On Wednesday April 10th 2019 you willprobably see the first-ever image of a black hole.
That's when the Event HorizonTelescope will be releasing their results and I haven't seen them yet butI think they're going to look something like this and I can be relativelyconfident because well it's gonna look a bit like a fuzzy coffee mug stain.
But ifyou are disappointed by this image I think that misses the gravity of thesituation.
From this image we should be able to tell whether the general theoryof relativity accurately predicts what happens in the strong gravity regimethat is what happens around a black hole what I want to do here is understandwhat exactly we are seeing in this image so here is my mock black hole of scienceand this sphere represents the event horizon.
That is the location from whichnot even light fired radially away from the black hole could be detected by anoutside observer.
All of the world lines end up in the center of the black holein the singularity once you're inside here there is no coming backnot even for light.
The radius of the event horizon is known as theSchwarzschild radius.
Now if we were just to look at a black hole with nothingaround it we would not be able to make an image like this because well it wouldjust absorb all electromagnetic radiation that falls on it but the blackhole that they're looking at specifically the one in the center ofour Milky Way galaxy, Sagittarius A* has matter around it in an accretiondisk.
In this accretion disk there is dust and gas swirling around here verychaotically it's incredibly hot we're talking to millions of degrees and it'sgoing really fast a significant fraction of the speed of light and it's thismatter that the black hole feeds off and gets bigger and bigger over time butyou'll notice that the accretion disk does not extend all the way in to theevent horizon.
Why is that? Well that's because there is an inner most stablecircular orbit and for matter around a non-spinning black holethat orbit is at three Schwarzschild radii now in all likelihood the blackhole at the center of our galaxy will be spinning but for simplicity I'm justconsidering the non spinning case.
You can see my video on spinning black holesif you want to find out more about that.
So this is the innermost orbit formatter going around the black hole if it goes inside this orbit it very quicklygoes into the center of the black hole and we never hear from it again butthere is something that can orbit closer to the black hole and that is lightbecause 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 anyorientation so it's a sphere of photon orbits and if you were standing there ofcourse you could never go there but if you could you could look forward andactually see the back of your head because the photons could go around andcomplete that orbit.
Now the photon sphere is an unstable orbit meaningeventually either the photons have to spiral into the singularity or spiralout and head off to infinity now the question I want to answer is what doesthis black quote-unquote shadow in the image correspond to in this picture ofwhat's actually going on around the black hole.
Is it the event horizon? Arewe simply looking at this? or is it the photon sphere? or the inner most stablecircular orbit? Well things are complicated and the reason is this blackhole warps space-time around it which changes the path of light rays so theydon't just go in straight lines like we normally imagine that they do I meanthey are going in straight lines but space-time is curved so yeah they go incurves so the best way to think of this is maybe to imagine parallel light rayscoming in from the observer and striking this geometry here.
Of course if theparallel light rays cross the event horizon we'll never see them again sothey're gone that will definitely be a dark region but if a light ray comes injust above the event Rison it too will get bent and end upcrossing the event horizon it ends up in the black hole.
Even a light ray comingin the same distance away as the photon sphere will end up getting warped intothe black hole and curving across the event horizon so in order for you to geta parallel ray which does not end up in the black hole you actually have to goout 2.
6 radii away if a light ray comes in 2.
6 Schwarzschild radii away it willjust graze the photon sphere at its closest approach and then it will go offto infinity and so the resulting shadow that we get looks like this it is 2.
6times 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 mapspretty cleanly onto onto the center of this shadow but if you think about itlight rays going above or below also end up crossing the event horizon just onthe backside.
So in fact what we get is the whole back side of the event horizonmapped onto a ring on this shadow.
So looking from our one point in space atthe black hole we actually get to see the entirety of the black hole's eventhorizon.
I mean maybe it's silly to talk about seeing it because it's completelyblack but that really is where the points would map to on this shadow.
Itgets weirder than that because the light can come in and goaround the back and say get absorbed in the front you get another image of theentire horizon next to that and another annular ring and then another one afterthat and another one after that and you get basically infinite images of theevent horizon as you approach the edge of this shadow.
So what is the firstlight that we can see? It is those light rays that come in at just such an anglethat they graze the photon sphere and then end up at our telescopes.
And theyproduce a shadow which is 2.
6 times the size of the event horizon.
So this isroughly what we'd see if we happen to be looking perpendicular to the accretiondisk but more likely we will be looking at some sort of random angle to theaccretion disk.
We may be even looking edge-on And in that case do we see thisshadow of the black hole? you might think that we wouldn't but the truth isbecause of the way the black hole warps space-time and bends light rays, weactually see the back of the accretion disk the way it works is light rayscoming off the accretion disk bend over the top and end up coming to ourtelescopes so what we end up seeing is something that looks like that.
Similarly light from the bottom of the accretion disk comes underneath getsbent underneath the black hole and comes towards us like that and this is wherewe get an image that looks something like the interstellar black hole.
it getseven crazier than this because light that comes off the top of the accretiondisk here can go around the back of the black hole graze the photon sphere andcome at the bottom right here producing a very thin ring underneath the shadow.
Similarly light from underneath the accretion disk in the front can gounderneath and around the back and come out over the top which is why we seethis ring of light here.
This is what we could see if we were very close to theblack hole, something that looks truly spectacular.
One other really importanteffect 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 usit's gonna look much brighter than if it's going away.
That's calledrelativistic beaming or Doppler beaming and so one side of this accretion diskis going to look much brighter than the other and that's why we're gonna see abright spot in our image.
So hopefully this gives you an idea of what we'rereally looking at when we look at an image of a black hole if you have anyquestions about any of this please leave them in the comments below and I willlikely be making a video for the launch of the first ever image of a black holeso I'll try to answer them then.
Until then I hope you getas much enjoyment out of this as I have because this has truly been my obsessionfor like the last week.
I guess what would be exciting is to watch it overtime how it changes, right? there's a lot of hope that there are blobs moving aroundand you know if you see a blob going round the front and then it goes around theback but you see it in the back image etc then that's gonna be kind ofcool.
