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# 14.13 Dust Extinction and Reddening

Even though space is a remarkably good vacuum by terrestrial standards, it is not perfectly empty and the few particles suspended in this vacuum mean that it's also not perfectly transparent. Tiny dust particles dim and redden the light from stars. This characteristic opacity — or ability to obscure light — also occurs in any discussion of the Sun's atmosphere or any other gaseous material. Opacity is a measure of the fraction of photons that penetrate a gas when they suffer collisions or can be absorbed. The Sun's opacity prevents us from seeing any deeper than the thin outer layer of the photosphere. Dust clouds in interstellar space have opacity too, preventing us from seeing through dusty nebulae.

Cosmic dust of theÂ Horsehead Nebulaas revealed by the Hubble Space Telescope. Click here for original source URL

The light intensity after passing through any material that scatters light is given by:

I = I0e

In this equation, I0 is the initial intensity, I is the intensity after passing through the material, and τ (the Greek letter tau) is the optical depth. The optical depth is just the amount of interstellar dust that the light must pass through, as you would expect. It doesn't matter whether the dust is thinly distributed in interstellar space or concentrated in a dense cloud. Starlight is affected either way.

Astronomers can calculate how much light is absorbed by dust by looking at the density and depth of a cloud of material. The combination of these two variables is referred to as optical depth. The fraction of light transmitted by a cloud rapidly declines as the optical depth increases. For τ = 0.5, I = 0.61I0. For τ = 1, I = 0.37I0. For τ = 2, I = 0.14I0. For τ = 4, I = 0.02I0, and so on. The fraction of transmitted light drops more rapidly than the optical depth increases — dust is very effective at quenching light.

There is a relation between optical depth to measurable properties of the particles in interstellar space. The optical depth is given by the simple equation:

τ = s N = (σr2) N

The optical depth is the product of the cross-sectional area of a single dust particle (the Greek letter sigma, where s = σr2 if we assume spherical particles, times the number of particles between us and the star. If we take the mean density of dust grains in a typical nebula like Orion, we find that τ = 1 over a distance of 0.5pc. For a typical nebula size of 5 pc, the number of dust grains encountered by starlight traveling through the nebula is 10 times higher, so τ = 10. This means that I = I0e = 5 × 10-5 I0. A star behind this nebula will be reduced to 0.005% of its original intensity!

Optical depth depends on the absolute number of dust grains encountered along a line of sight, but it does not depend on how the dust grains are distributed. In a nebula, the particles are relatively close together. (Although it is still much more rarified than the best terrestrial vacuum!) In interstellar space, the particles are more thinly distributed but the same extinction can be seen over a longer path. If interstellar space is 1000 times less dense than a typical nebula, it will take a 1000× longer journey for light to be extinguished by the same amount. So 0.5 × 1000 = 5000 pc through interstellar space will also give an optical depth of τ = 10. We cannot see more than about 16,000 light years through the Milky Way!

What about the reddening effect? It turns out that dust grains effect different colors of light with different efficiencies. Dust grains are not effective at scattering light with wavelengths much bigger than the grain size. A useful analogy is waves on a pond. If a wave is much smaller than an obstructing object like an island, the wave is blocked or reflected. However, if a wave is much larger than a small obstructing object like a pebble, the wave passes by with no effect. Long waves do not "see" small particles. Long wavelength (or red) light is not scattered as strongly as short wavelength (or blue) light. As a result, the farther starlight travels through a dust cloud or the interstellar medium, the more blue light is removed and the redder the star appears. Sometimes this scattered blue light reaches us indirectly — such as the reflected light from a nebula or the blue photons of sunlight that scatter in our atmosphere and make the sky look blue.

If we look at the scattering process in detail, the efficiency of scattering is inversely proportional to wavelength. UV light is almost entirely blocked, while dust extinction is much smaller at infrared wavelengths than at even for optical wavelengths. This is why astronomers use infrared techniques to study star-formation regions.