SETI question

[Junghalli]

I have a question relating to this paper, which discusses trying to detect the energy signals of the drives of alien starships as a possible avenue for SETI:

Link

Specifically, there's a section talking about the possibility of detecting cyclotron radiation from magsails braking against the interstellar medium, suggesting they might be detectable from thousands of light years with a large (several km) space-based antenna.

Here's a graph

Now, my question for any of you with knowledge of the physics of cyclotron radiation is, are they talking about directional or omnidirectional signals here?

It seems to me that they must be talking about directional signals, because the inverse square law would quickly drown out omnidirectional ones. I base this on a small sample calculation I did.

Let's say our typical starship is a 10,000 ton Bussard ramjet, it has a maximum speed of .9 c, and it decellerates from that to some low speed (a few hundred km/s or so) in the course of one year. Since the magsail transfers kinetic energy from the ship to the ISM and cyclotron radiation, doing some quick KE calculations I got an average transfer rate of 3.7 X 10^16 watts. I don't know how much cyclotron radiation that translates to, but I'm assuming for the sake of argument that all that energy becomes cyclotron radiation.

Now a star is a good example of an omnidirectional energy radiator. I used Teegarden's Star because it was only detected recently, so it seems safe to say that it's close to the limit of detectability for good present telescopes (around 8 meter mirror diameter IIRC, using the Subaru telescope in Hawaii). So, say a 4 meter radius telescope can detect Teegarden's Star at 20 light years. Teegarden's star is 1/300,000 the luminousity of Sol, so it emits about 35,000 as much energy as my example ship at minimum.

The graph on the paper I linked to suggests that a 6 km radius radio telescope should be able to detect my example ship at several thousand light years. Now an optical telescope with a 6 km mirror, compensating for the inverse square law and hoping I didn't screw up the math, should be able to detect Teegarden's star at 30,000 light years. It should therefore be able to detect my example ship at a little less than 1 light year.

I realize that an optical telescope and a radio telescope are not the same thing, but I imagine in terms of simple energy interception calculations the mechanics are the same. Correct me if I'm wrong.

So, based on this, I'm assuming magsail cyclotron radiation isn't an omnidirectional signal. Please correct me if I'm wrong. Yes, I realize I did lots of questionable and probably things in that calculation; I'm generally not very knowledgeable at all about this sort of physics, but am I right in that conclusion?

[Singular Intellect]

If detection isn't omnidirectional, you'd best fucking give up trying to pinpoint anything you don't already know the location of regarding the astronomical scale.

[Junghalli]

If detection isn't omnidirectional, you'd best fucking give up trying to pinpoint anything you don't already know the location of regarding the astronomical scale.

Yes, I know that. That's pretty much the reason I want to know.

[Kuroneko]

Forget about Teegarden's star; from Earth, it's not too much fainter than Pluto and brighter than Eris. Acceleration due to a magnetic field is perpendicular to the field and the charge velocity, F = q(v×B). In an inertial frame in which v/c is low, the emitted radiation varies as sin²θ, peaking in the transverse directions from acceleration. For a high-velocity charge, relativistic beaming will tend to distort the radiation peaks toward the v direction. So either way, no, it won't be omnidirectional.

[Junghalli]

Forget about Teegarden's star; from Earth, it's not too much fainter than Pluto and brighter than Eris. Acceleration due to a magnetic field is perpendicular to the field and the charge velocity, F = q(v×B). In an inertial frame in which v/c is low, the emitted radiation varies as sin²θ, peaking in the transverse directions from acceleration. For a high-velocity charge, relativistic beaming will tend to distort the radiation peaks toward the v direction. So either way, no, it won't be omnidirectional.

So, assuming you have a ramscoop-type ship with a "choked" magnetic scoop at the front that's slowing down/deflecting the ISM particles as they hit the magnetic field at some fraction of c, what directions would the radiation be concentrated in? A band at a 90 degree angle from the direction of acceleration? I unfortunately must admit the math is a little above me.

What I'm particularly interested in is whether the signal is more likely to spread out in a broad patten that will potentially cross many star systems and allow many opportunities for detection by distant observers, or more of a narrow cone where distant observers would have to get very lucky to be in its path.

[Kuroneko]

Well, it depends. Suppose you're a distant observer, with charges with low initial velocity relative to you, which will stay low as long as the ship deflects the charges rather than stopping them (relative to itself). Then, to a good approximation, radiation intensity will be proportional to sin²θ, θ angle with respect to the acceleration vector.

Suppose further that the acceleration is mostly along one direction. Then without loss of generality, we can work in spherical coordinates with zenith being the acceleration direction, deviation from which is given by the zenith angle φ, the peak therefore being at the equator (φ = π/2). The area element is dA = r² sinφ dφdθ, so the proportion of energy radiated in the equatorial bband (π/2-α,π/2+α) is F = Int_{π/2-α}^{π/2+α}[ sin³φ dφ ] / Int_0^π[ sin³φ dφ ] = sin α [ cos²α + 2 ]/2. In particular, about half the energy will be radiated in a ±20°band around the equator. Thus, while not omnidirectional, it's not exactly narrow either.

[Junghalli]

So it would look sort of like this:



With the cyclotron radiation coming off from a torus around the middle of the magsail, and a reciever would have to be in that cone to be able to pick it up at a distance (light years)?

[Kuroneko]

If the deflection of charges is actually used for propulsion, then yes, since the radiation is transverse to the acceleration of the charges, which would be parallel to the ship acceleration in that case.