<p>The size of cosmic dust grains is in general given not by some size, but by a size <em>distribution</em>. 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.</p>

<p>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 <em>modeled</em> assuming some distribution and composition. Often the composition needs not be assumed, but can be constrained from the <em>emission</em> of the dust at infrared wavelengths.</p>

<p>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 $r=100x$).</p>

<p>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.</p>

CC BY-SA 3.0
2017-08-14T09:14:12.480Z
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.
Robert Frost
CC BY-SA 3.0
2017-08-14T11:16:51.637Z
@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
CC BY-SA 3.0
2017-08-14T12:01:05.390Z
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?
Robert Frost
CC BY-SA 3.0
2017-08-14T13:06:07.240Z
@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
CC BY-SA 3.0
2017-08-14T15:42:43.310Z
@RobertFrost take a look at the equations for "The spot of Arago"  and related calculations for diffraction caused by a blocking "dot" which is the reverse of a blocking plate with a pinhole in it.  That may help you understand what people are telling you here.
Carl Witthoft
CC BY-SA 3.0
2017-08-15T08:42:44.080Z
@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
CC BY-SA 3.0
2017-08-15T16:48:25.510Z
@pela for your last statement to be pertinent you would have to mean the number of isolated atoms exceeds the number of atoms contained within collections of atoms such as rocks, stars and planets.  Is that really your claim? As that would seem surprising to say the least.
Robert Frost
CC BY-SA 3.0
2017-08-16T12:42:39.187Z
@RobertFrost: Yes, definitely! The typical metallicity in the Milky Way is ~0.02, i.e. ~2% of the elements are heavier than helium. Of this, roughly 1/3 is locked up in dust. Most hydrogen and helium is _not_ in dust (it is mostly Si and C). That means that of the order of 1% of the atoms are in dust grains. If building a dust grain of, say, r ~ 1 μ takes ~1e9 atoms, then the _number_ density of these grains is roughly 11 orders of magnitude smaller than the number density of atoms. Pebbles, boulders and planets use an increasingly higher number of atoms [cont'd below]
pela
CC BY-SA 3.0
2017-08-16T12:43:04.830Z
…and have correspondingly smaller number densities. Dust grains grow in the interstellar medium, but this growth is often counter-acted by intense radiation fields that tend to destroy the dust grains (apart from the very cores of molecular clouds that may be self-shielded), along with other destruction mechanisms. This makes it virtually impossible to grow to macroscopic sizes. The only place this happens is in stellar systems, but these are very small (a fraction of a parsec) compared to molecular clouds (tens to hundreds of parsec). [cont'd below]
pela
CC BY-SA 3.0
2017-08-16T12:43:16.777Z
…And the amount of gas locked up in stars/stellar systems is roughly half the amount in the interstellar medium by mass, and of this, by far most of the matter is in the star, not the pebbles, rocks, and planets around the star.
pela
CC BY-SA 3.0
2017-08-14T08:05:35.343Z
2017-08-14T08:05:35.343Z
pela
<p>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.</p>

<p>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.</p>

<p>How might we measure size from such distances?</p>

CC BY-SA 3.0
2017-08-14T15:44:14.113Z
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
CC BY-SA 3.0
2017-08-14T15:59:43.533Z
@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.
Robert Frost
CC BY-SA 3.0
2017-08-15T22:03:11.790Z
@RobertFrost Gravity is of negligible importance between dust grains.
ProfRob
CC BY-SA 3.0
2017-08-16T03:21:57.803Z
@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.
Robert Frost
CC BY-SA 3.0
2017-08-16T06:34:45.297Z
@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.
ProfRob
CC BY-SA 3.0
2017-08-16T07:36:17.423Z
@RobJeffries what is the reason?
Robert Frost
CC BY-SA 3.0
2017-08-16T07:41:26.410Z
@RobJeffries bear in mind the density of elements clumps similar elements  together in common orbits, drawing matter into rings. Gravity also draws matter into common plane, direction of rotation and speed making accumulation of dust much more likely than if its distribution was even among 3d space.
Robert Frost
CC BY-SA 3.0
2017-08-16T09:16:57.230Z
@RobertFrost Dust in the solar system (and others) is blown out by radiation pressure before it can form larger bodies. Only about 1% of the mass in the interstellar medium is in the form of dust and most of that is entrained with gas. Dust does not behave like individual, small gravitational bodies.
ProfRob
<nebula>
How big is nebula dust?
Robert Frost
# How big is nebula dust?

(Asked by: username_0 on 2017-08-14)

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?

**Tags:** nebula
> **Comments:**
> **username_1**: 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?)  
> **username_0**: @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.  
> **username_2**: @RobertFrost Gravity is of negligible importance between dust grains.  
> **username_0**: @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.  
> **username_2**: @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.  
> **username_0**: @RobJeffries what is the reason?  
> **username_0**: @RobJeffries bear in mind the density of elements clumps similar elements  together in common orbits, drawing matter into rings. Gravity also draws matter into common plane, direction of rotation and speed making accumulation of dust much more likely than if its distribution was even among 3d space.  
> **username_2**: @RobertFrost Dust in the solar system (and others) is blown out by radiation pressure before it can form larger bodies. Only about 1% of the mass in the interstellar medium is in the form of dust and most of that is entrained with gas. Dust does not behave like individual, small gravitational bodies.  

---

## 1 answers

### Answer by username_3 on 2017-08-14. Score: 9 | Accepted answer

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.

> **Comments:**
> **username_0**: 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.  
> **username_3**: @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.  
> **username_0**: 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?  
> **username_3**: @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.  
> **username_1**: @RobertFrost take a look at the equations for "The spot of Arago"  and related calculations for diffraction caused by a blocking "dot" which is the reverse of a blocking plate with a pinhole in it.  That may help you understand what people are telling you here.  
> **username_3**: @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 $n_\mathrm{atoms} \gg n_\mathrm{molecules} \gg n_\mathrm{small\,dust\,grains} \gg n_\mathrm{large\,dust\,grains} \gg n_\mathrm{pebbles} \gg n_\mathrm{boulders} \gg n_\mathrm{planets}$.  
> **username_0**: @pela for your last statement to be pertinent you would have to mean the number of isolated atoms exceeds the number of atoms contained within collections of atoms such as rocks, stars and planets.  Is that really your claim? As that would seem surprising to say the least.  
> **username_3**: @RobertFrost: Yes, definitely! The typical metallicity in the Milky Way is ~0.02, i.e. ~2% of the elements are heavier than helium. Of this, roughly 1/3 is locked up in dust. Most hydrogen and helium is _not_ in dust (it is mostly Si and C). That means that of the order of 1% of the atoms are in dust grains. If building a dust grain of, say, r ~ 1 μ takes ~1e9 atoms, then the _number_ density of these grains is roughly 11 orders of magnitude smaller than the number density of atoms. Pebbles, boulders and planets use an increasingly higher number of atoms [cont'd below]  
> **username_3**: …and have correspondingly smaller number densities. Dust grains grow in the interstellar medium, but this growth is often counter-acted by intense radiation fields that tend to destroy the dust grains (apart from the very cores of molecular clouds that may be self-shielded), along with other destruction mechanisms. This makes it virtually impossible to grow to macroscopic sizes. The only place this happens is in stellar systems, but these are very small (a fraction of a parsec) compared to molecular clouds (tens to hundreds of parsec). [cont'd below]  
> **username_3**: …And the amount of gas locked up in stars/stellar systems is roughly half the amount in the interstellar medium by mass, and of this, by far most of the matter is in the star, not the pebbles, rocks, and planets around the star.  

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