Check out Mike Brotherton’s the SF writer’s bookshelf. Full of excellent recommendations.
Binary Star evolution is complicated and not easily condensed down to a single sequence. A lot of binary stars are far apart from each other. They will evolve as independent stars. But there’s a category of stars that are very close to each other and can share mass.
In a binary system, each star controls a finite region of space bounded by the Roche lobes.
Langrangian points- There are points of special interest that LaGrange figured out some time ago. L1 is the center of mass where the gravity is balanced between the two stars. You can sit satellites there and they’ll remain with only minimal station keeping. Roche lobe is the gravitational sphere of influence. (This applies to something like the Earth/moon system as well as binary stars)
Roche lobes are relevant because the current case, the stars are encased in their own Roche Lobe. As we saw yesterday, stars can enlarge to giants past their Roche Lobe, which will allow mass transfer across the L1 point to the other star.
When we talk about planets of binary star systems, it’s thought generally that if the stars are far enough apart, they can have their own solar systems, not mixing. If they are very close, then the planets could rotate around the pair. (Tatooine would be circling a sunlike planet with a red giant in the distance.)
L1, L2 and L3 are unstable. If you put something there, it won’t move because it’s held by the gravity. But if they move off just a little, then they get sucked in so you just need a little rocket to nudge it back into place. L4 and L5 are very stable. If an item moves off a little, then it tends to drift back into place.
David explains it as balancing an item on the top of the bowl, versus the bottom of the bowl.
Stellar Evolution.
Here is a sample situation, but there are too many variables for this to apply to every binary system. If Star B is more massive than Star A, then it will evolve faster and become a Giant, filling it’s Roche lobe. It would lose mass to Star A. Star B loses mass and Star A gains mass. So the Roche lobes will change until they become equal OR Star A becomes more massive and loses mass back to the white dwarf that remains of Star B. The transfer stops when the mass in is inside the Roche Lobe.
There’s a model where the entire sequence happens in the space of a few months, totally absorbing one of the stars.
White dwarfs in Binary systems.
Binary consisting of white dwarf + main sequence or red giant star => WD accretes matter from the companion. The accreted matter forms a disk called accretion disk. The disk is made up of hot gas. A white dwarf is about the size of the earth.
Nova Explosions.
A nova is what happens when you accumulate hydrogen gas on the surface of a white dwarf. It sits there. At some point you reach critical conditions for fusion to happen. Hot enough, dense enough and when this happens its explosive. There’s a chain reaction that engulfs the entire star almost at once. The timescale is a few seconds to spread over the entire star. Novas only happen in binary system.
Recurrent Novae
In many cases, the mass transfer cycle resumes after a nova explosion. Cycle of repeating explosions every few years — decades.
The Fate of our Sun and the end of the earth.
Sun will expand to a red giant in 5 billion years. It expands to ~ Earth’s orbit. Earth will either be slowly toasted, outside, or be quickly toasted, inside. We expect the sun will form a planetary nebulae. And the suns carbon oxygen core will eventually become a white dwarf.
In more massive stars, we talked about the onion skin model. The very massive stars can continue to have fusion in the core with heavier and heavier elements. If we look at a 25-M star. It has enough H to burn for 7,000,000,000 years for 93.3% of its lifetime. It would have enough He for 500,000 years or 6.7% of lifetime. Carbon burns for 600 years, Oxygen burns for .5 years, Silicon for 1 day.
The Deaths of Massive Stars: Supernovae
If you’re greater that 8M you’ll form an iron core. The star can’t support itself. The inner part suddenly collapses and then you get all these crazy events happening that blows the outer part of the star apart. In the core collapse and the ensuing explosion that you get elements produced that are heavier than iron. If you are in the local environment, the neutrino flux is lethal within a couple of light years.
The core becomes either a black hole or neutron star depending on how much mass is involved in the core collapse. Greater than 3 solar masses are likely to end up in a black hole.
You could have a supernova in a binary system which would not destroy the other star in the explosion, but the other star could be pulled in to create a black hole or an accretion disk.
On the verge of being able to detect gravity waves.
The Crab Nebula formed from a Supernova from 1050 AD. The explosion continues expanding. We can see it in photos taken years apart.
Later in life they look like the Veil Nebula
In the x-ray, you can see the neutron star. You can’t see it in visible light, because it’s the size of Laramie.
Type I and II of Supernovae — If an accreting white dwarf exceeds the Chandrasekhar mass limit, it collapses, triggering a type Ia supernova. Type 1a is pretty much always the same. Type II are all over the map.
Neutron Stars
Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons.
Discovery of Pulsars
We already talked about the problem of angular momentum. If something large is spinning, when it collapses it spins faster (think ballerina.) Collapsing stellar core spins up to periods of a few milliseconds. Think of D.C. spinning around a few million times per second. Turns out that when we watch radio emission from some of these stars, we see regular pulsations. Which is why they are called pulsars.
These were first found in England doing some radio astronomy. Jocelyn Bell’s professor told her to build a radio telescope. She got regular pulses. Hm. Maybe we have aliens. They called them LGM1 (Little Green Men 1). They considered not publishing, because what if someone decided to contact them. They eventually decided that there were natural processes that could do that. So they published. the professor got the Nobel prize. Jocelyn Bell did not.
The Crab Pulsar. Crab Pulsar blinks in optical light and x-ray, not just radio.
We believe that they pulse because they do not have a magnetic axis aligned with their pole. So every time they spin, we see the magnetic pole, which causes a pulse.
When we get neutron stars in binary systems we get a lot of hard x-rays. Very energetic. The accretion process produces x-rays. In his example. Orbit is 1.7 days. Accretion disk material heats to several million => x-rays emission
Some pulsars have planets orbiting them. Just like in binary pulsars this can be discovered through variations of the pulsar period. They didn’t expect pulsars to have planets, because they’d thought the supernovae would have destroyed them. Mike says, “We’re good at radio timing” so they can find small planets in this setup.
Black Holes
When you get over 3M, we know of no mechanism to halt the collapse of a compact object. It will collapse into a single point — a singularity: A black hole.
You can think about black hole in terms of escape velocities. It’s 11.6km/s to escape from Earth and since gravitational forces decreases with distance, in theory you could escape more easily at the end of a large pole. If you could compress Earth to a smaller radius you’d need a larger escape velocity.
There is a limiting radius where the escape velocity reaches the speed of light, c:
Rs = 2GM/c2 Because the Schwarzschild Radius scales linearly, you can easily calculate the mass for other objects.
Schwarzschild Radius defines the event horizon. If you are within it, you can’t escape because you can’t go faster than the speed of light. No object can travel faster than the speed of light. Nothing, not even light, can escape from inside the Schwarzschild Radius. We have no way of finding out what’s happening inside the Schwarzschild Radius
Greg Egan has some technically correct fiction, The Plank Dive, that happens inside the event horizon that makes Mike’s head hurt.
10 billion M is observationally the largest Schwarzschild Radius.
“Black Holes Have No Hair”
Super-theoretical relativists argue about this. They stop having color, chemical compositions, any reasonable structures. They are determined by three properties. Mass, angular momentum, (electric charge)
As they spin, they will drag the space around with them. It’s called frame-dragging.
If you had a really massive electric charge, it ought to attract ions to equalize it. We don’t think you can have a massive electric charge in space without it neutralizing.
Black holes warp space, we know exactly how they warp space according to relativity. We know how things would look, for instance in this picture of a black hole in front of Harvard.
“Flatland”
General Relativity Effects Near Black Holes
An astronaut descending down towards the event horizon of the black hole will be stretched vertically (tidal effects) and squeezed laterally. Spaghetiffying effect. It would pull you apart like taffy. Lots of blood and guts and then ripped down to component atoms.
Time dilation
If we were to watch a clock falling into the event horizon, it would move more and more slowly until it stopped. But not from the perspective of the clock, which would be stretched apart.
Gravitational Redshift. Light coming from the vicinity of the black hole are redshifted. All wavelengths of emissions from near the event horizon are stretched. Frequencies are lowered.
Observing Radio Holes
No light can escape a black hole so they can’t be observed directly, so we observe their effect on the environment. They can accrete gas, which heats up to an enormous degree becoming quite luminous. If an invisible compact object is part of a binary, we can estimate its mass.
Gamma-ray bursts are cool and weird. Everyday we had gamma-ray bursts from space and didn’t know what they were. Military found them first, they’d built a machine to detect nuclear explosions and when they turned it on they found all sorts of explosions in space. So they went to the astronomers.
Massive stars emit them in what they call Hypernova. The collapsing core of a massive star drives its energy along the axis of rotation because the rotation of the star slows the collapse of equatorial regions. Within seconds the remaining parts of the star fall in. Beams of gas and radiation strike surrounding gas and generate beams of gamma rays. The gamma-ray burst fades in seconds, and a hot accretion disk is left around the black hole.
They have satellites that detected gamma ray bursts and transmit a signal to earth to a whole bunch of little telescopes. Within minutes, these are all pointed at that portion of the sky and taking constant pictures. With this, they get visual correlation which fade within a few hours or days.
Very cool stuff.