September 30, 2019 100

How to Understand the Black Hole Image

How to Understand the Black Hole Image

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

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