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Stephanie came up to me after the last lecture, and we discussed cultural construction of p-prim a little more. I feel more comfortable with her conclusions now; she says she is looking at how often the research pops up in different settings, and is aware of the fact that many scientists in her field (and others) have a tendency to forget that things need to be seen cross-culturally before they can be diagnosed as human traits. At any rate, she says, these things certainly seem to be true in our culture–which I absolutely agree with. (My hesitation relates to wondering how many of these things are shaped by human culture very, very early on in infancy. Most cultures may shape people in similar ways, but that doesn’t make the results innately human as long as there are exceptions. I don’t have a problem with the idea that there are innate human tendencies, or p-prims, or anything like that, but I feel that there is a tendency to declare things innate without substantial enough proof, and thus I approach most claims with skepticism. It’s just things like, if you have to teach kids not to touch the stove–which I hear parents complaining they do–then how do we accept that kids automatically know that heat sources are hottest at their centers? I picked a more exotic example in class, but they abound here.)
Now, stars! Mike Brotherton on stars again.
We want to take a step into the physics that provides stars with the pressure to resist gravitational collapse: the fusion processes in cores of stars, and how understanding them is fundamental to understanding stellar evolution.
Stars produce energy by nuclear fusion of hydrogen and helium. In the sun, this happens primarily through the proton-proton (PP) chain. The reason that turning hydrogen into helium, which you do by combining four hydrogens into a helium, produces energy is that a helium atom has less mass than four hydrogen atoms. You can turn four hydrogen into helium and you wind up with a little less mass, and that mass has been converted into energy in the process. That energy is kinetic and high energy gamma rays (neutrinos). This is called a proton-proton chain because you stick two protons together, only it’s not that simple. At the same time, you need help from the nuclear weak force to get two of these protons to turn into a neutron and produce a neutrino. If the first step was easier, then the sun would burn through its fuel much faster, and wouldn’t live as long. You need high temperature to force really strong collisions that will force hydrogen to stick. Net effect–start with four hydrogens, end one helium, with a release of energy and a couple neutrinos.
For stars about 20 times more massive than the sun, there’s something called the CNO cycle, which is something else that turns four hydrogens into a helium, but it does so with different chemical processes that don’t have that difficult, slow first step. You need higher temperatures to make the sequence of chemical reactions that happens in this more massive star to occur. These higher temperature reactions happen faster, and so the star burns through its much higher volume of fuel much faster than the sun burns through its fuel.
We’re pretty sure about the physics. For a long time we thought there weren’t enough neutrinos coming from these suns, but now we’ve realized that the neutrinos change properties on their way to us. Only about 1/3 of them remain neutrinos.
In a sun more massive than 8 solar masses, you can do more fusion. It turns out that you can fuse elements into heavier and heavier elements until you get to iron.
Hydrostatic equilibrium–you balance gravity with pressure. You do this computationally to solve for the structure of a star by building a computer model that solves for the equilibrium at every concentric sphere.
Outward pressure force must exactly balance the weight of all layers above everywhere in the star. This condition uniquely determines the interior structure of the star. This is why we find stable stars on such a narrow strip (the main sequence) in the H-R diagram.
Stellar models–the structure and evolution of a star is determined by the laws of 1) Hydrostatic equilibium, 2) energy transport, 3) conservation of mass, 4) conservation of energy.
The life of a star on the main sequence we understand well. Stars do evolve in time on the main sequence. Stars will migrate, getting brighter over time. The sun itself has gotten about30 or 40% brighter since it was first born, because when you change hydrogen into helium, you change four particles into one particle. Gas pressure changes because gas pressure depends on how many gas particles you have zooming around. What happens is you have fewer particles, gravity crushes it down more until the remaining helium has replaced the hydrogen, which is hotter to have more oomph, you get a little hotter, burn a little faster, and overall luminosity goes up. Bud points out that the stars get brighter, but cooler, although Mike notes that while this is true, they don’t get that much cooler.
That’s burning hydrogen on the main sequence.
2 solar masses has a lifetime about 1/6th of the sun, but is 11x as luminous.
O stars live maybe a million years. The sun lives on the order of ten billion years. M stars about 56 billion years. Massive stars on the order of millions of years, least massive ones essentially forever.
The end of a star’s life: when all the nuclear fuel in a star is used up, gravity wins over pressure, and the star dies. High-mass stars die first, in gigantic explosions called supernovae. Less massive stars die in less dramatic events.
Evolution off the main sequence: expansion into a red giant– hydrogen in the core completely converted into helium, hydrogen burning (i.e. fusion of hydrogen into helium) ceases in the core, hydrogen burning continues in a shell around the core. The helium core plus the hydrogen-burning shell produce more energy than needed for pressure support. Expansion and cooling of the outer layers of the star become a red giant. A star could start at like 5 solar masses, but as hydrogen fusion stops in the core and moves into the shell, it slowly expands over a few hundred million years until it is 70 solar masses.
So we have all those giant stars sitting on the right hand side of the H-R diagram. Those come from main sequence stars that finish burning their hydrogen, and evolve into red giant stars. The sun will eventually evolve into one, moving up and to the right on the H-R diagram. All the stars cool and get big, although the luminosity stays high because their surface area is also increasing. When the sun expands into a red giant, it may well go out beyond earth’s orbit. Even if it doesn’t, we’re toast…you know, about 5 billion years from now.
Degenerate matter– matter in the helium core has no energy source left, and this means there’s not enough thermal pressure to resist and balance gravity. Collapse is stopped at some level by degenerate electron pressure. Matter assumes a new state called degenerate matter.
Red giant evolution–there will come a point in the evolution where the core gets denser and hotter until the next stage of nuclear burning can begin in the core. Helium fusion turns on in the core with a helium flash at which point the star settles on the helium main sequence (the line where red giants settle on the h-r diagram). This is a shorter-lived sequence. The helium fusion is called the triple-alpha process. We find this out through theory and by looking at a lot of stars.
Evidence for stellar evolution: star clusters. Stars in a cluster all have approximately the same age. They don’t all turn on at exactly the same time, but they’re about the same age. More massive stars evolve more quickly than less massive ones. If you put all the stars of a star cluster on an HR diagram, you can test the assertions about star evolution. What you find is that the most massive stars in the upper left will be missing.
In an HR diagram of a star cluster, high-mass stars evolved onto the giant branch. Low-mass stars are still on the main sequence. But the massive stars will be gone, having burned through their fuel already.
He gave us a bunch of examples which were really cool but I couldn’t transcribe fast enough. It looks like this and you can see how the age of a star cluster will determine what kinds of stars are present.
Red dwarfs don’t expand to giants, and never have helium burning.
Sunlike stars devlop a helium core and expand to red giants during a hydrogen shell burn phase. We do ignite helium burning in the helium core. and we form a core of degenerate carbon or oxygen.
White dwarfs: degenerate stellar remnants have carbon or oxygen cores. They’re extremely dense, 1 teaspoon has a mass of 16 tons! A chunk of white dwarf material the size of a beach ball would outweigh an ocean liner. A white dwarf has a mass similar to solar mass (a bit less) but highly condensed, and their temperature is about 25,000 kelvins, like you took off the outer layers to reveal the bright, shining core. The luminosity is about 1/100th that of the sun. The temperature is higher. They tend to be about the size of the earth.
The goldilocks zone around them would be what, asks Bud? Mike answers, essentially nonexistent.
Mike says these cool over time. They’re done with their fusion processes. They don’t cool quickly, but they do cool. They’re balls of really dense material that just cool over time.
There could be nonradiating dead white dwarfs out there, asks Bud? Yes, says Mike, but we think in our own galaxy we’ve found the faintest, coolest ones out there. It takes billions of years for them to cool, and the ones we see are consistent with the age of the universe. They seem to be sunlike stars that became white dwarfs and cooled, but the ones the age of the universe are still visible.
How do stars move from being sunlike stars that end up with carbon or oxygen cores that they can’t burn, to being white dwarfs? The process has to do with a phase where the outer envelope is thrown off. This phase would toast any surrounding planets. So, science fiction wise, there shouldn’t be anything around a white dwarf, because it would have been toasted by the red giant phase, or by the phase when it became a white dwarf. You could put something there, but it would have to be close to the star.
The chandrasekhar limit indicates that the more massive a white dwarf is, the smaller it is. The pressure in the star becomes larger, until electron degeneracy pressure can no longer hold up against gravity. The least massive white dwarfs (1/10 solar mass) have a radius 2% of the sun. As we increase the mass, the radius gets smaller. This is counterintuitive because we think of more stuff as being bigger, but the idea is that as you add more mass to the white dwarf core, gravity is squeezing it more and more and more and squeezes it down until almost nothing. The size scale is tens of kilometers across, the size of Laramie or a bit bigger. The Chandrasekhar limit indicates how massive or how small a white dwarf can be.
The final breath of sun-like stars: planetary nebulae phase, which is how we go from a red giant to a white dwarf with an exposed core. These have nothing to do with planets. They’re called planetary nebulas because when astronomers first looked at them through telescopes they looked like little, resolved disks, which looked more like planets than stars. They didn’t move like planets; they’re not planets; but they were glowing objects that looked like the disks of planets. These are remnants of stars with the radii of .2 to 3 light years. They expand 10-20km/s into space. And you typically see a planetary nebula phase that lasts about 10,000 years.
There’s an instability that ends up blowing off the outer layers of the red giant and exposing the white dwarf core. One of the reasons this happen sis red giants get so huge with changing masses that the outer parts of them are not rotationally bound very much to the core. They’ve gotten far away from the concentration of the mass so it’s easy to get them to blow off.
The formation of planetary nebulae. They look like disks to us, but if we were able to look in 3 dimensional space, they’d look like spheres.
The outer layers of the red giant star are not that tightly bound to the stellar core. Escape velocity is not that high. Stellar winds happen, and the outer layers just start blowing out. As this happens, you start losing some of your shielding. The reason the outer layers can sit there in the first place is because of the layers between them. Take that away, and the gas starts blowing off, and the core becomes more exposed. Radiation from the core starts driving away the inner part. As this happens, it forms the planetary nebula which lasts about 10,000 years.
You get interesting pretty things that aren’t all spheres like the ring nebula. Sometimes they’re hourglasses or other interesting shapes. The egg nebula. The cat’s eye nebula. The clown face nebula. We think these may happen because of things like binary stars.
Is this an explosion, asks Ian? Mike answers that it’s an explosion that lasts 10,000 years. Then he analogizes it to me sneezing. Snifffle. Snuff.
Planetary nebulas are not super-common objects because they don’t last very long.
The flash that Mike mentioned earlier, is that visible, asks Ian? It’s not Mike’s area of expertise, but he says he doesn’t think so. If there is, it would be fast.
The photons in the core of the star take hundreds of thousands of years to work to the surface, in the case of the sun. So even if there were an explosion of photons, it would take a long time to see. It’s fast in terms of the age of the star, but not in terms of human vision.
White dwarfs are just the exposed, degenerate cores of sunlike stars.
NGC–galaxy catalog. The planetary nebula were lumped in with galaxies initially. At the time they didn’t know that spiral galaxies were really galaxies.
Mass transfer in binary stars: in a binary system, each star controls a finite region of space, bounded by the roche lobes (or roche surfaces). Some of the stars form quite closely together, even in contact with each other. There are scenarios in which one star can suck up another, or material can slosh back and forth between stars during their evolution. If you have two stars, they each have a gravitational area of influence. There will be a point at which they’re balanced, the lagrangian point.
Recycled stellar evolution–mass transfer in a binary system can significantly alter the stars’ masses and affect their stellar evolution. Imagine there is a star A and star B. Star B is more massive, evolves faster, goes into a red giant phase. It expands and beocme a teardrop shaped giant star. The edge of its envelope will fall into the gravitational influence of star A, which will then suck off the gases. Star A gets more massive now, triggering a runaway effect where star A is now more massive than star B and still on the main sequence. Star B is now a weird semi-giant star with little mass. Star A can then itself become a giant and start transferring mass back to star B. You can have a sort of strange dance, with much more complicated scenarios for stellar evolution.
Novas are different from supernovas. Novas happen when a white dwarf star in a binary system is accreting a very hot, dense layer of surface hydrogen which is an unstable situation. If you dump mass on them from the other star, then they suddenly hit fusion conditions, and a nuclear explosion happens, exploding the outer layers out into space. It does not destroy the white star, does not necessarily destroy the companion star, but it does make a bright explosive event. It’s not as bright as a supernova which can outshine a whole galaxy, but it is big, bright, explosive. Some of these are recurrent, so we know the companion star isn’t destroyed–instead, it keeps pouring mass onto the white dwarf, which then has enough mass that it reaches fusion conditions again and–boom. We have seen systems that every few years, to every few decades, go nova.
The fate of our sun and the end of the earth–the earth will be incinerated!