Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mrao.cam.ac.uk/~kjbg1/lectures/lect4.pdf Дата изменения: Mon Oct 20 20:52:14 2003 Дата индексирования: Tue Oct 2 03:15:10 2012 Кодировка: Windows-1251 Поисковые слова: п п п п п п п п п п п п п п

Dust
Dust pervades atomic and molecular hydrogen clouds in the Universe: we know this because of extinction of distant sources seen through the galactic plane -- roughly an extinction of 1 mag per kpc in the optical.

diffuse lines in optical and IR spectra attributed to dust absorption

far infrared and submm emission from gas clouds, often polarised

?



polarisation of starlight reflection nebulae diffuse scattered light in the ISM gas-phase depletion of metals relative to solar abundances

hot dust in HII regions gives rise to mid-IR (10 ) emission


The Extinction Curve
Extinction is due to scattering and absorbtion from the dust.

Main constraints on dust models come from the extinction as a function of wavelength in the UV to IR wavelength range.

There is an obvious feature at 220nm identified with a resonant absorption by graphite (C-C bonds). Many other solid-state resonances can also be seen at other wavelengths. Can estimate the total extinction at a par ticular wavelength, , from the differential extinction between two wavelengths if observing towards a star of known spectral type.

Е Ѓ? ?

?

There is a very approximate scaling: extinction the visible and UV ranges.

ї

? ? ? ? ? ?

in


Grain Optics
need to consider emission, scattering and absorption by nonspherical grains of sizes comparable to an optical wavelength. define the scattering, absorption and total extinction efficiencies for spherical grains of radius through

The albedo of a grain is the ratio of scattering to total extinction, . For single scattering the optical depth for extinction is then

where is the number of grains per unit volume and is the path length. This then results in an extinction in magnitudes of

P I4 ! HG "! F

g

ba `Y X V U 1T S @ @ @r

E# DC 5B A

hg f DC 5B A ed c

@2 5& 98 70 %

#

# 6 54 ! 3





D

P @y xw vu ts hr q p

# ba `Y 1X WV "U 1T S

2 10 )( '& %

HC 5B A R RQ P 54 !

# ba `Y X i

$# "!

dc




Calculating Q - The Mie Theory
The Mie Theory predicts and for spheres (and other shapes) as a function of radius a, wavelength and complex permittivity . These calculations involve solving Maxwell's equations for the fields subject to the boundary conditions at the grain surface. In general these have a complex form, but in the infrared when the wavelength is typically bigger than the grain size, we find

in the far infrared we can often ignore scattering altogether.

x

wv ut Hs r q p

and equals about the albedo is very small at long .

at 100 , i.e.



6 5

lk ji gh

g



"

fe " F

e 6 5

on

d

e " @m P I

y


Emission from Dust
.

HII regions: dust heated to about 200 K, so we see strong mid-infrared (10 ; 30 THz) emission. In molecular clouds, dust heated to temperatures from 10 K away from heating sources, up to maybe 60 K near embedded stars. Emits strongly 50-300 (6-1 THz). For tracing cool dust, the submillimetre ( 300 GHz) is of great impor tance because the emission is optically thin.



because the flux at the surface of a body of brightness .







" o ` Е " ~

"

Kirchoff 's Law by a grain per unit frequency is

. Thus the power radiated



~} @} H} |



{

Dust is destroyed above much emission shor t of a few

so we don't expect





5



3









z z z z z

is


Emitted spectrum
P? ?   З З + Г
Consider a dust cloud at uniform temperature tion optical depth, . , absop-

For , this is often known as a greybody spectrum: it lies below the same temperature blackbody spectrum and approaches it when the dust becomes optically thick.

In the far infared/submm, the dust emission is almost always optically thin. Also assuming the Rayleigh-Jeans approximation, we obtain an emergent intensity

Thus a greybody has a longwavelength spectral index in the range for typical values of .

?

Typically find in range 0 to 2. Theoretically metals and and crystalline dielectric substances; amorphous, layer-lattice materials.

И

e? О Ж Е

P? Е К

?

Н

М ~Л И

? ЖЕ

З

Г

Ж Е

+

6? Е К

ДГ

Often write

h? ?

?А h? ?? e? ?' ? ? е

ћ ч

ЙR Ѓ ?

З

В

?

ПњИ

 1Е ?

 DЃ ?

?

where

.

P? ?

'R Ѓ u? ?+ wѓ @' ї fњ I? R

3Ѓ Б ?

wѓ @' ?ї Е ?

?

long wavelengths

?

Fћ  ч ?

 DЃ ?





ignore scattering.

for for






Mass Estimates
is the mass absorption coefficient where for a density . It is the total cross section per unit mass of material and has has units .

Equation for emergent intensity becomes

Can then estimate the mass from

фу Pт Ес Кр eп о зн У чм цх Ц

~й Hг ж

Ха

б иЯ Э ЬЫ ?Ъ Щ Ш зж ег 7д г

у Pт ?с р п о н У м У С ы Щ ъ

в

У

У

У кы

а

эЦ х

б

б

Х

щ

Щ

аС

Х

щъ

Х фу Pт Ес Кр eп о зн У м л

ь

Х

Х

ХаС

Typical values are

,

У ЧС Ц

ХУФ

в

а

б

б

oа С

Я ЮЭ ЬЫ eЪ Щ Ш Х УС ш ь ю

Х Ук

Ц

У ТС Р Р

GHz.

Р Р


Temperature
Equate the incident and radiated fluxes to find temperature. For a single grain at a distance from a point source of specific : luminosity

Most of the absorption term comes in the optical/UV. Waveis indepenlength much smaller than grain size, so dent of . Emission is mainly in the Far IR/submm. Since

in the infrared, large grains emit more efsmall grains warmer than large ficiently than small grains ones. For then the dust temperature falls off as .

% ! 43 ? 2 1Ѓ "! 0) ( ' їЕ  Ѓ $

& 5! 6) (

5!

?

?

&



% Е Ѓ$ #? ? "! їЕ  Ѓ

D

їS B CR QP CI HG Е F B 7 "! E 6) ( 7 я3

CB A@ 9 8 7 "!

?? ?



?

?

я

я я


Models of Dust
different models needed for different environments. Dust grains evolve through interactions with other grains, molecules and photons. fit the extinction curve using the Mie models varying the size and shape distribution, and physical composition also some constraints from interplanetary dust gathered by spacecraft and from meteorites.

grains are usually negatively charged: this is due to the different collision cross sections for heavy positive ions and light fast electrons.

fe dc bU bU a

typical grain size is

("soot" sized, rather than dust!)

`Y XU WV U

T T T T T T

mass fraction in dust in the Galaxy is about

.


Composition
Much of this information comes from IR spectroscopy where we can see characteristic bond stretch frequencies and vibrational emission. The grains have refractory cores of

polycrystalline amorphous carbon, perhaps hydrogenated (HAC), seen in 7.6 absorption

Polycyclic Aromatic Hydrocarbons - PAHs - (large molecules or small grains?) fit many IR bands very well e.g. 3.3, 6.2, 7.7, 11.3 Cold grains in molecular clouds can accrete ice mantles leading to depletion of gas phase molecules. e.g. water, CO , ammonia, methanol,

h

amorphous silicates of Mg, Fe, Si, O, seen in 9.7 and 20 absorption bands

i

h

h

g g g g g

crystalline graphite: seen in 220 nm bump


Grain Alignment and Polarisation
Extinguished starlight is linearly polarised, and the degree of polarisation is well correlated with the visual extinction.

Mechanism

In equilibrium, the rotational KE is equipar titioned: , so that the angular momentum vector is ; this points preferentially towards propor tional to the minor axes.

x

z y



t ї y y r

t 's r

Consider prolate grains elongated about the axis, with for . There are two effects to consider:

q

f w w b u u r t #s s r p y xr w t vu r

w

p p

Millimetre wave dust emission is also polarised.




B

In a magnetic field a grain prefers to spin with its spin axis parallel to B: in this orientation, the magnetisation M is constant in the grain. For or thogonal spin and magnetic field axes, M fluctuates and thus dissipates rotational KE. We conclude that grains align themselves perpendicular to the magnetic field. (NB this simplified theory may not be the whole story: still a matter for debate.) If true however, we expect grain to absorb and emit the electric field preferentially along their long axes.

Polarised dust emission should have a plane of polarisation perpendicular to B.

Polarisation by Scattering
Even spherical grains produce optical/IR polarisation by scattering. In reflection nebulae, a circularly symmetric pattern can be seen. This can be used to locate the illuminating star.



Polarisation by extinction gives polarisation parallel to B


Summary

Dust emits with a greybody spectrum between 300 GHz - 30 THz.

An ellipsoidal dust grain will align perpendicular to magnetic field. Therefore: - emission has plane of polarisation perpendicular to B. - extinction has plane of polarisation parallel to B.

Scattering also impor tant (and produces polarisation) at shor t wavelengths; is negligable in the far infrared.

e d



Dust absorbs in the UV to IR with extinction

.


Dust

f

f f f

Emission as result of thermal excitation. Emitters in thermal equilibrium Polarised e.g. -- star forming regions -- optical extinction and polarisation through the galaxy -- diffuse scattered light from the Inter-Stellar Medium