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View Full Version : Why is It Necessary for a Star to Be Massive Before Producing a Black Hole?



Fiery Phoenix
2014-Sep-04, 03:26 AM
I imagine this is a rather basic question. I understand that a star generally has to be somewhere between 3-5 solar masses before having any chance of going supernova and, potentially, turning into a black hole. I also understand the basic concept behind the Schwarszchild radius (http://en.wikipedia.org/wiki/Schwarzschild_radius). However, I don't really get why a star has to be that massive before it can potentially produce a black hole. Is it due to the amount of 'stuff' present being insufficient to create a powerful enough gravitational force such that light cannot escape? Or is there more to it?

Jens
2014-Sep-04, 03:42 AM
Is it due to the amount of 'stuff' present being insufficient to create a powerful enough gravitational force such that light cannot escape?

That's basically it. There is something called "degeneracy pressure", where particles resist being compressed. If the weight of the object is big enough to overcome this pressure, then the object collapses into a singularity and light can no longer escape.

Jeff Root
2014-Sep-04, 04:52 AM
The Schwarzschild radius is very small compared to the size of a
star. How would enough mass get inside that radius? It would
have to be compressed. The gravity of the matter will compress
it, but thermal motions, electric and nuclear forces resist the
compression. So it takes a certain amount of gravity to overcome
that resistance. The gravity of a few solar masses will do it when
fusion dies down so that the thermal motions die down, too.

-- Jeff, in Minneapolis

ben m
2014-Sep-04, 05:09 AM
I imagine this is a rather basic question. I understand that a star generally has to be somewhere between 3-5 solar masses before having any chance of going supernova and, potentially, turning into a black hole. I also understand the basic concept behind the Schwarszchild radius (http://en.wikipedia.org/wiki/Schwarzschild_radius). However, I don't really get why a star has to be that massive before it can potentially produce a black hole. Is it due to the amount of 'stuff' present being insufficient to create a powerful enough gravitational force such that light cannot escape? Or is there more to it?

It's not quite "not enough stuff". Any amount of stuff, if sufficiently compressed, would have the light-cannot-escape property that makes it a black hole. The Earth would be a black hole if you could squeeze it into a sphere of 9mm radius.

Two problems: one, how you ever get "sufficiently compressed"? Stars are made of electrons and nuclei, which resist compression due to atomic- and nuclear-physics forces as well as thermal pressure. The compression comes primarily from gravitational attraction. You're never going to become a black hole unless from the starting point of atomic/nuclear matter the gravitational compression is strong enough to overwhelm atomic and nuclear. If you can get 1.4 solar masses of atomic matter into a cold ball, gravity will overcome all of the the atomic forces. If you can get ~2 solar masses of neutrons into a cold ball, gravity will overcome all of the nuclear forces.

Second, you have to consider the actual stellar dynamics. When someone says "a star of size X ends up as Y", that's a specific statement about "a star that starts its life as X amount of hydrogen and helium, and burns them by nuclear fusion in the core, etc."---as opposed to a generic statement about "any possible blob of mass X". To understand the fate of a star of a given mass, you need to understand what temperatures and pressures are, or are not, generated by its own nuclear-fusion capabilities; how it responds when its nuclear fuel runs out; etc. The statement that (say) "a 50 solar mass star makes a black hole" has a whole lot of stellar physics going into it, and does not tell you something fundamental about 50 solar mass black holes.

WayneFrancis
2014-Sep-04, 05:24 AM
I'll expand on what Jen said a bit.

Take a star like our sun. As it goes through its life cycle it fuses lighter elements into heavy element. It does this in stages. The gravity of the star pulls everything together. Most of this in a star is Hydrogen. As the hydrogen compresses, from the gravity of all that material, it heats up. At a certain point the hydrogen starts to fuse into helium releasing energy which works against the gravity. This goes on for a long time. Low mass stars can do this for orders of magnitude longer then our sun. Basically the bigger the star the faster it burns its fuel.
Anyway the star "burns" read that as fuses element into heavier elements. Hydrogen into Helium. Helium into Carbon. Carbon into things like neon, sodium and magnesium and the process goes on as long as there is enough mass that the gravity can compress the material to a point where it starts fusing.

This is a simplistic view but each stage end when there isn't enough fuel to keep up the outward pressure against the gravity within the star. While there is enough fuel the star is in a state of equilibrium where the energy from fusion balances with the inward pull of gravity. When the star can't convert enough of the current fuel gravity starts winning. This causes the core of the start to again start to contract. Which in turn heats up the core until it is hot enough to burn the material produced from the last stage. If the star is big enough this will continue to happen until the star is producing iron. The problem is that anything heavier then iron takes more energy to fuse then it releases which means gravity again would win.

In a star like ours there is not enough mass to compress carbon to a point where it will start to burn. So what will happen is a core of carbon will build up to a point that the sun will shed the remaining amount of lighter element in its outer shell in a nova and the carbon core will be left as a white dwarf. This is where you hear pop science talk about a star made of diamond.

If a star is more massive then it can burn the carbon and produce even heavier elements in its core. Eventually it will not have enough mass to burn what is at the core and it will collapse. Eventually the star will go supernova and shed the outer material. This could end up with a core that gravity was so strong that it turned all the protons into neutrons and it is left as a VERY dense neutron star. There isn't enough mass withing the Schwarszchild radius to form a black hole.

Increase the mass and instead of a neutron star there could be enough mass in the core that as it collapses to a neutron star and then even further it is now within the Schwarszchild radius of that amount of mass and you end up with a black hole.

It is possible to take a neutron star and add material on to it to take it over the edge and form a black hole too. This can happen when it is in a multiple star system where one of the other stars is close enough that the extreme amount of gravity of the neutron star pulls material off of the companion star.

The actual process is much more complicated but the basics is just how big the star starts out as will dictate if it ends up being a black hole.

If you had a bunch of iron and let it collapse from gravity you'd could produce a black hole without any significant fusion ever happening. The iron would collapse and start to glow. It would form a neutron star at about 1.4 solar masses and at some point after about 2 solar masses it would produce a black hole.

Grey
2014-Sep-04, 02:13 PM
Just as an aside, if you can figure out a way to make a smaller black hole in the first place, it's stable (well, apart from Hawking radiation). So if there were some process that could make mini or micro black holes (http://en.wikipedia.org/wiki/Micro_black_hole) (some people have hypothesized that it might have been possible shortly after the Big Bang, when the overall density of the universe was still very high), you could have smallish black holes floating around. We haven't seen any evidence of such, but it's at least a theoretical possibility for them to exist.

Ken G
2014-Sep-05, 09:10 PM
Another point that should be made is that, ironically, the main thing you have to achieve to get a black hole is you have to get the electrons, which are going to end up being responsible for the pressure that resists gravity, to be going at the speed of light (or very close to it). It might seem counterintuitive that the way to get a gravitational collapse is to get the particles moving as fast as possible, but remember that what gets the particles moving fast (when we are talking about a gravitational gravitational contraction of a star) is gravity, so of course the gravity will be extremely strong by the time the particles get moving that fast. So what actually matters is, as heat is lost and the object contracts, how much of the gravitational energy piles up in those particles, and how much needs to be lost to get the contraction to continue?

While the gas responsible for the pressure (which is eventually the electrons, due to their degeneracy they steal the kinetic energy from the protons) is not moving close to the speed of light, it turns out that half the gravitational energy that is released goes into the kinetic energy of the particles, and half goes into the heat that must escape to allow all this to happen. But as the particles bump into the speed limit of c, almost all the gravitational energy that is released goes right into the kinetic energy of the particles, and very little needs to be lost as heat. This means there is no waiting around for the heat to escape, the smallest loss of heat makes for a big amount of contraction. That is the basis of the necessary collapse to a black hole.

(ETA: I should perhaps also explain why, as the particles become more relativistic, more gravitational energy ends up in the particles rather than needing to be removed from the system to get the contraction to occur. This is because what relativity changes is the relationship between kinetic energy and momentum, and pressure is all about how the particles carry momentum around. So you could say that what resists contraction in almost any star is the rate at which the particles carry momentum around, given the amount of energy they have. The momentum transport rate, for a given energy, is the momentum times the speed of each particle, and so if we fix the energy E, the momentum times the speed is 2E if it's nonrelativistic, but only E if it's relativistic. So relativistic gas is not as good at making pressure as nonrelativistic gas, for given E. What this means is, as contraction occurs, if a relativistic gas is to maintain a force balance with the growing gravity, it needs to keep all the released gravitational energy, none has to be lost. But a nonrelativistic gas must find a way to lose half of the liberated energy, or it will end up with too much pressure and will reverse the contraction. This need to lose energy to get contraction of a nonrelativistic gas is the reasons that stars just sit there for long periods of time-- heat loss is generally rather slow. Not so for relativistic gases-- there's no waiting for heat loss, so any loss of heat suffices to get them to fall into themselves, unless degeneracy prevents any loss of heat.)

This process seems inevitable, because heat is always being lost, so any gas should eventually reach relativistic speeds and need little heat loss to continue contracting. But gravity has a dire enemy: degeneracy. Degeneracy is not a source of pressure, as is often erroneously claimed, it is way to keep the object from losing heat. Once the electrons occupy the "ground state" of the star, they cannot lose heat any more. So if they are not relativistic yet, they are not going to ever be, and the contraction ends, yielding a white dwarf. Or, this can also happen after a supernova has occurred, if the electrons and protons are turned into neutrons, and then neutron degeneracy can prevent further loss of heat. But the one way that gravity can still win is if it can be increased by the adding of more mass, which causes contraction without the need for heat loss because the gravity is just plain getting stronger. When the mass gets high enough, the gas is relativistic enough to not need any heat loss in order to collapse to a black hole.