Lesson Plan - The Interstellar Extinction Curve

Suggestions for Instructors

This exercise is designed to give the students a feel for how astronomers use theoretical models to interpret the light they measure in their telescopes. It can also be used as part of a lesson dispelling the misconception that space is "empty".

It is important to stress to students that this is only one tool out of many. Constraints of cosmic abundances (how much carbon is actually available), and the polarization of light are also used to help deduce what the material causing extinction in the galaxy is made of.

Also, while we cannot travel to distant galaxies, we can gather particles in near Earth orbit, which can give us a clue as to what is between the stars.

References

• Draine and Lee, Optical Properties Of Interstellar Graphite And Silicate Grains, The Astrophysical Journal, 285:89, 1984.
• Mathis, J. et. al. The Size Distribution of Interstellar Grains, The Astrophysical Journal, 217:425, 1977.
• Rouleau and Martin, Shape And Clustering Effects On The Optical Properties Of Amorphous Carbon, The Astrophysical Journal, 377:526, 1991.
• Whittet, D.C.B., Dust in the Interstellar Medium, Institute of Physics Graduate Series in Astronomy, 1992.

Solutions

1. Try matching the shape of the interstellar extinction curve with a single grain size of a single material. Is it possible to get a close match to the extinction curve in this way?
   The closest will be small graphite particles, which will have a peak at the same wavelength as the interstellar extinction curve, and large silicate grains will have an uneven peak but will not match the far-UV region of the spectrum but no single grain material will explain the spectrum seen in interstellar extinction.
2. What is the effect of changing the grain size?
   Absorption increases, so in order to have the same absorption you must have fewer total particles (lower column density). Absorption shifts towards the red end of the spectrum.
3. What is the effect of changing the material?
   Each material has unique features. Silicate can have many spectral features at different wavelength, depending on size, and in general absorbs well in the far UV. Small graphite particles have strong absorption at a wavelength of 0.22 microns (1/wavelength ~ 5). Amorphous carbon tends to have a smooth spectrum, and large particles absorb well in the visible and near infrared.
4. What are the basic characteristics of the extinction curve of small graphite grains?
   Small graphite particles have strong absorption at a wavelength of 0.22 microns (1/wavelength ~ 5).
5. What are the basic characteristics of the extinction curve of large graphite grains?
   Large graphite grains have a rapid rise in extinction from the infrared to the visible, and a reasonably uniform extinction throughout the ultraviolet, with small features.
6. What are the basic characteristics of the extinction curve of small silicate grains?
   Small silicate grains have little absorption in the IR, visible, and near UV, but has strong absorption in the far UV.
7. What are the basic characteristics of the extinction curve of large silicate grains?
   Large silicate grains have multiple peaks in the near UV, and flat extinction in the far UV.
8. What are the basic characteristics of the extinction curve of small amorphous carbon grains?
   Similar to silicate, small amorphous carbon grains have strong far UV extinction, but also have a moderate amount of near UV extinction.
9. What are the basic characteristics of the extinction curve of large amorphous carbon grains?
   Large amorphous carbon grains have a rapid rise in extinction from the IR to the visible, and then levels off through the UV.
10. How well do each of the above match the interstellar extinction curve? Can you find a mixture of the three that matches the curve?
    Each individually fail, but large amorphous carbon matches the visible part of the spectrum, small graphite particles match the near UV part of the spectrum, and small silicate particles match the far UV part of the spectrum.

    A reasonable fit using this model can be made with the following parameters:

    Amorphous Carbon:

    Grain Size: 0.82

    Column Density: 8.59e9

    Graphite:

    Grain Size: 0.01

    Column Density: 2.2e12

    Silicate:

    Grain Size: 0.019

    Column Density: 1.37e11