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On Wednesday April 10th 2019 you will probably see the first-ever image of a
black hole. That's when the Event Horizon Telescope will be releasing their
results and I haven't seen them yet but I think they're going to look something
like this and I can be relatively confident because well it's gonna look a
bit like a fuzzy coffee mug stain. But if you are disappointed by this image I
think that misses the gravity of the situation. From this image we should be
able to tell whether the general theory of relativity accurately predicts what
happens in the strong gravity regime that is what happens around a black hole
what I want to do here is understand what exactly we are seeing in this image
so here is my mock black hole of science and this sphere represents the event
horizon. That is the location from which not even light fired radially away from
the black hole could be detected by an outside observer. All of the world lines
end up in the center of the black hole in the singularity once you're inside
here there is no coming back not even for light. The radius of the
event horizon is known as the Schwarzschild radius. Now if we were just
to look at a black hole with nothing around it we would not be able to make
an image like this because well it would just absorb all electromagnetic
radiation that falls on it but the black hole that they're looking at
specifically the one in the center of our Milky Way galaxy, Sagittarius A*
has matter around it in an accretion disk. In this accretion disk there is
dust and gas swirling around here very chaotically it's incredibly hot we're
talking to millions of degrees and it's going really fast a significant fraction
of the speed of light and it's this matter that the black hole feeds off and
gets bigger and bigger over time but you'll notice that the accretion disk
does not extend all the way in to the event horizon. Why is that? Well that's
because there is an inner most stable circular orbit and for matter around a
non-spinning black hole that orbit is at three Schwarzschild
radii now in all likelihood the black hole at the center of our galaxy will be
spinning but for simplicity I'm just considering the non spinning case. You
can see my video on spinning black holes if you want to find out more about
that. So this is the innermost orbit for matter going around the black hole if it
goes inside this orbit it very quickly goes into the center of the black hole
and we never hear from it again but there is something that can orbit closer
to the black hole and that is light because light has no mass it can
actually orbit at 1.5 Schwarzschild radii. Now here i'm representing it with a ring
but really this could be in any orientation so it's a sphere of photon
orbits and if you were standing there of course you could never go there but if
you could you could look forward and actually see the back of your head
because the photons could go around and complete that orbit. Now the photon
sphere is an unstable orbit meaning eventually either the photons have to
spiral into the singularity or spiral out and head off to infinity now the
question I want to answer is what does this black quote-unquote shadow in the
image correspond to in this picture of what's actually going on around the
black hole. Is it the event horizon? Are we simply looking at this? or is it the
photon sphere? or the inner most stable circular orbit? Well things are
complicated and the reason is this black hole warps space-time around it which
changes the path of light rays so they don't just go in straight lines like we
normally imagine that they do I mean they are going in straight lines but
space-time is curved so yeah they go in curves so the best way to think of this
is maybe to imagine parallel light rays coming in from the observer and striking
this geometry here. Of course if the parallel light rays cross the event
horizon we'll never see them again so they're gone that will definitely be a
dark region but if a light ray comes in just above the event
Rison it too will get bent and end up crossing the event horizon it ends up in
the black hole. Even a light ray coming in the same distance away as the photon
sphere will end up getting warped into the black hole and curving across the
event horizon so in order for you to get a parallel ray which does not end up in
the black hole you actually have to go out 2.6 radii away if a light ray comes
in 2.6 Schwarzschild radii away it will just graze the photon sphere at its
closest approach and then it will go off to infinity and so the resulting shadow
that we get looks like this it is 2.6 times bigger than the event horizon. You
say what are we really looking at here? what is this shadow? well in the center
of it is the event horizon. It maps pretty cleanly onto onto the center of
this shadow but if you think about it light rays going above or below also end
up crossing the event horizon just on the backside. So in fact what we get is
the whole back side of the event horizon mapped onto a ring on this shadow. So
looking from our one point in space at the black hole we actually get to see
the entirety of the black hole's event horizon. I mean maybe it's silly to talk
about seeing it because it's completely black but that really is where the
points would map to on this shadow. It gets weirder than that
because the light can come in and go around the back and say get absorbed in
the front you get another image of the entire horizon next to that and another
annular ring and then another one after that and another one after that and you
get basically infinite images of the event horizon as you approach the edge
of this shadow. So what is the first light that we can see? It is those light
rays that come in at just such an angle that they graze the photon sphere and
then end up at our telescopes. And they produce a shadow which is 2.6 times the
size of the event horizon. So this is roughly what we'd see if we happen to be
looking perpendicular to the accretion disk but more likely we will be looking
at some sort of random angle to the accretion disk. We may be even looking edge-on
And in that case do we see this shadow of the black hole? you might think
that we wouldn't but the truth is because of the way the black hole warps
space-time and bends light rays, we actually see the back of the accretion
disk the way it works is light rays coming off the accretion disk bend over
the top and end up coming to our telescopes so what we end up seeing is
something that looks like that. Similarly light from the bottom of the
accretion disk comes underneath gets bent underneath the black hole and comes
towards us like that and this is where we get an image that looks something
like the interstellar black hole.
it gets even crazier than this because light
that comes off the top of the accretion disk here can go around the back of the
black hole graze the photon sphere and come at the bottom right here producing
a very thin ring underneath the shadow. Similarly light from underneath the
accretion disk in the front can go underneath and around the back and come
out over the top which is why we see this ring of light here. This is what we
could see if we were very close to the black hole, something that looks truly
spectacular. One other really important effect to consider is that the matter in
this accretion disk is going very fast, close to the speed of light and so if
it's coming towards us it's gonna look much brighter than if
it's going away. That's called relativistic beaming or Doppler beaming
and so one side of this accretion disk is going to look much brighter than the
other and that's why we're gonna see a bright spot in our image. So hopefully
this gives you an idea of what we're really looking at when we look at an
image of a black hole if you have any questions about any of this please leave
them in the comments below and I will likely be making a video for the launch
of the first ever image of a black hole so I'll try to answer them then. Until
then I hope you get as much enjoyment out of this as I have
because this has truly been my obsession for like the last week.
I guess what
would be exciting is to watch it over time how it changes, right? there's a lot of
hope that there are blobs moving around and you know if you see a blob going
round the front and then it goes around the back but you see it in the back
image etc then that's gonna be kind of cool
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How to Understand the Black Hole Image

18 分類 收藏
林宜悉 發佈於 2020 年 3 月 29 日
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