PDA

View Full Version : The upper limit to a black hole



Vanamonde
2008-Apr-02, 10:22 AM
In another thread about "cosmic downsizing", there was mention of many things, one being that a black hole cannot have more than between 10^9 and 10^10 times the mass of the sun.

I open this thread to ask what is this upper limit and why?

What happens when a black hole was reached this limit and stuff still falls into it?

I believe only occur in the center of a rather large active galaxy, right?

I believe these questions are all related and within the proper scope of a thread.

antoniseb
2008-Apr-02, 12:06 PM
...a black hole cannot have more than between 10^9 and 10^10 times the mass of the sun.
... what is this upper limit and why?

This is an observed upper limit. As far as we know, there is no actual upper limit. What tops off these black holes is that there is no other matter handy to fall into them... There is other matter near them, in the form of a galaxy or proto-galaxy, but this matter is in too high an orbit to be able to fall into the black hole in any serious quantity.


What happens when a black hole was reached this limit and stuff still falls into it?

As I said before there is no physical limit based on the properties of a black hole, the limiting factor is available mass.


I believe only occur in the center of a rather large active galaxy, right?

Giant black holes appear only in the centers of large galaxies. This is most likely because they are a result of the process of forming galaxies in the early universe.

BTW, it is also thought that the larger the black hole the faster it consumes the available matter around it, so the more nearby quasars and other active galaxies will tend to be based on smaller central black holes, unless they are also recently involved in a galactic collision, providing much new material to the central core.

Vanamonde
2008-Apr-18, 07:44 AM
Giant black holes appear only in the centers of large galaxies. This is most likely because they are a result of the process of forming galaxies in the early universe.

Should that be "Giant black holes have only been detected in the centers of large galaxies"? If a black hole finished off a galaxy and stayed away from any others, it would be very hard to detect.

Neverfly
2008-Apr-18, 08:07 AM
Should that be "Giant black holes have only been detected in the centers of large galaxies"? If a black hole finished off a galaxy and stayed away from any others, it would be very hard to detect.

Finished off a galaxy?

Vanamonde
2008-Apr-18, 10:58 AM
Finished off a galaxy?

Sorry, that was sloppy. I mean has that it has accreted all of the matter in a galaxy and not longer close to any significant amount of matter that can be added to the black hole. It would then only radiate a very small amount of Hawking radiation.

parejkoj
2008-Apr-18, 05:16 PM
Sorry, that was sloppy. I mean has that it has accreted all of the matter in a galaxy and not longer close to any significant amount of matter that can be added to the black hole.

Not gonna happen. There is essentially no way to get stars that are more than a couple light years to fall into the central black hole. Gas and dust can fall in as the orbits decay due to frictional losses, but stars interact almost exclusively through gravitation, so there is no way to lose significant amounts of energy.

Just like the Earth won't fall into the Sun, or the Moon won't fall into the Earth, stars orbiting in the outer reaches of the galaxy won't fall into the center.

And antoniseb is right: we haven't observed black holes larger than a certain size, but there is no reason to think they couldn't grow indefinitely, theoretically.

Vanamonde
2008-Apr-19, 10:29 AM
Not gonna happen.

Mmmm. I can accept that is very improbable. But I wonder. If you had a big active galaxy with it's stars and a big black hole in the center and it made it's way to a large cloud of gas, could it not sweep all of the near stars and such unto the hole? Never? Not in 13.7 billion years or even 100 trillion years?

I wonder would would be the probable limit for a truly black hole? We find something responible for things like gravitional lensing effects, unseen compact objects.

But never? Hard to accept. Not even counting the Many Worlds Interpretation.

Neverfly
2008-Apr-19, 10:35 AM
Mmmm. I can accept that is very improbable. But I wonder. If you had a big active galaxy with it's stars and a big black hole in the center and it made it's way to a large cloud of gas, could it not sweep all of the near stars and such unto the hole? Never? Not in 13.7 billion years or even 100 trillion years?

I wonder would would be the probable limit for a truly black hole? We find something responible for things like gravitional lensing effects, unseen compact objects.

But never? Hard to accept. Not even counting the Many Worlds Interpretation.
Exactly. And this is a common misconception where black holes are treated like vacuum cleaners.

They are not hoovering up galaxies.

mugaliens
2008-Apr-20, 06:26 AM
This is an observed upper limit. As far as we know, there is no actual upper limit. What tops off these black holes is that there is no other matter handy to fall into them... There is other matter near them, in the form of a galaxy or proto-galaxy, but this matter is in too high an orbit to be able to fall into the black hole in any serious quantity.

Bingo. This is 10,000,000,000 (ten billion) times the mass of our Sun. There is no upper limit. It's just that there aren't that many stars in a galaxy which might fall into the black hole!

Vanamonde
2008-Apr-20, 06:36 AM
This is an observed upper limit.

Maybe better to say, this is an observed maximum size?

Occams Ghost
2008-Apr-20, 03:38 PM
There is no upper limit. Heck... this is what allows controversial theories like the universe being a black hole to exist. They can be as big as nature wishes. But the smallest black hole must be in accordance with the Planck Mass given as:

(hc/2piG)

Where h is Planck's Constant, c is the speed of light and G is the Gravitational Constant. Mini black holes seem to be the best chance for scientists. There is simply no way we could create a minimum sized hole with a mass of about 22 micrograms because we would need about 10^16 TeV just to produce it, which is many magnitudes higher than we can produce today. A mini black hole would have a radius of about 2 x 10^-19m – very small – with a very large temperature of 1.5 x 10^14 K, or about 25 billion times hotter than the Sun!

To properly understand how we come to calculating black hole masses, comes directly from Newtons equations. Newton developed his work from Kepler’s Law which describes the motions of planets. By working off Kepler’s work, he found that the planetary paths where nearly circular and they were used to describe the force causing the motion.
Kepler’s three laws state:
1. All planets follow elliptical trajectories with the sun in central frame
2. A line between the sun and a planet sweep out equally
3. The ratio of the cube of the radius to the square of the period of revolution is the same for all planets. This gives us k=R^3/T^2
He found that the force of attraction of the sun for a planet is equal to the product of mass and centripetal acceleration.
F_SP=m_Pa_P=m_P(4π^2R/T^2)
Because of this, Newton started to postulate an inverse-square law of attraction. When he expressed the form of the famous inverse-law, he made it form Kepler’s third law and used R and m only;
k=R^3/T^2 and stated T^2=R^3/k
So the force is usually given as;
F_SPOH=m_P(4π2R/R3/k)=mP(4π2k/R2)
Newton introduced G into his equations, and the value of the Gravitational Constant has been found to be something like 6.67 x 10^-11 . Mathematically, the value of G was stated as,
F=Gm1m2/R2
One interesting thing is that no one actually knows how Newton arrived at value of the Gravitational Constant. Newton also showed that force is related to mass and distance. If we consider for a moment the projectile motion of a thing, we use the equations:
x=v_OHand y=v_OV-gt
They are called ‘’parametric equations,’’ and they have a parameter given as . Solving the parameter in the first equation, we should get x/vOH. Substituting  in the other equation and we get a parabolic equation;
y=v_OV(x/v_OH)-g(x/v_OH)= v_OH/v_OV x-g(x/v_OH)=v_OH/v_OV x-g/2v_OH x
The force of gravity is what is known as the net force on a projectile. The path of a projectile is then called the parabola. Gravity is then said to be acting on the thing along the path it takes.
Even though Newton knew of the equations that described free fall, none of his equations ever required them, until Einstein’s theory of relativity came around. Suppose that M was the mass of the earth and m is the mass of a building, like the legendary Leaning Tower of Pisa, the motion given by the famous F=Ma equation, must abide by the rules of gravitation,
F=GMm/r
If m under the law of gravitation is the same value as the m under the motion of gravity, then we say,
ma=GMm/r
Which allows for m to be cancelled out completely, leaving,
a=GM/r
Where a is acceleration.


Remember, a free falling object will have the force of gravity totally cancelled out as it’s that weak. We know that from Newton’s Force Equation is derived as f= ma, where this also shows an inertial system to derive the acceleration due to gravity. So the gravitational acceleration is the mass of a gravitationally warped object M, and the distance d from it. Also, instead of working out the mass of a black hole you can work out its mass against the gravitational acceleration formula, by; M=gd^2/G
We use the same method to work out the mass of the earth. The G is Newtons universal gravitational constant (6.710^-11 m3/(kg sec2). We find the Earth's mass = 9.8 (6.410^6)^2 / (6.7 10^-11) kilograms = 6.0 10^24 kilograms. A black hole need to be of Planck Mass at smallest size 2x10^-8kg.

Not all the variables showed up. Sorry.