physics of the interstellar and intergalactic medium · 2016-01-11 · lecture 6: dust grains dr...
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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.