# How big is nebula dust?

Whenever I see the term dust for the particles of a nebula, I ask myself whether this is actually based on some reliable measure of particle size. Of course we can all agree it looks like dust from this distance. And we all know how such appearances often lead to assumptions which are incorrect and whose incorrectness we are often blind to.

Is there any reliable evidence by which this "dust" is known not to be pebbles, rocks, boulders etc.? Which in reality would seem vastly more likely.

How might we measure size from such distances?

• Why do you think larger particles are more likely than small? What assumptions are you making about the source of the dust (and are those assumptions based on technical reports?) – Carl Witthoft Aug 14 '17 at 15:44
• @CarlWitthoft Knowing human nature as I do, I think the appearance of being dust-like has the capacity to bias us towards an assumption of dust, in the absence of any evidence that is so. Since dust is at the smaller end of the scale, any such assumption would be a downwards-biased estimator and as such, particles larger than dust would be a better estimator, statistically speaking. From a physics point of view, the law of gravity biases dust towards accumulating into larger bodies over time. For the moment however I present no opinion and ask if such an assumption has been made. – samerivertwice Aug 14 '17 at 15:59
• @RobertFrost Gravity is of negligible importance between dust grains. – Rob Jeffries Aug 15 '17 at 22:03
• @RobJeffries it depends over what timescale, and also a huge cloud of trillions of times of dust has more gravity than two dust grains. The Earth and all the planets were once dust. – samerivertwice Aug 16 '17 at 3:21
• @RobertFrost True enough, but the reason there is little dust in the solar system today is not because of gravity and not because it has clumped to form larger bodies. – Rob Jeffries Aug 16 '17 at 6:34

The size of cosmic dust grains is in general given not by some size, but by a size distribution. The only direct measurements of such a distribution are made on dust collected on plates of satellites, which is of course a very local measurement. When we think that distributions look similar — though not exactly alike — in other locations of the Universe, so far away that we will never be able to go there, it is because we know how a given distribution and composition affects light traveling through an ensemble of dust grains.

A particle has a given probability of absorbing a photon with a given wavelength, and in general this probability peaks around wavelengths of the order of the size of the particle (for small particles). Thus, if we know how the spectrum of some light source looks if there were no dust around (and we do for many sources, e.g. stars), then the difference between the known intrinsic spectrum and the observed spectrum can be modeled assuming some distribution and composition. Often the composition needs not be assumed, but can be constrained from the emission of the dust at infrared wavelengths.

Usually, the model that fits best the observations is a steep power law of the form $P(r)\propto r^{-a}$ with an index of roughly $a\sim3.5$; that is, the probability of finding a small grain is much larger than the probability of finding a large grain (more precisely, for $a=3.5$, grains of size $r=x$ is $10^{3.5}\simeq3\,000$ times more common than grains of size $r=10x$, and $10^7\!$ more common than grains of size $r=100x$).

For very large grains, the probability of absorbing a photon becomes independent of the wavelength of the photon. Whereas the small grains as described above have a "color preference", large grains are said to be "gray". This is the case for boulders, rocks, pebbles, and even sand-grain-sized particles. Thus, if a cloud consisted of such particles, the spectrum of a background source would simply be diminished by a constant factor at all wavelengths. This is very rarely observed — rather the sources are diminished much more at the short wavelengths than at the long wavelengths, as expected if there are more small grains than large grains.

• This is all good logic but I am not convinced the following is not true... light passing a great distance through a field of pebbles, stones etc., can be diffracted repeatedly around the edges of the multitude of particles it passes by (or even reflected off at a very obtuse angle), in such a way as to colour the light. – samerivertwice Aug 14 '17 at 9:14
• @RobertFrost: For such large grains, the ratio of diffracted-to-absorbed photons will be negligible. The circumference of a pebble with radius, say, 1 cm that will diffract a photon, is a thin ring with a width of perhaps 1 $\mu$ and so has a cross-sectional area of $2\pi(1\,\mathrm{cm})\times1\,\mu\sim10^{-5}\,\mathrm{cm}^2$, i.e. a fraction of $\sim10^{-6}$ of the total cross section of the pebble. – pela Aug 14 '17 at 11:16
• I think that conclusion requires some further facts, namely that the distance of nebula through which light has passed, and density of particles is such that the light will not have passed by $\sim10^6$ particles. The conclusion for any given nebula could therefore be estimated by analysing the overall transmittivity of the nebula. A low transmittivity would imply more of the light we see has passed close to some particle and been impacted by reflection or refraction. Are nebulae generally quite transparent? – samerivertwice Aug 14 '17 at 12:01
• @RobertFrost: That would be true for extremely low signal-to-noise ratios, but in general, if pebbles were responsible for the extinction, then on average the same fraction of photons would make it through the cloud at all wavelengths, whether there is one, 1e6, or 1e18 particles. Your last question depends on the wavelength you consider; some nebulae transmit close to no light at all in the UV, but are quite transparent in the IR. – pela Aug 14 '17 at 13:06
• @RobertFrost: Producing anything larger than single atoms is not easy; it requires high densities (so that particles meet) and low temperatures (so that they stick together), conditions that are met only in the vicinity of stars. In general, smaller structures are easier to create than larger. This is at least part of the explanation why $n_\mathrm{atoms} \gg n_\mathrm{molecules} \gg n_\mathrm{small\,dust\,grains} \gg n_\mathrm{large\,dust\,grains} \gg n_\mathrm{pebbles} \gg n_\mathrm{boulders} \gg n_\mathrm{planets}$. – pela Aug 15 '17 at 8:42