Synthetic Extinction Curves

Weingartner & Draine (2001) and Li & Draine (2001) have developed a carbonaceous-silicate grain model which successfully reproduces observed interstellar extinction, scattering, and infrared emission. The model consists of a mixture of carbonaceous grains and silicate grains, each with a broad size distribution extending from a = 3.5 Angstrom ultrasmall grains (containing tens of C atoms) to micron-sized particles. The size distribution includes two log-normal distributions, with characteristic radii a_0=3.5 Angstrom and 30 Angstrom, and width parameters sigma=0.4 (see Weingartner & Draine 2001, eq. 2,3), plus two modified-power-law size distributions with smooth cutoffs at large sizes (see Weingartner & Draine 2001, eq. 4-6)

The smallest carbonaceous grains have the optical and physical properties of PAH (polycyclic aromatic hydrocarbon) molecules. The larger (a > 100 Angstrom) carbonaceous grains are assumed to have the optical properties of graphite spheres. The silicate grains have optical properties appropriate to amorphous olivine, with the far-infrared opacity adjusted to reproduce the observed far-infrared and submm emission from interstellar dust (see Li & Draine 2001).

Draine (2003a) discussed the available evidence for dust extinction per unit H column in regions with different extinction curves. Based on this discussion, we have renormalized the size distributions of Weingartner & Draine (2001). For R_V=3.1, we have reduced the grain abundance per H by a factor 0.93 For R_V=4.0, we have taken the "A" model of Weingartner and Draine (2001) and increased the grain abundance per H by a factor 0.93*1.27=1.18. For R_V=5.5, we have taken the R_V=5.5 "A" model of Weingartner & Draine (2001) and increased the grain abundance per H by a factor 0.93*1.52=1.42

Dielectric functions were recently revised by Draine (2003b,c), including realistic structure at X-ray absorption edges of C, O, Mg, Si, and Fe.

As described in Draine (2003a) and Draine (2003b), extinction, absorption, albedo, <cos(theta)>, and <cos^2(theta)> have been calculated for wavelengths from 1 cm (30 GHz) to 1 Angstrom (12.4 keV), for selected mixtures of carbonaceous grains and amorphous silicate grains:

  • Milky Way, R_V = 3.1: Weingartner & Draine (2001) Milky Way size distribution for R_V=3.1 with C/H = b_C = 60 ppm in log-normal size dists, but renormalized by a factor 0.93 (now has C/H= 60*0.93 = 55.8 ppm in log-normal size distributions). This grain model is considered to be appropriate for the typical diffuse HI cloud in the Milky Way.
  • Milky Way, R_V = 4.0: Weingartner & Draine (2001) Milky Way size distribution "A" for R_V=4.0 with C/H = b_C = 40 ppm in log-normal size dists, renormalized by a factor 1.18 (now has C/H = 40*1.18 ppm = 47.2 ppm in log-normal size distributions).
  • Milky Way, R_V = 5.5: Weingartner & Draine (2001) Milky Way size distribution "A" for R_V=5.5 with C/H = b_C = 30 ppm in log-normal size dists, renormalized by a factor 1.42 (now has C/H = 30*1.42 = 42.6 ppm in log-normal size distribution).

    These older results continue to be available, based on the size distributions and dielectric functions as described in Weingartner & Draine (2001):

  • Milky Way, R_V = 3.1: Weingartner & Draine (2001) Milky Way size distribution for R_V=3.1 with C/H = b_C = 60 ppm in log-normal size dists.
  • Milky Way, R_V = 4.0: Weingartner & Draine (2001) Milky Way size distribution "B" for R_V=4.0 with C/H = b_C = 40 ppm in log-normal size dists.
  • Milky Way, R_V = 5.5: Weingartner & Draine (2001) Milky Way size distribution "B" for R_V=5.5 with C/H = b_C = 30 ppm in log-normal size dists.
  • HD 210121: Weingartner & Draine (2001) HD 210121 dust model with C/H = b_C = 40 ppm in log-normal size dists.
  • LMC avg: Weingartner & Draine (2001) "LMC average" size distribution with C/H = b_C = 20 ppm in log-normal size dists.
  • LMC 2: Weingartner & Draine (2001) "LMC 2" size distribution with C/H = b_C = 10 ppm in log-normal size dists.
  • SMC bar: Weingartner & Draine (2001) "SMC bar" size distribution with C/H = b_C = 0 in log-normal size dists.

    for wavelengths running from 0.01 micron to 1 cm. Here b_C = total C/H in the two log-normal size distributions of ultrasmall carbonaceous grains.

    N.B.: The tabulated opacity K_abs is the ratio (dust absorption cross section)/ (dust mass). To obtain the ratio (dust absorption cross section)/(total mass), the tabulated K_abs should be divided by (1+M_gas/M_dust). For the Milky Way dust mixtures, (1+M_gas/M_dust) = 125.

    References:

  • Draine, B.T. 2003a, "Interstellar Dust Grains", Ann. Rev. Astr. Ap., 41, 241-289 (pdf)
  • Draine, B.T. 2003b, "Scattering by Interstellar Grains. I. Optical and Ultraviolet", Astrophys. J., 598, 1017-1025 (pdf)
  • Draine, B.T. 2003c, "Scattering by Interstellar Grains. II. X-Rays", Astrophys. J., 598, 1026-1037 (pdf)
  • Li, A., & Draine, B.T. 2001, "Infrared Emission from Interstellar Dust. II. The Diffuse Interstellar Medium", Astrophys. J., 554, 778-802 (pdf or gzipped PostScript)
  • Weingartner, J.C., & Draine, B.T. 2001, "Dust Grain Size Distributions and Extinction in the Milky Way, LMC, and SMC", Astrophys. J., 548, 296-309 (pdf or gzipped PostScript)
  • The URL of this page is http://www.astro.princeton.edu/~draine/dust/dustmix.html

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