3.1. Extinction (Scattering, Absorption) and Polarization

3.1.1. Interstellar Extinction and Polarization Curves

"The extinction curve is a sharp discriminator of
(dominant) size, but a very poor discriminator of composition."

-- H.C. van de Hulst [1989]

The most extensively studied dust property may be the interstellar extinction. The main characteristics of the wavelength dependence of interstellar extinction - "interstellar extinction curve" - are well established: a slow and then increasingly rapid rise from the IR to the visual, an approach to levelling off in the near UV, a broad absorption feature at about ^-1 4.6 µm^-1 ( 2175 Å) and, after the drop-off, a "final" curving increase to as far as has been observed ^-1 8 µm^-1. We note here that the access to the UV was only made possible when observations could be made from space, first by rockets and then by satellites (OAO2 and IUE).

The optical/UV extinction curves show considerable variations which are correlated with different regions. ⁽¹¹⁾ Cardelli, Clayton, & Mathis (1989) found that the extinction curves over the wavelength range of 0.125 µm 3.5 µm can be fitted remarkably well by an analytical formula involving only one free parameter: R_V A_V / E(B - V), the total-to-selective extinction ratio. Values of R_V as small as 2.1 (the high latitude translucent molecular cloud HD 210121; Larson, Whittet, & Hough 1996) and as large as 5.6 (the HD 36982 molecular cloud in the Orion nebula) have been observed in the Galactic regions. More extreme extinction curves are reported for gravitational lens galaxies: R_V = 1.5 for an elliptical galaxy at a lens redshift z_l = 0.96 and R_V = 7.2 for a spiral galaxy at z_l = 0.68 (Falco et al. 1999). The Galactic mean extinction curve is characterized by R_V 3.1. The optical/UV extinction curve and the value of R_V depend on the environment: lower-density regions have a smaller R_V, a stronger 2175 Å hump and a steeper far-UV rise (^-1 > 4 µm^-1); denser regions have a larger R_V, a weaker 2175 Å hump and a flatter far-UV rise.

The near-IR extinction curve (0.9 µm 3.5 µm) can be fitted reasonably well by a power law A() ~ ^-1.7, showing little environmental variations. The extinction longward of 3 µm is not as well determined as that of 3 µm. Lutz et al. (1996) derived the 2.5-9 µm extinction law toward the Galactic Center (GC) based on the ISO observation of the hydrogen recombination lines. They found that the GC extinction law has a higher extinction level in the 3-8 µm range than the standard Draine (1989a) IR extinction curve. ⁽¹²⁾

Existing grain models for the diffuse interstellar medium are mainly based on an analysis of extinction (Mathis, Rumpl, & Nordsieck 1977; Greenberg 1978; Hong & Greenberg 1980; Draine & Lee 1984; Duley, Jones, & Williams 1989; Mathis & Whiffen 1989; Kim, Martin, & Hendry 1994; Mathis 1996; Li & Greenberg 1997; Zubko 1999a; Weingartner & Draine 2001a). All models are successful in reproducing the observed extinction curve from the near IR to the far-UV. The silicate core-organic refractory mantle model and the (modified) silicate/graphite model are also able to fit the HD 210121 extinction curve which has the lowest R_V value (Li & Greenberg 1998d; Larson et al. 2000; Clayton et al. 2000; Weingartner & Draine 2001a) and the Magellanic clouds extinction curves (Rodrigues et al. 1997; Zubko 1999b; Clayton et al. 2000; Weingartner & Draine 2001a). The fact that so many different materials with such a wide range of optical properties could be used to explain the observed extinction curve indicates that the interstellar extinction curve is quite insensitive to the exact dust composition. What the extinction curve does tell us is that interstellar grains span a size ranging from ~ 100 angstrom to submicron (Draine 1995).

The general shape of the polarization curve is also well established. It rises from the IR, has a maximum somewhere in the visual (generally) and then decreases toward the UV, implying that the aligned nonspherical grains are typically submicron in size, and the very small grain component responsible for the far-UV extinction rise is either spherical or not aligned.

The optical/UV polarization curve P() can also be fitted remarkably well by an empirical function known as the "Serkowski law", involving the very same free parameter R_V as the Cardelli et al. (1989) extinction functional form through _max, ⁽¹³⁾ the wavelength where the maximum polarization P_max occurs: P() / P_max = exp[-K ln²( / _max)] (Serkowski 1973; Coyne, Gehrels, & Serkowski 1974; Wilking, Lebofsky, & Rieke 1982). The width parameter K is linearly correlated with _max: K 1.66 _max + 0.01 (Whittet et al. 1992 and references therein). ⁽¹⁴⁾

The near IR (1.64 µm < < 5 µm) polarization has been found to be higher than that extrapolated from the Serkowski law (Martin et al. 1992). Martin & Whittet (1990) and Martin et al. (1992) suggested a power law P() ^- for the near IR ( > 1.64 µm) where the power index is independent of _max and in the range of 1.6 to 2.0, 1.8 ± 0.2. ⁽¹⁵⁾

The observed interstellar polarization curve has also been extensively modelled in terms of various dust models by various workers. The silicate core-organic mantle model (Chlewicki & Greenberg 1990; Li & Greenberg 1997), the silicate-graphite model (only silicate grains are assumed to be efficiently aligned; Mathis 1986; Wolff, Clayton, & Meade 1993; Kim & Martin 1995, 1996), and the composite model (Mathis & Whiffen 1989) are all successful in reproducing the mean interstellar polarization curve (_max = 0.55 µm).

However, the processes leading to the observed grain alignment are still not well established. A number of alignment mechanisms have been proposed. The Davis-Greenstein paramagnetic dissipation mechanism (Davis & Greenstein 1951) together with other co-operative effects such as suprathermal rotation (Purcell 1979), superparamagnetic alignment (Jones & Spitzer 1967; Mathis 1986), radiative torques on irregular grains due to anisotropic starlight (Draine & Weingartner 1996, 1997) seems to be a plausible mechanism for dust in the diffuse ISM. In dense molecular clouds, non-magnetic alignment mechanisms such as streaming of grains through gas (Gold 1952; Purcell 1969; Lazarian 1994), through radiation (Harwit 1970), through ambipolar diffusion (Roberge 1996) have been studied.

The wavelength dependent albedo (the ratio of scattering cross section to extinction) measured from the diffuse Galactic light, reflecting the scattering properties of interstellar dust, provides another constraint on dust models. The silicate core-organic mantle model (Li & Greenberg 1997) and the silicate/graphite-PAHs model (Li & Draine 2001b) are shown to be in good agreement with the observationally determined albedos, whereas the albedos of the composite grain model (Mathis 1996) are too low (Dwek 1997).

Scatterings of X-rays by interstellar dust have also been observed as evidenced by "X-ray halos" formed around an X-ray point source by small-angle scattering. The intensity and radial profile of the halo depends on the composition, size and morphology and the spatial distribution of the scattering dust particles (see Smith & Dwek 1998 and references therein). A recent study of the X-ray halo around Nova Cygni 1992 by Witt, Smith, & Dwek (2001) pointed to the requirement of large interstellar grains, consistent with the recent Ulysses and Galileo detections of interstellar dust entering our solar system (Grün et al. 1994; Frisch et al. 1999; Landgraf et al. 2000).

¹¹ Greenberg & Chlewicki (1983) found that the strength of the 2175 Å hump and the far-UV extinction can vary both independently and with respect to the visual extinction. This may imply that the 2175 Å hump and the far-UV extinction are produced by two different dust components. Back.

¹² The silicate core-organic refractory mantle model (Greenberg 1989; Li & Greenberg 1997) may provide a better fit to the 3-8 µm extinction curve than the silicate-graphite model (Mathis et al. 1977; Draine & Lee 1984) because the carbonaceous organic material is IR active at > 5 µm due to C = C, C = O, C - OH, C N, C - NH₂ stretches; CH, OH, and NH₂ deformations, and H wagging (Greenberg et al. 1995). Back.

¹³ R_V (5.6 ± 0.3)_max (_max is in micron; see Whittet 1992); i.e., the wavelength of maximum polarization _max shifts with R_V in the sense that it moves to longer wavelengths as R_V increases which is the effect of increasing the particle size. Back.

¹⁴ The far-UV polarization observations only became available in recent years as a consequence of the Wisconsin Ultraviolet Photo-Polarimetry Experiment (WUPPE) (Clayton et al. 1992) and the UV polarimetry of the Hubble Space Telescope (Somerville et al. 1993, 1994; Clayton et al. 1995). It is found that (1) lines of sight with _max 0.54 µm are consistent with the extrapolated Serkowski law; (2) lines of sight with _max 0.53 µm show polarization in excess of the extrapolated Serkowski law; (3) two lines of sights show a polarization feature which seems to be associated with the 4.6 µm^-1 extinction hump (Clayton et al. 1992; Anderson et al. 1996; Wolff et al. 1997; Martin, Clayton, & Wolff 1999). Back.

¹⁵ Martin et al. (1999) proposed a more complicated formula - the "modified Serkowski law" - to represent the observed interstellar polarization from the near IR to the far UV. Back.