This is going to be a two-part discussion of the collapse of high(ish)-mass stars into neutron stars and the subsequent explosion we call a supernova.
It all starts with a heavy star, over around eight solar masses (random aside: it turns out that if these stars weren't constantly blowing away their outer layers, a star would only need to be around four solar masses to collapse into a neutron star). Over time, as the star ages, its core runs out of hydrogen to fuse. Here the massive star behaves kind of like the stars I mentioned yesterday, but instead of relying on degeneracy pressure to fuse helium, it's massive enough to be able to fuse helium stably, and keeps going. Over time, the star develops an onion structure, with layers of different elements and fusion processes. Close to the surface the star burns hydrogen. This is a very efficient reaction, because protons are much happier to be in helium nuclei than hydrogen, because of the higher "binding energy per nucleon" in helium. Unfortunately, that's a topic that will have to wait for another day. For now, take my word for the fact that hydrogen burning is very efficient, while the burning of higher-mass atoms is less so. Anyhow, layers closer and closer to the center are hotter and denser, and can thus fuse larger and larger nuclei. All the way down through silicon fusing into iron and nickel. But iron-56 is the most stable nucleus in the universe, so there is will take energy to fuse it into heavier atoms or break it up into smaller ones. This star therefore accumulates an iron core. Eventually, this iron core becomes so massive that the degeneracy pressure of the electrons inside it isn't enough to support it against gravity. At this point (at least in the example I saw recently), the core has a radius of around 10,000 km. Now that there's less supporting pressure, the star collapses inwards and gets hotter (this is a fascinating example of negative specific heat, in which a loss of energy produces an increase in temperature). This is hot enough to break down iron and helium in an endothermic reaction, which consumes much of the increase in temperature and means that the star's core is once again relying solely on degeneracy pressure for support. But the density is so high that degeneracy pressure just doesn't cut it anymore.
Instead, the core begins a phase called electron capture, in which the electrons and protons in the core are pushed together so hard that they merge into a neutron and a neutrino in the reaction $p+e\to n+\nu_e$. This electron capture happens in just a few seconds, and suddenly the core is just 20 km across. It has a density of $8\cdot10^{17}$ kilograms per cubic meter. That means that in just a cubic centimeter (the volume of a measly gram of water), the ex-iron-core has around the mass of a respectable mountain! This is called a neutron star, and apart from being generally awesome, they're also the most perfectly spherical objects in the universe (that we know of, anyway). What happens to the non-core part of the star is a topic I hope to explore in a post soon.
I probably won't be able to post tomorrow or over the weekend, but look forward to returning to awesome physics at the beginning of next week.
Thursday, March 28, 2013
Helium flash
Stars between around 0.5 and 2.5 solar masses happily 'burn' hydrogen for most of their lives. Once one runs out of hydrogen, it suddenly isn't producing enough energy in its core to support its outer layers, and the star collapses under gravity. The first thing that happens here is that the density increases, so the star starts fusing hydrogen in layers outside the core, which causes the outer layers to expand outwards. The star becomes a red giant, but its core and inner layers continue to collapse under gravity. The two main forces that prevent any star from collapsing inward are thermal pressure (fusion inside emits radiation and prevents nearby layers from encroaching) and degeneracy pressure (a quantum effect - no two fermions (like electrons or hydrogen atoms) can occupy the same quantum state, so the star can't collapse any further than that). Since the core is now fusing much less hydrogen than before, the thermal pressure is dwarfed by degeneracy pressure. The pressure is high enough to initiate helium fusion, which increases the temperature. But because the core is primarily supported by degeneracy pressure, this increase in temperature does almost nothing to expand (and thus cool) the helium-fusing portion of the star. So the helium fusion becomes a runaway reaction in what's called the helium flash. This phase of the star's life only ends when the temperature finally rises enough to overwhelm degeneracy pressure. At this point, the star expands and cools a bit. Helium continues to burn, but in a more regulated manner, and thermal balance reigns once more.
Stars with less mass don't heat up enough to go through helium burning, and instead become helium white dwarfs. Stars with more mass are able to start helium burning before the core becomes degenerate, so there's no runaway helium flash. These eventually become neutron stars and supernovae - a topic for another day.
Stars with less mass don't heat up enough to go through helium burning, and instead become helium white dwarfs. Stars with more mass are able to start helium burning before the core becomes degenerate, so there's no runaway helium flash. These eventually become neutron stars and supernovae - a topic for another day.
Tuesday, March 26, 2013
Tops and precession
Remember playing with tops when you were younger? It turns out that they're interesting not only to children but also to physicists. Take precession. If you spin a top, as it slows down, it starts to wobble. In the simplest case, the handle of the top just spins around tracing out a rough cone. It's called precession, and it affects all sorts of things, from electrons to the Earth.
Here's how it works. You have a top, which is spinning and thus has some angular momentum. If the top is adequately symmetrical, then the angular momentum just points along the spin axis, either upwards or downwards, depending on the direction you spun it. The direction is determined by the right-hand rule, so if the top is spinning clockwise if you look at it from above, the angular momentum vector points down. Similarly, counterclockwise means the angular momentum points up. For now, let's suppose that the angular momentum is pointing upwards. If the top is completely vertical, then the top spins merrily onwards, and nothing interesting happens. Luckily, in the real world, nothing is ever so exact as to be totally vertical. Random perturbations happen, and the top tilts slightly. In any case, once this happens, gravity tries to pull the top downward further, which (treating the top's point of contact with the table as our pivot) creates a torque according to the cross product $\vec\tau=\vec r\times\vec F$ ($\vec\tau$ is torque, $\vec r$ is the radius vector from the point of rotation to the point on which the force acts - in this case, the center of mass of the top, and $\vec F$ is the force, in this case from gravity). If the top is tilted to the right, then the torque vector points away from us. If the top wasn't spinning, it would just topple over under the influence of gravity. But because it's spinning, and because angular momentum is conserved, it can't just topple like that. So what happens?
Recall that $\vec\tau=\frac{d\vec L}{dt}$, that is, torque causes a change in the angular momentum. And it's a vector relationship - since the torque is pointing away from us, after a very short time $dt$, the angular momentum is pointed slightly more away from us than originally. But observe that the torque is always perpendicular to the angular momentum. So while the angular momentum changes direction, it does not change length. Thus the top continues spinning happily, but its axis of rotation precesses around a cone. Neat!
So why is this precession only apparent when the top slows down? The length of the angular momentum vector is proportional to the speed of rotation. When the top is spinning really fast, the angular momentum vector is so long that it dwarfs the contribution of the torque from gravity, so the wiggles are tiny. As the top spins on and on, it's rubbing against the floor or table, and friction slows down its rotation. As that happens, the torque is less tiny compared to the angular momentum, so the wiggles become more and more noticeable, and eventually, the top spins out of control and falls over.
Here's how it works. You have a top, which is spinning and thus has some angular momentum. If the top is adequately symmetrical, then the angular momentum just points along the spin axis, either upwards or downwards, depending on the direction you spun it. The direction is determined by the right-hand rule, so if the top is spinning clockwise if you look at it from above, the angular momentum vector points down. Similarly, counterclockwise means the angular momentum points up. For now, let's suppose that the angular momentum is pointing upwards. If the top is completely vertical, then the top spins merrily onwards, and nothing interesting happens. Luckily, in the real world, nothing is ever so exact as to be totally vertical. Random perturbations happen, and the top tilts slightly. In any case, once this happens, gravity tries to pull the top downward further, which (treating the top's point of contact with the table as our pivot) creates a torque according to the cross product $\vec\tau=\vec r\times\vec F$ ($\vec\tau$ is torque, $\vec r$ is the radius vector from the point of rotation to the point on which the force acts - in this case, the center of mass of the top, and $\vec F$ is the force, in this case from gravity). If the top is tilted to the right, then the torque vector points away from us. If the top wasn't spinning, it would just topple over under the influence of gravity. But because it's spinning, and because angular momentum is conserved, it can't just topple like that. So what happens?
Recall that $\vec\tau=\frac{d\vec L}{dt}$, that is, torque causes a change in the angular momentum. And it's a vector relationship - since the torque is pointing away from us, after a very short time $dt$, the angular momentum is pointed slightly more away from us than originally. But observe that the torque is always perpendicular to the angular momentum. So while the angular momentum changes direction, it does not change length. Thus the top continues spinning happily, but its axis of rotation precesses around a cone. Neat!
So why is this precession only apparent when the top slows down? The length of the angular momentum vector is proportional to the speed of rotation. When the top is spinning really fast, the angular momentum vector is so long that it dwarfs the contribution of the torque from gravity, so the wiggles are tiny. As the top spins on and on, it's rubbing against the floor or table, and friction slows down its rotation. As that happens, the torque is less tiny compared to the angular momentum, so the wiggles become more and more noticeable, and eventually, the top spins out of control and falls over.
Spin is angular momentum
If you've taken an introductory chemistry course, chances are good that you've heard of a property of particles called spin angular momentum, or spin for short. In chemistry, spin is particularly relevant to the way that electrons can pile into atomic orbitals. More generally, in quantum physics (or particle physics), all fundamental particles have spins, and spin plays a huge role in the interactions between particles.
In any case, the spin statistics theorem (which basically describes the difference between leptons, which are the standard particles you hear about (electrons, quarks, etc.), and bosons, which carry forces) is a topic for another day. Instead, I want to briefly mention a really cool property of spin. I've heard it called 'spin angular momentum' for a long time, and it has some distinct parallels with orbital angular momentum. It's also almost always described as a tiny little particle rotating around its axis. But until recently, I didn't realize how very angular-momentum-ey spin actually is. There's this effect called the Einstein-de Haas effect that shows very clearly how spin is part of the total angular momentum of an object.
Imagine that we have a long(ish) thin cylinder of a ferromagnetic material like iron suspended from a twistable wire or thread. Wrap a conducting wire around this cylinder many times to create a solenoid (but don't let the solenoid touch the cylinder - that would a) short out the circuit and b) make it hard for the iron to rotate). Now run a current through the solenoid, which creates a roughly uniform magnetic field inside the cylinder, pointed along the cylinder. Because the cylinder is a ferromagnet, this polarizes the spins of the electrons inside along the magnetic field. All this is old news. The fascinating thing, and the fact that makes it clear that spin really is angular momentum, is that in order to conserve angular momentum now that all the spins are pointed in the same direction, the ferromagnetic cylinder starts to rotate in the opposite direction. This is the Einstein-de Haas effect, and it was theorized and observed by (surprise surprise) Einstein and de Haas in the early 20th century.
The reverse is also true, in what's called the Barnett Effect. That is, if you rotate a ferromagnetic material, it can spontaneously develop a magnetic polarization! So the angular momentum of the object is partially cancelled out by an alignment of the spins, which produces a net magnetization in the material.
Physics is awesome.
In any case, the spin statistics theorem (which basically describes the difference between leptons, which are the standard particles you hear about (electrons, quarks, etc.), and bosons, which carry forces) is a topic for another day. Instead, I want to briefly mention a really cool property of spin. I've heard it called 'spin angular momentum' for a long time, and it has some distinct parallels with orbital angular momentum. It's also almost always described as a tiny little particle rotating around its axis. But until recently, I didn't realize how very angular-momentum-ey spin actually is. There's this effect called the Einstein-de Haas effect that shows very clearly how spin is part of the total angular momentum of an object.
Imagine that we have a long(ish) thin cylinder of a ferromagnetic material like iron suspended from a twistable wire or thread. Wrap a conducting wire around this cylinder many times to create a solenoid (but don't let the solenoid touch the cylinder - that would a) short out the circuit and b) make it hard for the iron to rotate). Now run a current through the solenoid, which creates a roughly uniform magnetic field inside the cylinder, pointed along the cylinder. Because the cylinder is a ferromagnet, this polarizes the spins of the electrons inside along the magnetic field. All this is old news. The fascinating thing, and the fact that makes it clear that spin really is angular momentum, is that in order to conserve angular momentum now that all the spins are pointed in the same direction, the ferromagnetic cylinder starts to rotate in the opposite direction. This is the Einstein-de Haas effect, and it was theorized and observed by (surprise surprise) Einstein and de Haas in the early 20th century.
The reverse is also true, in what's called the Barnett Effect. That is, if you rotate a ferromagnetic material, it can spontaneously develop a magnetic polarization! So the angular momentum of the object is partially cancelled out by an alignment of the spins, which produces a net magnetization in the material.
Physics is awesome.
Friday, March 22, 2013
Betelgeuse
Rather than a general physics fact, I thought it'd be fun to share a few facts about a star familiar to many stargazers: Betelgeuse, the left shoulder of Orion (you know, the guy with the belt). If it were in our solar system centered at the Sun, its boundary would extend well past the orbit of Mars - that's one big star. It's a supergiant, which means that its surface is cooler than smaller stars like the sun. So it appears noticeably red, even for stargazers in the light-pollution capital of the world, Los Angeles.
To complicate matters, it seems that Betelgeuse also grows and shrinks periodically, and experiences corresponding changes in brightness and color. And all of this is hard to see, because it's surrounded by a very strangely-shaped cloud (remember the interstellar medium?), which interferes with observations. Experimentalists are really impressive!
To complicate matters, it seems that Betelgeuse also grows and shrinks periodically, and experiences corresponding changes in brightness and color. And all of this is hard to see, because it's surrounded by a very strangely-shaped cloud (remember the interstellar medium?), which interferes with observations. Experimentalists are really impressive!
Thursday, March 21, 2013
Fragmentation
Often, when we look out into space, we see clusters of young stars. These seem puzzling at first - why would so many stars form in the same area? Isn't there a limited amount of stuff available to form stars in a given region?
The answer has to do with the way that stars form. It all starts with a cloud of interstellar medium. The two main forces acting on it in bulk are gravity, which tries to pull all the mass of the cloud inwards towards the center, and temperature/pressure, which tries to push the cloud outward, preventing its collapse. For a cloud to collapse, then, its mass needs to exceed a critical mass, called the Jeans mass, after Sir James Jeans OM FRS MA DSc ScD LLD (this guy had a lot of titles). The Jeans mass is a function of the density, mass, and temperature of the cloud. A cloud with more mass will collapse. A cloud with less mass won't.
To understand why a cloud can form clusters of stars instead of just one, we need to take a slightly closer look at what the Jeans mass really says. I won't go into the math here, but conceptually, all else being equal, an increase in the temperature of the cloud will mean it takes more mass to overcome the warmer material pushing outward. More subtly, an increase in the density of the cloud reduces the Jeans mass, essentially because gravity has an easier time bringing everything together.
Suppose that we have a cloud with sufficient mass to begin collapsing. As the dust and hydrogen collapses inwards, the density naturally increases. But the extra energy the atoms gain is predominantly radiated off, and the cloud isn't dense enough to be opaque, so the energy doesn't go into the cloud. This means temperature stays roughly constant at the start of collapse. Because of these changes, the Jeans mass drops, and suddenly a whole bunch of regions of the cloud have the necessary mass to collapse in on themselves. Because the cloud cannot possibly be completely homogeneous, little pockets of collapsing dust form in a process called fragmentation. These will eventually become the young stars we can observe in a cluster.
Why, you ask, does the fragmentation stop? Why doesn't the cloud just keep dissolving into smaller and smaller bits of collapsing material? That's because eventually, the collapsing regions' density increases enough to start absorbing their own radiation, which causes the temperature of the protostar to rise, and cancels out the density effect.
The answer has to do with the way that stars form. It all starts with a cloud of interstellar medium. The two main forces acting on it in bulk are gravity, which tries to pull all the mass of the cloud inwards towards the center, and temperature/pressure, which tries to push the cloud outward, preventing its collapse. For a cloud to collapse, then, its mass needs to exceed a critical mass, called the Jeans mass, after Sir James Jeans OM FRS MA DSc ScD LLD (this guy had a lot of titles). The Jeans mass is a function of the density, mass, and temperature of the cloud. A cloud with more mass will collapse. A cloud with less mass won't.
To understand why a cloud can form clusters of stars instead of just one, we need to take a slightly closer look at what the Jeans mass really says. I won't go into the math here, but conceptually, all else being equal, an increase in the temperature of the cloud will mean it takes more mass to overcome the warmer material pushing outward. More subtly, an increase in the density of the cloud reduces the Jeans mass, essentially because gravity has an easier time bringing everything together.
Suppose that we have a cloud with sufficient mass to begin collapsing. As the dust and hydrogen collapses inwards, the density naturally increases. But the extra energy the atoms gain is predominantly radiated off, and the cloud isn't dense enough to be opaque, so the energy doesn't go into the cloud. This means temperature stays roughly constant at the start of collapse. Because of these changes, the Jeans mass drops, and suddenly a whole bunch of regions of the cloud have the necessary mass to collapse in on themselves. Because the cloud cannot possibly be completely homogeneous, little pockets of collapsing dust form in a process called fragmentation. These will eventually become the young stars we can observe in a cluster.
Why, you ask, does the fragmentation stop? Why doesn't the cloud just keep dissolving into smaller and smaller bits of collapsing material? That's because eventually, the collapsing regions' density increases enough to start absorbing their own radiation, which causes the temperature of the protostar to rise, and cancels out the density effect.
Wednesday, March 20, 2013
More ISM, and the hyperfine structure of hydrogen
The interstellar medium (which I introduced yesterday) is really cool in a lot of ways, so I thought it merited another post.
The ISM is made mostly of hydrogen (something like 90% or so), with a bit of helium (~8%), and some other stuff (around 2% heavier things, which astrophysicists lump into the 'metal' category). It turns out to be a lot easier to tell how much dust (granules of atoms, typically (I think) the heavier atoms) is present in a cloud than, say, how much hydrogen there is. We just look at how opaque a cloud is, which can tell us roughly how much dust is between us and the stars behind the cloud. But we can also get a good measure for the amount of neutral single hydrogen present in a cloud by looking at what's called the 21-cm line. You may have heard of emission/absorption lines. Every element has a characteristic signature, because in essence it can only emit photons with energies equal to energy level differences for its electrons. So, for instance, the photons emitted by neutral hydrogen when an electron drops from the third energy level to the second all have pretty much identical wavelengths of around 656 nanometers, which appears to us as red light. But the 21-cm line isn't from the electron energy levels you learn about in high school chemistry. Instead, imagine a hydrogen atom, just an electron 'orbiting' its proton, in which the spins of the electron and proton are aligned. This state of hydrogen has a slightly higher energy than the state in which the proton and electron have opposite spin. This division of the ground state of hydrogen into two sub-states is called hyperfine structure, and it occurs because of the interactions of the magnetic moment of the electron due to its spin and its orbital angular momentum. When an atom of hydrogen drops from the slightly-excited, spin-aligned state, it emits a photon with a wavelength of 21 cm, which, as a microwave, propagates freely through clouds of gas that are otherwise opaque to visible and infrared light.
The hyperfine energy levels of the ground state of hydrogen are so close together that a decay from the spin-aligned state to the spin-unaligned state takes the average atom around 10 million years. That's a rare decay, so it's really hard (impossible?) to observe on Earth - just regular heat-based interactions of materials interfere with it - but it turns out there's a heck of a lot of cold neutral hydrogen out there in space.
The 21-cm line is uniquely narrow, which means that it's really easy to pick up any Doppler shifting caused by the movement of the emitting hydrogen. That allows us to do things like map out how fast the various arms of the Milky Way are moving away from us. Pretty neat.
The ISM is made mostly of hydrogen (something like 90% or so), with a bit of helium (~8%), and some other stuff (around 2% heavier things, which astrophysicists lump into the 'metal' category). It turns out to be a lot easier to tell how much dust (granules of atoms, typically (I think) the heavier atoms) is present in a cloud than, say, how much hydrogen there is. We just look at how opaque a cloud is, which can tell us roughly how much dust is between us and the stars behind the cloud. But we can also get a good measure for the amount of neutral single hydrogen present in a cloud by looking at what's called the 21-cm line. You may have heard of emission/absorption lines. Every element has a characteristic signature, because in essence it can only emit photons with energies equal to energy level differences for its electrons. So, for instance, the photons emitted by neutral hydrogen when an electron drops from the third energy level to the second all have pretty much identical wavelengths of around 656 nanometers, which appears to us as red light. But the 21-cm line isn't from the electron energy levels you learn about in high school chemistry. Instead, imagine a hydrogen atom, just an electron 'orbiting' its proton, in which the spins of the electron and proton are aligned. This state of hydrogen has a slightly higher energy than the state in which the proton and electron have opposite spin. This division of the ground state of hydrogen into two sub-states is called hyperfine structure, and it occurs because of the interactions of the magnetic moment of the electron due to its spin and its orbital angular momentum. When an atom of hydrogen drops from the slightly-excited, spin-aligned state, it emits a photon with a wavelength of 21 cm, which, as a microwave, propagates freely through clouds of gas that are otherwise opaque to visible and infrared light.
The hyperfine energy levels of the ground state of hydrogen are so close together that a decay from the spin-aligned state to the spin-unaligned state takes the average atom around 10 million years. That's a rare decay, so it's really hard (impossible?) to observe on Earth - just regular heat-based interactions of materials interfere with it - but it turns out there's a heck of a lot of cold neutral hydrogen out there in space.
The 21-cm line is uniquely narrow, which means that it's really easy to pick up any Doppler shifting caused by the movement of the emitting hydrogen. That allows us to do things like map out how fast the various arms of the Milky Way are moving away from us. Pretty neat.
Tuesday, March 19, 2013
Interstellar Medium
When you look up at night, you see a bunch of little bright points in the sky. They're called stars, and they're enormous balls of glowing plasma/gas that are tremendously far away. But you knew all that. What you might not have known is that there's also a ton of stuff between us and them. It's called the interstellar medium (actually, that's mostly within galaxies. Between galaxies is the intergalactic medium, and it's even less dense). It's made of incredibly diffuse molecules - on average, there's only around one to three molecules per cubic meter. Think about that for a second. At standard temperature and pressure (pretty close to the room you're in right now, probably), there are around $10^{28}$ molecules per cubic meter. So the interstellar medium doesn't really have much stuff in it. In fact, it's a better vacuum than any that we can create here on Earth. This opens up all sorts of interesting lines of inquiry, like how chemistry works when molecular collisions are so rare. Physics is cool.
Monday, March 18, 2013
Solar convection
It's been a while, but here's a new fun physics fact!
The two main means of heat dissipation in stars are radiation, in which light transfers energy away from the center of the star, and convection, in which hotter areas of the star bubble upward, carrying their heat with them and expanding as they rise.
Convection is a much more effective means of heat transfer than radiation, but only kicks in when the stellar temperature decreases outwards with radius more slowly than the convective bubble's temperature as it moves outward (this means that if a bubble of hotter material rises a bit, when it expands and cools, it remains hotter than its surroundings - if it didn't, it would just sink again, and convection wouldn't occur). In this case, convection carries heat outward very quickly, drowning out radiative heat transfer.
Convection occurs in the outer 30% or so of the Sun, and is visible on the surface of the sun as granules (around the size of North America) of bright, hot material rising to the surface surrounded by boundaries of darker, cooler material sinking downward.
Also, according to Wikipedia, just below the surface of the sun are supergranules - convective regions that are larger than the entire Earth!
The two main means of heat dissipation in stars are radiation, in which light transfers energy away from the center of the star, and convection, in which hotter areas of the star bubble upward, carrying their heat with them and expanding as they rise.
Convection is a much more effective means of heat transfer than radiation, but only kicks in when the stellar temperature decreases outwards with radius more slowly than the convective bubble's temperature as it moves outward (this means that if a bubble of hotter material rises a bit, when it expands and cools, it remains hotter than its surroundings - if it didn't, it would just sink again, and convection wouldn't occur). In this case, convection carries heat outward very quickly, drowning out radiative heat transfer.
Convection occurs in the outer 30% or so of the Sun, and is visible on the surface of the sun as granules (around the size of North America) of bright, hot material rising to the surface surrounded by boundaries of darker, cooler material sinking downward.
Also, according to Wikipedia, just below the surface of the sun are supergranules - convective regions that are larger than the entire Earth!
Friday, March 8, 2013
Limb darkening
Given a cloud of gaseous stuff, we can describe absorption and emission of radiation in terms of a quantity called the mean free path. The mean free path is the distance a single photon in the cloud can expect to travel before it is absorbed. It turns out that when we look at something like the sun, what we actually see is a distance of one mean free path below the 'surface' (note that the surface isn't actually very well defined - the sun has less and less dense material further away from its center, all the way out to the orbit of Jupiter or so).
The interesting thing about this is that because of the spherical nature of the sun, in which the temperature decreases as radius increases, one mean free path below the surface in the center of the sun's disk is a lot brighter than one mean free path below the surface at the edge, since the edge is cooler. And since the color of radiation is related to the temperature of the radiating surface, the edges of the sun appear darker and redder than the center. This is true of other stars, too, and the phenomenon is called limb darkening, as the edge of the star is called its limb.
Thursday, March 7, 2013
Fusion!
Main sequence stars produce most of their energy by hydrogen fusion (also called hydrogen burning). The net reaction here is that four protons (hydrogen nuclei) and a couple of electrons fuse into a single helium nucleus - two protons and two neutrons - along with a heck of a lot of outgoing radiation and neutrinos. But this same net reaction can happen along two very different pathways: the proton-proton chain (PPC) and the carbon-nitrogen-oxygen cycle (CNO cycle). The proton-proton chain reaction works basically as you would expect:
1. Two protons fuse into a deuteron (deuterium nucleus - a proton and a neutron), a positron, and an electron neutrino
2. A deuteron and a proton fuse into a He-3 nucleus and an outgoing photon
3. Two He-3 nuclei fuse into a He-4 nucleus (just an alpha particle) and two protons
The net reaction here is just four protons -> one alpha particle, and it has an efficiency of around 0.7%. Not too high, but when you consider how much hydrogen there is in a star, you start to understand how they can radiate so much. In order for the PPC to work, the temperature of the star's core (where fusion is actually taking place) needs to be above around 2*10^6 K.
The CNO cycle has the same net reaction as the PPC, but it is catalyzed by carbon-12. It's a 6-step process in which carbon fuses with a proton to create a nitrogen, which decays into a heavier carbon. The heavier carbon then fuses with another proton to produce stable nitrogen-14 and some radiation. The nitrogen fuses with a third proton to produce an unstable isotope of oxygen, which then decays into nitrogen-15. Finally, the heavy nitrogen fuses with a fourth proton to produce a carbon-12 atom and an alpha particle. The net reaction here is the same, so the net efficiency (energy produced out of the total mass energy of the constituent parts) is the same as for PPC. But CNO has a much stronger dependence on the temperature of the star (T^19.9 as compared with T^4 for PPC) and doesn't kick in until temperatures around 10^7 K.
It turns out that the sun mainly burns hydrogen by PPC, as its core temperature is not quite high enough for the CNO cycle.
1. Two protons fuse into a deuteron (deuterium nucleus - a proton and a neutron), a positron, and an electron neutrino
2. A deuteron and a proton fuse into a He-3 nucleus and an outgoing photon
3. Two He-3 nuclei fuse into a He-4 nucleus (just an alpha particle) and two protons
The net reaction here is just four protons -> one alpha particle, and it has an efficiency of around 0.7%. Not too high, but when you consider how much hydrogen there is in a star, you start to understand how they can radiate so much. In order for the PPC to work, the temperature of the star's core (where fusion is actually taking place) needs to be above around 2*10^6 K.
The CNO cycle has the same net reaction as the PPC, but it is catalyzed by carbon-12. It's a 6-step process in which carbon fuses with a proton to create a nitrogen, which decays into a heavier carbon. The heavier carbon then fuses with another proton to produce stable nitrogen-14 and some radiation. The nitrogen fuses with a third proton to produce an unstable isotope of oxygen, which then decays into nitrogen-15. Finally, the heavy nitrogen fuses with a fourth proton to produce a carbon-12 atom and an alpha particle. The net reaction here is the same, so the net efficiency (energy produced out of the total mass energy of the constituent parts) is the same as for PPC. But CNO has a much stronger dependence on the temperature of the star (T^19.9 as compared with T^4 for PPC) and doesn't kick in until temperatures around 10^7 K.
It turns out that the sun mainly burns hydrogen by PPC, as its core temperature is not quite high enough for the CNO cycle.
Wednesday, March 6, 2013
Scattering particles
It turns out that the $\Delta^{++}$ particle (capital delta with a double '+' superscript, pronounced "Delta plus plus"), which is typically discussed as a composition of three up quarks, is actually just a resonance in scattering experiments. That is, we know it exists because if we're shooting pions at protons, for certain energy pions, we see way more scattering than for nearby energies. This is explained as the pion and the proton combining to create a new particle, the $\Delta^{++}$, which almost instantaneously decays into a proton and a pion. The new proton and pion can head off in basically whatever direction they want, so scattering cross section is very high. But the decay happens so fast that it's impossible to directly observe the $\Delta^{++}$ particle; it really is just a resonance!
This same resonance is observed in a variety of experiments involving different scatterers, and based on the width of the scattering peak, we can find out the mass and lifetime of the particle.
On a related note, the $\Delta^{++}$ is a member of the delta family, which consists of four baryons (particles composed of three quarks) involving only up and down quarks, the same basic ingredients as protons and neutrons. That includes the $\Delta^{+}$ (uud) and the $\Delta^0$ (udd) baryons, which have the same quark composition as protons and neutrons, respectively. The distinction is that in the delta family, the spins of all three constituent quarks are aligned, for a net spin of 3/2, rather than 1/2 for the proton and neutron. This spin alignment is a higher-energy state than the 'ground-state' nucleons, which is manifested in the delta family's higher masses and shorter lifetimes.
This same resonance is observed in a variety of experiments involving different scatterers, and based on the width of the scattering peak, we can find out the mass and lifetime of the particle.
On a related note, the $\Delta^{++}$ is a member of the delta family, which consists of four baryons (particles composed of three quarks) involving only up and down quarks, the same basic ingredients as protons and neutrons. That includes the $\Delta^{+}$ (uud) and the $\Delta^0$ (udd) baryons, which have the same quark composition as protons and neutrons, respectively. The distinction is that in the delta family, the spins of all three constituent quarks are aligned, for a net spin of 3/2, rather than 1/2 for the proton and neutron. This spin alignment is a higher-energy state than the 'ground-state' nucleons, which is manifested in the delta family's higher masses and shorter lifetimes.
Magnets!
Whoops, forgot one for yesterday... here it is!
Materials spontaneously order the spins of their component atoms in the presence of a magnetic field. My understanding is that all materials exhibit either paramagnetism (creation of a weak magnetic field that works in parallel with the external field, attracting the object to the source) or diamagnetism (creation of a weak magnetic field opposing the external field, which causes the source to repel the object). In both cases, the spin alignment of the atoms dissolves quickly after the external field is removed, due simply to thermodynamic effects.
This is in contrast with ferromagnetism, in which an object such as iron aligns the spins of its atoms with the external magnetic field and maintains this alignment after the magnetic field is removed, which allows one to make a (weak) permanent magnet out of a paper clip, for instance.
But it turns out that some very special materials have a fourth spin-ordered state, called antiferromagnetism. In this state, the spins of adjacent atoms are opposite, so moving along the lattice we see atoms that are spin-up, spin-down, spin-up, spin-down, and so on. These materials only attain this ordered state at temperatures below what's called the Neel temperature, and it is believed that learning more about antiferromagnetism could lead to the development of room-temperature superconductors.
Cool, huh?
Monday, March 4, 2013
Sunscreen!
The way that sunscreen works is using a certain molecule, oxybenzone, which can absorb UV photons and reemit lower-frequency photons. Based on the fact that it absorbs photons with around 100-nm wavelengths, we know that the energy difference between its ground state and its first excited state is exactly the energy carried by such a photon, which is simply $\frac{hc}{\lambda}$. So we can actually calculate the probability that any given oxybenzone molecule is in an excited state at beach-temperature (independent of the incoming UV, which is greatly reduced by the atmosphere). It turns out that only about one in 10^200 oxybenzone molecules is in its excited state because of the ambient temperature (around 300K). That's a seriously small fraction, and speaks to the effectiveness of sunscreen.
Another convenient thing about oxybenzone is that it is soluble in most organic solvents (nonpolar) and less so in water, so it's fairly water-resistant.
Sunday, March 3, 2013
Phun Physics Phact of the Day
Physics is really cool. I'm not sure how long this will last, but I'd like to share some fun facts. Here's one:
Castor, one of the twin stars in Gemini (as in the constellation, not a movie star who plays a twin in a TV show called Gemini), is actually six stars. Castor A and B are a visual binary, which means that using a powerful telescope, one can see that there are really two separate stars. Further investigation reveals that Castor A and Castor B are actually both spectroscopic binary systems.* That makes the system a quadruple star system. But wait, there's more! There's another, far dimmer, system called YY Gem that is much further away from the quadruple we've already discussed. And did I mention that it's a binary system too? Basically it is far enough away from the other stars that it responds to Castor A/B as if the collection of four stars is just a large massive object, and is in a 'binary' system with them. And this whole thing manages to stay gravitationally bound. Fun, right?
* Spectroscopic binary systems are detected by examining the Doppler shift of spectral lines as the brighter of the two stars wiggles back and forth in response to the orbit of the dimmer one - as it wiggles towards us, the spectral lines are all slightly blueshifted, and they're redshifted as it wiggles away from us. It's useful for detecting binary systems in which the two stars are very close together, which makes them difficult or impossible to distinguish visually. The really amazing thing about this measurement is that the amount of blue or redshifting that occurs is generally smaller than the natural width of the spectral line. Observational astrophysics is awesome.
Note: A binary star system is one in which two stars orbit their mutual center of mass. There are a variety of ways to detect them (see the Wikipedia page for a fairly comprehensive explanation), and it's believed that something like 60% of stellar systems are actually binary star systems. So our single-star solar system is actually in the minority!
Castor, one of the twin stars in Gemini (as in the constellation, not a movie star who plays a twin in a TV show called Gemini), is actually six stars. Castor A and B are a visual binary, which means that using a powerful telescope, one can see that there are really two separate stars. Further investigation reveals that Castor A and Castor B are actually both spectroscopic binary systems.* That makes the system a quadruple star system. But wait, there's more! There's another, far dimmer, system called YY Gem that is much further away from the quadruple we've already discussed. And did I mention that it's a binary system too? Basically it is far enough away from the other stars that it responds to Castor A/B as if the collection of four stars is just a large massive object, and is in a 'binary' system with them. And this whole thing manages to stay gravitationally bound. Fun, right?
* Spectroscopic binary systems are detected by examining the Doppler shift of spectral lines as the brighter of the two stars wiggles back and forth in response to the orbit of the dimmer one - as it wiggles towards us, the spectral lines are all slightly blueshifted, and they're redshifted as it wiggles away from us. It's useful for detecting binary systems in which the two stars are very close together, which makes them difficult or impossible to distinguish visually. The really amazing thing about this measurement is that the amount of blue or redshifting that occurs is generally smaller than the natural width of the spectral line. Observational astrophysics is awesome.
Note: A binary star system is one in which two stars orbit their mutual center of mass. There are a variety of ways to detect them (see the Wikipedia page for a fairly comprehensive explanation), and it's believed that something like 60% of stellar systems are actually binary star systems. So our single-star solar system is actually in the minority!
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