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Giovanni Covone » 9.Properties of the interstellar dust

First evidence for dust extinction

Trumpler (1930) demonstrated the existence of interstellar absorption by comparing luminosity distances and angular diameter distances of a sample of open clusters.

Trumpler’s main conclusions:

angular diameter distances are systematically smaller than luminosity distances;
discrepancy increases with distance;
distant clusters are redder;

On that basis,

he estimated an absorption of about 2 magnitudes per kpc;
he attributed it to Rayleigh scattering due to tiny grains (size about 25 $\AA$ ).

A more appropriate term would be smoke: indeed, the particle sizes are much smaller than in terrestrial dust.

Distances of open clusters

Trumpler's comparison of the luminosity and diameters distances for 100 open clusters. Credit: Trumpler (1930).

Dust extinction

Extinction by small particles.

Light absorption along a line of sight the relation between apparent and absolute magnitude is:
$m = M + 5 {\rm log} \frac{r}{10 {\rm pc}} + A \, ,$
where $A \geq 0$ is the extinction.

Exctinction is proportional to the distance travelled by light:
$A = a \, r \, .$

Constant $a \sim 2 \, {\rm mag/kpc}$ .

Extinction depends strongly on the direction (up to 30 mag towards Galactic center).

Dust extinction. Extinction is due to dust grains that have diameters about the wavelength of the light.

Gas extinction by scattering, but its scattering efﬁciency per unit mass is much smaller.

Dust extinction (cont.)

Extinction by ISM particles:

by absorption, radiant energy into heat;
by scattering, the direction of light propagation is changed.

Geometrical cross section of spherical particle : $\pi a^2$ .
The extinction cross-section of the particles:
$C_{\rm ext} = Q \, \pi a^2 \, ,$
where $Q$ is the “extinction efﬁciency” factor.

Volume element with length $dl$ and cross section $dA$ ; particle density $n$ . Number of particles in the volume element: $n \, dl \, dA$ .

Extinction and optical depth: $d I = - I d \tau \, .$

So:
${\rm d} \tau \, = \frac{n {\rm d}A {\rm d}l C_{\rm ext} }{d A} \, = \, n C_{\rm ext} d l \, .$

Total optical depth:
$\tau (r) = \int_0^r d \tau \, = \int_0^r n \, C_{\rm ext} d l \, = C_{\rm ext} \bar{n} r \, ,$

where ${\bar n}$ : mean particle density along the line of sight to the source at distance $r$ .

Evidence of interstellar dust

Evidence of interstellar dust comes from interaction with starlight and from emission of light.

Interaction with incident starlight

Radius of dust grains: $a \simeq \frac{\lambda}{2 \pi}$

Extinction of background stellar light (“holes in the heavens”).
Reflection of light from nearby stars (producing reflection nebulae).
Polarization of light (by scattering or by interaction with aligned dust grains).

Evidence of interstellar dust (cont.)

Evidence from emitted light

Dust clouds can be revealed by means of light emitted by dust grains.

Thermal continuum emission from grains at radiative equilibrium (MIR and FIR radiation).
Thermal continuum emission from non-equilibrium heating (NIR and MIR radiation).
Infrared emission bands from heated dust grains.
Radio continuum emission.

Reflection and dark nebulae

A complex ISM system with blue reflection nebulae (NGC 6726/6727 & IC 4812) and a dark nebula. Credit: Martin Pugh.

Gas and dust in spirals

A face-on spiral (M74) and an edge-on spiral (NGC 4013). Credit: NASA/Hubble Space Telescope.

Other evidence for dust in the ISM

Less direct evidence for dust in the ISM:

Presolar grains preserved in meteorites
Depletion of some elements from the interstellar gas (missing atoms presumed contained in dust grains?)
Abundance of $H_2$ in the ISM and catalysis on dust grains.
The temperature of interstellar diffuse HI and $H_2$ : effect of heating by photoelectrons ejected from interstellar grains.