Lecture 6: Dust Grains

Dr Graham M. Harper

School of Physics, TCD

Tutorial: Jan 16 Mon 14:00-15:00

PY4A04 Senior Sophister

Physics of the Interstellar and

Intergalactic Medium

Lecture 6: Dust Grains

Dr Graham M. Harper

School of Physics, TCD

PY4A04 Senior Sophister

Physics of the Interstellar Medium

6. Dust Grains (soot and stardust)

Evidence for dust

Depletion, condensation sequence

pre-solar dust grains

extinction of starlight

polarization (extinction and emission)

Formation and Destruction

Optical Properties

Extinction, scattering, albedo, phase

Dust grain temperatures

3

Element Depletion LISM

•Compare abundances observed in the gas with the cosmic standard (solar abundance)

• Typically there are deficiencies in the abundances and it is assumed that these ions are trapped on dust grains

Dust condensation sequence

50% element

condenses out

in solid form

Star stuff & the pre-solar nebula

Credit Busso et al. 1999 ARAA, 37, 239

Diamond

Diamond

1000 atoms

Isotopic xenon and

nitrogen abundances

suggest supernova

origins

Photo credit T. Daulton

Graphite

Graphite

<20 μm (micron)

Onion like structure

Asymptotic giant

branch (AGB),

massive star, or

supernova origin

Photo credit S. Amari

Silicon carbide

Silicon carbide

0.1-20 μm

Most carbon rich AGB

stars, supernovae and

nova

Aluminium Oxide (Al2O3), Spinel (MgAl2O4),

Titanium Oxide (TiO2)

Aluminium oxide

(shown)

3 μm

Oxygen rich red giants

and AGB stars

Less well studied

Extinction (refresher)

ApcdMm 10log5 10

m = apparent magnitude of star

M = absolute magnitude

d = distance (pc)

Aλ= the extinction due to dust

Ad

dm

2

110log5

E(λ1-λ2) = color excess 212121 AAmmE

Compare a reddened star to a nearby one with same spectral-type

LCn extd Dust optical depth

Extinction and optical depth

A086.1

3.58.2:1.3~)(

rangeVBE

AR V

V

τ = dust optical depth, nd = dust density, L = path length

Cext(λ)= extinction cross-section

RV is ratio of total to selective extinction and depends of the

nature of the dust, and as dust extinction decreases at long

wavelengths, e.g., infrared, we have

E(B-V) Johnson colour system

)(

lim

VBE

VERV

Interstellar dust extinction

More than one grain type present

Polarization by extinction

Linear polarization

Starlight has been observed up to 7% polarized

Circular polarization is much weaker

minmax

minmax

II

IIP

Linear polarization

Starlight has been observed up to 7% polarized

Circular polarization is much weaker

Implies non-spherical grains, AND not randomly oriented

[Serkowski Figure] maximum polarization 0.55 μm

For dielectric grains of radius, a

For refractive index, m=1.5 (silicates) this implies

minmax

minmax

II

IIP

amm 1255.0max

ma 18.0

Why is dust Polarized?

Polarization by Absorption Polarization by Emission

~ FIR - mm ~ UV - NIR

Diagrams after A. Goodman: http://cfa-www.harvard.edu/~agoodman/ppiv/

P (sub-mm)

orthogonal to

P (extinction)

CSO:

OMC-2 (Orion)

350 m

SHARC+ polarimeter

Polarization by emission

Different wavelength properties

Whittet 2004

Dust Formation I

Formation within the ISM (standard argument)

Consider initial grain of radius r(0) – the “seed”

density of solid = s (mass per unit volume)

mass = mi and thermal velocity vi

sticking coefficient = ϵ

equate mass increase associated with change in radius, dr

then calculate the rate of sticky collisions

dnmsdrr i24

2rndt

dnii dtrndr

m

srii

i

224

Dust Formation II

Time to grow from an initial seed to radius 0.1μm

BIG PROBLEM!

This also assumes that the abundance of

sticking atoms is not depleted which occurs on

when nH=20 cm-3

could be even shorter for molecular clouds

Whence stardust? High densities, and

supersaturated vapours and condensation

sequence implies stellar winds and shocks

yrt

9103

ts

mnrtr iii

40

yrtatom

7104

Dust Destruction

[1] High dust temperature causes molecules to sublimate

from grains, Tdust > 20-40 K

[2] Sputtering: collisions with thermal atoms and ions

more important for coronal ISM

[3] Absorbing high energy photons 5-13 eV can liberate a

molecule from the grain

[4] Shattering - grain-grain collisions: head-on collision at

few km s-1 with evaporate both grains – shocks

[2] and [4] destroy, and [4] create a dust size distrubution

Grain optical properties I

extinction efficiency Qext defined as

2

,

a

aCQ ext

ext

scaabsext QQQ

The extinction is broken down into pure absorption and scattering.

The albedo is defined as

ext

sca

Q

Q

In thermal equilibrium the emission coefficient for grains of radius a is

solidabsd TBaQnj 2

scaabsrp QgQQ 1Cross-section for radiation pressure

Mie Scattering theory

Spheres of radius “a” and complex index of refraction m=n+ik

Dielectric constant ϵ=m2

Boundary value problem

Define the dimensionless parameter: x

m: large limiting case

m=1.33 : ice particles at visual wavelengths

m=1.33 + 0.09i : ice with impurities = dirty ice

m=1.27 + 1.37i : spheres of iron

ax

2 Circumference

Wavelength

Scattering

Rayleigh Scattering

When x << 1 (particles small compared wavelength)

And |mx| << 1

2

2

24

2

1

3

8

m

mxQsca

2

1Im4

2

2

m

mxQabs

Rayleigh scattering λ-4

Absorption decreases

Aside: Dust Distributions

In practice we have to consider a range of dust radii:

Mathis-Rump-Nordsieck (MRN) form for 0.005< a<0.25μm

daadaan 5.3

a

a

ext daaCan ,Need to include distribution in

optical depth

Grain properties II

extinction efficiency Qext often approximated by

with

and β is between 1-2

for crystalline dielectrics β=2 at low frequencies

for metallic material β=2

amorphous 3-D structures β=2

graphite (layered) or amorphous carbon β=1

00

0

0

0

forQ

forQQabs

12

1 00 xa

candQ

Grain temperatures

Steady equilibrium between

absorbed galactic radiation and

dust emission

dJQE absdustabs

0

4

dTBQE dustabsdustemis ,40

Example: dust clouds

illuminated by hot stars

(like reflection nebula)

part scattered, part heated

Grain temperatures II

Radiation field given by (sum of) dilute hot blackbody(s)

4

*,4

1TBzWdIJ

W = radiation dilution factor: fractional solid angle subtended by star

R R

2

112

1

R

R

R

RW

Grain temperatures

Temperature for grains of size a

dTBQdTBQzW dustabsdustabsdust ,4,40

*

0

Example for gray extinction Qabs = Constant (β =0), and dust

cloud illuminated by hot star (like reflection nebula)

Recall

41

*

44

* WTTTTW dustdust

4

0

, dustSBdust TdTB

Table 4.1 Dyson & Williams

Grain Material Radius (μm) Temperature (K)

graphite 0.05 45

silicates 0.10 42

olivine 0.05 22

0.10 20

fused quartz 0.05 19

0.10 17

Silicate (0.05)+ ice mantle 0.10 14

Different grain sizes will have different temperatures Qabs(λ,x)

Stochastic small grain heating

Small grains have

different heat capacity

compared to large

solids. UV photons

can heat individual

grains 100’s K.