Study of interstellar extinction andcircumstellar dust properties with composite
porous grains
Ranjan Gupta
Inter University Center for Astronomy and Astrophysics
Pune-411007, India

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Abstract
Its is well known that the interstellar dust plays the mostimportant role in which the light seen form stars suffers
extinction. Conventional models assume Mie theoryof light scattering with solid spheres and other shapesof silicate and graphite particles of different sizes. An
extension of this theory was Effective Medium Theory(EMT) which tries to explain some of the observed interstellar properties.

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Abstract ... contd.
Recent space probes have confirmed that the dust
grains are highly porous and fluffy (i.e. aggregatesor clusters) rather than having regular shapes (spherical,cylindrical or spheroidal) and homogeneous in composition and structure. Since their is no exact theory
for calculation of scattering properties of such irregular, inhomogeneous particles, recently our group has
used Discrete dipole approximation (DDA) method andthe results of this investigation will be discussed. The
model uses a composite fluffy dust grain for explaining most of the observed interstellar extinction curves

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Abstract ... contd.
Further, our composite dust model also explains theIR emission from circumstellar dust.
In the near future, there are a few space missions
planned by ISRO and ESA viz. ASTROSAT and GAIA
which will provide extensive platform for large coverageof UV sky and render interstellar extinction measurements where above models will be useful.

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Plan Of The Talk
Images of effects of dust and its composition
Light Scattering Basics
Scattering properties of composite grains andinterstellar extinction – REAL DUST in
Astrophysical Context
Linear polarization calculations
Abundance constraints
IR emission from dust
Laboratory Studies
Future outlook

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Dust in Astrophysical & Atmospheric Environments
Dust is a very important constituent in many astrophysical environments – though at most situations, its only
1% of the total mass in the ISM! Despite the fact that
dust grains have relatively small contribution to the total
mass, the remarkable efficiency with which such grains
scatter, absorb, polarize and re-radiate the starlight –ensures that they have significant impact on our viewsof the universe.

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Pillars of Dust
Nebula shows evaporating gaseous globules (EGGs)
emerging from pillars of molecular hydrogen gas anddust

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Bernard 68 Dark Cloud
The dependence of dust extinction at different
wavelengths (B,V,I,J,H & K bands) for a dark cloud –background stars are seen more easily in longer
wavelengths

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Rosette Nebula
Inside the Rosette nebula lies an open cluster of brightyoung stars designated NGC 2244. These stars
formed about four million years ago from the nebularmaterial and their stellar winds are clearing a hole in
the nebula’s center, insulated by a layer of dust andhot gasStudy of interstellar extinction and circumstellar dust properties with composite porous grains – p.9/81

Star forming cloud
The bright central source of heavily reddened starformation complex W3, which is completely invisible atvisual wavelengths due to heavy dust obscuration, is
one of the brightest stars in the Galaxy

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Trifid Nebula
Clouds of glowing gas mingle with lanes of dark dustin the Trifid Nebula, a star forming region towards theconstellation of Sagittarius. In the center, the threehuge dark dust lanes that give the Trifid its name allcome together

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Horse Head Nebula

The Horsehead is a plume of dust rising in front of abackground of glowing ionized gas off in one part of
the Orion Molecular Cloud complex
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Atmospheric Dust

Atmospheric dust effect seen during an eclipse

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Views of a typical Sunset

Dust and its effect seen during a typical sunset

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Dust Storm Onset

Onset of a dust storm – funnel like structure seen on a
typical hot summer day

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Sahara Dust Storm

An approaching major dust storm to be followed by athunder storm and possible rain

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Volcanic Dust
Another source of natural dust – may persist for manyweeks – spread all over the globe by winds

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Global Warming

Source of man-made dust and its effect on global
warming
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Role of Dust
The main role of dust is to obscure the light from thebackground source which could be starlight or othergeneral nebulosity. Dust causes the extinction of the
background light; affects the polarization and also
provides abundance contraints.
All the three aspects:(1) Extinction(2) Polarization(3) Abundance contraints
have been studied in the past decade by our group.
Further recently, we have used composite silicate
grains to explain the IR emission from circumstellar
dust.
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Light Scattering Basics
Average total extinction = Av = 1 magnitude kpc−1
Dust particles radius = a ∼ λExtinction Law ∝ λ−1
Extinction Cross-section = Cext = Qext π a2
Extinction Efficiency = Qext = Qsca + Qabs
(depends on 2 πa/λ & m = n - ik)
Density of Dust = ρ ∼ 1.2 × 10−23 kg m−3
Gas to Dust Ratio = ρ(dustparticles)/ρ(gas) ∼ 10−2

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Light Scattering Basics .. contd.
Number density per unit volume along the line ofsight to a distant star = ndLength of Cylinderical Column = L
Number of Grains contained in a cylindericalcolumn of length L and unit cross-section area =Nd = nd L
If instead of constant radius a, we have a size
distributionZNd =n(a)daStudy of interstellar extinction and circumstellar dust properties with composite porous grains – p.21/81

Light Scattering Basics .. contd.
Number of Dust grains per unit volume having
radius in the range of a and a+da = n(a)da∝ a−3.5 da(Mathis et.al. 1977 – power law grain size
distribution – MRN Law)
Total Extinction =2Q
Aλ = 1.086NC=
1.086N
πa
ext
ext
d
d
Z
= 1.086π a2 Qext n(a)daZ a2=πa2 Qext a−3.5 daa1

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References on Dust Modeling by
our group
Vaidya & Gupta, A & A, 328, 634 (1997)
Vaidya & Gupta, A & A, 348, 594 (1999)
Vaidya, Gupta, Dobbie & Chylek, 375, 584 (2001)
Gupta, Mukai, Vaidya, Sen & Okada, A & A, 441,
555 (2005)
Gupta, Vaidya, Dobbie & Chylek, Astrophys. Sp.
Sci., 301, 21 (2006)
Vaidya, Gupta & Snow, MNRAS, 371, 791 (2007)
Vaidya & Gupta, JQSRT, 110, 1726 (2009)
Roy, Sharma & Gupta, JQSRT, 110, 1733 (2009)
Roy, Sharma & Gupta, JQSRT, 111, 795 (2010)
Vaidya & Gupta, A&A, 528, 457 (2011)

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SolidSpheres
Spheroids

v/s

Solid

Extinction efficiencies Qext (spheroid)/Qext (sphere) v/s
Wavelength for different grain sizes and axial ratios for
Silicate and Graphite grains with T-Matrix.
Oblates have axial ratios > 1.0 and Prolates have axial
ratios < 1.0 and sphere has axial ratio=1.0
Gupta et al., A&A, 441, 555 (2005)

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Silicate Spheroids

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Graphite Spheroids

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Graphite Bump Region

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Interstellar Extinction(Solid grains)

CurvesComparison of Observed Interstellar Extinction curves
with the best fit model combination curves ofspheroidal silicate and graphite grains with various
axial ratios using T-Matrix

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Int. Ext. Curve .. contd.
Bump Region

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Extinction and linear polarization(Solid Grains)
Interstellar Extinction (Qext ) and Linear Polarization(Qpol ) for aligned oblate spheroids (silicates andgraphites) with grain size a=0.1µ. Various axial ratios(AR) and orientation angles of alignments have been
computed.

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T-Matrix computations .. contd.
Interstellar Extinction (Qext ) and Linear Polarization(Qpol ) for aligned prolate spheroids (silicates andgraphites) with grain size a=0.1µ. Various axial ratios(AR) and orientation angles of alignments have been
computed.

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Observed Interstellar Extinction
Curve
Observed Interstellar Extinction is compared with thebest fit model curve of a combination of silicate andgraphite grains with axial ratio AR=1.33 using a grain
size distribution of 0.005-0.250µ in steps of 0.005µ.
Lower panel highlights the UV bump region.

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EMA & T-Matrix
Fitting of Observed Extinction curve with Effective
Medium Approximation (Maxwell-Garnet mixing rule)and T-Matrix computation

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Discrete-Dipole(DDA) Basics

Approximation

Computation for solid spheres which are homogeneous andisotropic (cylinders and some more shapes are also possible) could be done by Mie scattering theory. It is clear that
dust grains cannot be solid spheres or of same composition since observation of interstellar and other polarization
requires non-spherical grains. T-Matrix and some other exact methods can be used to model non-spherical grains but
usually of single composition.

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DDA for computing light scattering of particles – originallydeveloped by Purcell & Pennypacker (1973) can handle
non-spherical grains. DDA replaces the solid grain by anarray of N point dipoles, with the spacing between the
dipoles small compared to the wavelength. Each dipole
has an oscillating polarization in response to BOTH an
incident plane wave and the electric fields due to all of theother dipoles in the array (see Draine, ApJ, 333, p848-872,
1988 for more details on DDA method).

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"Spherical" Dipole Arrays

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Dipole Polarization within the"Spherical" Arrays

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Validity Criteria fo DDA
Grain volume V is represented by an array of N
discrete dipoles – physical size of the grain ischaracterized by the "equivalent radius"
aeq = (3V /4 ∗ π)1/3 – i.e. radius of a sphere ofequivalent volume. The nearest neighbour distance
between the dipoles is d = aeq ∗ (4 ∗ π/3N )1/3
(a) The DDA is valid only when the N is large enough(d is small enough compared to the aeq ) such that theboundary of the cubic array satisfactorily approximates
the desired grain shape.
(b) Another criteria is |m|kd < 1 – where m is the complex refractive index; k is π/λ and d is the lattice spacing.
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Validity Criteria .. contd.

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Validity Criteria .. contd.
Table 1: DDA validity criteria in Optical/UV
λ (µm)

3.40002.20001.00000.70000.55000.30000.20000.15000.1000N=9640 14440 25896
a(µ)
a(µ)
a(µ)
4.00
5.00
6.00
2.50
3.50
4.00
1.20
1.40
1.60
0.80
1.20
1.00
0.60
0.96
0.80
0.40
0.50
0.45
0.22
0.30
0.25
0.14
0.20
0.16
0.10
0.16
0.12
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Validity Criteria in IR
Table 2: DDA validity criteria showing the |m|kd ≤1 values for each model in IR region for maximum
grain size of a=0.250µ.
λ (µm) N=9640

5.0
10.0
15.0
20.0
25.0

0.041
0.021
0.015
0.011
0.005

14440 25896
0.030 0.022
0.014 0.011
0.011 0.005
0.007 0.003
0.002 0.001

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Porosity
Porosity P is defined as:
P = 1 − Vsolid /Vtotal ; where Vsolid is the volume of thesolid material inside the grain and Vtotal is the total volume of the grain. Porosity varies between 0 < P < 1

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Axial Ratios & No. of Inclusion (no. of dipoles/inclusion)

Inclusions

Inclusion

Fractions

N=9640

f=0.1

f=0.2

AR=1.33

32/24/24

16/12/12

1(1184)2(1184)8/6/6

6(152)

11(152)16(152)

4/3/3

38(16)

76(16)

114(16)

N=25896

f=0.1

f=0.2

f=0.3

AR=1.50

48/32/32

12/8/87(432)

13(432)19(432)

6/4/4

54(56)

108(56)

162(56)

3/2/2

216(8)

432(8)

648(8)

N=14440

f=0.1

f=0.2

f=0.3

AR=2.00

48/24/24

16/8/83(536)

6(536)

8(536)

12/6/66(224)

11(224)16(224)8/4/423(64)

46(64)

68(64)

f=0.3

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Orientation Averaging
β from 0 to 180 degrees in 3 steps
θ from 0 to 90 degrees in 3 steps
φ from 0 to 180 degress in 3 steps

Total 27 orientations are good enough

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Composite Grains
It is very unlikely that interstellar grains have regularshapes (spherical/cylinderical/spheroidal) or that they
are homogeneous in compostion and structure. It has
been proven that (from balloon observations and otherflyby missions) the real dust grains are porous; fluffy
and non-spherical – rather than solid spheres as was
assumed in Mie theory for computation of light scattering properties by dust grains.

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Composite Grains .. contd.

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Composite Grains .. contd.

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Composite Grains .. contd.

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Composite Grains .. contd.

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Aerogel Dust Tracks from Impact
missionStudy of interstellar extinction and circumstellar dust properties with composite porous grains – p.50/81

Simulated Grains
Multi-component-composite; size distribution andporous etc.

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Simulated Grains .. contd.

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Composite Grains with Inclusions
A typical Non-spherical Composite grain with a total of
N=9640 dipoles with the inclusions embedded in thehost spheroid such that only the ones placed at outer
periphery are seen. (Gupta et al., Astrophys. Space
Sci., 301, 21 (2006))

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Composite Grains with Inclusions .. contd.

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Showing the Inclusions

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Interstellar Extinction with composite grains
Gupta et al., Astrophys. Space Sci., 301, 21 (2006)

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Int. Ext. .. contd.

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Cometary Polarization
3D plots of Scattered Intensity (S11) and Linear Polarization (P) for Composite Spheroidal Grains (N=14440& 152) with silicate as host sphere and 20 % graphite
as inclusion. The vertical axes are for S11 and P; theaxes marked as θ denotes the Scattering angle (X 10◦ )in the range 0 to 180◦ and the third axis is for the grain
size a=0.0-1.0µ. The wavelength for these calculationsin the K-band at 2.2 µm.

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Cometary Polarization .. contd.

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Cometary Polarization .. contd.
Linear Polarization (P) for Spheroidal Composite
Grains (N=25896, 14440 and 152) with silicate as hostsphere and graphite as inclusion and comparison withthe observed Polarization data for comets

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Cometary Polarization .. contd.
Note that some comets show the negative branch ofpolarization at large scattering angles (i.e. > 150◦ ) but
not all comets show this negative branch in the K-band(Kelly et.al. 2004). Our models do not show this negative branch but the overall curves resemble well withthe observations. Calculations are in progress for using
fractal aggregate monomers as a model for dust grains
which can reproduce the negative branch of polarization.

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Interstellar Polarization by Composite Grains
Linear Polarization for N=9640 dipoles and twovolume fractions (f=0.05 & 0.10) and comparison with
Serkowski’s Law (Vaidya et al. 2007, MNRAS, 371,
791)

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Abundance Constraints & Carbon Crisis
Table 3: Abundance Ratios
Abundance Ratio ISM Other Models Our Model
(ppm)
C/H
110
254
160
Si/H
17
32
25
ISM Value: Estimated by Mathis, JGR, 105, 10269(2000)
Other Models: Li & Draine, ApJ, 554, 778 (2001)
Our Model (Vaidya et al. 2007, MNRAS, 371, 791)

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Abundances .. contd.
Calculations with our models predict lower values for
Carbon and Silicon abundances as compared to othercomposite models but a further reduction is warranted
to match the estimated ISM values and this could beachieved by introducing a 3rd component in thecomposite grain like SiC, amorphous carbon and
PAH’s etc.
The calculations have been done by using the VolP P
ume Extinction Coefficient Vc =V/ Cext (λ) for ob-

taining the abundances for our models (spheres andspheroids) with various axial ratios and porosities etc.

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Light Scattering Codes
http://www.astro.spbu.ru/staff/staff/ilin2/SOFTWARE/
http://www.astro.princeton.edu/∼draine/DDSCAT.html
http://www.giss.nasa.gov/∼crmim/t_matrix.html

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IR emission from circumstellar
dust
Composite grain model has been used to compute IR
fluxes in the 5-25µm region at several dust temperatures T=200-350◦ K and compared with the IRAS-LRS
average observed curves and also for two other typicalstars which are known to have strong Silicate emission
features at 10 and 18 µm.

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IR flux comparison with composite models and observed fluxes
Best fit χ2 minimized composite grain models (silicateswith graphite inclusions) plotted with the averageobserved infrared flux for IRAS-LRS curve and twoother stars (A&A, 528, 457, 2011)

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Analytical formulae for Interstellar Extinction

Figure 1: Analytical formulae fit to the observed
averaged Extinction Curve – JQSRT, 111, 795(2010)
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Extinction modeling in various
galaxy directions
12
Si+0.1Gr N=25896

10

Si+0.2Gr N=9640

8
6
4
2
12

HD93222

HD96042
Si+0.3Gr N=14440

10

Si+0.1Gr N=14440

8
6
4
2
12

HD37021

HD13267
Si+0.1Gr N=14440

10
8
6
4

HD37903

2
3

4

5

6

73

4

5

6

7

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Conclusions & Future Outlook
We have demonstrated that Spheroidal Composite
Grain models can explain the observed interstellar
extinction curve, the observed linear polarization
curve and also provides a lower estimates for the
Carbon abundance which brings closer to theobserved ISM values.
Several workers have recently reported thatporous and spheroidal composite dust grains of
the type proposed in our models may be the best
option for explaining the above observed
parameters:

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Future Outlook .. contd.
Padoan et. al., ApJ, 649, 807 (2006)
Perets & Biham, MNRAS, 365, 801 (2006)
Stark et. al., A&A, 457, 365 (2006)
Pelkonen et. al., A&A, 461, 551 (2007)
Iati et. al. MNRAS, 384, 591 (2008)
We are have also attempted to compute the IR
emission with the spheroidal composite dust
model to explain the IRAS observations as well as
the COBE data on diffuse IR emission (Dwek, ApJ,
484, 779, 1997). This will further constrain theInterstellar Dust models (Zubko et. al., ApJS, 152,
211, 2004)

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Future Outlook .. contd.
Upcoming dedicated space missions(ASTROSAT-UVIT and GAIA) will bring out large
data base of extinction measurements in many
directions of the galaxy and would help in the
study of dust distribution within the galaxy by fittingthese measurements with Spheroidal Composite
dust models. (Bora et al. MNRAS, 384, 827, 2008
– using simulated data for expected output of
TAUVEX/ASTROSAT bands – obtain interstellar
extinction and Bora et al. New Astronomy, 14, 649,
2009)

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Extinction Estimate

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Future Outlook .. contd.
X-ray scattering is a powerful toll for measuring thesize distribution and composition of interstellar
dust. Smith & Dwek 1998 (ApJ, 503, 831) havestudied the soft X-ray scattering of dust halosaround Nova Cygni 1992 using Mie theory, buthave mentioned that DDA can be used for thisstudy since 1keV photon has only λ = 1.24 Åwhich is substantially smaller than the radius ofany grain.

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Future Outlook .. contd.
Thus X-ray scattering will be affected by the grain’s exact morphology. X-ray observations from ASTROSAT
for similar objects and corresponding modeling efforts
using composite DDA grains in the X-ray region can
provide better insight for understanding the dust behaviour.

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Dark Star Forming Clouds CB3

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Dark Star Forming Clouds CB25

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Dark Star Forming Clouds CB39

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Normal BVR Photometry

Correlation of Polarization v/s Extinction
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Strömgren Photometry5

Observed Linear Polarization (%)

Piehl et al., 2009, submitted to AJ
4

uvbyHbeta photometry: R=0.81
CB3(16), CB39(1), CB25(2), CB52(4), CB54(19), CB246(2)

3

2

1

0
-0.5

0

0.5
E(B-V)

1

1.5

Correlation of Polarization v/s Extinction
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Thanks!

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