Dust in AstrophysicsGian Luigi Granato

•Generalities

•Radiative transfer and dust.

•Dust models

•The importance of dust in Stars, Galaxies,

AGNs.

In a galaxy only »10-22 of vol. is in stars.

The Interstellar Medium (ISM), provides 5–10% of the

baryonic mass of the galaxy in form of gas mixed with

tiny solid particles: dust grains

Size distribution: from a few Å (PAH molecules) to »1-10

mm, with max at »0.5 mm (the l of visible light)

Composition: C, Si, O, Mg, Fe. two main groups

carbonaceous (graphite and/or amorphous C) and

silicate (Mg+Fe+Si+0, eg olivine) grains

Typically from 0.5 to 1% of ISM mass is in dust at z=0,

but about ½ of heavy elements are depleted to dust

Dust is relevant in many astrophysical environments.

Examples (in chronological order):

• zodiacal light (last century);

• comet tails (Arrhenius 1900);

• evolved stars (from Loreta 1934);

• interstellar extinction (Hoyle and Wickramasinghe

1962);

• IR emission of galaxies and AGNs (IRAS early ‘80);

• unified models for AGNs (say from Antonucci and

Miller 1985)

Silva, Granato, Bressan & Danese 1998

Modelling obscured emission by stars and galaxies

Ivison et al 2000

850 µm contours of sub-mm sources onUBI images of Abell1835

Orion SF MCOrion SF MC

Optical

NearIR

FIR and Sub-mm surveys are very

effective in detecting obscured star

formation at high-z, due to the expected

steep shape of the SED from about 100

to 1000 micron rest frame

The “k-correction” compensates for

cosmological dimming, so that the

observed FIR and sub-mm flux nearly

constant between z=1 and 10

far-IR and sub-mm

surveys

Optical flux

Interactions between Dust and Radiation:

Radiative Transfer (RT) with dust

I º~r ;! ; t́dE

dº ddAdt

dE

dA ? ! dt

dº d !

The radiation field is affected by the presence of matter:

True absorption: the energy of photons is turned into

other forms (internal energy of matter or fields)

True emission: the opposite

Scattering: the energy flow of photons is ‘deviated’ into

other directions. Usually in RT is treated as absorption

from one direction + emission in another one (possibly at

different n)

Dust scattering is elastic (= no changes of n)

True abs. + Scattering abs = extinction

I º

! ² r I º~r ;! ¡ ®º~r ;! I º~r ;! j º~r ;!

dI º

ds ¡ ®º I º j º

Displacement is

along the ray ()

Extinction coefficent

(true abs + sca abs)

Emission coefficent

(true em + sca em)

In most practical cases, an integro-differential equation

d¿º ´ ®º ds ¿º ´

Z s

so

®º ds

¿º

< < > >

Sº ´ j º =®º

Sº B ºT

dI º

d¿º ¡ I º Sº ;

e¿º ! dI º e¿º

Sº e¿º d¿º

I º¿º I ºe¡ ¿º

Z ¿º

e¡ ¿º¿0ºSº¿

0ºd¿0

º

Sº

I ºT

I º¿º I ºe¡ ¿º

º ¿º e¡ ¿º

< ¿º > ´

Z 1

¿º e¡ ¿º d¿º

In a microscopic model of absorption particles with

density n each presents an effective cross section sn,:

orn Nn n n n s s

where s is the geometrical cross section (pr2 for

spheres) and Qn,e , Qn,a and Qn,s are extinction, absorptionand scattering efficiencies. In optical-UV Qn,a»Qn,s»1, in

IR Qn,s<<Qn,a/l-1.5¥ 2

( )e a sQ Q Qn n n ns s s

For dust grains it is common to writeColumn

density

The albedo n=Qn,s/Qn,e, i.e. the fraction of extinguishedlight scattered rather than absorbed:

The total absorbing area presented by absorbers is (n sn dA ds).

thus energy absorbed out of the beam -dIn dA dW dt dn

is given by In (n sn dA ds) dW dt dn

then dIn = - n sn ds, which compared to the RT equation with no

emission yields n= n sn

Therefore for dust (single population)

enQn n s

The emission coefficient includes true emission

and elastic scattering: jn,= jn,em+ jn,s

True emission of dust grains is thermal ) Kirchoff’s

law holds (jn,em=n,a Bn(T) )

( )em aj nQ B Tn n ns

The elastic scattering component is

4

1ˆ ˆ ˆ ˆ( ) ( ) ( )

4s sj Q n I f dn n n n

p s

p

W

fn is the phase function of the incidence–scattering

angle. It’s clear that both jn,emand jn,s depend on In

Both terms of the emission coefficient depend on the

radiation field. True emission jn,em depends on it trough

grain temperature T, since their heating is almost always

dominated by the radiation field.

Thus a primary task is to compute T given the radiation field. In any case, grains sublimate at T &1000¥2000 K

Two different cases depending on grain’s size.

1.Grains big enough (&100 Å), don’t cool in the time

between absorption of two photons, so reach thermal

equilibrium with the RF.

T is determined by solving the energy balance equation:

( )a aQ J d Q B T dn n n nn

n

n n

Absorption EmissionAngle

averaged In1

( )4

J I dn n p

W

Note that equilibrium grain T depends weekly on

radiation field

Indeed, absorption occurs mainly in optical–UV whereQn,a»1, while emission is in IR where Qn,a/ l-g with

g'1.5¥ 2. Thus, as an order of magnitude we get

4( ) ( )a rad aQ J d J d U Q B T d B T d Tg g

n n n n n nn n

n n

n n n n n

1/(4 ) 0.17

rad radT U Ug

e.g. to double T would require an increase of U by 60!

The SED of optically thin dust emission is relatively

stable.

2. Small grains (.100 Å) fluctuate in temperature

between two photons and a probability distribution

P(T)dT to find a grain between T and T+dT has to be

computed with more complex statistical techniques

(e.g. Guhathakurta & Draine 1989, Siebenmorgen et

al. 1992).

Once this is done:

( ) ( )max

min

T

em d absT

j n Q B T P T dTn n ns

( )em aj nQ B Tn n ns replacing

PT Ti PiA f i

i f 6 i

Ti

dPf

dt

X

i6f

A f iPi ¡ Pf

X

g6f

A gf X

i

A f iPi

A f f ´ ¡P

g6 f A gf

Pi

( Pi A f iPi Pi Pi

f

Effect of temperature fluctuations

Predicted P(T)

Predicted spectrum

Neglecting

fluctuations

With

fluctuations

Astrophysical dust is believed to be a mixture particles

with different size, shape, and composition. All the

equations must be summed and/or integrated over all

the species. For instance for spherical grains with

different compositions, labelled by the index i, and

corresponding distributions of radii ni(a)da:

2

,( ) ( )i i e

i a

n a Q a a dan n p

2

, , ( ) ( ( )) ( )em i a i

i a

j a Q a B T a n a dan np n

To treat the effects of a dusty medium on the radiation

field we need knowledge of Qn,a, Qn,s and fn. They

depend on the chemical composition, size and shape of

grains.

Exact solutions exist for homogeneous spheres (Mie’s

theory) and infinite cylinders, and good approximation in

most realistic cases.

These complex computations are the subject of entire

books (e.g. Bohren and Huffman 1983)

Moreover we may be interested into modelling the

effects of dust on polarization, which requires transfer

equations for the 4 Stokes parameters….

Rule of thumb:

•when l.a, Qn,e»1,

•when l'a there are

features due to resonances

in the grain lattice

•when l>>a, Qn,e/ l-(1.5¥2)

(exponent depends on grain

material and T)

2

,( ) ( )i i e

i a

n a Q a a dan n p

2

, , ( ) ( ( )) ( )em i a i

i a

j a Q a B T a n a dan np n

, ,4

1ˆ ˆ ˆ ˆ( ) ( , ) ( ) ( , )

4s s i i

i a

j Q a n I f a dn n np

n s p

W

( )a aQ J d Q B T dn n n nn

n

n n

dII S

d

nn n

S jn n n d dsn n

0( ) (0)exp( ) exp( ) ( )I I S d

n

n n nn n n n n n

Summary sheet of dusty RT equations

Models of Interstellar Dust

The first models where developed to reproduce the

extinction curve, which describes how dust extinction

changes with l: before IRAS dust properties could be

tested mainly by the dimming of stellar light.

Further constraints now come from dust emission

Suppose to observe the optical light from a source through a dust

veil. The emission is negligible because dust emits only in the IR,

and scattering from other lines of sight is unimportant. Thus the

formal solution is no more formal and gives

exp( )(0)

I

I

nn

n

2 5(0) 1 08

ln10A m ml l l n n

where In(0) is (also) the intensity we would

measure in absence of the veil. Taking 2.5

the log of both members we get the

interstellar extinction in magnitudes:

The extinction curve is all but universal: even in the Milky Way,

where it is best studied, depends on the line of sight and

environment. Moreover data on other few nearby stellar

systems shows a variable behaviour, in particular in UV.

The main characteristics of extinction curves:

•A growth in the optical–near UV, linear with x=1/l•A bump around 2175 Å.

•A more than linear rise in FUV.

•Two features at 18 and 9.7 mm

To explain these properties a mixture of grains, with

different sizes and compositions, is required:

•The visible extinction can be explained by grains ofa»0.1mm. However they cannot account for the growth

in UV, requiring smaller grains with a»0.01mm

•Silicates are necessary for the 9.7 mm and 18 mm

features. The large width of these features suggest

silicates with many impurities (dirty or astronomical

silicates).

•Silicates have an excessive albedo in the optical. Here

graphite or amorphous carbon grains, mainly produced

in the atmospheres of carbon stars, are proposed as

main absorbers. This material has a resonance at

2175Å, good also to explain the observed UV bump.

Graphite grains

Silicate grains

PAHs

Theoretical extinction curve decomposed

extinction

albedo

Many models, usually with the above requisites, have

been proposed to successfully reproduce the extinction

curve. Besides the similarities (above all the role of

carbonaceous and silicate grains) the differences are

substantial: the extinction curve alone do not constrains

enough the properties of interstellar dust.

The classical model in this context is the MRN model by

Mathis, Rumpl & Nordsiek (1977), slightly revised by

Draine and Lee (1984), with a power law size distribution

of silicate and graphite grains:

3 5 for 0 005 m 0 25 msil gra Hsil gra

dnA n a a

dam m

Refinements are motivated to explain the emission

properties of (possibly specific) dusty systems:a

universal model of dust is unreasonable. For instance:

•Very big grains 1 mm.a.10 mm to explain the sub-mm

emission of carbon stars, or properties of AGNs, and in

general in denser environment (MCs);•Very small grains 10 Å.a.100 Å explain the observed

emission in galactic cirrus;

•PAHs (Polyciclyc Aromatic Hydrocarbons) molecules

may explain the interstellar emission bands (UIB) at 3.3,

6.2, 7.7, 8.6 and 11.3 and 12.7 mm (and now other

longer l) seen in many objects;

•Porous grains are possible solution of the carbon crisis;

Very small grains, stocastically heated grains to account MW

cirrus emission

MNR –DL model,

grain radii >50ÅModel with graphite grain radii

extended down to 10Å

9Å

30Å

60Å

100Å

• absorption featuresdue to Silicates.

• strong emissionfeatures at 3.3, 6.2,7.7, 8.6, 11.3 mm =UIBs

UIBs

Sil.

l(microns)

(Sturm et al. 2000)

NeII

[ArII]

PAHs (polyciclyc aromatic hydrocarbons) are a family of very

stable planar molecules, based on benzene ring which has an

aromatic bond in which a p orbital is shared in the chain.

UIB commonly interpreted by C-C and C-H vibration modes,due to the absorption of a single uv photon, in large planarPolycyclic Aromatic Hydrocarbons (PAHs) molecules, with size~ 10 Å and containing ~ 50–100 C atoms. But the issue ismcomplex.

PAH vibrational spectra resembles those of emission bands in several (not all!)

astrophysical objects

PAH emission features originate mainly in the so-called photo-dissociation

regions, i.e. in the interfaces between molecular clouds and the HII regions,

illuminated by the high energy field of the young stars. There are evidences that

in denser environments and stronger UV field intensities the PAHs could be

depleted.

In the circum-nuclear dusty regions around AGNs PAH emission is not

observed.

A constraint for dust models is the abundance of the

elements depleted into dust grains. Of course it can not

be greater than the cosmic abundances of the

corresponding elements minus their amounts estimated

in the gas phase (both things quite uncertain).

This could be a problem with classical models.

The DL84 model has 282 atoms of C per million H atom

(ppM). This is 80% of recent estimates of solar

abundance, so there is little room for C in gas phase(»150 ppM?). Moreover, solar values are believed to be

greater than the average values: Carbon Crisis.

A possible way out are porous grains are: available C is

used more effectively to produce opacity

Grain production & destruction

The mechanisms of birth, growth and destruction of grains are a very active

field of research. Given the importance of dust reprocessing to interpret

observations, dust evolution models begin to be incorporated in many galaxy

formation models (monolithic, semi-analytic, numerical simulations)

The first tentative account of most relevant processes in the dust life cycle was

Dwek (1998). For more recent treatments, see e.g. Hirashita+ 2015 and

rerefences therein.

Computations of dust emission/radiative transfer

Given the optical properties of dust and the geometry (both

difficult things), one can predict the spectra of dusty systems.

From a computational point of view we can distinguish two cases:

•If the emission is not self-absorbed, i.e. if the system is optically

thin in IR, the emitted radiation is simply the volume integral of the

local emissivity

This is in general the case for the IR galactic cirrus. Still there maybe important scattering radiative transfer effects at l.1mm

•Otherwise (e.g. tori in AGNs, Molecular Clouds) one has the

difficult task to solve the transfer equation. In any practical cases

this can be done only with numerical techniques, such as the

lambda-iteration method, a straightforward application of the

formal solution.

A very flexible approach, but much more time-consuming, is

Montecarlo.

Monte Carlo method

The life of many photons is followed through dust. Its fate is

derived in a probabilistic way by tossing random numbers. In

essence:

do until Signal/Noise good enough:

Draw the position where a photon is emitted with probability distribution

given by the adopted distribution of sources, and with direction assigned

assuming some phase function (usually isotropic)

On the path the probability for a photon to avoid absorption and scattering

is exp(-n). Derive a random optical depth along the path where interaction

occurs using this probability distribution. Here the photon can be either

absorbed or scattered (scattering probability = albedo = n= Qn,s/Qn,e).

If scattered, the phase function is used as the probability distribution for the

angle between the old and the new travelling direction.

End do

But in practise many numerical tricks to speed up things

Full SED of a simulated galaxy

gasstars

RT predicts

SED and

optical

image

Images of

(another)

simulated

galaxy from

FUV to FIR

(Dominguez

et al 2014)