.

As we will see in Sect. 2.2.1.3, the X-ray regime can provide interesting constraints on the dust properties. The most important missions are: ROSAT (1990-1999; $⌀=0.84$ m; $\lambda =0.06-30$ nm;  Aschenbach, 1991), XMM-Newton (1999-; $⌀=0.7$ m; $\lambda =0.1-12$ nm;  Jansen et al., 2001) and Chandra (1999-; $⌀=1.2$ m; $\lambda =0.1-12$ nm;  Weisskopf et al., 2002). The Advanced Telescope for High ENergy Astrophysics (ATHENA; $\simeq 2030$;  Wilms et al., 2014) will revolutionize the field.

2.1.1.5 Grain-Collecting Spacecrafts

(a) Aerogel honeycomb matrix	(b) Aerogel dust track	(c) X-ray image of a grain

Electromagnetic waves are not the only vectors of information about ISD we can get. The motion of the heliosphere relative to the local interstellar cloud creates an inflow of ISD through the Solar system (at 26 km/s; e.g.  Krüger et al., 2019, for a review). Contrary to interplanetary grains, this interstellar flow is important at high ecliptic latitude, allowing us to discriminate grains from extrasolar origins. Several spacecrafts have collected actual interstellar grains, and analyzed them in situ or returned them to Earth.

Ulysses

(1990-2009;  Bame et al., 1992) was a spacecraft designed to analyze the Solar wind. It was the first mission to capture dust grains from interstellar origin.

Galileo

(1989-2003;  Johnson et al., 1992) was a spacecraft sent to study Jupiter and its satellites. It detected interstellar grains on its way.

Cassini

(1997-2017;  Matson et al., 2002) was a spacecraft sent to study Saturn and its satellites. It embarked an instrument called the Cosmic Dust Analyzer (CDA), recording the size, speed, direction and chemical composition of interstellar grains. It identified thirty six of them, smaller than 200 nm (Altobelli et al., 2016). They appeared to be essentially Mg-rich silicates with iron inclusions.

Stardust

(1999-2006;  Brownlee et al., 2003) was a spacecraft that captured grains in a low-density aerogel, and returned them to Earth for laboratory analysis (Fig. 2.5). It identified seven interstellar grains (Westphal et al., 2014). Those were Mg-rich silicates, with sizes $\gtrsim 1$ $\mu m$. Two of them had crystalline structures.

2.1.2 Chronology of the Main Breakthroughs

In what follows, we present the main discoveries about ISD. We order the discussion by themes. Table 2.1 puts all these breakthroughs in chronological order. This is a partial and incomplete review. We refer the reader to van de Hulst (1986), Dorschner (2003), Whittet (2003), Li & Greenberg (2003) and Li (2005), for more complete historical reviews.

2.1.2.1 Obscuration and Dimming of Starlight

The discovery of dark nebulae. The first evidence of ISD came through the obscuration of visible starlight. There was a debate during the whole XIX${}^{\mathrm{th}}$ century about the reality of this obscuration.

• Sir William HERSCHEL, in his treaty on The Construction of the Heavens (Herschel, 1785), reported“an opening or a hole” in the Scorpius constellation. This hole was later identified as the Ink Spot nebula, B$$86 (Fig. 2.6.a; cf. Steinicke, 2016, for the historical branching out of this discovery).
• Edward BARNARD’s photographs of Ophiucus showed dark lanes through the nebula (Barnard, 1899). They were at the time interpreted by Agnes CLERKE, as “glades and clearing” in the stellar distribution (Clerke, 1903).
• Twenty years later, Edward BARNARD (Fig. 2.7.a) realized these black patches were actually “real, obscuring masses, most probably dark nebulae” (Barnard, 1919).

The reddening of starlight. The selective extinction of starlight provided the first consensual evidence of ISD. This was realized at the beginning of the 1930’s.

• Already in the middle of the XIX${}^{\mathrm{th}}$ century, Friedrich Georg Wilhelm STRUVE found that the stellar volume density is decreasing with distance from the Sun (Struve, 1847). This decrease could be explained by a $\simeq 1$ mag/kpc absorption by interstellar material. This is a factor of $\simeq 2$ from the actual value, which is wavelength-dependent.
• Dark nebulae and the extinction of starlight were both understood by Henry N. RUSSELL (Russell, 1922). In advance on his time, he noticed that “in certain instances stars embedded in dense luminous nebulosity are abnormally red”. He finally deduced that this “obscuration of light in space, therefore, whether general or selective with respect to wave-length, will be produced mainly by dust particles a few millionths of an inch in diameter” (i.e. $\simeq 0.03-0.1$ $\mu m$).
• The seminal study of Robert J. TRUMPLER (Fig. 2.7.b; Trumpler, 1930) provided the first solid evidence of ISD. His study was based on the observation, at the Lick observatory, of 100 open clusters. He found that the diameter distances (assuming all clusters have the same diameter) are always smaller than the photometric distances (based on the stellar spectral types), and this discrepancy increases with distance (Fig. 2.6.b). This allowed him to interpret stellar color excesses as selective extinction by fine dust particles. He inferred particles of average mass $10^{-19}$ g or larger ⁴. At the same time, Schalén (1929, 1931) independently arrived at a similar conclusions, at the Uppsala observatory.

(a) The Ink Spot nebula	(b) Trumpler (1930)’s relation

2.1.2.2 The Dust Continuum

The Shape of the extinction curve. The investigation of the spectral shape of the extinction curve started right after Trumpler’s study.

• A series of papers (Rudnick, 1936; Hall, 1937; Greenstein, 1938; Stebbins et al., 1939) concluded that $\kappa \left(\lambda \right)$ was roughly proportional to $1∕\lambda$ in the $\lambda =0.3-1\mu m$ range. By the end of the 1930’s, it was thus clear that the grains responsible for the visible light extinction were not in the Rayleigh regime (${\kappa }_{\mathrm{sca}}\left(\lambda \right)\propto 1∕{\lambda }^4$; Sect. 1.2.2.3).
• Stebbins & Whitford (1943) extended the study of extinction curves to the $0.35\mu m<\lambda <1.03\mu m$ range, and found deviations to the $1∕\lambda$ behavior, due to the now well-known far-UV rise and NIR knee (Sect. 2.2.1).
• During the 1950’s and 1960’s followed a discussion on the universality of the shape of the extinction curves (cf. references in Li, 2005).
• Starting in the 1960’s, the first airborne and space observatories opened the UV window, up to the Lyman break (York et al., 1973). The 2175 Å bump was discovered by Stecher (1965, cf. Sect. 2.1.2.3).
• The first UV extinction curves in the Large Magellanic Cloud (LMC) were measured by Borgman et al. (1975), and by Koornneef (1978) in 30 Doradus. In the Small Magellanic Cloud (SMC), it was first measured by Rocca-Volmerange et al. (1981). In both cases, the steepness of the curve and the weakness of the bump were noted.
• Cardelli, Clayton, & Mathis (1989) performed a mathematical fit to a collection of extinction curves toward different sightlines in the MW. They found that, over the $0.125\mu m<\lambda <3.5\mu m$ range, the shape is universal and controlled by a single parameter, $R\left(V\right)=A\left(V\right)∕\left(A\left(B\right)-A\left(V\right)\right)$ (where $A\left(\lambda \right)$ is the magnitude extinction; cf. Sect. 2.2.1).
• ISO observations of the Galactic center exhibited a flatter MIR curve (Lutz et al., 1996), confirmed by Indebetouw et al. (2005) with Spitzer data.

Polarization by dichroic extinction. Hall (1949) and Hiltner (1949) found that starlight was linearly polarized.

• Davis & Greenstein (1951) proposed that this polarization is due to dichroic extinction by non-spherical particles aligned on the magnetic field (cf. Sect. 1.2.2.5).
• Serkowski (1973) determined the wavelength dependence of the polarization fraction, known as the Serkowski curve (cf. Sect. 2.2.1.4).

(a) Edward E. BARNARD	(b) Robert J. TRUMPLER	(c) Hendrik C. VAN DE HULST
(1857–1923)	(1886–1956)	(1918–2000)

Dust emission. The thermal emission of heated grains started to be observed in the 1960’s. The presence of very small grains or large molecules with $a\lesssim 1$ nm was speculated by Platt (1956, they are known as Platt particles).

• Greenberg (1968) first realized that small grains must be stochastically heated.
• Andriesse (1978) reported the first observational evidence of such transiently heated Platt particles in M 17. The spectral shape of the MIR spectrum was indeed constant over the region, and much wider than a single grey body emission, consistent with temperatures up to 150 K.
• Similarly, the NIR continuum and 3.3 $\mu m$ feature emission of several reflection nebulae was shown by Sellgren et al. (1983) to be consistent with small grains fluctuating up to 1000 K.
• The presence of small grains in the diffuse ISM was clearly evidenced by the 12 and 25 $\mu m$ IRAS emission (Boulanger & Perault, 1988). It was observed by numerous studies afterward in all types of interstellar regions and galaxies.

2.1.2.3 Identification of Dust Features

The confirmation of the presence of various solid-state and molecular features was important to better constrain the dust composition.

Silicates. The first identification of silicates was reported by Woolf & Ney (1969), in absorption toward M giant and supergiant stars. Kemper et al. (2004) provided a $2\%$ upper limit on the crystalline silicate fraction, based on ISO observations toward the Galactic center. The MIR features, proper to crystalline silicates were indeed not detected.

Carbonaceous grains. MIR aromatic emission features were first detected in the Planetary Nebula (PN) NGC 7027 by Gillett et al. (1973, cf. Fig. 2.8.a). They were called at the time Unidentified Infrared Bands (UIBs). They were attributed to the bending and stretching modes of PAHs ten years later (Duley & Williams, 1981; Léger & Puget, 1984; Allamandola et al., 1985, cf. Fig. 2.8.b). The 3.4 $\mu m$ aliphatic feature in absorption was first detected toward the Galactic center by Willner et al. (1979).

(a) First detection of UIBs	(b) Attribution of UIBs to PAHs

Ices. Ice absorption features have been searched for since the 1940’s and the dirty ice model (cf. Sect. 2.1.2.5).

• The 3.1 $\mu m$ H${}_2$O ice band was finally detected by Gillett & Forrest (1973).
• Lacy et al. (1984) provided the first observational identification of CO ice absorption.
• CO${}_2$ ice absorption was discovered in ISO/SWS spectra (de Graauw et al., 1996; D’Hendecourt et al., 1996; Guertler et al., 1996).

X-ray edges. The absorption of X-ray photons by inner electronic shells can provide information on the crystalline configuration of solids (e.g. Forrey et al., 1998; Draine, 2003c, for the theoretical predictions). The first X-ray absorption edges were detected in Chandra and XMM-Newton data (Paerels et al., 2001), but their interpretation remained problematic. More recent studies have been able to constrain grain structures using these features (e.g. Lee et al., 2009b).

2.1.2.4 Dusty Epiphenomena

Diffuse Interstellar Bands. There are unidentified, ubiquitous absorption features in the $\lambda \simeq 0.4-2$ $\mu m$ range, called Diffuse Interstellar Bands (DIBs; cf. Sect. 2.2.1.5).

• They were first reported by Heger (1922a,b).
• It was only Merrill (1934) who showed their interstellar nature.
• More than 400 of them have been identified toward a diversity of sightlines, even in external galaxies (Hobbs et al., 2009). They remain largely unidentified, although four of them have been attributed to C${}_{60}^{+}$ (Campbell et al., 2015; Walker et al., 2015).

Extended Red Emission. The Extended Red Emission (ERE) is a broad emission band, found in the $\lambda \simeq 0.6-0.9$ $\mu m$ range of a diversity of Galactic environments. It is attributed to dust photoluminescence (e.g. Witt & Vijh, 2004), but the nature of its carriers is still debated. Photoluminescence is a non-thermal emission process in which, subsequently to the absorption of a UV photon, a grain is brought to an excited electronic state. After partial internal relaxation, a redder photon is emitted, bringing the electron back to its fundamental state. The ERE was first reported in the Red Rectangle reflection nebula (Schmidt et al., 1980).

Spinning Grains. The radio emission of fastly spinning dust grains was predicted by several authors (Erickson, 1957; Hoyle & Wickramasinghe, 1970; Ferrara & Dettmar, 1994).

• Kogut et al. (1996) detected an Anomalous Microwave Emission (AME) in the COBE/DMR data. This excess could not be explained by thermal dust, free-free and synchrotron emissions.
• Draine & Lazarian (1998a,b) showed the AME could be explained by the rotational emission of small, charged, fastly rotating grains.

2.1.2.5 Dust Models

First models. The first dust models of the 1930’s, following Trumpler’s study, were mainly speculative.

• The first assumptions about the dust composition were made by analogy with micrometeorites. Schalén (1936) and Greenstein (1938) assumed grains were made of $a=0.01$ $\mu m$ iron particles. Lindblad (1935) had assumed dust could form by condensation in space.
• The dirty ice model (Oort & van de Hulst, 1946; van de Hulst, 1949) was the first attempt to base the dust composition on the abundant atoms: H, C, N, O. These atoms would form various ices (H${}_2$O, CH${}_4$, NH${}_3$) nucleating on grain seeds. The predicted dust temperature of this model was $\simeq 15$ K, close to the actual value ($\simeq 18$ K).
• Several studies hypothesized that graphite could be a major dust constituent, explaining the polarization of starlight, because of its anisotropic crystalline structure (Cayrel & Schatzman, 1954; Hoyle & Wickramasinghe, 1962). Graphite was supported by the discovery of the 2175 Å bump (Stecher, 1965; Stecher & Donn, 1965).
• Donn (1968) hypothesized that PAHs could be responsible for the 2175 Å bump, which was supported by the laboratory measurements of Joblin et al. (1992).
• The MRN model (Mathis, Rumpl, & Nordsieck, 1977) was the first attempt at fitting the average extinction curve of the MW with a mixture of graphite and silicate grains, with a power-law size distribution:

  $$f\left(a\right)\equiv \frac{dN}{da}\propto a^{-3.5}\text{ for }{a}_{-}<a<a_{+},$$

  (2.1)

  where $\left[a_{-},a_{+}\right]=\left[0.005,1\right]$ $\mu m$ for graphite and $\left[a_{-},a_{+}\right]=\left[0.025,0.25\right]$ $\mu m$ for silicates.

Calculation of the optical properties. Dust models rely on the computation of optical properties. The techniques have improved with time. The laboratory measurements on the most relevant compounds also expanded.

• Mie theory (cf. Sect. 1.2.2.3) was independently developed by Gustav MIE and Peter DEBYE (Mie, 1908; Debye, 1909).
• The DDA method (cf. Sect. 1.2.2.4) was developed by Purcell & Pennypacker (1973).
• Draine & Lee (1984) presented the first UV-to-mm optical properties of astronomical silicate and graphite. These properties have been refined by numerous studies afterward.
• Similarly, synthetic optical properties of a mixture of astronomical PAHs were presented by Li & Draine (2001) and updated by Draine & Li (2007).
• The properties of various amorphous carbon compounds were inferred from laboratory data by Rouleau & Martin (1991) and Zubko et al. (1996). Jones (2012a,b,c) presented a physical parametrization of the optical properties of a-C(:H).

Elemental depletions. Elemental depletions (cf. Sect. 2.2.3) are an important set of constraints on the dust mass and on the stoichiometry of the dominant grain compounds. Greenberg (1974) laid the ground for such studies. Savage & Bohlin (1979) showed that the depletion strength correlates well with the average density of the gas. Several studies have refined this approach. Jenkins (2009) presented a unified view, showing depletions were controlled by a single parameter, correlated with the column density.

Modern panchromatic models. With the COBE and IRAS data, dust models started to have the possibility to be constrained by both the emission and the extinction. These simultaneous constraints are important to break the degeneracy between the composition and the size distribution.

• The Désert, Boulanger, & Puget (1990) model (hereafter DBP90) was the first silicate-carbon-PAH model, fitting the extinction and emission of the Galactic diffuse ISM (Fig. 2.9). This model had three components: the PAHs, the Very Small Grains (VSG; small carbon grains) and the Big Grains (BG; large carbon-coated silicates).
• Dwek et al. (1997) built the first model constrained by the fine spectral sampling of the COBE data (DIRBE broadbands and FIRAS spectrum).
• Zubko, Dwek, & Arendt (2004) added the elemental depletions to the emission and extinction, to constrain more accurately the grain composition.
• Jones et al. (2013, 2017) developed the The Heterogeneous Evolution Model for Interstellar Solids (THEMIS). This model is physically parametrized to account for the known evolution of the dust mixture as a function of the physical conditions.
• Guillet et al. (2018) presented a dust model accounting for the polarized emission observed by Planck.

2.2 The Current Empirical Constraints

We now review the current empirical constraints that are used to build dust models. These models are calibrated on observations of the diffuse Galactic ISM. This medium indeed presents several advantages.

• It is optically thin. No radiative transfer is thus needed.
• It appears to be rather uniformly illuminated. The mixing of heterogeneous physical conditions along the sightline is probably limited.
• Dust properties of the diffuse ISM appear rather uniform.
• It benefits from a wealth of observations.

Observations of the diffuse Galactic ISM are thus the most important ones. Extragalactic constraints are the focus of Chap. 3. It is currently impossible to gather the same type of data set, at the same level of accuracy, in external galaxies.

Several reviews discuss the available dust observables (e.g. Draine, 2003a; Dwek, 2005; Draine, 2009; Galliano et al., 2018; Hensley & Draine, 2021). We have represented on Fig. 2.10 most of these observables on top of the typical SED of a gas-rich galaxy.

2.2.1 Extinction

Dust extincts light from the X-rays to the MIR. The effect of dust extinction on a background source is sometimes referred to as reddening. It is indeed more important on the blue side of the visible window.

2.2.1.1 UV-to-NIR Extinction

The extinction magnitude. We saw in Sect. 2.1.2.1 that the first dust studies were performed in extinction, in the visible range. Consequently, extinction properties were characterized by quantities depending on the magnitude system. The magnitude, $m\left({\lambda }_0\right)$, of a star of flux $F_{\nu }\left({\lambda }_0\right)$, observed through a photometric filter centered at wavelength ${\lambda }_0$, is:

where $F_{\nu }^0\left({\lambda }_0\right)$ is the reference flux or zero-point of the photometric filter. The zero-point is a calibration quantity, independent of the observed source. Two important bands for characterizing extinction are the B and V bands, centered respectively at ${\lambda }_B=0.44\mu m$ and ${\lambda }_V=0.55\mu m$ (Table B.5). The total extinction or extinction in magnitude is defined as:

where the index “obs” refers to the observed quantity, and “int” refers to the intrinsic quantity, that is the quantity not affected by dust extinction. In the MW, the average V-band extinction over the distance to the star, $d$, is $A\left(V\right)∕d\simeq 1.8{\text{kpc}}^{-1}$ (e.g. Whittet, 2003). $A\left({\lambda }_0\right)$ can be linked to a more physical quantity, the optical depth:

The expression above has been derived assuming homogeneous properties along the sightline (cf. Sect. 3.1.1 for a more rigorous definition of $\tau$). The observed flux can conveniently be expressed as a function of the optical depth:

The selective extinction. The spectral shape of the extinction curve varies among sightlines. It can be quantified by the selective extinction, $E\left(\lambda -{\lambda }_0\right)\equiv A\left(\lambda \right)-A\left({\lambda }_0\right)$. In the MW, Cardelli, Clayton, & Mathis (1989) showed that the UV-to-NIR extinction curves follow a universal law, parametrized by the sole visual-to-selective extinction ratio:

This parametrization is demonstrated in Fig. 2.11.a. We see that $A\left(V\right)$ is a scaling parameter quantifying the amount of extinction along the sightline. According to Eq. ($2.5$), $A\left(V\right)\propto Z_{\mathrm{dust}}\times N_H$. In the MW, there are no drastic dustiness variations, thus $A\left(V\right)\propto N_H$. On the other hand, $R\left(V\right)$ is a shape parameter. It typically varies between $R\left(V\right)\simeq 2$ and $R\left(V\right)\simeq 5$. On average, $R\left(V\right)\simeq 3.1$ in the MW. Curves with $R\left(V\right)\gtrsim 3.1$ tend to be flatter.

The most notable features of the UV-to-NIR extinction curves are the following (cf. Fig. 2.11.a).

The Far-UV (FUV) rise

is mainly due to the absorption by small grains, in the Rayleigh regime ($A\left(\lambda \right)\propto 1∕\lambda$; cf. Sect. 1.2.2.3).

The 2175 Å bump

is attributed to small sp${}^2$-hybridized C bonds (cf. Sect. 1.1.4).

The optical knee

is mainly due to scattering by larger grains.

The NIR extinction

can be approximated by a power-law: $A\left(\lambda \right)\propto {\lambda }^{-\alpha }$, with $\alpha \simeq 2.27$ (Maíz Apellániz et al., 2020).

Measuring extinction. The original method to measure the wavelength dependence of the extinction curve is the pair method (Stecher, 1965): two stars of the same spectral type are observed, one with a low, and one with a high foreground extinction. The extinction curve is directly derived from the differential SED or spectrum, assuming the dust properties are uniform along both sightlines. An alternative to this method consists in replacing the reference star by a synthetic spectrum, knowing the precise spectral type of the star (e.g. Fitzpatrick & Massa, 2005). This is demonstrated in Fig. 2.11.b.

UV-visible scattering. Observations of starlight scattering by ISD can constrain the average albedo, $\tilde{\omega }$, and asymmetry parameter, $⟨\cos <!--\; FUNCTION\; APPLICATION\; -->𝜃⟩$, of the grains (cf. Sect. 1.2.2.3). Two types of observations are usually favored to that purpose.

The Diffuse Galactic Light

(DGL) is the scattering of the general ISRF by dust. It is the diffuse visible light seen in ISM regions without associated stars. The DGL was first detected by Elvey & Roach (1937). Henyey & Greenstein (1941) built their scattering phase function (cf. Sect. 1.2.2.3) to explain this phenomenon.

Reflection nebulae

are obvious objects to measure $\tilde{\omega }$ and $⟨\cos <!--\; FUNCTION\; APPLICATION\; -->𝜃⟩$, as the visible light comes from a nearby star or cluster, and is scattered on the surface of a cloud facing us.

Both methods converge toward qualitatively consistent results:

2.2.1.2 MIR Extinction

The MIR continuum. The spectral shape of the MIR extinction is harder to constrain than its UV-visible counterpart. The MIR range is indeed the domain where the stellar and dust SEDs intersect (cf. Fig. 2.10). It is therefore difficult to precisely model the background sources toward which the extinction is measured.

• The Rayleigh-Jeans continuum of old stars, peaking in the NIR, such as G and K-type stars, can be used (e.g. Xue et al., 2016).
• Otherwise, H recombination lines (e.g. Lutz et al., 1996) or H${}_2$ rovibrational lines (e.g. Bertoldi et al., 1999) provide an alternative. The ratio of a series of these lines can indeed be reasonably well modeled. Differences between the theoretical and observed ratios result from the extinction.

In the ISO days, there was a controversy about the 4-to-8 $\mu m$ continuum, which seemed to be following the extrapolation of the NIR power-law trend (e.g. Bertoldi et al., 1999). However, Lutz et al. (1996) showed this continuum toward the Galactic center was relatively flat (cf. Fig. 2.12.a). This has been confirmed by ulterior observations with Spitzer, WISE and AKARI (e.g. Indebetouw et al., 2005; Xue et al., 2016; Gordon et al., 2021). It seems to be a general feature of a wide variety of sightlines. The new synthetic extinction of Hensley & Draine (2021) reproduces this flat continuum (cf. Fig. 2.12.a).

Silicate features. The observed profiles of the Si–O stretching and O–Si–O bending silicate features, at 9.7 and 18 $\mu m$ (cf. Sect. 1.1.4), are not perfectly matching those of olivine and pyroxene. This is the reason of the introduction of the concept of astrosilicates by Draine & Lee (1984).

• Interstellar silicates are indeed a mixture of different varieties of compounds, with different stoichiometry, and probably metallic inclusions.
• Interstellar silicates are predominantly amorphous. The interstellar crystalline silicate fraction seems to be $\lesssim 2\%$ (Demyk et al., 1999; Kemper et al., 2004; Do-Duy et al., 2020).

There are uncertainties about the profile of the features and its potential variations between sightlines.

The 9.7 $\mu$m feature

has on average a FWHM of $\simeq 2.2$ $\mu m$. $A\left(V\right)∕\tau \left(9.7\right)\simeq 9\pm 1$ toward the GC (Kemper et al., 2004), but is higher when averaged over sightlines: $A\left(V\right)∕\tau \left(9.7\right)\simeq 19$ (Roche & Aitken, 1984; Mathis, 1998). The synthetic extinction of Hensley & Draine (2021) has $A\left(V\right)∕\tau \left(9.7\right)=20$.

The 18 $\mu$m feature

is weaker than the 9.7 $\mu m$, making its characterization more uncertain. The depth ratio of the two features is $\tau \left(9.7\right)∕\tau \left(18\right)\simeq 2$ (Chiar & Tielens, 2006).

Ices. In regions shielded from the stellar radiation, some molecules can freeze out to form icy mantles onto grains (cf. e.g. Boogert et al., 2015, for a review). The dominant species are H${}_2$O, CO and CO${}_2$. They are responsible for several MIR absorption bands, shown in Fig. 2.12.b. These ice features are not observed in the diffuse ISM. They start appearing at higher values of $A\left(V\right)$, different compositions having different melting points. They are observed in dense regions, toward molecular clouds, Young Stellar Objects (YSO) or AGNs.

2.2.1.3 X-Rays

X-ray halos. Although the opacity of typical interstellar grains peaks in the UV (cf. e.g. Fig. 1.19), grains extinct significantly X-rays. In this regime, photons have wavelengths approaching the size of the atoms in the grain. Dust grains, when present along the sightline of an X-ray point source (such as a low-mass X-ray binary), scatter the radiation at small angles, creating an X-ray halo (Overbeck, 1965; Smith & Dwek, 1998). The properties of this halo are complex, as they depend on the grain properties: composition, porosity and maximum size (e.g. Smith, 2008). Such studies are limited by the uncertainty on the distance of the intervening dust and the background source. They however confirm the low abundance of grains larger than $\simeq 0.1$ $\mu m$ (e.g. Valencic & Smith, 2015).

X-ray absorption edges. Atoms, whether in the gas phase, or locked-up in grains, exhibit X-ray absorption features at specific wavelengths, called X-ray photoelectric edges (cf. Fig. 2.13). These edges correspond to the binding energies of the inner electrons, the letter (K or L in our case) corresponding to Bohr’s orbitals (cf. Table 1.2). The important point is that the energy and the spectral shape of these edges depend on the way the atom is paired (e.g. Draine, 2003c). It is thus possible, using X-ray spectroscopy, to differentiate atoms in the gas and dust phase, but also the crystalline structure of the grains (e.g. Lee et al., 2009a). For instance, Zeegers et al. (2017) studied the Si K edge along the line of sight of a Galactic X-ray binary. They were able to constrain the column density and the chemical composition of the silicate grains. This method was used to show that interstellar silicates are essentially Mg-rich, whereas the iron content is in metallic form (Costantini et al., 2012; Rogantini et al., 2019; Westphal et al., 2019). Finally, the crystalline fraction of silicates has been estimated to be in the range $\simeq 11-15\%$, using X-ray spectra (Rogantini et al., 2019, 2020). This is significantly higher than the $\simeq 2\%$ upper limit derived from MIR spectroscopy (cf. Sect. 2.2.1.2). This discrepancy might originate in the challenges of X-ray spectroscopy, which requires both high spectral resolution and high signal-to-noise ratios.

2.2.1.4 Dichroic Extinction

The light from a background source seen through a cloud containing elongated grains, with their rotation axis aligned along the magnetic field, is partially polarized (cf. Sect. 1.2.2.5). In the MW, the wavelength-dependent polarization fraction follows the empirical law of Serkowski (1973), shown in Fig. 2.14.a. It runs from the near-UV (NUV) to the NIR, peaking around $\lambda \simeq 0.55$ $\mu m$. It is well reproduced by models with elongated grains (cf. Fig. 2.14.a and Guillet et al., 2018). The polarized extinction fraction, $p\left(\lambda \right)$, is often quoted: $p\left(\lambda \right)\equiv C_{\mathrm{pol}}\left(\lambda \right)∕C_{\mathrm{ext}}\left(\lambda \right)$, where $C_{\mathrm{pol}}$ and $C_{\mathrm{ext}}$ are the polarized and total cross-sections.

2.2.1.5 Diffuse Interstellar Bands

DIBs are ubiquitous absorption features in the $\simeq 0.4-2$ $\mu m$ range (cf. Fig. 2.14.b). They are too broad to originate in atoms or simple molecules. They have to come from large molecules and/or small grains. Over 500 of them have been detected in the ISM (Fan et al., 2019). They are empirically associated with dust, as their strength correlates with $E\left(B-V\right)$ at low values, but they disappear in denser sightlines (e.g. Lan et al., 2015). To first order, DIBs correlate with each other, but there are some notable differences, suggesting that they have different carriers (Herbig, 1995). For instance, the so-called C${}_2$ DIBs (Thorburn et al., 2003) appear to be found preferentially in diffuse molecular clouds. They remain largely unidentified, although four of them have been attributed to the ionized buckminsterfullerene, C${}_{60}^{+}$, a football-shaped carbon molecule (Campbell et al., 2015; Walker et al., 2015). The MIR transitions of this molecule, as well as C${}_{70}$, had been detected in the ISM, a few years before (Cami et al., 2010).

2.2.2 Emission

As we have discussed in Sect. 1.2.4, dust emits thermally in the IR. This thermal emission is also partially polarized. We will see in this section that there are also non-thermal emission components.

2.2.2.1 Infrared Continuum and Features

Observations of the diffuse ISM. Fig. 2.15 represents the NIR-to-cm SED of the diffuse Galactic ISM. Those are the observations used to constrain the dust models we will discuss in Sect. 2.3. The challenge of building such a data set is ensuring that these fluxes correspond to the emission of the most diffuse regions of the MW, characterized by its H column density ($N_H\simeq 10^{24}$ m${}^{-2}$). The disk of the MW contains the densest regions (cf. Fig. 2.4.b). It is also important to ensure avoiding denser regions, as grain properties evolve, probably due to the accretion of mantles (e.g. Ysard et al., 2015). These observations therefore focus at high Galactic latitude, $b$, and low $N_H$. For instance, Compiègne et al. (2011) used data at $\left|b\right|>6^{\circ }$ and $N_H<5.5\times 10^{24}$ m${}^{-2}$. Hensley & Draine (2021) gives a more a complete discussion about the homogenization of the different datasets. At these emission levels, there are several contaminations that need to be subtracted.

The zodiacal foreground

is the MIR emission from the interplanetary dust in the Solar system disk.

The CIB

that we have already discussed in Fig. 1.28 is the accumulated emission of background galaxies. Its SED is very similar to the emission of the MW, and thus difficult to subtract.

The CMB

is the mm emission shown in Fig. 1.28.

MIR features. The average MIR spectrum of the diffuse Galactic ISM is represented in Fig. 2.15 (in blue). This particular spectrum corresponds to a smaller patch of the sky, and is scaled on the DIRBE 12 $\mu m$ photometry (Flagey et al., 2006; Compiègne et al., 2011). There are indeed no MIR spectroscopic all sky surveys. The MIR constraints of dust models prior to Compiègne et al. (2011) were only the DIRBE broadbands. This difference in MIR coverage has consequences on the derived abundances and profiles of the aromatic feature carriers that we will discuss on Sect. 2.3. The profiles and relative intensities of the main aromatic features can alternatively be constrained by a combination of laboratory data and the emission of nearby gas-rich galaxies (e.g. Draine & Li, 2007; Hensley & Draine, 2021).

2.2.2.2 Polarized Emission

We have seen in Sect. 1.2.2.5 that elongated grains emit polarized IR radiation. Although the polarized submm emission of the ISM had been measured from various balloon-borne observatories (Benoît et al., 2004; Bennett et al., 2013), the Planck satellite provided the first all sky survey in several bands (Planck Collaboration et al., 2015b). These observations point toward one major result: large ISM grains have homogeneous properties. In other words, the IR emission can not originate in the mixing of several heterogeneous grain populations. Small grains have a negligible polarization effect. The models of Guillet et al. (2018), which account both for total intensity and polarization, indeed provide the best fit for a single population of large composite astrosilicates with a-C mantles. In parallel, Planck Collaboration et al. (2020b) showed that the polarized SED was consistent with a single MBB with $\beta \simeq 1.5$ and $T\simeq 20$ K.

2.2.2.3 Non-Thermal Emission

Spinning Grains. The AME is a centimeter continuum excess that can not be accounted for by the extrapolation of dust models, free-free, synchrotron and molecular line emission (Fig. 2.10). It was first detected in the MW (Kogut et al., 1996). Draine & Lazarian (1998a) promptly proposed that it was arising from the dipole emission of fastly rotating ultrasmall grains. The candidate carriers were thought to be PAHs. The Wilkinson Microwave Anisotropy Probe (WMAP; $\lambda \simeq 3.2-13$ mm; 2001-2010) and Planck data of the Galaxy were successfully fitted with spinning dust models, including PAHs (Miville-Deschênes et al., 2008; Ysard & Verstraete, 2010; Planck Collaboration et al., 2011b). The cm SED in Fig. 2.15 is dominated by spinning grain emission. In the MW, the AME correlates with all tracers of dust emission (e.g. Hensley et al., 2016). However, the AME intensity increases with the ISRF intensity, while PAHs are destroyed in high ISRFs. Hensley et al. (2016) thus proposed that the carriers of the AME could be nano-silicates, rather than PAHs. Refining the modeling of the MIR SED, Bell et al. (2019) showed that AME correlates better with the emission from charged PAHs, in the Galactic region $\lambda$-Orionis. This will be discussed in more details in Sect. 3.2.2.2.

Photoluminescence. We have seen in Sect. 2.1.2.4 that the ERE excess emission was thought to originate in the photoluminescence of dust grains. In reflection nebulae, ERE appears to be excited by FUV photons ($11\text{eV}\lesssim \mathit{h\nu }\lesssim 13.6\text{eV}$; e.g.  Lai et al., 2017). It disappears if the exciting star has an effective temperature $T_{\mathrm{eff}}\lesssim 10^4$ K. The conversion efficiency, that is the rate of photoluminescent photons per absorbed UV photon, seems to be around $\simeq 1\%$. ERE being seen in reflection nebulae, it is expected to be a general property of interstellar grains. There is however a debate about the detection of ERE toward cirrus clouds and its conversion efficiency (cf. the discussion in Hensley & Draine, 2021). ERE is observed in C-rich PNe (containing predominantly carbonaceous grains) and not in O-rich PNe (containing predominantly silicates grains;  Witt & Vijh, 2004). The carriers should thus be carbon grains, such as PAHs.

2.2.3 Elemental Abundances in Grains

The logarithmic abundance of an element E, relative to H, is often noted:

$N_E$ being its column density. The number abundance ratio can also be noted E/H instead of $N_E∕N_H$, when it is not directly derived from the measure of a column density. An element in the ISM belongs either to the gas or to the dust phase. If we know the total or reference abundance of an element E in the ISM, we can thus infer its abundance locked in dust grains, by measuring its abundance in the gas phase. This difference is the depletion. The logarithmic depletion of an element E is defined as (Jenkins, 2009):

The observable $\delta \left(E\right)$ is a measure of the ratio between the abundance of an element E observed in the gas phase to its total assumed abundance. The abundance of element E, locked in grains, is thus:

Note that, in Eq. ($2.10$), we do not differentiate the origin of H, as H is predominantly in the gas phase: $H_{\mathrm{ref}}\simeq H_{\mathrm{gas}}»H_{\mathrm{dust}}$.

2.2.3.1 Measuring ISM Abundances

Solar abundances. The abundance of elements and their isotopes are the most accurately known in the Solar system (e.g. Asplund et al., 2009, for a review). Those are thus used as a reference in the ISM. The abundances of the protosolar nebula, at the time the Sun formed, 4.56 Gyr ago, can be determined the two following ways.

Meteorites,

analyzed with mass spectroscopy, provide the most precise abundances. The most primitive meteorites are the carbonaceous (CI) chondrites. The issue with meteorites is that the most volatile elements (i.e. the lightest ones and the noble gases) have been depleted due to high-temperature processes within the Solar nebula (e.g. Hellmann et al., 2020).

Solar photosphere

absorption spectroscopy is less precise, as it requires some modeling. It however provides more reliable abundances of the volatile elements.

These abundances are compared in Fig. 2.16. We see that both tracers are in very good agreement, except for the volatile elements. It is common to define the mass fractions of H, He, and elements heavier than He ($M_{\mathrm{ISM}}$ being the total ISM mass):

In the literature, the ratio $Z$ is unanimously called metallicity. Some even call the elements heavier than He, metals, which is even worse, knowing what we have learned in Sect. 1.1.3.1. This is one of the worst choices of terminology in the whole history of sciences. It is however difficult to avoid using the term metallicity. We will thus reluctantly use it in the rest of this manuscript.

Present-day Solar abundances. The abundances displayed in Fig. 2.16 are present-day photospheric values. They are however not perfectly representative of the present-day abundances of the Solar neighborhood ISM. To go from the former to the latter, a factor $+0.03$ dex has to be added to the heavy element abundances of Fig. 2.16 to account for diffusion in the Sun (Turcotte & Wimmer-Schweingruber, 2002). This provides protosolar abundances. Present-day abundances can then be inferred by modeling the chemical evolution of the MW during the last 4.56 Gyr (e.g. Chiappini et al., 2003; Bedell et al., 2018). This leads to correcting each element with a different factor, up to $\simeq 0.2$ dex (cf. e.g. Hensley & Draine, 2021, for the correction of the major dust constituents). The present-day Solar photospheric abundances are (Asplund et al., 2009):

To put it in words, three quarters of the gas mass is made of H, one quarter is made of He, and only $1.3\%$ is made of heavy elements, in the MW. Besides H and He, the most abundant species in the ISM are O and C ($M_O∕M_{\mathrm{ISM}}\simeq 8.0\times 10^{-3}$ and $M_C∕M_{\mathrm{ISM}}\simeq 2.8\times 10^{-3}$). These abundances can be used as references in Eq. ($2.9$). Alternatively, B stars or young F and G stars can provide a more direct estimate of the abundances in nowadays ISM. These abundances are however more difficult to estimate accurately.

2.2.3.2 Depletions

The depletion strength. The abundances in the gas phase are most reliably measured by absorption spectroscopy toward stars. Gas atoms in the neutral ISM are essentially in their ground state. Most of the corresponding transitions are in the UV ($\lambda =0.0912-0.3$ $\mu m$). Jenkins (2009) compiled and homogenized the abundances of 17 elements measured along 243 sightlines, throughout the literature, to propose a unified representation of the depletions in the MW. Jenkins (2009) showed that the logarithmic depletions of each element are all linearly related, and controlled by a single parameter, $F_{\star }$, called the depletion strength factor:

The factors $A_E$ and $B_E$ are empirically determined for each element. The depletion factor accounts for the fact that depletions are different along different sightlines. They however vary according to Eq. ($2.13$). This effect is due to dust growth in the ISM. It is supported by the good correlation between $F_{\star }$ and the average density of the ISM, demonstrated on Fig. 2.17.a. When the density of the ISM increases, the collisional rate of a grain with heavy elements increases. A fraction of these elements stick on the grain surface and grow mantles.

• When $F_{\star }\simeq 0$, we are in the most diffuse ISM, the depletion is $\delta \left(E\right)\simeq B_E$.
• When $F_{\star }\simeq 1$, such as toward $\zeta$ Oph, we are sampling the dense ISM. The amplitude of the depletion, $A_E$, reflects the composition of the grain mantles.

Volatile and refractory elements. Not all the most abundant elements in the ISM enter the dust composition. Some elements such as N or the noble gases are not significantly depleted. Fig. 2.17.b shows a general relation between the depletion amplitude and the condensation temperature of the most abundant heavy elements. The most depleted elements are those which have a high condensation temperature. For that reason, elements are often classified in the two following categories.

Volatile elements

are the elements with low condensation temperatures (C, N, O, noble gases). A moderate temperature is sufficient to remove them from the grains. These elements thus exist mainly in the gas phase.

Refractory elements

are the elements with high condensation temperatures (those are essentially the metals). They can be present in grains up to high temperatures. Their abundance in the gas phase therefore exhibits large variations as a function of environment.

We note that, although C and O are two of the main dust constituents, these elements are classified as volatile. These elements are indeed mainly in the gas phase, as their depletion is moderate (cf. Fig. 2.18.a). However, this modest depletion is sufficient to account for a large fraction of the dust mass.

Inferred dust composition. Since the individual depletion of each element can be inferred, it provides the unique prospect of constraining the average composition of dust grains. This composition changes with density, as mantles grow. Following Hensley & Draine (2021), we quote depletions for $F_{\star }=0.5$ as they correspond to $⟨n_H⟩\simeq 0.3$ cm${}^{-3}$, which is appropriate for the diffuse ISM. From this vantage point, the dustiness of the diffuse Galactic ISM is:

The dust-to-metal mass ratio is thus:

The results of Jenkins (2009) indicate that the dustiness is $\simeq 2.7$ times higher at $F_{\star }=1$ than at $F_{\star }=0$. The number and mass abundance in grains is represented in Fig. 2.18. The carbonaceous-to-silicate mass ratio is:

Finally, we can have an idea of what the stoichiometry of silicates should be:

We note it results in a higher Si:O ratio than in olivine (1:4) and pyroxene (1:3) (cf. Sect. 1.1.4). It is currently difficult to understand where all the depleted oxygen is, even if it also forms various oxides, such as Fe${}_2$O${}_3$, Al${}_2$O${}_3$, etc.

(a) Number abundance, relative to H	(b) Grain composition, in mass