Download Speck-ulations on Big Dust

SPM inclusions
Speck-ulations on Big Dust
Alyssa A. Goodman
Harvard University Astronomy Department
Essential Physical Properties of Dust
Size Distribution
– MRN: N(a) ~ a-3.5... how often applicable?
Composition
– effects emissivity, Q
» QFIR~λ−β
β=0 for pure blackbody; β~1 for amorphous, layerlattice material; β~2 for metals & crystalline dielectrics
Shape (“Fluffiness”, “Compactness”)
– effects surface area & sticking properties
Size: Which Grains Matter Most?
2

a
F = N 2 Q B (T )
D 
Q
x=2πa/λ
ISM: N(a)~a-3.5
Grain Size Distribution in the ISM
–N(a)~a-3.5
(Mathis, Rumpl & Nordseick 1977)
–BUT both slope and
upper & lower size
cutoffs can effect RV
observed
–RV is observed to vary
substantially in ISM!!
(recall: AV=RV E(B-V))
Cardelli, Clayton & Mathis 1989.
Size Distributions: What’s In-Between?
20
10
ISM Dust (MRN)
15
Relative Number
10
10
10
5
10
0
?
10
-5
10
-10
10
-15
10
Kuiper Belt Objects (Jewitt & Luu)
-6
10
-4
10
-2
10
0
10
2
10
4
10
6
10
8
10
Particle Size [cm]
? Asteroids, Interplanetary Dust, “Big” Interstellar Dust
SEDs & Mass Determination
Flux at for N particles of size a:
 a 
F = N 2 Q B (T )
D 
2
B (T ) =
2
2 hc
5
1
exp (hc kT ) − 1
QFIR ∝
−
 =0 blackbodies

lattice =1 amorphous,
layer materials

& crystalline
 =2 metals
dielectrics
Flux at for a distribution with Na particles of each size a:
 a2 
(Note: same flux can be achieved using different
F (obs) =
Na  2 Q , a B (T )
∑
combinations of size distribution and emissivity law!)
D 
grain distribution
Mass determination:
4sF D2  a 
Mdust =
 
3B (Tdust )  Q 
Using "appropriate
average" of a/Q .
"Wien's Law":
peak
 5  −1
≈ 3000 
T

 + 5
Peak flux moves to
longer λ for smaller β.
Mdust (true ) =
∑
grain &
temperature distribution
4 sF D2  a 


3B (Tdust ) Q ,a 
N = number of grains
a = "typical" grain size
D = distance from observer
Tdust = dust temperature
Q = emissivity
s = density of grain material
Composition: Changes
Wavelength [cm]
2
1
10
-8
10
0
10
-1
10
-2
10
-3
10
Maximum emissivity is for
pure blackbody, =0
SED peaks move to longer
for smaller
Decreasing gives you
more flux at any
so...
10
-10
10
-12
10
-14
10
-16
10
Pure Blackbodies
-18
10
Emissivity-Weighted, =1.5
14
arbitrarily normalized at 10 Hz
-20
10
8
10
9
10
10
10
11
10
12
10
Frequency [Hz]
13
10
14
10
– overestimating will mean
more mass required to
produce observed flux
WARNING: In theory, is only a
property of individual grains, but
in “practice” it has come to
include size distribution
Essential Physical Properties of Dust
Size Distribution
– MRN: N(a) ~ a-3.5... how often applicable?
Composition
– effects emissivity, Q
» QFIR~λ−β
β=0 for pure blackbody; β~1 for amorphous, layerlattice material; β~2 for metals & crystalline dielectrics
Shape (“Fluffiness”, “Compactness”)
– effects surface area & sticking properties
Evidence for Grain Growth in
Cirucumstellar Environments
Modification of “ ”, a.k.a. “dust opacity index”
– opacity ~ ~
~
– ISM: ~ 2
– Disks around Young Stars:
<< 2
» more opacity at longer wavelengths in disks than ISM
» (e.g. TTS Disks ~ 0.6; Mannings & Emerson 1994, see also
Beckwith & Sargent 1991)
– Low ’s are easily Inconsistent with N(a)~a-3.5
Flux Density [MJy]
The Data: Low-β and Free-Free
ν2.1, β=0.1
free-free
ν-0.1
Frequency (GHz)
Chen, Zhao & Ohashi, 1995
Disk
Masses
from SEDs
Uncertain
by ~ x100
Plots show χ2 for
disk masses derived
from fits of
Mannings &
Emerson (1994)
Axes: Mass vs. β
Typical β~0.6
How (Big) Solids are Formed
More Obvious Scenario: Direct Coagulation of
Material, in-situ (Goldreich & Ward 1973; Cameron
1975, etc.)
Less Obvious Scenarios: Mixtures of
Materials formed in Hot/Cold Environments, on
Varying Timescales
– e.g. as accomplished through star/disk-formation/
outflow process (see F. Shu et al.)
or... some of both?
Making Big Dust(balls) by Coagulation
Requirements
– substantial rate of low-speed collisions
– “sticky” material (ices good)
– melting & other exotic possiblities
Dangers
– equilibrium established short of “big” dust
– evaporation & destruction by high T & h
» within several A.U. of forming stars
– destruction by high-speed collisions
» e.g. infall, supersonic turbulence, etc.
Single Particle: Aggregate
of Similar Particles
Recall:
cm/s
100
1000
10000
100000
Ice
km/s
0.001
0.01
0.1
1
Single Particle :Aggregate
of Similar Particles
Quartz
Single Particle: Aggregate
of MRN-like Particles
Ice
Aggregate:Aggregate
(Each made of like particles)
Ice
Grain Growth
in Cores?
Some, but not
too much.
Weidenschilling &
Ruzmaikina (1994)
find “...weak turbulence
results in few collisions
and preserves [original
particle size distribution,
while] strong turbulence
tends to produce net
destruction, rather than
...growth]”
For a Proper Model of Big Dust around YSOs...
We’d need, all as functions of 3D position (and time)...
– “Initial” Size Distribution
– Velocity Distributions (of dust and gas)
» including effects of binaries & shocks
– Temperature Distribution
» including effects of “cloud surface” heating,
transient grain heating & shocks
– Composition Distribution
» e.g. more ices in colder regions?
– Serious Dedication & Brilliance
Observations to Constrain a Model
Total Flux at a given wavelength
Integrated (unresolved) SED
Spatially resolved SED
Spatially resolved multi-λ polarimetry
Spatially resolved maps of ice features
Record in meteorites, comets & asteroids
Questions to Consider
How to make big dust?
– How long does it last in a given environment?
How to best detect big dust?
How much big dust makes how much of a
difference in:
–
–
–
–
SEDs
mass calculations
chemistry
ISM