> “Black holes are where God divided by zero.” -Stephen Wright
Yesterday, I told you about all the evidence for the Black Hole at the center of our galaxy. In particular, we see multiple stars orbiting a single point that emits no light of any type at all.
And, perhaps unsurprisingly, the comments became very active. So let’s take a look at some of what was said, and let’s see what we can further learn about black holes from answering your questions.
> I see the stars orbiting on their own orbits, but I mean, all orbits seem quite different to me, there´s no central point they are orbiting around… or is there?
This is actually a great one! Kepler was the first to figure out that orbits weren’t about a central point, but rather in an ellipse-shape, with a mass at one focus of an ellipse.
This is true for all planets, comets and asteroids around the Sun, for the Moon around the Earth, and for each of the stars near the galactic center. In fact, if we ask where is this “focus” for each of the ellipses near the galactic center, we remarkably get the same location for each one, below.
> So, a lead sphere that was about the diameter of the earth’s orbit would fulfil both criteria. [Dense/massive enough and dark.]
So the question is – what measurements have we taken that would invalidate this ‘big lead ball’ model?
Sure – a big lead ball might not fit our current model of stellar formation … but I’m interested in whether it contradicts our measurements?
There are two surprising problems with this. First off, there’s a maximum size that something that doesn’t emit light can have, and it isn’t given by the density of lead. As planets get more massive, they get bigger. Earth is bigger than Mars, Uranus is bigger than the Earth, Saturn is bigger than Uranus, and Jupiter is bigger than Saturn.
But not by that much! Jupiter is about 3 times as massive as Saturn, but only about 15% bigger! What’s going on?
As you get more and more mass together, gravity starts working its magic, and starts compressing the atoms at the center. Bodies much more massive than Jupiter will actually start to shrink in size, and will compress! By the time you get up to about a Solar Mass of lead, you’re talking about something around the size of the Earth, similar to a white dwarf star.
But even white dwarfs have a limit. You get about 40% more massive than our Sun in a white dwarf, and the atoms can’t stand up to the intense gravitational pressure, and they collapse. (This limit is known as the Chandrasekhar mass limit.)
But we can go even farther! Even if you took a Mercury’s-orbit-sized region of space and filled it with a sphere of lead, you can calculate what the escape velocity would be. Guess what you find?
Yup. It’s bigger than the speed of light, which means you’d get a black hole anyway!
> am also quite unconvinced that mathematical artifacts of General Relativity (=singularities) trump Quantum Mechanics (discreteness of space-time rules out singularities). Maybe Ethan could give us the view of an astrophysicist on this?
Technical time; look out, folks! There are a bunch of different types of energy in the Universe. Matter, radiation, and what we call “vacuum energy”, which is the same stuff we believe dark energy is made out of. If, when you try to collapse to a singularity, you start producing vacuum energy, you can avoid the mathematical “inevitability” of a singularity. See, for instance, this wikipedia page.
> You don’t have to go to the galacatic center. The blue giant star HDE 226868 is much closer, and it is also orbiting a dark object much more massive then any neutron star can get. And it coincides with the position of a strong X-ray source.
(From Birger Johansson.)
Okay, check this out.
Cygnus X-1, to which Birger refers, is an 8.7 solar mass object, emitting X-rays, and with another, visible star orbiting it. It is too dense and doesn’t have the right properties to be either a white dwarf or a neutron star, and appears to be a black hole with an event horizon of radius 26 km. This system, discovered in 1964, was the subject of a famous bet between Kip Thorne and Stephen Hawking, about whether it was a black hole or not. Hawking, loser of the bet, conceded in 1990 that it was a black hole.
> I thought the accretion disks of black holes would be quite bright (including in visible light). Shouldn’t we see that?
Brightness is relative.
Compared to the black hole itself, sure the accretion disk is relatively bright. But the actual amount of light coming from it? Unless you’ve got something like a super-duper-massive one, like a quasar,
you’re not going to “see” anything. (Image credit: here.) Most of the emitted “light” isn’t in the visible part of the spectrum, unfortunately. But the radio waves (quasars stand for quasi-stellar-radio-sources) and the x-rays are, in fact, how we detect these guys in the first place!
Thanks for some great comments! I’m sure you’ll have more for me, and I hope I’ve gotten to answer some of the more interesting ones!
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