Nobody has yet, so the problem is clearly hard enough to be interesting.
Einstein tackled quite a few hard problems, and came up with useful solutio ns for some of them, enough to make him famous. There were problems that st umped him (and everybody else) at the time, some of which have since been s olved by other people (helped by observations that were made after Einstein had died).
Speculating how Einstein would have made out if he'd lived until now isn't a useful activity, except in as far it distracts Cursitor Doom from posting links to fatuous right-wing propaganda.
Edges that sharp are implied in the observed visibility function when it is combined with the prior knowledge that the sky does not have regions of negative emission. To take a trivial example if you only measured the DC and cos(kx) components and found them to be both amplitude A.
Then the linear reconstruction of what the sky looks like would be
sky(x) = A + A.cos(kx)
But if you add the additional constraint that the sky brightness function must be everywhere positive then the non-linear reconstruction with N terms is unique and in the limit N->inf becomes a delta function centred on the origin.
sky(x) = N.A.delta(0) lim N-> inf
In reality signal to noise affects the resolution of the image with sharp edges against bright components more precisely resolved than low brightness regions.
It didn't take me long to find a PPT for a seminar given by Katie Bouman who is one of the image processing specialists behind the technique used on this together with various theoretical models of what a BH might look like when viewed with their baselines and noisy data and what they would be able to reconstruct with the method. It does remarkably well too...
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She has rather suddenly found herself in the news.
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And for balance some other Japanese researchers with a rival imaging algorithm for handling the same data and their tests on known targets. This one also includes the so-called dirty map which is what you get if you naively invert the measured U-V plane coverage by FFT.
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The various groups all agree on the structure having worked independently using their own preferred imaging methodology.
More than pot luck, since that implies a reasonable chance. AFAIK, I was right in the middle of the only and small hole in the clouds:)
I prefer not to believe it, but I know that luck plays a significant part in far more than astronomical observations.
In some ways it would be comforting if the world was more predictable and good outcomes were the result of skill rather than brute force and luck. But t'ain't so.
Read Townes' book, How The Laser Happened. He had to fight the establishment, and almost lost his lab funding, to demonstrate what is now obvious: inverted energy population states are possible and, in fact, easy. Once he confounded the old-fart orthodoxy, all sorts of people had permission to make all sorts of masers and then lasers.
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John Larkin Highland Technology, Inc
lunatic fringe electronics
Of course the original pic was made from terabytes of noisy data so wouldn't be coarsely pixellated; pixels are cheap. But it had resolution corresponding to a coarse array.
It looks like the popular press further enhanced the pix to sharpen the edges of the black hole. As if it hadn't been enhanced already.
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John Larkin Highland Technology, Inc
lunatic fringe electronics
That would be a world that's simpler, with few weird and amazing things to discover or invent. That world would be a lot more academic and institutionalized than ours, with less use for mavericks (and for luck.)
I remember "computer dating" from way back. You'd fill out a questionare and a big IBM mainframe (or maybe just a card sorter) would find your ideal mate. It didn't work, even for people who believed in computers.
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John Larkin Highland Technology, Inc
lunatic fringe electronics
Presumably a Keysight UXR 110GHz BW, 256GS/s, 10-bit Real-Time 4 channel Oscilloscope would speed that up to a just under 4 hour job. That makes its 1,300,000 dollar/euro asking price look like a real bargain in that context.
Mind you, after watching that YT tear down video, I'd already reached that conclusion anyway. :-)
for anyone here who hasn't already seen the video. Just a head's up, it might be a good idea to keep a box of tissues handy to soak up the drool, just in case... even if you don't normally drool. :-)
Tom Gardner wrote in news:p_AtE.162172$ snipped-for-privacy@fx19.am:
I can shoot pool without touching the table. Including the break shot. I literally stroke the shot with both hands in mid air. And we are talking one two three and four rail banks like they are candy. I am extremely precise.
I call it 'the harlem globtrotter effect'. Hitting that exact, precise point on a ball up to 9 feet away just amazes me.
I can also curl around balls that are in my shot path (not quite as successfully). I call it mild masse. That dude on the Lincoln commercial ain't got nuthin' on me. And he had to do that in way more than one take. I just see the shot and walk up and shoot it.
Pixels are *NOT* cheap when you are making each one by a complicated non-linear algorithm from 1PB of raw data. They will use the absolute minimum number of pixels that they can safely get away with.
I have found one of her public access papers that isn't too mathematical and includes some samples of various target model images and the results of reconstructing them with CLEAN (still most radio astronomers default tool of choice), a couple of other non-linear methods and her CHIRP.
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Jupiter - a large bright disk with faint dark markings on remains the most difficult target for all radio astronomy imaging algorithms.
No they didn't. How the dark edges against strong emission looks so sharp is a feature of the non-linear method of reconstruction.
Her facebook profile has a picture of her looking very pleased with the first cut phase solution on her laptop warts and all. Looks to me like there is a ghost of the ring shifted about a diameter downwards but the main ring structure and the hole in the middle is already very clear.
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It looks a bit more like a horseshoe at this stage. I wish they hadn't cropped the published image quite so tightly. One of the knots nearby might actually be a real shock front in the plasma and significant.
If it is there or slightly further away next time they do it then we will know it is real. I am waiting to see what they get on SgrA*.
Martin Brown wrote in news:q96oje$jpl$ snipped-for-privacy@gioia.aioe.org:
Isn't it slightly tilted away from us?
Would that not make energys from the far side less likely to get discerned.
Yes, I know... how does one declare a black hole tilted? Well, they (some) do spin, and this one does, so it has an axis. The generally coincide with the axis of the galaxy they are found at the center of.
We do not see the black hole itself. We see (some of) the 'shimmering' around it, which ends up defining the position and size of the SMBH it surrounds.
That we can see a relativistic beamed optical jet with apparent 6x super luminal motion towards us puts a fairly tight constraint on the angle between us and the object spin axis. We have to be looking down onto one pole give or take
Its all very messed up with rays looping round the BH several times before escaping and starting out as much higher energy photons deep in the gravitational potential well being redshifted as they escape.
I would still like to see one imaged where we know that we are looking at it more or less edge on to the accretion disk. Cygnus A or similar - snag is they need another 5x improvement in resolution. I think M82 is the only other well known nearby supermassive black hole galaxy candidate within the capabilities of their instrument (and there are a few other targets of opportunity there first seen by Jodrell in 2010).
Most are expected to have non-zero angular momentum and be spinning vigorously (which does strange things to magnetic field lines which find themselves frozen into the surface).
Its a fair bit more complex than that. We are looking at the glowing accretion disk plasma distorted by the peculiar ray paths that photons escaping from it are forced to travel along. They used an MHD code to work out what the accretion disk would be like and then GR ray tracing to work out what it would look like to a distant observer.
The theoretical results are astoundingly close to the observations.
At Monday's symposium, pointing out the image is of photons close to the event horizon, strongly bent by the high gravity, and streaming toward us, they said the brightness was due to the rotation of the black hole, dragging the photo flux.
The explanation wasn't very clear. Maybe they simply don't know for sure.
I think they have a pretty good idea how the frame dragging will help boost photons going round in the same sense as the black hole. Explaining it in a publicly accessible way is a different matter. One thing they don't know is how close to the maximum possible spin the thing is. The maths is complex but relatively well understood (or so we think).
It is a variation of relativistic beaming but in a region close to the event horizon where the gravitational distortion of photon paths is also extreme. If you are interested in a look see there is a library of animated simulations as well as a few snapshots on their website:
The "pixel" size is determined by the VLBI telescope resolution, which is determined by the wavelength and the distance between individual antennas. Unfortunately the Earth diameter is quite small (about 12700 km) so the baseline (maximum distance between telescopes) is about
10000 km, so this limits the VLBI resolution to 20-25 uas.
As such, it is remarkable that they got VLBI images at 230 GHz.
Of course, using some space antennas, you could extend the baseline significantly, but unfortunately for instance RadioAstron works only up to 22 GHz. .
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