Astronomical-wavelength radio (AWR) transmissions between cosmic plasmas? My son asked me if electromagnetic waves longer than radio exist. I told him that even though physics permits such waves, there are no antennas long enough to radiate or detect them.
However, on further thought I realized that is not quite correct.
Supernovas like the Crab Nebula, as well as other astronomical phenomena such as cosmic jets, routinely create continuous plasmas with conductive lengths ranging from planetary distances to light years across. Such plasmas are also often in violent motion. Without (yet) attempting any detailed calculations, I'm pretty confident that violent motion in such giant conductive constructs should cause them to radiate in astronautical wavelength radio bands (AWR, and yes, I just now made that up), possibly powerfully.
But how would one detect such emissions, even if they do exist?
That's where the hair-of-the-dog-that-bit-you principle comes in: A sufficiently powerful AWR broadcast should be received and converted into large-scale plasma currents by any nearby cosmic-scale plasmas of the same general type.
So, my question if anyone who is willing to take a whack at something this speculative:
If AWR emissions exist and are powerful enough to create slowly alternating, long-duration current flows within cosmic-scale plasmas, are there experimentally detectable optical or short-radio phenomena -- e.g. polarization effects, or faster cooling of transmitting plasmas due to unexpected energy losses, or unexpected energy gains in receiving plasmas -- by which the emission or receipt of AWR could be detected?
I realize this is as much an astronomy question as a physics question, but if my physics argument is drastically wrong somewhere, or is correct but does not produce experimentally detectable phenomena, the astronomy part doesn't matter much.

2013-06-08 -- The discussion is interesting, but perhaps drifted a bit towards the question of much shorter (and directly detectable) VLF waves. Eduardo make the excellent point that the interstellar medium is opaque to VLF. By simple generalization of VLF behavior to far lower frequencies, that may also mean that astronomical-scale EM waves are also not possible.
It's worth emphasizing that even if something within the astronomy zoo is able to generate powerful AWR band emissions, and even if such transmissions could make it to earth, I'm pretty sure no antenna on earth would be able to pick up those transmissions.
That in turn emphasizes that the only readily apparent way to detect AWR band energy transfers, if they exist at all, would be by them enabling unexpected modes of transfer of energy between visible astronomical plasmas that would act as both AWR generators and receivers.
Eduardo's excellent point about the opacity of the interstellar plasma may provide the simplest answer: AWR cannot exist because interstellar plasmas will never allow it to.
However, that same VLF opacity issue brings up at least two more questions:


*

*Opacity at VLF may not necessarily guarantee interstellar opacity in the AWR band, which after all would be orders of magnitude lower in frequency. Speculating wildly, AWR might for example be so gentle in its ion-level impact that the interstellar plasma ends up being largely transparent to it. And yes, that really is just a wild speculation, nothing more.

*Even if the interstellar plasma is highly absorbing of AWR, any major generator of AWR band energy would still likely result in some sort of unexpectedly higher or faster outward transfer of energy surrounding the AWR generator. More specifically: if (big if_ AWR exists and can be generated at high power levels by self-excitation of currents in violently moving astronomically sized plasmas (think Crab Nebula), but is also absorbed very quickly by the interstellar medium, it should still be indirection detectable by its enabling of otherwise inexplicable increases in the rate or speed at which energy dissipates outward from the event into the surrounding interstellar plasma. Such an effect would be indirectly detectable by a lack of explanation for it from other known and well-modeled energy transfer modes.
I realize this has likely turned into an unfair question at this point, since the range of issues that would need to be analyzed is pretty high. It seems likely the idea of a AWR band that could (maybe!) exist, and even have indirectly observable effects on visible phenomena such as supernova cloud expansions, has not been explored much, if at all. That's interesting all by itself.
I'll probably either award Eduardo the answer soon for best coverage of the issue so far, or perhaps I'll even try a bonus. I am a bit intrigued by this one.
 A: This is not an answer, but merely some information to put you on the right track, too long to be in a comment. I am curious too, to see what other users with more information about the question may answer.
Cold plasma models (where the analysis is not complicated by thermal motions) consist essentially in electrons that are nearly free to move among heavier ions. There is an associated quantity $\omega_{p}$, the plasma frequency:
$$\omega_{p}^2 = \frac{n e^2}{\epsilon_0 m_e}$$
where $n$ is the number density of electrons. For a propagating electromagnetic wave, this relation holds:
$$ \omega^2=\omega_p^2 + k^2 c^2 $$
as derived in 8.13 in Choudhuri 2010
So that, for an EW with much bigger frequency than $\omega_p$,
$$\omega=k c$$
as with any usual EW, which means that the electrons are too massive to respond to such a high frequency, thus the plasma is transparent for such waves.
But if the frequency is lower than $\omega_p$, there is no real solution for $k$. I guess that means that the incident wave is partially absorbed as an evanescent wave, and the rest is reflected back, but I am no expert on this. The question is that low frequency waves cannot propagate within plasma, because the electrons are light enough to "dance" with the frequency of the incoming wave, thus absorbing (and re-radiating?) the energy.
Another question is the movement of a supernova plasma sphere, as you say in your comment... well, that's a bit like cheating. In the same sense, Voyager II is a metalic object that has been slowly moving along 1 light-day during the last decades. That is a loooong, (incredibly weak) EW what it has created, right? (yeah, -1 for this paragraph!). If I understood your question, you probably are wondering if there is in nature something big enough, electrically non-neutral at that size scale, that moves fast enough to create that giant EW. A binary black hole?
Books have data about $\omega_p$ for ionospheric plasma and things like that. I wonder what is the value of that free electron density of interstellar medium in Chris's comment (again, I am no expert on this). But I remember to have read that there is a delay in pulsar signals for low frequencies, that is attributed to the interaction with free electrons along the line-of-sight. I would be happy to read something more technical from any user.
