Annu. Rev. Astron. Astrophys. 1990. 28: 37-70
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4. SCATTERING FROM DUST

Scattering from grains provides another diagnostic for their nature and composition, since cross sections for scattering at any angle (the ``phase function'') can be computed for a given material in much the same way as for extinction. However, the relative locations of the illuminating sources, scattering grains, and the observer are very important in determining the actual intensity of scattered radiation. The presence of fluorescent emission (Section 3.2.1) complicates the interpretation of red and NIR scattering, but there seems to be little fluorescence in the range lambda < 0.5 µm (139).

In practice, the geometry is so uncertain that one attempts to determine only two quantities characterizing the scattering process: the albedo, or fraction of the extinction that is scattering; and g, the mean value of the cosine of the angle of scattering. For isotropic scattering, g = 0; for completely forward-throwing scattering, g = 1.

Scattering can be observed in three general situations: (a) The ``diffuse galactic light'' (DGL) - i.e. scattering by the diffuse dust of the general incident interstellar radiation field - which is strongly concentrated to the galactic plane, since the dust has a relatively small scale height; (b) reflection nebulae, with a known source of illumination (usually an B or A star, because of their favorable luminosities); and (c) scattering of the general interstellar radiation field by a dark cloud, seen at high enough latitudes so that it contrasts with a relatively dark sky background.

The DGL in the optical part of the spectrum has been analyzed (110, 173). It is quite faint and asymmetric in its angular distribution, and requires careful correction for the contribution of faint stars, airglow, and (especially) zodiacal light. Its advantage is that the geometry of the sources and scatterers is well known, in contrast to reflection nebulae. Witt (174) quotes a study (158) from Pioneer 10 at 3 AU (so that both the airglow and zodiacal light are negligible) in which Toller (158) finds the albedo at 0.44 µm to be 0.61 ± 0.07, and g = 0.60 ± 0.22. Grains exhibit strong forward throwing scattering in the optical.

In the UV, there are surprising spatial fluctuations in the diffuse brightness of the sky, with background intensities ranging over an order of magnitude at the same wavelength (cf (77, 103, 120, 127, 155). The minimum N(H I) in the sky corresponds to A(V) approx 0.05 mag (100), or a scattering optical depth of ~ 0.06 at 0.16 µm. This translates into a sky brightness which is comparable to that observed. There may be an extragalactic component (which, in fact, is a common interpretation of the observed brightness). Clearly, the properties of grains or the intensity of any extragalactic component cannot be analyzed until the scattered intensity is known.

Reflection nebulae, in which a bright star illuminates a nearby scattering cloud, have been analyzed in some detail by various authors. Their advantages over the DGL and scattering by clouds are that they are much brighter, and that they are reflecting light from well-studied early-type stars, whereas the DLG and the clouds (discussed below) are illuminated by the much less well known interstellar radiation field (especially at UV wavelengths). Reflection nebulae suffer from three disadvantages: (a) The geometry of the star and scattering particles is not well known, and the placement of a given grain relative to the star and observer is crucial for determining how much light it scatters into the observer's line of sight. Simple geometries used in modelling the scattering, such as plane-parallel or spherical, are not so appropriate as one would like. (b) The patchiness of the dust is more serious for the reflection nebula than for the DGL or the clouds. For clumpy objects, mean values of the albedo and g determined for the clump may not represent the values for a single scattering from an individual grain. (c) Some of the scattering is at large angles, in which case the assumed form of the phase function becomes important in the analysis. Astronomical observations of scattering have been interpreted by theoretical analyses employing the simple analytical Henyey-Greenstein (HG) phase function (69), which is computationally convenient but has no physical basis. The HG function is suitable for analyzing scattering at small to modest angles (< 1 rad), in which case the important quantity is the fraction of the light thrown almost in the forward direction, but the HG function is not realistic for large-angle scattering.

Whether the advantages of reflection nebulae for determinig the scattering properties of dust outweigh the disadvantages is a matter of opinion. I feel the geometrical uncertainties are such that results should be taken with considerable caution. Witt (174, and references therein) disagrees, arguing that the brightest reflection nebulae must have a common geometry in which the intensity of scattered light is maximized. He also points out that in the UV there might be three wavelengths at which the extinction optical depth is the same (two on each side of the bump and one more in the steeply rising part of the extinction law at very short wavelengths; see Figure 2). In this case, differences in the scattered light relative to illuminating star's luminosity directly reflect changes in the grains' albedo. His conclusion that g is smaller (more isotropic scattering) at lambda < 2000 Å than for longer wavelengths seems correct.

Possibly small, relatively isolated interstellar clouds (``globules'') contain dust that is more like outer-cloud dust than diffuse dust, but the determination of their optical properties is still of considerable interest. The geometry of scattering from globules at high enough latitude to be seen against a dark background (free from the DGL in the plane) is better known than for other reflection nebulae. At optical wavelengths, a cloud is seen strongly limb brightened from scattered radiation from behind (52), which is a direct indication of highly forward-scattering by the grains in the optical. If the scattering were isotropic, the center of the cloud (with the greatest optical depth) would be brightest. Mattila (116) determined an albedo of ~ 0.6 and g approx 0.75 by comparing the brightnesses of two globules at different latitudes and assuming that their dust is intrinsically similar.

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