3.2.2. Dust Temperatures and IR Emission

The temperatures of interstellar dust particles depend on their optical properties and sizes (i.e., on the way they absorb and emit radiation) as well as on the interstellar radiation field (ISRF). ⁽²³⁾ Most of the visible and UV radiation in galaxies from stars passes through clouds of particles and heats them. This heating leads to reradiation at much longer wavelengths extending to the millimeter. On the average, in spiral galaxies, ~ 1/4 - 1/3 of the total stellar radiation is converted into dust emission (Cox & Mezger 1989; Calzetti 2001). The converted radiation is a probe of the particles and the physical environments in which they find themselves.

There is a long history in the study of grain temperature (and emission) since Eddington's demonstration of a 3.2 K black body equilibrium dust temperature assuming a 10⁴ K interstellar radiation field diluted by a factor of 10^-14 (Eddington 1926). Van de Hulst (1949) was the first to provide a realistic dust model temperature, ~ 15 K for dielectric particles. A subsequent extensive investigation was made by Greenberg (1968, 1971) where the temperatures were calculated for various grain types in regions of various radiation fields. The first step to study the shape effects on dust temperatures was taken by Greenberg & Shah (1971). They found that the temperatures of non-spherical dielectric grains are generally lower than those of equivalent spheres, but insensitive to modest shape variations. Later efforts made by Chlewicki (1987) and Voshchinnikov, Semenov, & Henning (1999) essentially confirmed the results of Greenberg & Shah (1971).

The advent of the IRAS, COBE, and ISO space IR measurements provided powerful information regarding the far-IR emission of the large particles (the so-called "cold dust"). The "cold dust" problem has received much attention since it plays an important role in many astrophysical subjects; for example, the presence of "cold dust" would change the current concept on the morphology and physics of galaxies (Block 1996).

The presence of a population of ultrasmall grains was known long before the IR era. Forty-six years ago, Platt (1956) proposed that very small grains or large molecules with radii 10Å may be present in interstellar space. Donn (1968) further proposed that polycyclic aromatic hydrocarbon-like "Platt particles", may be responsible for the UV interstellar extinction.

These very small grains - consisting of tens to hundreds of atoms - are small enough that the time-averaged vibrational energy <E> is smaller than or comparable to the energy of the starlight photons which heat the grains. Stochastic heating by absorption of starlight therefore results in transient "temperature spikes", during which much of the energy deposited by the starlight photon is reradiated in the IR. The idea of transient heating of very small grains was first introduced by Greenberg (1968). Since then, there have been a number of studies on this topic (see Draine & Li 2001 and references therein).

Since the 1980s, an important new window on the "very small grain component" has been opened by IR observations. The near-IR continuum emission of reflection nebulae (Sellgren, Werner, & Dinerstein 1983) and the 12 and 25 µm "cirrus" emission detected by IRAS (Boulanger & Pérault 1988) explicitly indicated the presence of a very small interstellar dust component since large grains (with radii ~ 0.1µm) heated by diffuse starlight emit negligibly at such short wavelengths, whereas very small grains (with radii 0.01µm) can be transiently heated to very high temperatures ( 1000 K depending on grain size, composition, and photon energy). Subsequent measurements by the DIRBE instrument on the COBE satellite confirmed this and detected additional broadband emission at 3.5 and 4.9 µm (Arendt et al. 1998).

More recently, spectrometers aboard the Infrared Telescope in Space (IRTS; Onaka et al. 1996; Tanaka et al. 1996) and ISO (Mattila et al. 1996) have shown that the diffuse ISM radiates strongly in emission features at 3.3, 6.2, 7.7, 8.6, and 11.3 µm.

"PAHs, they are everywhere!"

-- L.J. Allamandola [1996]

These emission features, first seen in the spectrum of the planetary nebulae NGC 7027 and BD+30°3639 (Gillett, Forrest, & Merrill 1973), have been observed in a wide range of astronomical environments including planetary nebulae, protoplanetary nebulae, reflection nebulae, HII regions, circumstellar envelopes, and external galaxies (see Tielens et al. 1999 for a review for Galactic sources and Helou 2000 for extragalactic sources). Often referred to as "unidentified infrared" (UIR) bands, these emission features are now usually attributed to PAHs which are vibrationally excited upon absorption of a single UV/visible photon (Léger & Puget 1984; Allamandola, Tielens, & Barker 1985) although other carriers have also been proposed such as HAC (Duley & Williams 1981; Borghesi, Bussoletti, & Colangeli 1987; Jones, Duley, & Williams 1990), QCC (Sakata et al. 1990), coal (Papoular et al. 1993), fullerenes (Webster 1993), and interstellar nanodiamonds with sp³ surface atoms reconstructed to sp² hybridization (Jones & d'Hendecourt 2000).

The emission mechanism proposed for the UIR bands - UV excitation of gas-phase PAHs followed by internal conversion and IR fluorescence ⁽²⁴⁾ - is supported by laboratory measurements of the IR emission spectra of gas-phase PAH molecules (Cherchneff & Barker 1989; Brenner & Barker 1989; Kurtz 1992; Cook et al. 1998) and by theoretical investigations of the heating and cooling processes of PAHs in interstellar space (Allamandola, Tielens, & Barker 1989; Barker & Cherchneff 1989; d'Hendecourt et al. 1989; Draine & Li 2001a).

The near-IR (1-5 µm), mid-IR (5-12 µm) emission spectrum along with the far-IR ( > 12 µm) continuum emission of the diffuse Galactic medium yields further insights into the composition and physical nature of interstellar dust; in particular, the PAH emission features allow us to place constraints on the size distribution of the very small dust component.

Attempts to model the IR emission of interstellar dust have been made by various workers. Following the initial detection of 60 and 100 µm cirrus emission (Low et al. 1984), Draine & Anderson (1985) calculated the IR emission from a graphite/silicate grain model with grains as small as 3Å and argued that the 60 and 100 µm emission could be accounted for. When further processing of the IRAS data revealed stronger-than-expected 12 and 25 µm emission from interstellar clouds (Boulanger, Baud, & van Albada 1985), Weiland et al. (1986) showed that this emission could be explained if very large numbers of 3-10Å grains were present. A step forward was taken by Désert, Boulanger, & Puget (1990), Siebenmorgen & Krügel (1992), Schutte, Tielens, & Allamandola (1993), and Dwek et al. (1997) by including PAHs as an essential grain component. Early studies were limited to the IRAS observation in four broad photometric bands, but Dwek et al. (1997) were able to use DIRBE and FIRAS data.

In recent years, there has been considerable progress in both experimental measurements and quantum chemical calculations of the optical properties of PAHs (Allamandola, Hudgins, & Sandford 1999; Langhoff 1996; and references therein). There is also an improved understanding of the heat capacities of dust candidate materials (Draine & Li 2001) and the stochastic heating of very small grains (Barker & Cherchneff 1989; d'Hendecourt et al. 1989; Draine & Li 2001), the interstellar dust size distributions (Weingartner & Draine 2001a), and the grain charging processes (Weingartner & Draine 2001b).

Li & Draine (2001b) have made use of these advances to model the full emission spectrum, from near-IR to submillimeter, of dust in the diffuse ISM. The model consists of a mixture of amorphous silicate grains and carbonaceous grains, each with a wide size distribution ranging from molecules containing tens of atoms to large grains 1 µm in diameter. The carbonaceous grains are assumed to have PAH-like properties at very small sizes, and graphitic properties for radii a 50Å. On the basis of recent laboratory studies and guided by astronomical observations, they have constructed "astronomical" absorption cross sections for use in modelling neutral and ionized PAHs from the far UV to the far IR. Using realistic heat capacities (for calculating energy distribution functions for small grains undergoing "temperature spikes"), realistic optical properties, and a grain size distribution consistent with the observed interstellar extinction (Weingartner & Draine 2001a), Li & Draine (2001b) were able to reproduce the near-IR to submillimeter emission spectrum of the diffuse ISM, including the PAH emission features at 3.3, 6.2, 7.7, 8.6, and 11.3 µm.

The silicate/graphite-PAH model has been shown also applicable to the Small Magellanic Cloud (Li & Draine 2002a; Weingartner & Draine 2001a).

Li & Draine (2002c) have also modelled the excitation of PAH molecules in UV-poor regions. It was shown that the astronomical PAH model provides a satisfactory fit to the UIR spectrum of vdB 133, a reflection nebulae with the lowest ratio of UV to total radiation among reflection nebulae with detected UIR band emission (Uchida, Sellgren, & Werner 1998).

²³ Originally, the ISRF was represented by a 10⁴ K black-body radiation diluted by a factor of 10^-14 (Eddington 1926) which is undoubtedly too crude but serves as a simple and adequate approximation for some purposes. Many attempts have been made to obtain a more reasonable determination of the ISRF either on the basis of direct measurements of the UV radiation from the sky or by calculating the radiation of hot stars using model atmospheres. Van Dishoeck (1994) has summarized the typical ISRF estimates (Habing 1968; Draine 1978; Gondhalekar et al. 1980; Mathis, Mezger, & Panagia 1983). As illustrated in Fig. 2 of van Dishoeck (1994), the various estimates agree within factors of two. The latest work on the local far-UV ISRF by Parravano, Hollenbach, & Mckee (2002) led to a value quite close to Draine (1978). Back.

²⁴ PAHs are actually excited by photons of a wide range of wavelengths (Li & Draine 2002c). Back.