21. A Telescope at the Solar Gravitational Lens: Problems and Solutions

[Music] [Music] [Music] our next speaker is well known to this community this is dr. Jeff Landis after sending undergraduate MIT received a PhD and from Brown University he went to work as a senior researcher at Lois research some time ago and now he made the transition to the dark side became a civil servant and continues to research there I've known Jeff a long time I made a presentation in 2014 of a concept I thought was original only to find out later he thought of the whole thing thirty years earlier so Jeff please go good morning so Slava gave an excellent presentation about why the solar gravitational lens is interesting now I will do a presentation about why it is difficult the solar gravitational lens is a fascinating object but getting images from the gravitational lens is not going to be easy the background is something that Slava has already talked about the fact that a massive body the fact that a massive body deflects light is of course one of the classic consequences of general relativity and because of that it can act as a lens and as mentioned since 1979 there have been people proposing you can use this lens it is in a sense a giant telescope and telescope that's actually an area smaller than the Sun but that's much larger than actual physical telescopes so can we use it to image extrasolar planets well yes the theoretical magnification is high enough to image not merely the planet but to map the surface but there's practical difficulties here the challenge of the mission is tough 550 au is difficult but it is interesting to us precisely because it's difficult there's not a whole lot to look at this far from the Sun so it is a potential interstellar precursor of course elsewhere in this meeting people are talking about to get there but I just want to show a couple of the proposals even back in 1987 JPL did a conceptual design for this one the thousand astronomical unit mission which would go out to a distance of the gravitational lens here's something that I like perhaps a little bit better the idea of solar or laser pushed light sails here's a concept in fact that Greg Matloff has been talking about quite a bit where a solar sail comes in very close to the Sun in order to get high-intensity sunlight to push it out toward the gravitational lens well here's the physics perhaps I shouldn't go too much into detail here but the interesting thing to note is that because you can only image light which does not pass through the Sun itself you need the Einstein ring to be outside the surface of the Sun that puts a minimum distance of about 550 astronomical units for the focus it's worth noting of course that as you get further and further away the focus is not a single place it's not a point focus but it is a line of focus this is actually good in some sense it means you don't have to stop at a point in order to focus but if you're traveling out at tens or possibly even hundreds of AU per year you stay in a gravitational focus as long as you're going radially outward from the Sun well let's see what some of the difficulties here are the lens is pointed at a target exactly on the far side of the Sun ah so if you want to re aim at a different target say one degree away you have to move one degree which at five hundred fifty au or further is a long distance to get one degree of pointing of your telescope you'd have to move ten astronomical units the distance to Saturn what this means is essentially if the telescope is not we pointable you pick your target before you launch ah and you are then set on that target it is a single purpose telescope ah it also means that to aim at a target far away you need to position yourself extremely well you're at a distance of own the order of maybe 90 trillion kilometers and you need to find your point to within a distance of something like 10 kilometers just to image the planet here's the geometrical optics of it uh if we're now looking at the Sun as just a lens and don't think too much about what type of lens it is it's a lens with a focal length of greater than 550 astronomical units all of you telescope users out there know that magnification is proportional to the focal length so the gravitational lens produces an image at a conceptual focal plane and you can figure out how big that images and here's how big it is for it uses an example a planet 10 light-years away so I've always used an example of a hundred so you can do the multiplication in your head but 10 would be the distance roughly of Epsilon Eridani about the closest sort of distance you might want to image an extrasolar planet so the image of the planet on the focal plane is 12 and 1/2 kilometers in diameter the thing to note is that this means that it isn't acting like an ordinary telescope we have an image of focal plane imager what it means is that the image at the focal plane is actually bigger than your spacecraft is it's kind of the opposite that image is no longer inside the telescope but the telescope is now inside the image this has consequences so you're not imaging the whole planet you image a small fraction of the planet unless you have a focal plane of course as many kilometers in diameter an example case a one meter telescope would one meter in dimension would image about a kilometer on the planet of course that isn't what you image because of the focal blur so imaging the whole planet would require a huge away array well how could you do that well one thing is you could raster across the planetary disc another might be however talking about things like star shot where we send out perhaps hundreds maybe thousands of tiny spacecraft well we might be able to just send one spacecraft out to each point in the focal plane so we send out a thousand spacecraft and each one looks at a point on the planet it may not be an insuperable problem but a problem is the motion of the image the magnification is high and the planet is moving the plane is orbiting if it's orbiting at Earth's velocity 30 kilometers a second that one kilometer part will Traverse in 33 milliseconds but the entire diameter of the planet more to the point will pass across a given focal plane in about 42 seconds so the planet does not stay in the particular place for very long if you were talking at the hundred kilometer sorry the hundred light year distance it would be a lot slower it would be 420 seconds but that's still not very long well what does that mean well the first is you might be able to use that feature because I'm saying that we have to raster in order to get the whole planet well but the planet in one dimension rasters by itself it moves across the focal plane so now we only need a line detector in order to raster the full planet because the planet will move in the second dimension so it's a bug 42 seconds is not very long but it's also a feature it's a feature that we might be able to use well let's calculate gain Slava gave us some information on theoretical gain at the diffraction limit unfortunately the gravitational lens telescope is not diffraction limited in fact actually Jim Benford just mentioned one of the reasons it's not diffraction-limited is that the variations in index refraction of the corona of the Sun in fact completely destroys the wavefront the blurring due to that alone is going to hurt your image beyond the diffraction limited but let's look at the geometrical magnification a lot of the old papers on gravitational lenses said oh we can't calculate the focal blur due to geometrical optics because it's theoretical infinite well actually it isn't infinite it's infinite only for an infinitesimal point but nothing is an infinitesimal point just a couple of vocabulary words amplification will define as flux at the focus divided by the flux that would have been received without the lens gain is the same as amplification it's usually expressed in logarithmic units but I will flip back and forth I'll use gain an amplification really they're the same thing just whether the units are logarithmic or linear magnification is the area of the object divided by the area of the object without the system turns out we're interested in area magnification but there's a brightness theorem that says that amplification and magnification are actually the same thing you don't increase the brightness you just increase the apparent area so here is a view of what we're actually looking at this is the Einstein ring of a distant galaxy surrounding a star and there's more of the galaxy that we can see because the Einstein wearing is amplifying that distant galaxy here it is in schematic we're looking at the Einstein ring and that blue ring on the outside here this is the image of the planet as was shown in the video so at the minimal focus design star knowing is exactly touching the surface of the Sun as you get further and further out the Sun gets smaller the Einstein wearing also gets smaller but not as fast so the Einstein wearing seems to be further away from the surface of the Sun so look an example case if we're doing the Tim Lightyear planet the magnification is just the error the total area of this ring there it is divided by the area of what the planet would be if it weren't smear it across the Einstein ring that's relatively easy to calculate there's the the calculation that's relatively straightforward for this particular case the earth diameter planet at 10 light years distance the area of that ring divided by the original area the planet is an amplification of about 6400 so you getting 6400 times more light but there's a difficulty here difficulties the solar corona actually I was looking at the solar corona just what was that about a month and a half ago I'll help most of us were looking at the corona it was actually a magnificent sight but we've been saying well the Einstein ring has to be outside of the surface of the Sun which is here blocked by the moon but actually if it's outside the surface of the Sun there's still quite a bit of light so here's the corona seeing during eclipse so the disk of the Sun has to be blocked so the first thing is we do need a coronagraph that's gonna complicate the mission a little bit it's more than just a image detector aiming at the Sun it's an image detector that's blocking the Sun itself but you also have to block the coronal light in fact if you only block the Sun this part the corona itself would be brighter than the planet you wouldn't see the planet so you have to be more distant than 550 au here's a view of the stolen from an old paper of how bright that solar corona is I here very close to the Sun at about 1.2 solar radii it's actually as bright as de sky here actually out almost a four solar radii the brightness of the corona is as bright as the sky when the moon is full but actually astronomers don't usually do observations when the moon is full because they consider that too bright you cant see dem stuff when the moon is full but we're gonna have to deal with this anyway because we'd have to go out to two times the radius of the Sun which means that you'd have to be four times the distance away you'd have to be at 2200 astronomical units in order to get that Einstein ring separated from the Sun by two solar radii that's probably too far 550 au is hard 2200 au is a bit harder let's go back and think about image brightness as I said you can calculate the image brightness from geometry it's a factor of about 64,000 so that means that the one meter diameter light if you have a one meter telescope at the gravitational lens you're collecting the same light as an 80 meter telescope without the lens for that planet that's at 10 light-years away but it moves past the focal plane pretty quickly in that 40 seconds astronomical telescopes actually don't just take snapshots it's not like your point-and-shoot camera that you point you shoot and you see the image you usually camp on one image for a long time you take long exposures that for Deep Field images these can even be days worth of exposure where's the planet moves past the imaging plane in 40 seconds so this means that since long integration times are needed to increase the signal-to-noise ratio here's the noise the signal is a little dot in there to increase the signal-to-noise ratio you want long integration times so actually the fact that it moves across very quickly gives you bad problems with signal-to-noise ratio well let's look at the line of focus I showed this graph before every point about this line is a focus but I also want to point out that while this point is focusing all these red lines all of these light is out of focus at the focal point so that actually turns out to be the definition of spherical aberration that as you go further away from the lens you are focusing to a different point ah I'm not sure what that ray is but as you go further away the focus is to a different point so that blurs the image here the image here is this plus it's all of these other rays which are increasingly out of focus so this is a lens with spherical aberration is actually negative spherical aberration because the further out points on the lens are actually focusing further away so that gives you focal blur and that focal blur actually is very easy to calculate it comes just from looking at the area of the Einstein ring but the interesting thing is the amplification is 1 over radius so the further you get out so you'd think well that goes toward infinity at the axis it doesn't because an area of say 1% of the area sorry yeah point 1 of the radius which is 1% of the area gives you only 1% of the light sorry only 10% of the light so the focal blur actually turns out to be half the radius of the planet imaged and that's purely due to the spherical aberration inherent in the lens so let's think about that although the center part of the planet is intensified relative most of the light doesn't come from that center spot well the first thing you say is well in a lens that we use for ordinary purposes we correct that out we correct out spherical aberration unfortunately correcting spherical aberration would require a lens that's roughly as big as your telescope so in this case it would require a lens that could resolve the width of the Einstein ring but if you could resolve the width of the Einstein ring you could just resolve the planet you wouldn't need the gravitational lens so the spherical aberration for our purposes is inherent in the system you can't resolve it out well but let's look a little bit more of the structure of the Einstein ring I have another paper I present at the aerospace sciences conference that gives the the math of this but if you look at a particular stripe of the Einstein ring what is that stripe well this planet has been smeared out into the Einstein ring but this stripe of the planet is imaged in that part of the Einstein ring so it was this stripe of the planet is mapped to that part of the Einstein ring so every portion of the planet is mapped onto a portion of the Einstein ring and you should be able to deconvolution lead at deconvolution all the stripes include the center point so this is how it is that the center point is amplified relative to the edge points is that the further out you go with the more narrow the portion of the Einstein ring that's included well so let's take a look at that if you're not on the center of the planet what if you're not aimed toward the center then this stripe of the planet NOW images that stripe of the Einstein ring so as the planet moves you're looking at different stripes across the planet on different portions of the Einstein ring so in principle looking at different flight stripes of the Einstein ring enough information could be acquired to do a computer deconvolution to reconstruct the plane and I see now Slava has adopted that under his baseline program good that helps how much well here's just an example and this is again not to scale because when you do things to scale everything gets very tiny but this is actually showing one arcsecond rings around a a planet so if you have one arcsecond in your telescope you can get maybe 13 different slices of that einstein ring so with deconvolution maybe you could get a 13 by 13 centimeter pixel well one arcsecond isn't a particular limit in a telescope here's the Hubble Space Telescope 2.4 meter mirror in principle at all to get 0.5 0.05 arc seconds of resolution actually gets about 0.1 arc second no telescopes are actually completely diffraction limited but if you could do that you would be able to resolve about a hundred points around the outside of the ring well I didn't mention but this let's go back a little this fact that you have multiple things this is resolved but there's an ambiguity this slice contains light from this slice of the planet so it contains the left and the right side and it's merged together since you can't resolve that this part of the Einstein ring which is the mirror image of that also has both sides that gives you a mirror ambiguity if you're trying to resolve it this way but the easiest way to resolve that mirror ambiguity is to look at the planet and half phase so half of the planets missing or even better in crescent phase so here's the Crescent planet so this stripe now maps on to this part of the Einstein ring and there's no longer a mirror ambiguity there is part of it is light from this part of the planet but that part of Planet is dark it doesn't matter so using it this way with multiple parts of the Einstein ring being resolved on a crescent planet you could resolve more of the planet look at a crescent planet helps a little bit more a focal blurr is less of a problem on a crescent planet it still technically half the planets diameter but most of the plant is dark so the fact that this focal blur includes a lot of region around it is less important because the dark part doesn't contribute so just looking at conclusions the gravity lens can be used as a telescope but there's many difficulties which are going to make it hard to do this mission the required pointing is extremely difficult you're pointing at a very small object very far away with very high precision it means that over your distance of a hundred trillion kilometres you have to have a precision of about ten kilometers the size of the image and the focal plane is a problem it means that you are now having a telescope that's smaller than the image rather than the other way around the motion speed is a real problem the planet moves across your focal plane so that you cannot integrate with long periods of time you need an occult err people haven't really looked into that problem up until very recently but this complicates the design you're not merely looking at a light bucket but you're looking at a light bucket staring into the brightest object in the sky when you first got your telescope when you were perhaps 10 years old the first thing they told you is don't point it at the Sun well okay here you have to point it at the Sun the signal to noise ratio produced by the brightness of the solar corona is really going to limit your resolution it does not have a good signal to noise ratio and in astronomy ultimately signal to noise ratio is everything and finally of course the inherent aberration of the lens means the focal blur will be equal to half the diameter of the planet but these all these aren't necessarily fatal you can use clever approaches and there may be even more clever approaches to resolve some of the problems in particular I've proposed this idea that you can use slices across the Einstein ring that'll allow the planets just to be resolved but you're not going to get that thousand by thousand pixel image ah you might be able to get perhaps as much as a hundred by hundred pixel image but that's gonna be very hard to do because you'd have to use the rotation of the planet in order to build up the whole picture and of course if the planet has clouds that clouds are going to be blurring blurring everything so the main comment is the missions a lot more complicated than a Shulman and Maconie and some of the original people proposed it's not a case of just oh we go out to this distance stare back at the Sun and voila here's an image of the planet it's a very complicated mission that's gonna be very hard to do with a essentially Hubble class telescope sent to the distance of the gravitational lens you might be able to get an image of perhaps as good as a hundred pixels by a hundred pixels with a lot of averaging over the rotation of the planet so okay some of these calculations are in this paper if you want more of the details I it was presented at the AI double-a there's an older version of the paper on archive that's easy to find doesn't have all the corrections on it but more of the details are in that paper thank you and I should mention will be discussing this again this afternoon in the Sagan seminar with a couple of other people experts coming up on a panel so we'll talk about in much more detail okay thanks excellent you mentioned of course the motion of the planet and you did not mention the proper motion of the solar system here and there and these numbers are not known very accurately and so you're having to do dead reckoning pointing from a place where you can't see the target no matter what what do you do about this how could you acquire it it's true all of the motions are important the motion of the solar system we can cancel out just say well you know we use the Sun as the reference point but it would be the motion the proper motion of the target so you're going to have to have some method of doing well fine correction at the end to make sure you hit that correct 10 kilometer spot where the planet is and not perhaps the spot just a little bit off where the planet isn't that's going to be tricky could be could be tricky it's a sellable problem but it may not be an easy problem just a quick one is when you get out not all the way to 1,200 a you would say a more reasonable intermediate distance between 558 is the corona a problem in all wavelengths of observation pretty much the corner actually does a very odd thing it has a negative index of refraction so the corona D focuses the light fortunately the D focus is very strongly dependent on the wavelength and it's almost trivial at optical wavelengths but if you start getting into radio wavelengths actually it there comes a point where the light isn't focused at all because it's not come completely D focused by the permit would the speed of the rotation or even the direction rotation in fact any of this well the direction of rotation would affect it a lot if you happen to be sort of pole onto the planet because you'll never get the Crescent so yeah it matters but whichever way the speed and rotation is faster rotates the better of course because you're trying to use the rotation to raster the plan across the that the image so the faster is better and the direction matters but it's not a it's not a main factor it's a minor factor thank you [Applause] [Music] you

Channel: TVIW

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Rating: 5 out of 5

Keywords: Astrophysics, Interstellar, TVIW, Symposium

Id: nlcNB8gjcEg

Length: 29min 54sec (1794 seconds)

Published: Sat Nov 04 2017