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In gym class, I loved playing tug-of-war. Our teacher would divide us into 2 nearly
equal teams and give us a thick rope with a ribbon tied in the middle. We’d tug and
pull, but the two teams would balance each other out for a while. The ribbon would hardly move.
Then one of the teams
would either lose their footing or tire out, and then the rope would suddenly collapse
toward one side or the other.
The universe is a little bit like this. There are a lot of opposing forces that balance
each other out in a kind of celestial tug-of-war, until they sometimes don’t.
When it comes to stars, the two opposing forces are gravity which tries to collapse the star
inward, and outward pressure due to the energy of fusion. This tug of war can remain in a
stalemate, or relative balance for billions of years.
But what happens when large stars run out of fuel and gravity overwhelms that outward
pressure? This can cause a cataclysmic collapse, resulting in a colossal explosion called a
supernova. And what remains is sometimes a neutron star or a black hole. But how does
a sudden collapse result in such a powerful explosion, and why does a neutron star or
black hole form? The fascinating story of the birth of a neutron star and
a black hole is coming up right now…
To
understand how a neutron star or a black hole results after a supernova, let’s briefly
review the process of a supernova explosion: A star creates outward pressure against gravity
by the energy from fusion. It fuses increasingly higher mass elements, starting with fusing
hydrogen to helium, then fusing helium to carbon, then neon, progressing up through
the periodic table until a core of iron and nickel is produced. Fusion stops there because
the fusion process creating iron consumes more energy than it produces.
Note that not all stars produce Iron before they run out of fuel. For example, our sun
will not get to this stage. It will run out of fuel before any iron is produced. But if
the star is large enough, then its fusion will eventually end with iron.
When this happens, no energy gets produced, and so the outward thermal pressure decreases,
allowing gravity to collapse the star. The core contracts. For a time, electron degeneracy
pressure keeps the core from collapsing further. What is electron degeneracy pressure? It has
to do with the Pauli exclusion principle. This principle states that two or more identical
electrons cannot occupy the same quantum state. The same quantum state also includes the volume.
Since electrons can have two different types of spins making them non-identical,
a simpler way to state this is that no more than 2 electrons can be in the same
orbital in an tom. What does this mean? Usually atoms have plenty
of space to move around in. But in a collapsing star, gravity pushes the atoms together and
limits the atoms to their maximally compacted state. So what happens is that the electrons
in the outermost shell of the atoms, next to electrons in the outermost shell of the
neighboring atoms, create a physical barrier keeping the atoms from compressing any further.
You might think that this physical barrier is due to the electrostatic repulsion of electrons
in the outer shell of neighboring atoms, because like charges repel. But theoretical physicist
Freeman Dyson showed in 1967 that this physical barrier to compression of atoms exists due
to the Pauli exclusion principle, and not due to repulsion of neighboring electrons
or neighboring nuclei. There are simply no other free quantum states
for electrons to occupy, so there is no physical possibility of compressing more. This is the
electron degeneracy pressure. And this pressure will pick up from where the radiation pressure
fell off, and take up the fight with gravity to try to prevent a further collapse of the star.
Once a star is in this degenerate state, gravity cannot compress it any more, because quantum
mechanics dictates that there is no more available space to be taken up. So the core of the star
survives, not by the outward pressure of fusion, but by quantum mechanical principles that
prevent its complete collapse. This core of a star where the electron degeneracy
pressure keeps it from collapsing further, is called a white dwarf. This is what will
happen to our sun after billions of years, after it runs out of fuel in its red giant
state. After much of its mass floats away, its inner core will be such a white dwarf.
It will be the remains of our sun. It would be only about the size of earth, but will
be about 200,000 times more massive. To give you an idea of how heavy this is, Jupiter
is only about 320 times as massive as earth. The sun is about 300,000 times more massive
than earth, but is also 110 times wider. But, there is a limit to the amount of mass
that such a white dwarf can have. Indian-American physicist, Subrahmanyan Chandrasekhar discovered
this limit to be about 1.4 times the mass of the Sun. This is known as the "Chandrasekhar
limit." So what this means is that if the mass of
the collapsed star exceeds of 1.4 times the mass of the sun, even this electron degeneracy
pressure is not enough to keep the star from further collapse.
The extra mass can come from further deposits of matter from the outer shells of the star.
Once the Chandrasekhar limit is exceeded, it will keep collapsing. And what happens
in this scenario is that the temperatures within the core soar to above 5 billion degrees
Celsius. At these temperatures gamma rays are produced. These are so energetic that
they break up the iron nuclei into helium nuclei, also called alpha particles. And this
raises the temperature even higher, to roughly
100 billion degrees Celsius. And at these conditions,
electrons combine with protons in a process called electron capture, to form neutrons.
This process also releases a flood of neutrinos. So essentially, once the Chandrasekhar limit
is exceeded, electrons are captured by the nucleus, creating a smaller ball of pretty
much nothing but neutrons, and no more atoms remain. The star becomes like a giant atomic
nucleus. This neutron star is even more dense than a white dwarf. Instead of earth sized,
it would only be about 10-20 km wide. And it’s density would be about 10^14 or 100
trillion times that of earth. So a teaspoon of this material would weigh as much as Mount
Everest. The Pauli exclusion principle which I talked
about earlier which causes electron degeneracy in White dwarfs, also applies to neutrons
in neutron stars. This is because this exclusion principle applies to all fermions, or quantum
objects with ½ spin. Electrons are fermions. And neutrons are made of quarks, which are
also fermions. So the same exclusion principle applies to them.
Again, assuming the Chandrasekhar limit is exceeded for the star, instead of an electron
degeneracy pressure, a neutron degeneracy pressure is formed, meaning that the star
cannot be compressed further because the neutrons are already maximally compressed.
The core of the star which is like one giant nucleus now, forms a kind of incompressible
wall. And since the infalling outer part of the star now has nowhere to go, the collapse
of its outer mass now bounces off this neutron core.
The energy of this sudden rebound causes a shock wave which disrupts the overlying stellar
matter, and pushes it to escape velocity. And this is what results in a supernova explosion.
The sudden compression of matter, and bounce outward releases enormous amounts of energy,
up to 10^46 Joules within 10 seconds. So all this energy is what we can see in our telescopes
and sometimes even with our naked eyes when such an explosion occurs in our own galaxy.
For a brief time, a supernova can be as bright as the entire galaxy. The most recent supernova
to be seen in our own Milky Way galaxy occurred in 1604. It showed up as a sudden distant
bright star, and was visible even during the day. It was noted by Chinese scholars and
was studied by Yohannes Kepler. It’s remnant identified in 1941, can still be seen with
our telescopes. You should know that there are actually several
different kinds of supernovae out there, and they have different mechanisms and different
durations. But in principle the mechanism is the same. What I have talked about here
are the most common core collapse supernovae. Now, I explained this step by step, so you
may get the impression that this happens over a long period of time, but that’s not really
the case. After the electron degeneracy pressure gives way, the core undergoes a cataclysmic
implosion within seconds. And without the support of this inner electron degeneracy
core, the outer core collapses very quickly reaching almost 25% the speed of light, before
it hits the wall of neutrons due to neutron degeneracy pressure.
Let me give you an idea of the overall timeline. It can take millions of years for a large
star to die, but less than a quarter of a second for its core to collapse. It then takes
a few hours for the shockwave to reach the surface. The explosion only lasts about 2
minutes, but their peak brightness remains for several months, and they can take a year
or more to fade away. What’s leftover from this process is a neutron
star, and it can remain a neutron star for billions of years. But you are probably wondering,
if electron degeneracy can be overcome by gravity, why can’t neutron degeneracy also
be overcome by gravity? Well, it can.
Just like the Chandrasekhar limit which when exceeded results in a Neutron star, there
is something called the Tolman–Oppenheimer–Volkoff limit (or TOV limit). If this TOV limit is
exceeded, it results in a Black hole. Theoretical work in 1996 placed the limit as about 1.5
to 3.0 solar masses. So if the remnant neutron star is 1.5 to 3
times the mass of our sun, gravity can overcome even the neutron degeneracy pressure, and
collapse it further to something even smaller
than a neutron star, theoretically, infinitesimally
small. It can form a black hole. This is a complete domination of gravity over every
other force. And is an object beyond the limits of our equations.
When a black hole forms, nothing can escape from it, not even light. So unless there is
infalling matter into the black hole, which gets compressed and heated to produce high
energy radiation like x-rays or gamma rays, which would be visible on our telescopes,
we would not see anything. That’s why it’s called a black hole.
So a white dwarf and neutron star are due to the same root effect: the Pauli exclusion
principle: two fermions cannot be in the same state, including position, so they form a
barrier to further compression. The difference is the type of fermion. In the case of white
dwarfs, it’s the electron. In the case of neutron stars, it’s a neutron.
In white dwarfs, as atoms get tightly packed together, the electrons’ wave functions
overlap more and more with neutrons’ wave functions, and so the probability of electron
capture increases. Eventually a white dwarf can thus become a neutron star when gravity
is high enough. The neutrons in neutrons stars, however, don’t
have anything to get captured by, so they can get very densely packed. But gravity seemingly
has no end, and can keep going if the star exceeds the TOV limit, to ultimately form
a black hole – beyond the limits of the quantum mechanical laws we know about. These
are some of the most interesting and fascinating objects in the universe.
Now, if you want to learn more about the science of gravity and black holes, there is a superb
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Now…the next video on this topic will be posted right up here. I’m going to talk
more about some astonishing facts about black holes such as how they can support many more
planets in stable orbits than stars like our sun. Some of this stuff is going to blow your
mind. So be sure to check out that video, And I will see you there my friend.