I didn’t plan to do a follow-up to yesterday’s post about the optics of sending messages with lasers, but then I starting idly thinking about detection, prompted in part by a bunch of conversations with my summer students about single-photon detectors. which led to scribbling on the back of an envelope, which led to Googling, and suddenly, I have a follow-up post.
So: as we said yesterday, if you want to send messages over a distance of ten light years, a relatively efficient way to do this might be to send them via lasers. This results in the light being spread over a pretty big area, though– the best you can do at a distance of 11 light-years is a spot around 160,000m radius– so how easy would that be to detect?
Well, we have the ability to detect single photons, so a good way to think about this would be to ask how many photons from that laser spot we could expect to collect with a telescope. The number of photons per second sent out by a laser will be equal to the laser power in watts divided by the energy per photon (a watt is one joule per second, remember). The photon energy depends on the wavelength, and yesterday’s estimates used a wavelength of 400nm, at the short end of the visible spectrum, which corresponds to around 5×10-19 joules per photon. So a one-watt laser would be sending out 2×1018 photons per second.
Yesterday, we said that the smallest spot you could hope to make at the far end is 1.6×105 meters in radius, so we need to spread those photons over that area, which works out to about 24,000,000 photons per square meter per second. If you were looking at that with a telescope having a mirror with a 10-meter radius, you’d expect to see something just under eight billion photons per second. That’s a pretty substantial rate, something you would easily be able to detect even without going to fancy single-photon counters.
Of course, it’s not quite as simple as just detecting those eight billion photons per second, because your communications laser is going to be coming from a region very close to your home star, so you’ll need to pick it out from that background. which is where we have to turn to Google, which turned up this discussion at CosmoQuest giving two different values: a very bright star produces something like two million photons per second per square centimeter, and a very dim one about 0.2 photons per millisecond per square centimeter. Doing a bit of multiplication gets us a total photon flux for our imaginary telescope of somewhere between 6×108 and 6×1012 photons per second, depending on the magnitude of the star the signal is coming from. At the low end, that would make our 1W laser clearly detectable; at the high end, not so much.
But then, it’s not as bad as it might seem, because a laser by definition is concentrated in a very narrow band of wavelengths, while the flux from a star is spread out in a black-body sort of spectrum. So if you were to focus on a very narrow region in the right range of wavelengths, the laser photons might very well stand out even against the background of light from the star. This will also depend somewhat on the character of the star– a violet laser would be more clearly detectable coming from the neighborhood of a reddish star. I’ve had enough mucking around with weird astronomical unit conversions, though, so I’m not going to try to figure out the details– call it extra-credit homework, which you can send to Rhett for grading.
Of course, that’s the optimum case, where you’re getting the smallest possible spot size at your distant target by launching your signal from a mirror with a radius of 100,000m, the size of a biggish asteroid. That might not be completely ludicrous for a civilization capable of launching an interstellar probe in the first place, but it’s not going to work for the probe itself. So what would the return signal look like, assuming you used the 10-m-radius detection mirror to send the return signal?
Well, from yesterday’s post, a 10m launch mirror gives you a beam at the far end with a radius of 1.3×109m. that’s a factor of 8000 or so bigger than you would get with the asteroid-scale mirror, which corresponds to an increase in the beam area by a factor of 66,000,000. Which means a 10m telescope back on Earth would pick up just 114 photons/s from a space probe equipped with a 1W laser at 400nm. That’s… more challenging. You might try using the same asteroid-scale mirror as a telescope to pick up the return signal, which would boost your laser photon counts back up to the same level as before. But, of course, that’s going to boost the photon rate from the background star by that same factor of 66,000,000, so it doesn’t actually help. If you wanted your laser flux to match the total background light from a dim star, you’d need to use a five megawatt laser to send the signal, which is a bit tricky. But I suppose you could run it off the magic compact fusion reactor you’re using to power your relativistic space probe in the first place…
So, anyway, there’s another blog post on the feasibility of using lasers to send messages between the stars. There are, of course, a lot of factors left out of this, chiefly the fact that I assumed perfect Gaussian beams for this (which you’re probably not going to get) and that I’ve ignored any effects of stuff along the beam line. Even interstellar space isn’t perfectly empty, and over the span of 11 light years, you might need to worry about that medium causing some distortion of your beam. In which case, you probably want to decrease all the laser photon count rates by an order of magnitude or so, probably more. But those calculations won’t fit on the back of any envelopes I have handy, so this is what you get.