The Gravitational Lens and Communications

by Paul Gilster on November 6, 2009

If we can get the right kind of equipment to the Sun’s gravitational focus, remarkable astronomical observations should follow. We’ve looked at the possibilities of using this tremendous natural lens to get close-up images of nearby exoplanets and other targets, but in a paper delivered at the International Astronautical Congress in Daejeon, South Korea in October, Claudio Maccone took the lensing mission a step further. For in addition to imaging, we can also use the lens for communications.

The communications problem is thorny, and when I talked to JPL’s James Lesh about it in terms of a Centauri probe, he told me that a laser-based design he had worked up would require a three-meter telescope slightly larger than Hubble to serve as the transmitting aperture. Laser communications in such a setup are workable, but getting a payload-starved probe to incorporate a system this large would only add to our propulsion frustrations. The gravitational lens, on the other hand, could serve up a far more practical solution.

Keeping Bit Error Rate Low

Maccone goes to work on Bit Error Rate, a crucial measure of signal quality, in assessing the possibilities. Bit error rate charts the number of erroneous bits received divided by the total number of bits transmitted. Working out the numbers, Maccone posits a human probe in Centauri space trying to communicate with a typical NASA Deep Space Network antenna (70 meter dish), using a 12-meter antenna aboard the spacecraft (probably inflatable).

Using a link frequency in the Ka band (32 GHz), a bit rate of 32 kbps, and forty watts of transmitting power (and juggling the other parameters reasonably), the math is devastating: we get a 50 percent probability of errors. So much for data integrity as we operate within conventional systems.

But if we send Maccone’s FOCAL probe to the Sun’s gravitational lens at 550 AU, we now tap the tremendous magnification of the lens, which brings us a huge new gain. Using the same forty watts of power, we derive a completely acceptable bit rate. In fact, Maccone’s figures show that the bit error rate does not begin to become remotely problematic until we reach a distance of nine light years, when the increase in BER begins slowly increasing.

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Image: Figure 4. The Bit Error Rate (BER) (upper, blue curve) tends immediately to the 50% value (BER = 0.5) even at moderate distances from the Sun (0 to 0.1 light years) for a 40 watt transmission from a DSN antenna that is a DIRECT transmission, i.e. without using the Sun’s Magnifying Lens. On the contrary (lower red curve) the BER keeps staying at zero value (perfect communications!) if the FOCAL space mission is made, so as the Sun’s magnifying action is made to work. Credit: Claudio Maccone.

Building a Radio Bridge

Now this is interesting stuff because it demonstrates that when we do achieve the ability to create a human presence around a nearby star, we will have ways to establish regular, reliable communications. A second FOCAL mission, one established at the gravitational lens of the target star, benefits us even more. We could, for instance, create a Sun-Alpha Centauri bridge. The bit error rate becomes less and less of a factor:

…the surprise is that… for the Sun-Alpha Cen direct radio bridge exploiting both the two gravitational lenses, this minimum transmitted power is incredibly… small! Actually it just equals less than 10-4 watts, i.e. one tenth of a milliwatt is enough to have perfect communication between the Sun and Alpha Cen through two 12-meter FOCAL spacecraft antennas.

This seems remarkable, but gravitational lenses make remarkable things possible. Recall that it was only months ago that the first tentative discovery of an extrasolar planet in the Andromeda galaxy (M31) was made, using gravitational lensing to make the observation.

Into the Galactic Bulge

Maccone goes on to work out the numbers for other interstellar scenarios, such as a similar bridge between the Sun and Barnard’s Star, the Sun and Sirius A, and the Sun and a Sun-like star in the galactic bulge. That third possibility takes us into into blue sky territory, but it’s a fascinating exercise. If somehow we could use the gravitational lens of the star in the galactic bulge as well as our own gravitational lens, we would have a workable bridge at power levels higher than 1000 watts.

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Image: Bit Error Rate (BER) for the double-gravitational-lens of the radio bridge between the Sun and Alpha Cen A (orangish curve) plus the same curve for the radio bridge between the Sun and Barnard’s star (reddish curve, just as Barnard’s star is a reddish star) plus the same curve of the radio bridge between the Sun and Sirius A (blue curve, just as Sirius A is a big blue star). In addition, to the far right we now have the pink curve showing the BER for a radio bridge between the Sun and another Sun (identical in mass and size) located inside the Galactic Bulge at a distance of 26,000 light years. The radio bridge between these two Suns works and their two gravitational lenses works perfectly (i.e. BER = 0) if the transmitted power higher than about 1000 watt. Credit: Claudio Maccone.

I’m chuckling as I write this because Maccone concludes the paper by imagining a similar bridge between the Sun and a Sun-like star inside M31, using the gravitational lenses of both. We’re working here with a distance of 2.5 million light years, but a transmitted power of about 107 watts would do the trick. This paper is a dazzling dip into the possibilities the gravitational lens allows us if we can find ways to reach and exploit it.

The paper is Maccone, “Interstellar Radio Links Enhanced by Exploiting the Sun as a Gravitational Lens,” presented at the recent IAC. I’ll pass along publication information as soon as the paper appears.

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Ron S November 6, 2009 at 13:20

I haven’t yet read the paper, but I want to mention a couple of things. The effective beamwidth of this antenna system is exceptionally narrow. That is unavoidable. What this means is that aiming — both initial and maintaining — is a huge challenge. Imagine if you will a million-times scope, and using it to locate a pinpoint source in your jittery and extremely-tiny field of view.

High BER in itself is not a killer issue, but the FEC (forward error correction) will degrade throughput (effective bit rate) by a lot. This is standard procedure for deep space probes. However as you can see in those curves, the knee where you go from good BER to unusable is pretty steep.

tacitus November 6, 2009 at 15:52

So, what are the odds that there is an automated alien spacecraft out there somewhere at 550AU, keeping an eye on Earth and transmitting the latest and greatest information back to its home planet? :-)

Adam November 6, 2009 at 17:54

Hi All

With a gravity lens an alien could probably stay home and observe Earth in high definition… but it is nice to think that we have a natural “Broad-Band between the Stars” available.

jeff millar November 7, 2009 at 12:28

…a very interesting paper. Communication engineers would like to know the effective gain of such an “antenna”, which would then translate into beamwidth, effective aperature size, etc.

Some other engineering points… The receiver at the focal point of this would be pointing directly at the star/Sun and would need to have a precision beam shape to block the radio noise from the Sun while receiving signals from a narrow ring around the sun. This may take a very large antenna at 550 AU by itself. It’s not just the signal strength that matters, it’s also signal to noise ratio.

To communicate with a specific location light year away, the spacecraft would have to keep itself in the gravitational focal point, which it certainly not the same as a natural orbit. This will take energy.

Ron S November 7, 2009 at 14:52

Solar noise drops rapidly above 1 GHz so if you operate up there there is no need to block the sun. Think of DTV from geosynchronous satellites: sun noise is only a modest annoyance for a few days around each equinox.

Just make sure the beam is not so narrow that it only illuminates the sun. Mind you, from 550 AU that isn’t difficult to achieve.

Now if instead there is an alien transponder at the sun’s gravitational focus, this is a concern — for them. They spy on Earth at their relatively-close vantage point and relay the intelligence back to their home. However since they must aim at the sun their signal may be detectable on Earth. Or perhaps not. The gravitational amplification towards their home allows for modest power levels, which when detected on Earth by the direct path could be a very weak signal, one that would require a directed search.

Dave Moore November 7, 2009 at 17:17

This paper is a game changer for SETI.
Most search strategies are based on the assumption that the exosapien civilization will use enormously powerful beams to either signal with us directly or to communicate with each other. This paper implies that the signals may be of a power much lower than we assumed, and just as we assumed an alien race would communicate at the Hydrogen frequency, the alien races might assume we would do our searches using gravitationally lensed telescopes.
We are going to have to think through all our SETI assumptions to see how this possibility will affect them.

Eniac November 8, 2009 at 15:23

As I understand, the gravitational focus of a star is not one point, but a line starting at 550 AU and going on outwards indefinitely. Going further simply increases the radius of the “aperture ring” around the star. Has anyone looked into using nearby stars as telescope lenses to observe anything that may happen to be in line of sight? If it works with galaxies, why not stars? What resolution would a solar system bound telescope need to sufficiently resolve the aperture ring around a nearby star?

Eniac November 8, 2009 at 16:00

Well, to partly answer my own questions, I dug up this 2004 article in PhysicsWorld: http://physicsworld.com/cws/article/print/19575. Not sure if it has been discussed here before, it certainly ought to have been.

Sorry about wasting the bandwidth if this is obvious…

Gravitational lensing brings extrasolar planets into focus

Jun 10, 2004

Astronomers have used gravitational microlensing to detect a cool planet orbiting a star some 15,000 light-years away

A major breakthrough in the search for new worlds beyond our solar system happened recently with the discovery of a planet using a technique known as gravitational lensing. The new planet is about 1.5 times the mass of Jupiter, and is about half way between the Sun and the centre of the Milky Way. This makes it the most distant extrasolar planet detected by astronomers to date.

The discovery, made by Ian Bond and co-workers in the MOA and OGLE collaborations, represents the debut of a new and faster technique for discovering cool planets that orbit stars at large distances from the Sun (Astrophys. J. at press). Most significant of all, however, is the unique capability of gravitational lensing to discover Earth-like planets from the ground.

[more ....]

Dave Moore November 8, 2009 at 17:08

“Maccone concludes the paper by imagining a similar bridge between the Sun and a Sun-like star inside M31, using the gravitational lenses of both. We’re working here with a distance of 2.5 million light years, but a transmitted power of about 107 watts would do the trick. This paper is a dazzling dip into the possibilities the gravitational lens allows us if we can find ways to reach and exploit it.”

Just a thought.

Gravitational lensing has already been used to detect a Jupiter-sized planet around a star in M31, the Andromeda galaxy. The technique is to scan the galaxy looking for changes in the brightness of stars. When a dwarf star (that we can’t detect) passes in front of a bright star the lensing effect causes the bright star’s brilliance to rise and fall in something like a normal curve. If the dwarf has a planet orbiting it, and the planet happens to be in line of sight alignment then the normal curve develops a shoulder to it.

If we scanned the Andromeda galaxy with a radio telescope on its focal line with respect to our sun, we could use a similar technique to scan for planets to look for radio signals. (We would be looking at planet around the object star not the lensing star.) If the dish was large enough to increase the signal detection threshold by a factor of 100 (assuming signal strength is directly proportional to receiver area then this would be a 120 meter dia. dish), then we would pick up a signal of 10 to the 5 watts, i.e., a signal the strength of commercial radio and TV.

One thing about gravitational lensing is that the field of view is minute, which means the scope would have to scan the galaxy. The signal strength from gravitational lensing rises and fall over a matter of weeks so the scope would only have to cover a given area every couple of days or so.

Picking up the signal would be a one-off event though, a tantalizing glimpse of a sentient technological society never to be repeated, but nevertheless we would know there is another sentience out there.

jeff millar November 9, 2009 at 2:43

Solar Flux actually increases significantly with frequency, see http://vk1od.net/calc/qsrf/index.htm.

I really want to read the article to understand the dimensions of the ring around the sun. This will set the required angular resolution of the antenna at the gravitation focus. I’m starting to think it will have to have a huge aperture to resolve the ring separately from the sun. As Enaic mentioned, the ring gets bigger further from the Sun. Which makes for a tradeoff between antenna size and distance beyond 550 AU. Let’s see a graph of arc-seconds of separation between gravitational ring and limb of Sun vs AU from the Sun.

…running some numbers (with a lot of chance for error)…The Sun subtends 16 micro radians at 550 AU or 3.5 arc seconds. The gravitational ring probably just grazes the sun at 550 AU. Moving it out to 1% of the sun’s diameter would require .035 arc second resolution. If I read the diffraction limit formula correctly, this requires a 50 km aperture for a 1 cm radio wavelength. I don’t know how to calculate what distance from the Sun moves the ring out to 1% of solar diameter…that’s a key thing to know.

This analysis does sound about right. Current radio astronomy can image at less than .1 arc second resolution when using VLBI.

One other approach would use a smaller antenna, let some of the Solar noise creep in and simply increase link power.

Pat Galea November 9, 2009 at 3:57

Eniac is correct. The gravitational lens focus starts at 550AU, but doesn’t end there. In this respect, it is unlike an optical focus.

In practise, what you’d probably do is launch your craft on a hyperbolic orbit, with the long “leg” of the orbit on the asymptote of the line you want to follow.

Pat Galea November 9, 2009 at 3:58

Also, we should remember that in reality the usable focus actually starts around 700AU, due to the solar corona mucking with photons passing through it.

Eniac November 9, 2009 at 10:35

While the Einstein ring get larger as you move away, I doubt it fully makes up for the increased distance, so the farther you go, the higher angular resolution you will need. If you want to work out details, the math seems to be presented quite well here: http://en.wikipedia.org/w/index.php?title=Gravitational_microlensing&action=edit&section=4

Ron S November 9, 2009 at 11:52

Jeff, you’re right. Mostly. There is more than one peak in the solar spectrum. The one at lower frequencies is due to electron noise (synchrotron radiation) in any excited gas — this is same thing that make the sky (even Jupiter) so generally noisy at low frequencies. As the frequency increases, and that noise declines, you eventually hop onto the rising black body radiation curve for the sun. Your reference appears to be in that intermediate range where the solar flux is strongly mediated by sunspot activity (such as the 10.7 cm solar flux reading that correlates to geomagnetic activity).

I was assuming (didn’t check) that the noise from that would be small at low microwave frequencies. That’s still generally true, but without getting into specific calculations I shouldn’t comment on how great a factor it would be!

Dave Moore November 9, 2009 at 20:37

Eniac,
The Einstein ring is not the object. It is a focal element. As you move away from the sun, the ring becomes larger, which is the equivalent of your scope’s aperture becoming larger. Therefore, the resolution improves in proportion to your distance from the sun.

Eniac November 10, 2009 at 3:00

I thought we were talking about the “scope” on board the spacecraft. If you are talking about the entire “giant telescope”, yes, larger distance gives wider aperture. However, lacking a telescope tube, the detector at the focus needs to “resolve” the Einstein ring itself, i.e. you have to separate light coming from the ring from other light, particularly that from the sun. Thus, your secondary scope, or “eyepiece”, if you will, needs to have fine angular resolution itself, if I am not mistaken.

As you increase the distance from 550 AU outwards, I think what will happen is that at first that resolution can be relaxed somewhat, because the apparent distance between the sun’s surface and the ring increases, but after a certain optimal distance, resolution needs to be increased again, because the ring will grow more slowly than its apparent size decreases with distance.

The hyperbolic trajectory, I think, will not work for communication. There will be too much lateral motion, i.e. the “beam” will shift. Relative motion of the target star will also be a problem. Perhaps the two can be made to cancel, but probably not for long. Which means that for communication, where you need to focus on a single spot for a long time, you need to expend propellant continuously.

Instead, the best configuration for a long term focal mission may be a circular orbit at 700-1000 AU, with the “beam” scanning along the sky like that of a lighthouse, with small, but very accurate course corrections made to sweep over interesting targets. Not useful for communication, but good for resolving the finite sizes and surface features of stars and exoplanets at insane magnification. To get 2-d images, a linear array of detectors would be needed. A thousand detectors could provide megapixel image resolution along an extremely thin ribbon of sky. Perhaps not little green men, but starspots, oceans and continents should be possible.

Come to think of it, though, any planet will race through the field of view rather quickly, if you can hit it at all. That could clearly be a showstopper. Perhaps deep field observation of the early universe, then?

Eniac November 13, 2009 at 11:44

Here are some back-of-the-envelope calculations on the solar gravitational telescope:

Assume we are at f = 670 AU ~ 1E14 m.
Assume the Einstein radius there is twice solar radius r ~ 1.5E9 m
Distance to object is d = 10 ly ~ 1E17 m
Wavelength of light lambda = 500 nm = 5E-7 m

1) The distance vs. focal length ratio is d/f = 1E3, one thousand. That means that a 1 meter pixel-to-pixel detector will have a resolution of 1 km at the target system, which is quite phenomenal. There are at least two things that can keep that from happening: a) the diffraction limit, and b) resolving the Einstein ring from the sun requires a pixel aperture much larger than a meter.

2) Diffraction limit: The resolution limit due to diffraction is 1.22*d*lambda/r ~ 4 m. Well below our pixel resolution, so we are good with that.

3) pixel size: we need to resolve the Einstein ring from the sun. Angular resolution for the pixel telescope needs to be r/f ~ 1.5E-5, requiring a minimum aperture of a = 1.22*lambda*f/r ~ 4 cm. We are good with that also.

So far, unless I have miscalculated, it looks like 1 km resolution is feasible and could even be improve by a factor of twenty or so to reach ~50 meters, based on diffraction and pixel size. There are, however, at least two more potential problems: light gathering power and tracking. These are somewhat more difficult to deal with, perhaps I’ll take a stab some other time. Anyone know if, how, and where these things have been worked out before?

Note that small lambda here has a very beneficial effect and things would look much less rosy in the radio range.

Steven R. Martin November 26, 2009 at 0:57

I attended Dr. Maccone’s lecture at the SETI Intstitute in Mountain View, CA today (11/25/09). He outlined the two parts of the new book – the FOCAL spacecraft concept; and the use of KLT as a way for SETI to increase the chances of detecting signals from noise.

Of note are the separate missions that the FOCAL spacecraft could perform. All distances must be greater than 550 AU from the sun in order to take advantage of the gravitational lensing effect. However, the frequency of observable radio emissions changes as the distance increases, enabling observations of phenomena such as the Cosmic Microwave Background (at approximately 750 AU).

Dr. Maccone suggests that the CMB mission might be useful in convincing the influential cosmology community to press for a real NASA spacecraft effort. My impression is that the only thing holding back NASA is the reality that there is not an available propulsion method that would not take many decades for the necessary distances to be reached.

Also of note is the reality that the precision of positioning and station keeping required for the FOCAL mission is currently prohibitive. An engineering solution does not exist for holding a truly interstellar spacecraft to within 100 meters of its required position.

Dr. Maccone mentioned that the charts from his presentation should be at the SETI website soon. I would advise you all to check them out! Very intriguing.

Serge Boisse February 25, 2011 at 6:36

Steven, I think you are wrong regarding precision of positioning and station keeping. This would be true if the craft were in the vicinity of the earth, but it is not the case. At 500 or 600 AU from the Sun, the gravity pulling aceleration from the sun is… remote. So the craft could simply NOT orbit around the sun, and just remain at a FIXED place (with respect to the sun) using only a tiny ion rocket engine to stay there !

Feld December 12, 2011 at 16:08

Serge, yes moving it with precision will be easy enough. Finding the right spot may not be. Unless you have a feedback mechanism telling you EXACTLY were you are then finding a particular exoplanet is a needle in a haystack.

Once you find it, then maintaining it in view should be easy with a little ion engine.

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