Interstellar Dust properties

While practicing for an upcoming examination, I ran into this problem:

Which of the following best describes dust grains in the interstellar medium:

1. They are a few hundred nanometers in size (size of optical light).
2. They are much larger than regular dust.
3. They are primarily composed of helium and hydrogen.
4. They emit large amounts of blue light.

I did some research and discovered that they scatter blue light, their size ranges form $$1 \ldots 100 {\rm \mu m}$$ while regular dust is about $$1 \ldots 100 \mu{\rm m}$$. Also, interstellar medium is composed of helium and hydrogen but that doesn't mean the same about dust. My guess: It is the first answer.

Is this correct? Any assistance much appreciated.

Yes, #1 is the correct answer.

1. ✅ For small particles such as dust grains and molecules, light generally interacts most easily with particles roughly the same size as its wavelength. This is seen as the maximum in the figure below. That is, the particle’s cross section doesn’t depend on its exact shape, but rather on the ratio between the size and the wavelength of the incident light: As the particles become larger, you enter the regime of “geometric” scattering, where the cross section approaches the geometric cross section (e.g. $$\pi r^2$$ for a sphere etc.), whereas as the particles become smaller, you enter the “Rayleigh regime”, where the cross section drops proportionally to the wavelength to the power of $$-4$$.

Since observationally we know that interstellar dust affects optical and, in particular, UV light significantly, we know that the dust grains must be roughly the size of that light’s wavelength. More carefull modeling shows that a typical cosmic dust size distribution can be described by a power law with the probability of size $$r$$ decreasing roughly as $$P(r) \propto r^{-3.5}$$ (Mathis et al. 1977). In other words, for every dust grain of size $$r$$, there are 3,000 times as many dust grains of size $$r/10$$.

2. 🚫 "Normal" dust particles are in the range 1–100 $$\mu\mathrm{m}$$ (thanks for the sources @uhoh & @PeterErwin, unless they mean dust bunnies which are more like mm- to cm-sized. At any rate, cosmic dust is not much larger than normal dust, so #2 isn’t correct.

3. 🚫 #3 also isn’t correct. While it’s true that 98% of the interstellar gas is hydrogen and helium, dust is composed of the last 2%. That is, iron, carbon, silicon, oxygen, etc.

4. 🚫 Finally, while it’s true that blue light is absorbed or scattered more efficiently by dust than red light, dust doesn’t emit blue light. If it’s absorbed, the energy goes into heating the dust and is then later re-emitted as infrared light. So #4 also isn’t correct.

In the figure below you can see how the cross section of a(n idealized) particle depends on the ratio between its size $$r$$ and the wavelength $$\lambda$$ of the incident light. Credit: Catslash, Public domain, via Wikimedia Commons with own annotations.

• +1 Light doesn't have any problem interacting with particles much much larger than a wavelength either. It's just that the scattering part is more reflection and less diffraction. Although if the metric is scattering per gram, then there is an optimum size of order the wavelength.
– uhoh
Mar 15 '21 at 22:32
• Also this (x-axis is microns) from Particulates shows that "regular dust" gets in the eye of the beholder. :-)
– uhoh
Mar 15 '21 at 22:39
• “The stuff you sweep off the floor, I.e mm- to cm-sized”? That’s sand and gravel, not dust. “Household dust” actually is in the range 1–100 $\mu$m. (E.g., airmidhealthgroup.com/images/micro-lab/published-data/…) Mar 16 '21 at 7:45
• @PeterErwin okay by "regular dust" I was thinking of dust bunnies. But thanks, I edited my answer.
– pela
Mar 16 '21 at 12:10
• Thanks for that source, @uhoh!
– pela
Mar 16 '21 at 12:38

Yes, it is correct.

As you said, interstellar dust particles have more or less the same size of terrestrial dust. We think they are primarily composed of carbon and silicates. Size and composition can be inferred from the absorption curve. The curve is telling you that interstellar dust absorbs a lot of blue/UV light, and once the grains reach an equilibrium temperature, they re-emit this energy in the infrared band.

• What is the y axis of the graph? What are $A_{\lambda}$ and $A_{V}$? What is the source of the graph, can you add a link to it, and perhaps copy/paste the caption as well? Thanks!
– uhoh
Mar 15 '21 at 22:35