Optical Properties of Interstellar Dust Grains

Bruce T. Draine, Dept. of Astrophysical Sciences, Princeton University

Dielectric Functions

As described by Draine & Lee (1984) and Laor & Draine (1993) we have constructed dielectric functions for "astronomical silicate", graphite, and silicon carbide for wavelengths from the far-infrared to X-rays.

Dielectric Function and Refractive Index for "Astronomical Silicate"

The "astronomical silicate" dielectric function comes in three versions:

The original "astronomical silicate" dielectric function constructed by Draine & Lee (1984). This used lab measurements of crystalline olivine in the vacuum ultraviolet, resulting in an absorption "feature" at 1/lambda = 6.5 um-1 which is not seen in astronomical objects, as noted by Kim & Martin (1995, Astrophys. J., 442, 172). This was extended into the X-ray region by Laor & Draine (1993).
A "smoothed astronomical silicate" dielectric function obtained by removing an absorption feature at 6.5 um-1 from Im(eps). Re(eps) is obtained from Im(eps) through the Kramers-Kronig relations. This version of "astronomical silicate" was used by Weingartner & Draine (2000).
The above dielectric function has been modified to include X-ray absorption edge structure for an assumed MgFeSiO4 composition, as discussed by Draine (2003b), including near-edge structure for olivine. This provides a dielectric function that obeys the Kramers-Kronig relations from submm to X-rays, and has the appropriate cumulative oscillator strength (i.e., "effective number of electrons") as a function of energy (see Draine 2003b). This is currently recommended. An electronically-readable file extending from 1e-5 eV to 2.0 keV is available for download: callindex.out_sil.D03

Dielectric Function and Refractive Index for Graphitic Carbon

The dielectric tensor for graphite has two eigenvalues: the dielectric function for E parallel to the c-axis, and the dielectric function for E perpendicular to the c-axis. (The "c-axis" is normal to the "basal plane"). The graphite dielectric functions are available in two versions:

The original graphite dielectric functions computed by Draine & Lee (1984), and extended into the X-ray region by Laor & Draine (1993).
The graphite dielectric functions have been reestimated by Draine (2003b), taking into account more recent estimates of the absorption cross section per C atom in the extreme ultraviolet and X-rays, with particular attention to near-edge absorption structure near the C K edge. This dielectric function satisfies the Kramers-Kronig relations from submm to X-rays, and has the appropriate cumulative oscillator strength (i.e., "effective number of electrons") when integrated over all wavelengths (see Draine 2003b). This is currently recommended.
Because graphite is a conductor, the dielectric function is separated into contributions from "bound electrons" and from "free electrons".
As discussed by Draine & Lee (1984), the total dielectric function

epsilon(E) = epsilon_{bound}(E) + epsilon_{free}(E),

where

epsilon_{free} = -(omega_p tau)^2/[(omega tau)^2 + i omega tau]

Expressions for omega_p and tau are given in Table 1 of Draine & Lee (1984) [note erratum ApJ 318, 485 correcting a typo in Table 1].
The damping time tau depends on the grain radius a; therefore we provide files for two radii, a=0.01um and a=0.1um.
Electronically-readable files of (epsilon-1) and (m-1) from Draine (2003b) are available for download:
callindex.out_CpaD03_0.01 (for E parallel to c, a=0.01 micron)
callindex.out_CpaD03_0.10 (for E parallel to c, a=0.10 micron)
callindex.out_CpeD03_0.01 (for E perpendicular to c, a=0.01 micron)
callindex.out_CpeD03_0.10 (for E perpendicular to c, a=0.10 micron)

Scattering and Absorption Cross Sections

We have also computed scattering and absorption cross sections for spherical grains of these materials, for radii ranging from 0.001 - 10 micron. Cross sections have been computed as described in Laor & Draine (1993). In brief:

Mie theory is used for |m|x < 1000, where m is the complex refractive index;
Rayleigh-Gans theory is used for |m|x > 1000 and |m-1|x < .001;
geometric optics approximation are used when |m|x > 1000 (too large for Mie theory), and |m-1|x > .001 (too large for Rayleigh-Gans theory);
for graphite (a uniaxial material), the spheres are assumed to be randomly oriented, and the "1/3-2/3" approximation is employed (for validity of this approximation see Draine & Malhotra 1993).

PAH-Carbonaceous Grains

As described by Li & Draine (2001), we approximate small carbonaceous particles as having PAH-like optical properties for N < 50,000 C atoms, going smoothly to graphitic properties for N >> 50,000 C atoms. The particle "radius" is defined in terms of the number of C atoms: N = 468*(a/.001micron)**3 We have tabulated optical cross sections for .000355 - .0010 micron radii, for 1000 - .001 micron wavelengths. For a < .005 micron, these cross sections show strong absorption features in the infrared, with the strongest features being a 3.3, 6.2, 7.7, 8.6, 11.3, 11.9, and 12.7 micron. The feature strengths depend on whether the PAH is neutral or ionized.

REFERENCES:

Draine, B.T. 2003b, "Scattering by Interstellar Dust Grains. II. X-Rays", Astrophys. J., 598, 1026 ( click here for pdf)
Draine, B.T., & Lee, H.M. 1984, "Optical Properties of Interstellar Graphite and Silicate Grains", Astrophys. J. 285, 89 ( click here for pdf)
Draine, B.T., & Malhotra, S. 1993, "On Graphite and the 2175A Extinction Profile", Astrophys. J., 414, 632. ( click here for pdf)
Laor, A., & Draine, B.T. 1993, "Spectroscopic Constraints on the Properties of Dust in Active Galactic Nuclei", Astrophys. J. 402, 441. ( click here for pdf)
Li, A., & Draine, B.T. 2001, "Infrared Emission from Interstellar Dust. II. The Diffuse Interstellar Medium", Astrophys. J., 554, 778-802 ( click here for pdf)
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 ( click here for pdf)

If you make use of the files listed below, please consider citing the appropriate references.

The following files are available:

PAH-Carbonaceous Grains (Li & Draine 2001)

PAHneu_30.gz: optical properties for PAH-graphite particles, 30 radii from .000355 - .0010 micron, wavelengths from .001 - 1000 micron
PAHion_30.gz: optical properties for PAH-graphite particles, 30 radii from .000355 - .0010 micron, wavelengths from .001 - 1000 micron

Graphite (Draine & Lee 1984; Laor & Draine 1993):

For the dielectric function and refractive index of graphite, please look above on this page.
Gra_21, Gra_21.gz, and Gra_81.gz: optical properties for graphite spheres, radii (either 21 or 81 values) from 0.001 - 10 micron, wavelengths from 0.001 - 1000 micron.
planck_Gra.gz, Planck-averaged absorption-emission cross sections for graphite spheres, for radii from 0.001 - 10 micron, and temperatures 10 - 50000K.

Original Astronomical Silicate (Draine & Lee 1984; Laor & Draine 1993):

eps_Sil and eps_Sil.gz dielectric function for the original "astronomical silicate".
Sil_21, Sil_21.gz, and Sil_81.gz: optical properties for "astronomical silicate" spheres, radii (either 21 or 81 values) from 0.001 - 10 micron, wavelengths from 0.001 - 1000 micron.
planck_Sil.gz, Planck-averaged emissivities for graphite, alpha-SiC, or "astronomical silicate" spheres, for radii from 0.001 - 10 micron, and temperatures 10 - 50000K.

Smoothed UV Astronomical Silicate (Draine & Lee 1984; Laor & Draine 1993; Weingartner & Draine 2000):

eps_suvSil and eps_suvSil.gz dielectric function for "smoothed astronomical silicate".
suvSil_21, suvSil_21.gz, and suvSil_81.gz: optical properties for "smoothed UV astronomical silicate" spheres, radii (either 21 or 81 values) from 0.001 - 10 micron, wavelengths from 0.001 - 1000 micron.
planck_suvSil.gz, Planck-averaged absorption cross sections for "smoothed UV astronomical silicate" spheres, for radii from 0.001 - 10 micron, and temperatures 10 - 50000K.

Silicon Carbide (Laor & Draine 1993):

eps_SiC and eps_SiC.gz: dielectric function for alpha-SiC.
SiC_21, SiC_21.gz, and SiC_81.gz: optical properties for alpha-SiC spheres, radii (either 21 or 81 values) from 0.001 - 10 micron, wavelengths from 0.001 - 1000 micron.
planck_SiC.gz, Planck-averaged absorption cross sections for SiC spheres, for radii from 0.001 - 10 micron, and temperatures 10 - 50000K.

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