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It's Official: Black Holes Have Lots Of Mass
KewlPC writes "Spaceflight Now reports in this article that some scientists have been able to measure the "weight" (yeah, yeah, it's actually mass, not weight) of a black hole that is (or was, 13 billion years ago) eating up the most distant known quasar, some 13 billion light years away."
this is how normal stars work too. The radiation pressure generated by the core keeps the core from collapsing into itself. - well not quite the same, but same idea.
But I haven't heard of the eddington limit before either. Neat.
You might be confusing neutron stars (pulars sometimes) with these quasars.
Neutron stars are prevented from collapsing into black holes because of nuclear repulsion / neutron degeneracy (instead of electron repulsion). In fact, there's so much pressure that the electrons get squeezed into the protons of the atoms - hence neutron stars.
Black holes have enough gravity to overcome nuclear repulsion and collapse further than neutron stars. I think there's a couple theories about just what happens inside the black hole, but the commonality is that particles don't mean much whether or not you're talking about a singularity, or the non-singularity quantum foam theories.
This page has some good info.
I'm right in saying "the Schwarzschild radius of a black hole is proportionate to its mass", but more properly it's directly proportional; i.e., the proportionality constant is 1.
Well, as long as I'm here, let's do some calculations. The article says the black hole's mass is 3 billion times that of our Sun, so multiply 3 km by 3 billion and you get 3 km * 3*10^9 = 9 billion km. To put things in perspective: the distance to Alpha Centauri is 3.8*10^16 m = 3.8*10^15 km, so this black hole's radius is only .0002% of the distance from here to the nearest star. Quite small, astronomically-speaking.
Atoms produce very specific patterns of absorption or emission in the light spectrum depending on species. A familiar example, is the solar spectrum, which is created by absorption of narrow bands in the spectrum by a large number of different elements in different states of ionization. Redshift causes the entire set of these lines to be moved towards the red end of the spectrum. They retain the spacing between themselves, so they can still be recognized in their new positions, and their new positions tell us how fast the object that created them is moving. Reddening caused by dust doesn't move these absorption lines. Instead it scatters light preferentially at the blue end of the spectrum, causing the entire end of that spectrum to dim, rather than creating narrow bands in it or moving narrow bands around. These two different processes are usually distinguishable.
"I'm so moist I'm sticking to the leather." -Kermit the Frog on The Late Late Show
To put it another way, it's not a stable limit, it's an unstable limit. If a black hole is accreting mass at a rate less than or equal to this limit, the black hole will shrink and evaporate; if a black hole is accreting mass at a rate greater than the limit, it will grow.
I'm curious as to whether black holes are compacted so much that most of the space between atoms (and even subatomic particles?) is gone, or whether the repulsions keeping them apart are even stronger than the force of the black hole's gravity.
Ok, first you get netron stars where the space between atoms is gone. The entire star becomes one big "nucleus". Then there are quark stars (I think they may still be uncertain about whether quark stars exist). In a quark star the space between subatomic particles (neutrons protons and electons) is gone.
THEN you get to black holes. Once you get within a certain distance of a black hole all laws of physics other than gravity effectively cease to exist. It isn't a question of gravity being stronger then the repulsion - the repulsion no longer exists. What happens is that the repulsive force itself gets pulled in by the gravity.
Think of it this way: Imagine the repulsive force is sound and gravity is wind. A black hole is where the wind is faster than the speed of sound. No matter how strong the repulsive sound is it gets carried inwards. It can't push outwards on anything.
We don't really understand what happens at this point. All known laws of physics break down within this region. We need to discover new laws of physics. The answer will probably be found in a theory of "Quantum gravity".
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Do we know the physical size or the particle density of black holes?
We know both. Err... we know one and we know what general relativity predicts about the other, but we don't know how to merge that with quantum dynamics. The density of the black hole is infinite. Every bit of mass inside it is concentrated into a point of zero size - the singularity. So yes, all of the space between particles is gone. But of course being at such a small size, GR is outweighed by the quantum effects and we don't have a theory of quantum gravitation yet. So we're not entirely sure on that one.
As for the physical size of the black hole, we have to be clear about what we mean by `black hole'. The `black' part of the hole is known as the event horizon. It is the point of no escape, after you've crossed that boundry you can't get out. No light can escape from inside the event horizon, hence the name of black hole.
Now when someone says `black hole' they mean `the event horizon and everything inside it'. Fortunately there is a rather simple formula for calculating the event horizon (also known as the Schwarzchild radius after the discoverer of the formula): R = 2*G*M / c^2 where G is the gravitational constant (6.67*10^-11), c is the speed of light (2.99*10^8 m/s) and M is the mass of the black hole.
From the radius we can find the `density' of the black hole, but being as all the mass is concentrated in a single point, it is a rather meaningless value.
Of course it gets more complicated when the black hole is spinning (it doesn't have to be spherical then) but even in that case we can express the dimensions in terms of the mass.
If a black hole is a sphere, doubling it's radius increases it's volume by a factor or about 33 1/2! Since mass only doubled, it's density just dropped by a factor of 17?
:-)
Correct. In your sphere example, a 2x mass increase will not yeld a 2x radius increase, since the relation between the two is not linear.
But a black hole is not a physical object, it's an abstraction. The radius of a blackhole is defined as the distance where the escape velocity equals lightspeed. And that distance is directly proportional to the black hole mass, hence the 2x radius increase.
but if anything it seems a black hole would condense to some maximum possible density, and it would maintain that maximum possible density regardless of how much mass you add to it
That's probably true, since in theory a black hole is empty, except a point in its center where all the mass is concentrated at inifite density - so if you double the mass, you get double infinite density, which is still infinite
Average density continues to drop as you add more mass. The black hole of the story, with billions of solar masses, is probably less dense than water...
Minor nit-pick with your analogy.
The speed of sound in a medium is a function of the average velocity of the molecules in that medium. This is based off of the ideal-gas law, utilizing the probability of direction of particles bouncing off one another.. Collision of gas molecules against solidly compacted forces (such as the front-end of an ship (air/boat), an explosion wave-front, etc) merely causes the molecules to divert their direction, and such ping-ponging causes neighboring molecules to divert, thereby causing an effective motion of the gas. When a large body of such molecules move in the same direction (on average), we call this a current.
Wind is such a current, rivers are such a current, electrons propagating along a conductor is such a current. In each of these cases, a single particle (molecule/electron) is not moving the entire length, but the net motion of all the colliding and direction-changing particles is.
Thus, as with the speed of light, for net-aggregate-velocities (current velocity) much much lower than the average velocity of a given particle in the medium, you can use linear superposition. Namely, if you are in a car moving at velocity x, and you through a book forward at velocity y, then until air-resistance slows you down, the book will have velocity x + y.
However, as you approach the average speed of a particle in your medium, the particles on your wave-front can't move forward fast enough to "get out of your way", so the apparent friction becomes non-linear (polynomial, in fact). You are now accelerating the particles in front of you, and apparently gaining mass (as far as propulsion is concerned). BUT, the key is that you are accelerating the particles in front of you.
I believe the formula for friction in an ideal gas is something similar to:
1 - V^2/Vavg^2
Which is related to the lorenz contraction factor.
Ideal gas law does not mean that no particle ever travels faster than the average.. In fact, if enough energy is released into the gas such that it's temperature (e.g. aggregate kinetic energy) rises, the it's average velocity is indeed increased.
Thus my nitpick is that for the analogy where a repulsive force is sound and gravity is wind.. As your "wind" velocity increases, you are, in fact, increasing the average velocity of particles. Any perterbations (shock waves, aka sound), now can propagate faster, though in a non uniform manner (the direction of the wave will be faster in the direction of the wind (parallel direction), average in orthogonal directions and dramatically attenuated in anti-parallel directions).
Further, if the auditory devices (sound-generator, and target) are carried along with the medium, then their relative velocities will be constant with respect to the medium, and sound will effectively probagate uniformly.
There is one tiny wrinkle in all this. Here, the max velocity is consdered to be Vavg and is changable. In quantum physics, Vavg is the speed of light and can never be exceeded (at least on average). Thus linear superposition breaks down. Increasing the velocity of the wind means that particles ricocheting forward can't produce a net propagation velocity twice as fast relative to a stationary transmitter/reciever.
Theoretically, all the quantum "forces" are effectively energy moving through space and time at different ratios. Plotting them together as a 4D space-time plot, the magnitude of the 4D coordinate should always equal c. Thus if you are traveling along the event horizon at c in any one direction, then you should have no remaining ability to travel in any other directions (including time). Thus perterbing the medium should be impossible. The event horizon would be like having a steel shell that is oblivious to outside disturbances (ignoring that steel allows for elastic collisions, including sound). I speculate (as a lay person) that the reasoning that event horizon particles are oblivious to anti-parallel disturbances is because they have
-Michael