Annu. Rev. Astron. Astrophys. 1990. 28: 37-70 Copyright © 1990 by Annual Reviews. All rights reserved

3.2 Continuum Emission

Continuum radiation from dust arises from two mechanisms: (a) fluorescence, giving rise to a red continuum; and (b) thermal radiation. The latter is observed either in the 1-60 µm range following the transient heating of a small grain by a single UV photon; or for > 100 µm, where the energy is reprocessed by steady-state emission of larger grains; or in the intermediate-wavelength range, where the effects compete.

3.2.1. RED CONTINUUM Grains in the ``reflection'' nebula NGC 2023 were found to produce a red continuum that peaks at about 6800 Å (178). Subsequent studies of many such nebulae confirm that there is an extended red emission in many of them (175 and ref. therein), typically contributing 30-50% of the flux in the I band (0.88 µm). In NGC 2023, the red emission is found in filamentary structures that spatially coincide with patches of H<sub>2</sub> infrared fluorescence and the 3.3-µm UIB emission (56) but not necessarily with the intensity of reflected light, which is determined by total dust density. IC 435, in the same molecular cloud, shows no red luminescence (174), nor does the Merope reflection nebula. A small patch of red fluorescent emission near the star Cas also shows a strong H<sub>2</sub> fluorescence in the UV (179). The ``Red Rectangle'' (HD 44179), a bipolar outflow excited by a central star, shows both strong UIBs and the red emission (140, 146).

The simplest interpretation of the red fluorescent emission is that it is excited by a strong UV flux incident upon hydrogenated carbon particles, either amorphous (46) or PAHs (32), thereby producing both the fluorescent red emission and the H₂ fluorescence. A strong enough radiation field will alter the carbon particles and dissociate the H₂, as might be the case in the Merope nebula.

3.2.2. 3-30 µm CONTINUUM In addition to the UIBs, there is a continuous emission in the NIR/MIR range that accounts for a large part of the radiation from reflection nebulae (151) and, presumably, from the Galaxy as a whole. A survey at 11 and 20 µm (132) found unexpectedly high diffuse galactic emission. IRAS mapped almost the entire sky at 12, 25, 60, and 100 µm and found the 12- and 25-µm intensities vary considerably relative to the 100-µm intensity (90, 91), which is roughly proportional to N(H I). The NIR/MIR emission arises from warm grains; simple considerations of the peak wavelength of the Planck function (and hence the emissivity of a grain) as a function of temperature show that this radiation must come from grains with temperatures of hundreds of Kelvins. By contrast, the mean local interstellar radiation field and optical constants for likely grain materials (carbon, silicates, organic refractory mantles) all suggest equilibrium temperatures of ~ 20 K for the grains having the sizes (> 0.01 µm) needed to account for the optical extinction (133). Grains of this size have large enough heat capacities so that their temperatures do not fluctuate appreciably after absorbing a single UV photon.

The NIR/MIR emission must be produced by grains in the size range 5-50 Å; such grains are large enough to have an almost continuous density of energy states. In this case they radiate a continuum rather than emission bands. A single UV photon heats the grain to a high peak temperature that depends upon the size of the grain and the energy of the photon (150). The grain emits the NIR/MIR radiation and cools to very low temperatures between photon absorptions. Calculations of thermal fluctuations (34, 41) have shown that very small grains can account for the spectrum of the emission. For clear discussions of the properties of small grains, see (4, 133).

3.2.3. FIR EMISSION Grains with sizes of 0.01 µm or more are cold (~ 20 K) and reradiate most of the energy they absorb into the FIR part of the spectrum. Hildebrand (70) has clearly explained the process of determining grain properties and cloud masses from FIR observations. Cox and Mezger (30), in a recent review of the galactic FIR/submillimeter radiation from dust, estimate that about 10¹⁰ L, or 30% of the total luminosity of the Galaxy, is radiated in the FIR, mostly from dust heated in H I regions by the interstellar radiation field of early-type stars (12).

The FIR provides important information regarding the spatial variations of the interstellar radiation field throughout the Galaxy and on how molecular clouds form stars and evolve into H II regions, but is of limited use as a diagnostic of dust because each line of sight samples grains with temperatures which depend upon their local radiation fields. However, for wavelengths much longer than about 150 µm (the peak of the emitted radiation), the FIR can be used to determine the relative opacities of the emitting grains. The Galaxy is optically thin at submillimeter wavelengths, in which case the intensity of emission, I, is proportional to the opacity, k times the Planck function, B(T). For long wavelengths, B(T) varies linearly with the temperature, and thus the wavelength dependence of I provides relative values of k. The results for diffuse radiation from the Galaxy (115) and from other galaxies (22) show that for > 100 µm, k is proportional to ^-2, which is predicted by theory (e.g., DL84). The constant in the proportionality is difficult to determine because it depends on an estimation of the column density of grains, or of hydrogen, along the line of sight of the observation. The theoretical opacities of DL84, based on a graphite-silicate model for grains, are approximately half of Hildebrand's estimate (70) based on a calibration in local dense globules (cf. 124). The uncertainties are probably at least a factor of two, if not more. Table 1 uses the Hildebrand value.

The mass of interstellar dust, and thereby an estimate for the mass of the ISM, is often determined from the FIR intensity, together with the opacity of grains per mass and an estimated grain temperature. It is important to realize (40) that this procedure is reasonably safe only if the observations are all on the long-wavelength side of the Planck function of the coldest grains -normally, in the submillimeter range. For instance, ``the temperature'' obtained from the ratio of the 60- and 100-µm intensities from IRAS is biased by a few warm grains that can provide almost all of the 60-µm emission. One can easily be off a substantial factor (>3) in the resulting mass estimate!

In dust surrounding very young objects, bipolar outflows, or the cores of giant molecular clouds, the flux suggets that the opacity even in the submillimeter range (400-1300 µm) might vary as ^-1 or ^-1.5 (145, 162, 181) instead of ^-2. The nebulae might be so optically thick that radiative transfer effects are important at submillimeter wavelengths. However, the grains in these extremely dense objects might not extremely small in comparison to 1 mm. Cometary grains also extend up to this size range. The growth of fractal grains (182; see Section 8) would explain the observations.