# What is the physics of the “spinning dust” contribution to Cosmic Microwave Background measurements?

The lengthy paper Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results mentions "spinning dust" about 51 times. It is a potential contributor to the measured spectrum and the details of its emission spectrum has more than one proposed model.

question: Is there a simple way to understand the physics behind the emission spectrum of spinning dust and how it would differ from non-spinning dust?

• Try Gold et al. 2011 where they talk about the spinning dust models and how they try to create masks to remove this emission from the WMAP results. Basically, the spinning dust produces synchotron radiation whereas non-spinning dust (and spinning dust for that matter) produces thermal radiation. What you're asking ultimately is about the different types of radiation emissions in which case any standard radiative physics textbook would cover these concepts. – zephyr Oct 4 '17 at 17:19
• You seem to have missed part of my point which was that this isn't a spinning-dust physics topic, its a synchotron radiation physics topic. If you understand how and why synchotron radiation is produced, you'll understand how and why spinning dust produces it. You're not likely to find detailed papers or textbooks on this very specific application of a general physics concept. – zephyr Oct 4 '17 at 18:18

"Spinning dust" is a mechanism proposed to explain a particular feature in the foreground emission of CMB; a bump around $\nu\sim20\,\mathrm{GHz}$.

Dust grains acquire charge through photoelectric emission and collisions with electrons and ions (Draine & Lazarian 1998). As zephyr comments, if the dust is a poor conductor, its charges will, in general, be unevenly distributed, causing small dust grains to exhibit an electric dipole moment $\mathbf{\mu}$. But the molecules making up the grains may themselves have a dipole moment, and even a perfect conductor will, in general, have its charge centroid displaced from the mass centroid (Purcell 1975).

Collisions and radiation may cause the grains to start spinning, and in the presence of magnetic fields (which are very common in the interstellar medium), this spin in turn causes the particles to emit radiation with a power $P$, according to Larmor's formula which for a rotating dipole can be written as: $$P = \frac{2}{3} \frac{\mu_\perp^2 \omega^4}{c^3}.$$ Here $\mu_\perp$ is the component of $\mu$ perpendicular to the rotation axis, $\omega$ is the angular frequency of the rotation, and $c$ is the speed of light.

The emitted radiation matches the rotation frequency which lies in the (tens of) GHz-region, corresponding to wavelengths in the microwave region.

In contrast, the radiation from non-spinning dust will be thermal, thus lying in the infrared.

The paper you link to (Bennett et al. 2013) shows the difference in Fig. 22 (although thermal radiation peaks outside the observational range of WMAP): The spinning dust peaks around $\nu\sim20\,\mathrm{GHz}$, while the thermal radiation peaks around $\nu\sim2\,000\,\mathrm{GHz}$.

Note that spinning dust also emits thermal radiation, and in fact thermal fluctuations within the grains cause the charges to shift around quite rapidly, changing $\mu_\perp$ and $\omega$ (Hoang et al. 2015), thus effective smearing out the spectral lines.

A symmetrical dust grain will arguably be hit by particles/photons, on average, as much from one side as from another. A mechanism to accelerate an asymmetrical grain's spin is proposed by Purcell (1975). Below is Fig. 1 from his paper. A particle that strikes in a concavity is more likely to interact with the grains twice. If the gas it colder than the grain, it will be heated and leave the grain with a larger velocity than it entered with, causing the grain in the figure to start spinning counter-clockwise; it the gas is hotter (which is more often the case), it will cause the grain to spin clockwise.

• @uhoh Because dust particles aren't conductive and can't reach electrostatic equillibrium easily. Not to mention they're constantly bombarded by photons and cosmic rays causing them to become (slightly) charged. The same is true of most non-conductive objects. It particularly matters for these dust particles because they're so tiny. – zephyr Oct 4 '17 at 17:15
• @uhoh $\mu$ is the electric dipole moment. And the dust grains can become charged, as I said, because they're hit with photons and cosmic rays which knock off electrons (e.g., the photoelectric effect). Again, as I said, dust grains are not conductive so the electrons cannot easily move around and reach electrostatic equilibrium meaning they maintain mostly constant separation of charge. As an analogous example, consider rubbing a balloon on your hair. Your hair becomes charged and remains charged for a while for the same reasons. – zephyr Oct 4 '17 at 18:25
• @uhoh You're really missing my points here. I mentioned hair in that it analogously holds its charge for a while, not for how it gets its charge. Besides, as I already said dust is constantly getting bombarded so even if it can reach equillibrium over long periods, it will be easily and quickly knocked back out. And I think you're assuming it is really easy to form monopoles. If the electric charge distribution is anything but perfectly spherically symmetric (which it always will be), you'll have a dipole induced. There's no possible way these dust grains will have only a monopole. – zephyr Oct 4 '17 at 18:38
• I edited my answer thanks to @zephyr's comments, and also corrected an error — the magnetic fields don't cause the rotation; that is caused by interactions with other particles. – pela Oct 4 '17 at 21:27
• @uhoh Thanks for the heads up, but I don't know enough about laboratory experiments to give a qualified answer. – pela Dec 17 '18 at 15:19