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
-
Draine, B.T., & Lee, H.M. 1984, "Optical Properties of Interstellar Graphite
and Silicate Grains", Astrophys. J. 285, 89
-
Draine, B.T., & Malhotra, S. 1993, "On Graphite and the 2175A Extinction
Profile", Astrophys. J., 414, 632.
-
Laor, A., & Draine, B.T. 1993, "Spectroscopic Constraints on the Properties
of Dust in Active Galactic Nuclei", Astrophys. J. 402, 441.
-
Li, A., & Draine, B.T. 2001, "Infrared Emission from Interstellar Dust. II.
The Diffuse Interstellar Medium", Astrophys. J., 554, 778
-
Weingartner, J.C., & Draine, B.T. 2001, "Dust Grain Size Distributions and
Extinction in the Milky Way, LMC, and SMC," Astrophys. J. 548, 296
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.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.gz
dielectric function for the original "astronomical silicate".
-
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.gz
dielectric function for "smoothed astronomical silicate".
-
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.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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