From original burst, fraction of stellar mass still surviving on Main sequence

From original burst, fraction of stellar mass still surviving on Main sequence

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Suppose that all stars in this galaxy were born in a single major-merger burst event about 10 Gyr ago. From this original burst, I want to compute the fraction of stellar mass still surviving as stars in the main sequence ? For this, I have got to use a Salpeter IMF, and a star formation range between 0.1 and 120 solar masses.

What I have done is starting from Salpeter IMF : $$Phi(m) ext{d}m=Phi_{0},m^{-2.35}$$

with $$Phi_{0}$$ a constant normalization.

From this, I integrate from $$m_{1}=0.1, ext{M}_{odot}$$ to $$m_{2}=120, ext{M}_{odot}$$


This result depends on the valeur of $$Phi_{0}$$ and I don't know how to deal with it in order to get $$N(0.1<> ?

Moreover, it seems that I have to take into account of the age of the major-merger burst event (10 Gyr).

From these 2 principles, how could I calculate the fraction of stars surviving in the main sequence ?

Any help is wlecome, Regards

When you are calculating fractions, rather than absolute numbers, the value of $Phi_0$ does not matter, since it will be a multiplying factor in both the numerator and denominator.

You have (almost, see below) successfully got an expression for the denominator of your fraction.

The numerator is found by calculating an equivalent integral from your lower limit to an upper limit that is instead defined by the most long-lived main sequence stars that are still "alive" - i.e. those with a lifetime equal to the age of our Galaxy.

Finally, you were asked to find the fraction of stellar mass surviving, not the fraction of stars. The stellar mass existing between two mass intervals is $$M_* = int_{m_1}^{m_2} mPhi(m) dm$$

Stellar Mass Loss

Is a Wolf–Rayet star the precursor to a supernova? This is still a controversial matter. It appears that the underluminous historical supernova, Cas A, which exploded apparently without notice in the 17th century, was one of these stars. It was probably a WO on the basis of the observed abundances in the optical filaments and the lack of hydrogen in the ejecta. While exceedingly energetic, the shocks from WO stars do not have much overlying matter as they transit the stellar envelope, so the ejected material cools rapidly without producing an optically bright blast wave. The normal Type II supernova arises from a less evolved stage of the star, for instance a red or blue supergiant. In these stars, the envelopes are massive and remain hot and luminous for much longer, nearly a year, before they become optically thin and cool rapidly. The long plateau observed in the normal SN II light curve is generally ascribed to this envelope structure. Thus, the stage that precedes a supernova is set up by the rate of stellar mass loss , so there is still considerable work to be done on the driving mechanisms for that phenomenon before definitive answers can be given to the questions concerning the presupernova stages of evolution. At least one type of γ-ray burst may result from hypernovae, in which up to 10 52 erg is released by the shock propagating through the WR wind.

The precise appearance of the stellar surface at the stage of Fe core formation is still a hotly debated question. Because of the role played by mass loss in the final stages of stellar evolution, the star may end up either as a blue or red star at the end of its life. The Wolf–Rayet stars are candidates for the final, presupernova state. However, it should be remembered that the precursor of SN1987A in the LMC was a B3 supergiant, and model calculations show that for a 15 to 25 M star the iron core forms while the star is a red supergiant. Clearly, the end stages of massive stars are a fruitful area for future work.

The formation of successively heavier nuclei by fusion cannot continue past the formation of Fe. The binding energy of this nucleus is the largest possible for a stable isotope, so that subsequent processing can only lead to destruction of the nucleus. This involves endoergic reactions, robbing the star of its gravitational energy and producing the rapid disintegration of the nuclei. Cooling proceeds via neutrino emission, which is rapid enough that the star cannot quasistatically adjust to the energy losses and begins to dynamically contract. The formation of Fe is, therefore, the beginning of the end for a massive star. After this stage, only dynamical collapse and the consequent supernova explosion are possible.


We present a cosmic perspective on the search for life and examine the likely number of Communicating Extra-Terrestrial Intelligent (CETI) civilizations in our Galaxy by utilizing the latest astrophysical information. Our calculation involves Galactic star formation histories, metallicity distributions, and the likelihood of stars hosting Earth-like planets in their habitable zones, under specific assumptions which we describe as the Astrobiological Copernican Weak and Strong conditions. These assumptions are based on the one situation in which intelligent, communicative life is known to exist—on our own planet. This type of life has developed in a metal-rich environment and has taken roughly 5 Gyr to do so. We investigate the possible number of CETI civilizations based on different scenarios. At one extreme is the Weak Astrobiological Copernican scenario—such that a planet forms intelligent life sometime after 5 Gyr, but not earlier. The other is the Strong Astrobiological Copernican scenario in which life must form between 4.5 and 5.5 Gyr, as on Earth. In the Strong scenario (under the strictest set of assumptions), we find there should be at least civilizations within our Galaxy: this is a lower limit, based on the assumption that the average lifetime, L, of a communicating civilization is 100 yr (since we know that our own civilization has had radio communications for this time). If spread uniformly throughout the Galaxy this would imply that the nearest CETI is at most lt-yr away and most likely hosted by a low-mass M-dwarf star, likely far surpassing our ability to detect it for the foreseeable future, and making interstellar communication impossible. Furthermore, the likelihood that the host stars for this life are solar-type stars is extremely small and most would have to be M dwarfs, which may not be stable enough to host life over long timescales. We furthermore explore other scenarios and explain the likely number of CETI there are within the Galaxy based on variations of our assumptions.

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Large Mass Stellar Death

The fates of large mass stars are quite different from those of the low mass ones. At first glance you might think that with more mass they will live longer - but no, they are just fuel guzzlers. As such, massive stars (O and B types on the Main Sequence) will have very short lives. To get a good idea of how a large mass star dies, let's look at what a really big one goes through.

Very massive stars are also very luminous, so they tend to have very strong stellar winds (since this is linked to their energy outputs). Due to this they may have a lot of gas around them that was blown off long ago. Sometimes it is easy to see these gas clouds, sometimes not. Like other mass ejection things we have already seen, the material can be spewed out in several ways, with the most common being bipolar outflow and rings. Figure 1 shows several different stages in the life cycle of stars, all in one convenient location.

Figure 1. A picture from the Hubble Space telescope showing stars in various stages of their lives. The lower right region (1) is a gas cloud from which stars form. Near the center (2) is a group of main sequence stars. Up and to the left of those is a large star (3) in the process of dying. The massive star has already ejected a ring of material as well as material out from it in a bipolar direction. In a way this image is just like a family portrait showing the oldest and youngest members of a family. Image credit: Wolfgang Brandner (JPL/IPAC), Eva K. Grebel (Univ. Washington), You-Hua Chu (Univ. Illinois Urbana-Champaign), and NASA.

Sometimes the outflow is even more energetic and at times confusing to astronomers. Some very massive O-type stars have such strong winds that they can completely screw up their evolutions - they lose so much mass that you have to take that into account in your calculations when trying to figure out how these stars will live their lives. Due to this uncertainty, we have a rather hard time predicting what a very massive star will do or even trying to figure out what one of them may have done in the past. Images of two such objects are shown in Figure 2. A recently observed massive star (with the exciting name of WOH G64) has lost so much material that a thick, dusty ring has formed around it. This star is very far away, in another galaxy in fact, so it is not possible to easily see the ring, but its presence is revealed by spectra and other instruments. You can learn about this massive star here. Even though it has lost a bunch of material, WOH G64 is still about 1500 times wider than the Sun.

Figure 2. Two very massive stars with very extreme mass loss episodes. On the left is the star WR124, a massive star ejecting material out at speeds of 100,000 miles/hr. Each blob of gas that it ejects out has a mass of more than 30 times that of the Earth's. To the right is the unusual star Eta Carina. Actually, the star is buried in the center of the two bubbles, which are thought to be from an eruption that occurred in 1847. Follow this link to see how the bubbles formed. During this outburst the two bubbles were ejected as well as a disk of material that can be seen between the bubbles. The speed of the material in this case is on the order of 1.5 million miles/hr. Image credits: Yves Grosdidier (University of Montreal and Observatoire de Strasbourg), Anthony Moffat (Universitie de Montreal), Gilles Joncas (Universite Laval), Agnes Acker (Observatoire de Strasbourg), Jon Morse (University of Colorado), and NASA.

All of these big time mass loss episodes are just a sneak preview of what is to eventually happen to these stars. These stars are more massive than the cut off for going into Planetary Nebula stages, so the death scenarios of the massive stars go down very different paths. Just how big can a star be? We're not exactly sure, but there is a limit to how much material can come together to form a single star, and conservative estimates put that at around 150 solar masses. However in 2010 astronomers from the Very Large Telescope in Chile announced the discovery of a star that may have a mass that is currently 265 times the mass of the Sun. What is really amazing about this star, with the cute name R136a1, is that it started out with a mass of about 320 solar masses! So it probably had some serious mass loss episodes in its life. In case you were wondering, this star is not even in our galaxy, but is in a neighboring galaxy.

We'll look at the life cycle of a 25 Solar Mass star to see what happens to one of these big beasts. It is more massive, so it can go through more burning stages than a low mass star. It can ignite the more massive elements due to the greater gravitational heating in the core (more mass means more gravity). Each burning stage takes less time. The data in the accompanying table is from Chieffi, Limongi, and Straniero (1998) based upon their computer model for such a star.

Fusion Process Main Fusion Products Duration of Fusion Process
H He 6 million years
He C, O 700,000 years
C Ne, O 1000 years
Ne O 9 Months
O S, Si, Ar 4 Months
Si Fe, Cr 1 day

When the star is burning hydrogen, it is on the Main Sequence. Every other burning stage after that has the star off the Main sequence and in the area of the H-R diagram populated by Supergiants. The stars just evolve through these various burning stages while they are Supergiants, sometimes blue supergiants, sometimes yellow supergiants, and sometimes red supergiants, so they will wander back and forth across the top of the H-R diagram during these later stages. If you click here you can see some evolutionary paths of such stars. The region that the supergiants inhabit isn't a clearly defined location on the H-R diagram, but is basically just the top part where the luminosity is very high.

Take a look at the numbers in the rightmost column. Why is each stage shorter than the previous stage? There are two reasons

  • There is less fuel available in each stage. After all, stars are originally made up of mainly hydrogen and helium, so all of the other material comes for the most part from previous burning stages. Only a fraction of the original star is made up of the elements heavier than hydrogen and helium that are used in the later burning stages.
  • There is lower efficiency in the later burning processes. Less energy is released when heavier elements are undergoing fusion, so the star needs to burn that material at a greater rate to produce enough energy to sustain the structure of the star (to maintain stuff like Hydrostatic and Thermal Equilibrium).

So now these dying massive stars will be seen as either Red Supergiants or Blue Supergiants, depending upon how hot or cool they are. Due to their very large radius they also tend to be extremely luminous. How large can the radii get? In 2005, astronomers discovered several red supergiants with radii that were much larger than that of Betelgeuse (shown above) - these stars had radii that are about 1500 times that of the Sun! To see how big these stars actually are, just take a look here. Obviously with the outer layers so stretched out, the fusion going on deep in the core is not going to be visible to anyone. Even though stars like this look like they are in the last stages of their lives, we can only see what is going on at the surface, not what is actually happening in the core. Of course the core is the interesting part!

Eventually the core of the massive star will look like a giant onion, with the densest material in the middle and the lowest density stuff on the top. Each shell of the onion will have some small amount of fusion still going on, but the energy that is being produced at this point is pretty pathetic.

All sorts of elements have been burning, and now we come to the last element to burn, iron (Fe). Does it burn? It sure does, but at a cost. Whereas previous fusion processes released energy, iron burning consumes energy. The energy that should go into holding up the star instead goes into burning the iron. Is this a problem? You bet your buttonhole it is! The iron fusion consumes energy, so there isn't enough energy to help support the star. Without support, gravity comes along and squeezes down the core. What happens when you squeeze stuff? It gets hotter. The iron core gets hotter and starts burning faster, which causes more energy to be sucked away, which removes more support against gravity, which causes the core to compress more and heat up more, which causes the iron to burn faster, which. I think you get the picture.

The core of the star collapses during the iron burning stage (since nothing is fighting the gravity), which takes only about 1/4 second. The collapsing process shrinks the core down to the size of the Earth. It gets very dense, up to the point of electron degeneracy (remember, that's what a white dwarf is like). Will the collapse stop? No, since the core is more massive than the Chandrasekhar limit (the iron core is about 1.5 solar masses in this case). The mass of the core is too much for the Chandrasekhar limit, so electron degeneracy will not stop the collapse - it will keep going. Gravity keeps crushing the star down until it reaches the point where the pieces of atoms are crushed together. This is not an easy thing to do, but as the protons (p + ) and electrons (e - ) are slammed together they form neutrons (n) and neutrinos (), which can be written out as

This reaction makes sense, because you combine a positive and a negative together and just get neutral stuff out in the end. All of this compression and atomic mushing results in the core of the star ending up as a big ball of neutrons. At this point the collapse can be stopped by neutron degeneracy (10 14 g/cc is the density of such material). Neutron degeneracy is much more extreme than electron degeneracy - greater density, more extreme rules of physics and so forth. Because of the degeneracy, the star will not get any denser so long as the neutron degeneracy can hold it up. In the case where the degeneracy can't hold it up, you end up with a black hole - more on this later.

The core that ends up as a ball of neutron degenerate material is called a Neutron Star. This is a star so small and compact that a 1.5 solar mass neutron star would be only about 20 km in size. Think of that - an object more massive than the Sun only the size of a large city! It would be incredibly dense, 10 14 gm/cc. This is sort like the density you'd get if you took 100 aircraft carriers and crush them down to the size of a sugar cube. Try putting that in a cup of tea!

In about 1/4 of a second the core has been crushed down, resulting in a neutron star, which are in most cases only a few solar masses in size. What happens to the rest of the star? Remember, the neutron star core at this point is only a small part of the total mass, so you still have quite a few solar masses to watch out for that is located beyond the star's core.

The core collapsed very quickly from a size close to that of the Sun's to only about 20 km, so there is a gap in the support of the rest of the star. What support? - there is NO SUPPORT! Nothing is holding up the rest of the star. This is sort of like when the Coyote runs off a cliff and doesn't immediately fall down - at least not until he realizes that he is off the cliff. The outer layers of the star don't really know that they have had their legs cut out from under them for a moment, but once they do - watch out. The upper layers will fall onto the ultra dense neutron degenerate core and the material will heat up to about 5 billion degrees. This high temperature and the corresponding high pressure will generate an incredible amount of energy. The energy that is generated by the slamming of the outer layers on the core is huge. This energy that is produced here in this small interval of time is the same amount as that given off by the Sun over its entire lifetime (10 billion years). This huge bottled up energy is released in a massive explosion that will blow off the outer layers - basically, the star explodes. That's how you produce a Supernova . This little animation shows a blue supergiant quickly collapsing down and then exploding as a supernova.

  • The explosion blows away almost all of the mass of the star. What is left behind may be only a few solar masses in size, though in the case of a black hole it can be larger.
  • The core that is left over is in the form of a neutron star or a black hole.
  • There is the release of a large amount of energy, so these things are very bright. A supernova produces the equivalent amount of energy as an entire galaxy (billions of stars), and it can stay bright for quite some time - weeks or months depending upon the distance. There have even been supernovae that were visible in the daytime.
  • The iron fusion and the huge amount of energy from the collapse of the star are so great that the fusion of even heavier elements occurs. All elements more massive than iron require huge amounts of energy to form, since like iron, their fusion processes consume energy. A supernova is the only thing that has energy to spare for the fusion of the heavy elements, so this is the only way that these things can be made. All of the copper, zinc, nickel, gold, silver, mercury, and other elements up to uranium are produced in supernovae (these include elements numbers 27 to 92 on the periodic table). The NuSTAR x-ray satellite has been studying the chemical distribution of material from a supernova that occurred only a few hundred years ago, some of this material is still radioactive.
  • During the formation of the neutron star there is the release of neutrinos, and at times these can be detected. Remember, there are neutrino detectors that are currently working to detect neutrinos from the Sun and these detectors are able to pick up supernova neutrinos as well.
  • A large shock wave is produced by the explosion. The shock wave can travel through space and can compress gas clouds, which will lead to new star formation. This can help explain why large scale star formation can continue on, since large stars die relatively quickly, usually near to the location where they were born. If one dies in a supernova near the location of its formation (near a Giant Molecular Cloud), the shock wave from the explosion can ignite new episodes of star formation in the GMC. The death of one star can lead to the birth of many more. Recent observations by the Spitzer telescope appear to support this scenario, with a region of star formation found near a likely supernova - you can see a schematic of the event here. Some people have even linked the explosion of supernovae to things on the Earth, such as climate changes or various large extinction events - but those are only theories.

Massive stars are pretty rare, so on average there is only one supernova occurring in a galaxy every century.

Now I'm going to complicate matters a bit. There are actually two main types of supernovae. One is the type that I just described the other occurs when a white dwarf is near its mass limit (the good old Chandrasekhar limit=1.4 solar masses) and is pushed over this limit when too much mass is dumped on it, usually in a binary system. You may want to refresh your memory on the stuff about novae in the previous set of notes. If the white dwarf star in the binary system is really big (close to 1.4 solar masses), rather than just going nova when mass is dumped on it, it will be too massive to hold itself up and may instead become a supernova. There is also a theory that if you had two white dwarfs in a binary system and they collide, it will become a type I supernova. Either way, the white dwarf ends up being too massive and collapses in on itself. Since there are two vastly different kinds of supernovae - and they have to be distinguishable, and they are, mainly because the object that explodes in each case is very different (massive star versus white dwarf). To distinguish between the two types, the following designations are given

  • Type Ia Supernova - a white dwarf going over the Chandrasekhar Limit
  • Type II Supernova - a massive star collapsing and then exploding when iron fusion starts

In general Type Ia supernovae are brighter by about two magnitudes or so than the Type II. You would have to know the distance to the supernova if you want to use the brightness as a way of categorizing it, so that isn't a good method. Fortunately it is possible to tell the two supernovae apart by looking at their spectra. The object that goes supernova is quite different in each case, so the spectrum from each type of supernova is distinct. A white dwarf is the burned out core of a dead star, so it is made mainly of stuff like carbon, oxygen, nitrogen, etc., but not a lot of hydrogen. A massive star, on the other hand, is still mainly made of hydrogen, so when it explodes its spectrum will be full of hydrogen. It is pretty easy to distinguish the two types of supernovae without knowing their distances. You'll notice that if you do know which type of supernova you have, you can then use its typical maximum brightness (from Figure 5 above) and the apparent magnitude that you observe to get its distance.

One very unusual Ia supernova is 2006gz. This has a spectrum just like a 'regular' Ia, but it was brighter than normal. It also had too much carbon and silicon, which led some astronomers to speculate that this was actually a collision of two white dwarfs. It has also been proposed that 2006gz came from a super-Chandrasekhar limit white dwarf - an abnormally large white dwarf. So far we do not know the answer to this unusual question, but it does show that sometimes very strange things do happen. There was also a recent study by the Chandra observatory that seemed to indicate that most type Ia supernovae are actually produced by the merger of two white dwarfs, rather than a single star. So until more evidence is found (because that's how science is done), we'll just have to use the general phrase "white dwarf going over the mass limit" - which could occur due to very different reasons.

You should be asking yourself Why is it 'Ia'? Why not just call it a 'I'?. Good question. A type I supernova has very little hydrogen in the spectra, but sometimes it is not because the star that exploded was a white dwarf. There are two other type I supernova, with the amazingly original names of Ib and Ic. Both are thought to come from large mass stars that have blown away most of their outer layers so there is not much hydrogen left in their spectra. The main difference between Ib and Ic is whether there is any helium left - a Ic has no helium in their spectrum, while a Ib still has some helium. Both the Ib and Ic are fainter than a Ia, and a bit rare since they only come from very massive stars. Unlike the massive stars involved in the type II supernova, these have lost too much of their mass to have a big blast. Generally when we talk about type I supernovae, we are referring to type Ia.

Recently astronomers have found that there are some supernovae that could be better described as super-supernovae - but that's sort of a silly name. The term hypernovae has been proposed for these extreme explosions. There is a bit of debate as to exactly what happens during a hypernova, since this is a relatively new idea and most of them have only been observed to occur at very great distances. One option is that a very massive star (more than 30 solar masses, possibly up to 150 solar masses) that had been previously losing mass eventually collapses in on itself, causes a massive explosion and eventually forms a black hole. Another option is the merger of unusual stars, such as two neutron stars, which results in a massive explosion (you'll learn more about neutron stars in the next set of notes). One side effect of such an event is the emission of a large amount of gamma-rays, which aren't normally observed from stars. Now a days such gamma-ray bursts can be spotted with the Swift telescope, and several possible hypernova have been discovered in that way - though it wasn't until after we look at them with other telescopes, light visible light or x-ray telescopes are we certain about their overall energy output. The overall energy of a hypernovae is generally 100 times greater than the energy given off by "normal" supernovae. Currently the record holder for the most powerful stellar explosion is the object known as SN2006gy (yes, that is a lame name), which was observed in 2006 and had an energy output that was greater than any other supernova. Here is a comparison of this objects brightness over time compared to other "normal" supernova. This is similar to Figure 5 shown above. Here is an animation showing the explosion based upon the x-ray and gamma-ray data from the region following the explosion. It is interesting that there are two large bubbles of material, which were given off by SN2006gy before the explosion occurred. This is very similar to what we see today in Eta Carina (Figure 2), an object in our own galaxy which might someday erupt as a hypernova. Several other stars are thought to have also had smaller outbursts before they blew themselves to pieces as supernova - sort of a hiccup before a really big belch! And in case you were wondering how you missed such an amazing explosion in 2006, don't worry, not too many people noticed it since SN2006gy occurred in a galaxy that is about 240 million light years away, so it was barely visible, except with the largest telescopes.

While most gamma-ray bursts are invisible to us (since gamma-rays cannot reach the surface of the Earth), it is still possible to "see" them, since the total energy given off is huge. Gamma-ray bursts give off light at all wavelengths, not just gamma-rays (remember hot objects give off light at many wavelengths even though they have only one peak for their emission). So when the Swift satellite observes a burst, the location is transmitted to regular ground based telescopes, both visible light and radio, in an effort to measure the light output in as many wavelengths as possible. In March 2008, there was a gamma-ray burst that was so powerful and concentrated that it could have been seen by the naked eye for about 15 seconds. That's pretty impressive considering that the object that produced the burst was about 7.5 billion light years away! A gamma-ray burst in 2013 was so long lasting as well as powerful that it broke records for total output. The 2013 burst lasted for hours, which is very unusual for such events. But it was at a great distance away, so you wouldn't have noticed anything.

Supernovae are sort of rare, so astronomers are only able to observe them occurring in distant galaxies. Currently about 200 or more supernovae are observed each year in other galaxies - in 2003, nearly 330 supernovae were discovered, some nearly a billion light-years away. While this may seem okay, the problem is that since these are very distant supernova, there isn't a lot of detail visible. For the most part, astronomers can figure out the type of supernova in a distant galaxy by obtaining a spectrum, but that's about all. Astronomers over the centuries have seen supernovae, some in our own galaxy, though in the old days they didn't know what they were. By looking at the records of various cultures, astronomers have figured out that some unusual astronomical events that mystified people in the past were actually supernovae. Here are some of the more famous ones -

  • 1054 A.D. - Chinese and Arabic astronomers observed a new star appear in the constellation of Taurus the bull - this is a very important supernova and we'll run across it later.
  • 1572 A. D. - Tycho Brahe made careful observations of one in the constellation of Cassiopeia
  • 1604 A. D. - Johannes Kepler (and many others) observed one in the constellation of Ophiuchus

Kepler's supernova (as it is sometimes called) was the last supernova that was observed to go off in our galaxy. We haven't seen a star become a supernova in our galaxy in about 400 years - we're long overdue for one! Of course, it is possible that other supernovae have occurred in our galaxy since Kepler's, but they may have happened in distant parts of our galaxy, and we couldn't see them. As you'll see there is good suspicion that this is the case.

While it is difficult to see a supernova in great detail today (since most are so far away), it is sometimes easy to find the material left over from the explosion. This is because there is not only a lot of material, but it stays relatively hot for quite a long time. The gas cloud left over from the supernova explosion is known as a Supernova Remnant ( SNR ). Like an explosion in a fireworks display, it takes a long time for the cloud to fade away, though in the case of a SNR, the cloud can hang around for thousands of years.

Figure 7. Various Supernova Remnants are shown. To the left is the Crab Nebula, the remnant from the Supernova observed by the Eastern astronomers in 1054 A. D. This visible light image is from the Very Large Telescope. In the center is the Cygnus loop, as seen by an x-ray telescope. This is a very old remnant, and it is also very large. The line in the lower right part of the picture is the width of the Full Moon. On the right is an x-ray image of the remnant that was Tycho's supernova (observed in 1572 A. D.). If you click on the Crab or Tycho images, you'll be able to see the Chandra x-ray image of those remnants. (Image credits: VLT, ROSAT, MPE, NASA, NASA/CXC/ASU/J. Hester et al., NASA/CXC/Rutgers/J. Warren & J. Hughes et al.).

These aren't just neat things to observe they can provide useful information about supernovae. This is done by measuring the velocity of the gas and combining that with the size of the object. Doing this provides astronomers with the age of the supernova (since velocity = size / time since explosion). Even though we might not have seen the explosion, we can estimate when it occurred. Many SNRs seen today are still rather hot even though they may have "gone off" hundreds of years ago. They often have x-ray emissions - which tells us that they are still really hot. The supernovae described earlier, like the one in observed in 1054 and those seen by Kepler and Tycho, all left behind large expanding gas clouds. The one seen in 1054 can be observed today as an object called the Crab Nebula (or, by its catalog name, M1).

Figure 8. Cas A, a supernova remnant. The image to the left is from the Very Large Array radio telescope (NRAO). The image to the right is from the Chandra x-ray telescope (NASA/CXC/MIT/UMass Amherst/M.D.Stage et al). Click on either image to see a larger view.

One rather confusing SNR is Cas A , a SNR in the constellation of Cassiopeia (that's where the "Cas" comes from in its name). This is a very strong radio source, as well as a strong x-ray source (see Figure 8). Obviously it is still rather hot. It is also relatively small. Combining this information with velocity and size data tells astronomers that this object blew up about 300 years ago. We haven't seen a supernova in our galaxy for about 400 years! Somehow, this thing blew up and no one noticed it! It also looks like we missed another supernova that was even more recent - only 150 or so years ago! Unfortunately it was in a rather messy part of the galaxy, so it would have been difficult to see even if we knew it was going on.

Another neat SNR is the Gum Nebula. This is a large gas cloud, and it is really large because it is really old. It is estimated that this object blew up sometime around 10,000 BC. Not only is it rather old, but it is also relatively nearby. Taking this into account, when this thing blew up, it would have been as bright as the Full Moon!

Let's see what we have got so far. Astronomers can study supernovae in other galaxies, but they are so far and faint that only the largest telescopes we have can see most of them. They can study supernova remnants to try to figure out what happened in the past when these things blew up. That's sort of boring, eh? It isn't all of the time. Actually, things in the astronomical community got rather crazy not too long ago, on February 23, 1987, to be exact. On that night there was the event of a lifetime - Supernova 1987A, or SN 1987A for short. Supernovae are named for the year (1987 in this case) and a letter for the order of their occurrence in the year. The first one of the year is A, the second is B, etc. In 1987, the first supernova seen was labeled SN 1987A.

Figure 9. Supernovae 1987A - image of the supernova at its brightest in the part of the sky it appeared in. In the upper left of the image is the Tarantula nebula, a large H II region. These objects are actually thousands of light-years away - around 160,000 light-years in fact. Image ESO, click on the link to see the larger version of the image.

What was the big deal about SN 1987A? This was the first naked eye visibility supernova observed since 1604 - you didn't need a telescope to see it that's how bright it was! While it did not occur in our galaxy, but in one of our neighboring galaxies (the Large Magellanic Cloud is the galaxy it happened in), it was still close enough that detailed studies of it could be carried out. The supernova was discovered, or perhaps a better word is "noticed," by Ian Shelton on the night of Feb 23, 1987. It is quite likely that others saw it but they did not recognize it for what it was.

When SN1987A went off, virtually every telescope that could observe it was used to study it. This included telescopes located in countries such as Chile, South Africa, and Australia, mainly because the Large Magellanic Cloud and the supernova are very southern objects. Satellites were also used - including the ultraviolet satellite, IUE (which made over 600 observations) and a variety of rockets that obtained x-ray images. The Hubble Space telescope wasn't in orbit at the time, but it has been looking at it since.

Figure 10. The brightness variation of SN1987A over time. This chart shows thousands of observations by both professional and amateur astronomers. The time scale at the bottom is in days, but uses a rather strange system. The entire graph covers a time corresponding to about 3.3 years. The magnitude scale is on the sides. Remember, the faintest that you can see with your eye is magnitude 6, so SN1987A was visible to the naked eye for about a year. Chart is courtesy of the American Association of Variable Star Observers (AAVSO).

Another added advantage to this supernova over others that are studied is that we knew which object blew up. This area of the sky is fairly well studied, so many stellar surveys were done and the star in question, Sanduleak -69 202 , was cataloged and its characteristics (color or temperature and luminosity) were known before it became a supernova. Why was that important? We knew what type of star exploded (temperature, luminosity, likely mass, composition, etc.), so information about it helped astronomers refine computer models of supernova events. The supernova was bright for a long time (visible to the naked eye for about a year), so its evolution was followed closely (and still is being followed) to see if our theories about supernova remnants are correct. The rate at which the supernova brightened and is fading away can also provide information for various computer models and can be compared to other supernovae.

The spectrum of the explosion confirmed the heavy element production (elements heavier than iron). This was seen in the way that various elements would appear and then decay over time. This was exactly in line with the theories about the heavy element production - a nice example where the theories that have been around for a long time finally were supported by observations. Also, by measuring the expansion velocity, we can determine the distance to the Large Magellanic Cloud galaxy in a very accurate manner - something that is very difficult to do. Probably one of the more exciting discoveries was of the neutrinos from the supernova. All of those neutrino detectors around the world were set up to look for neutrinos from the Sun. On the day of the supernova, these detectors were practically flooded with neutrinos. By "flooded" I mean they detected maybe six or eight neutrinos, which is considered a flood when compared to the normal number of neutrinos that are detected. This was another case of theory and observations coming together!

When you look at the supernova today, you can see several rings of material around its location. This material is not part of the supernova explosion, but was blown off by the star years before (you may want to go back up to the top of the notes to look at those big stars that are currently blowing off mass, especially Eta Carina). It wasn't until the supernova went off that the ring actually did something - in this case the rings lit up, because the light (energy) from the supernova traveled through them and heated up the gases.

Figure 11. How the area around SN 1987A looks today. The supernova is in the center of the multi-ring structure. The inner ring is less than a light-year from the supernova, while the other rings are a few light-years away. The rings are not part of the supernova, but are made of material that was blown out from the star before it went supernova. To see why the rings have the orientation that they do, just click on this link. Image credit: P. Challis (CfA).


Using the new photometric metallicity estimation technique described in the previous section, we estimated distances and metal abundances for individual stars in SDSS Stripe 82, which is one of the imaging stripes in SDSS that has been repeatedly scanned along the celestial equator. There are two photometric catalogs available in Stripe 82: the calibration or Standard Star catalog (Ivezić et al. 2007, hereafter calibration catalog) 15 and the co-add imaging catalog (Annis et al. 2011, hereafter co-added catalog). The calibration star catalog contains stellar magnitudes for approximately one million sources, where the magnitudes were averaged at the catalog level. The co-added catalog is based on the co-added image products and is about 0.5 mag deeper than the calibration catalog. Both catalogs, which were in principle produced from the same observations, obtained with the ARC 2.5 m SDSS survey telescope facilities, provide the most precise (

1%) photometry set available within SDSS, and therefore can be used to set the best available constraints on the photometric MDF of the Galaxy. Both catalogs were constructed on the Photo magnitude system. However, we directly employed our UberCal-based models in the parameter estimation using this photometry, because the global photometric zero-point differences between the two systems are negligible.

Below, we describe the selection of a photometric sample from Stripe 82 designed to minimize bias (Section 3.1) and evaluate the effects of unrecognized giants in the sample (Section 3.2). In the subsequent section (Section 4), we present an unbiased MDF of the Galactic halo, and test the hypothesis that the halo is composed of two overlapping sub-components, based on both metallicity and kinematic information for our sample stars.

3.1. Sample Selection and Bias

An unbiased sample of stars is, of course, an important ingredient for obtaining a representative MDF of the Milky Way's halo population(s). Although photometric samples are less susceptible to sample biases than spectroscopic studies that make use of metallicity or color in their sample selection, a bias still exists that needs to be taken into account, as discussed below.

In this work we adopted a sample selection based on stellar mass, as estimated using our isochrones. Figure 11 shows our color-calibrated models at [Fe/H] = −2.4, −1.6, −1.2, and −0.8 the thick solid lines indicate where 0.65 < M*/M < 0.75. This range of stellar mass is similar to what is adopted in this work (see below). Our choice for the mass-based sample selection was motivated by our reasoning that, in order to obtain a representative sample of the halo, stars at different metallicities should be sampled in identical mass ranges. We consider this to be a superior choice to the more commonly adopted color-based selections, because of the strong relationship between color, metallicity, and mass narrow color cuts in a stellar sample would produce a mix of stars, including less massive, lower metallicity stars and more massive, higher metallicity stars. Although colors can be used as a surrogate for temperatures, they have only a limited applicability for stellar masses, hence we believe our mass-based selection should produce a less biased sample of stars for the assembly of a valid halo MDF.

Figure 11. Range of stellar mass in the model considered in this work. Color-calibrated models are shown at [Fe/H] = −2.4 (13 Gyr leftmost), −1.6 (13 Gyr), −1.2 (13 Gyr), and −0.8 (9 Gyr rightmost), where solid lines represent 0.65 < M*/M < 0.75. The fiducial sequence of M13 is shown as a gray line for comparison.

Figure 12 illustrates metallicity–luminosity relations as a function of stellar mass, where the luminosity is expressed in terms of a maximum heliocentric distance that can be reached by a star at a specific magnitude limit. Note that we adopted an age of 13 Gyr for models at −3.0 ≤ [Fe/H] ≤ −1.2, and 4 Gyr at −0.3 ≤ [Fe/H] ≤ +0.4, with a linear interpolation between these two metallicity ranges (Section 2.1). The u-band magnitude limit was used in Figure 12, because of the strong sensitivity of this band on metal abundances. The umax = 20.6 (top panel) and umax = 21.0 (bottom panel) correspond to a median photometry error of σ ≈ 0.03 mag in the calibration and the co-added catalogs, respectively. The error size is similar to those adopted in the artificial star tests (Section 2.5).

Figure 12. Maximum heliocentric distance as a function of stellar mass that can be reached by a star at u < 20.6 mag (top panel) and u < 21.0 mag (bottom panel). These magnitude limits correspond to σu ≈ 0.03 mag error in u in the Stripe 82 calibration (top) and co-added (bottom) catalogs, respectively. The solid and dotted curves show distance limits at a number of different metallicity bins. The gray shaded region represents a mass–distance limit set for the halo sample in this work, which ensures that the sample is unbiased at [Fe/H] −1.2, has a stellar mass less than the turnoff mass of the [Fe/H] = −3 model, and is relatively free from thick-disk contamination (dhelio > 5 kpc).

At a given u-band magnitude limit, we computed a maximum distance to which each star can be observed at a given stellar mass and metal abundance. At a fixed mass, metal-poor stars are brighter than metal-rich stars, thus they can be observed at greater distances than metal-rich stars (see Figure 11). Note that a color-based selection would have the opposite consequence on the luminosity of stars that would be included at a fixed color (or temperature) stars are brighter at higher metallicity. It follows that, in a magnitude-limited survey such as SDSS, color-based selection would produce samples that are biased against more metal-poor stars at greater distances from the Sun.

The gray shaded region in Figure 12 indicates the mass–distance limit set in our halo sample. In both panels, these areas are surrounded by an [Fe/H] = −1.2 model to insure that the sample is unbiased at [Fe/H] ≤ −1.2. Our photometric halo MDFs should be less affected by this choice, since we generally expect to obtain relatively few halo stars outside this metallicity range. An additional constraint on the stellar mass has been applied to the sample, because main-sequence turnoff masses (the high-mass end points of each curve in Figure 12) are varying at different metallicities. Therefore, we imposed an upper mass limit, M* < 0.75 M, which is close to the main-sequence turnoff mass from an [Fe/H] = −3 model turnoff masses occur at higher masses for [Fe/H] > −3. The lower limit to the heliocentric distance (5 kpc) was set to exclude possible thick-disk interlopers in the sample this naturally results in a lower mass cut-off at

0.65 M. We further imposed a cut based on Galactic latitude (see discussion below in Section 4.1). The application of these constraints results in a relatively narrow parameter space (gray areas in Figure 12) in the stellar mass versus distance plane (5 kpc ≤dhelio 8 kpc for the calibration catalog 5 kpc ≤dhelio 9 kpc for the co-added catalog). In short, our sample selection (delineated by the gray regions in Figure 12) collects all of the stars at [Fe/H] −1.2 in a limited volume of the halo, given the magnitude limit set in a photometric catalog (σu < 0.03 mag in this work). The resulting distribution of our sample in Galactocentric distances is shown in Figure 13.

Figure 13. Distribution of Galactocentric distances for the final halo samples in the calibration and the co-added catalogs in Stripe 82.

We have carried out comparisons of our samples obtained by both the calibration and the co-added catalogs, using a search radius of 1''. As recommended in Ivezić et al. (2007), we only included sources in the calibration catalog with at least four repeated observations in each bandpass, for both the photometric comparisons and the following analysis, and proceed with the mean magnitudes and their standard errors. After carrying out iterative 3σ rejections, we found zero-point differences of −0.007 ± 0.022 mag, −0.001 ± 0.011 mag, +0.002 ± 0.013 mag, and +0.003 ± 0.015 mag, in ug, gr, gi, and gz, respectively, for stars with u < 20.6 and fainter than 16th magnitude in each filter bandpass see also photometric comparisons in Annis et al. (2011). The sense of these differences is that the ug color measurements in the co-added catalog are redder than those in the calibration catalog. We restricted our comparison to only include those stars with Galactic latitudes at |b| > 35°, to be consistent with the analysis of the halo MDF carried out below. The listed errors indicate the derived dispersions in color difference (rather than the errors in the mean), using

100, 000 objects in each comparison. Because fainter u-band measurements yield less strong UV excesses, the use of photometry from the co-added catalog would lead to systematically higher photometric metallicity estimates than in the calibration catalog (this is confirmed in the next section). The rms deviations of the color differences between the two catalogs are stable (σcolor < 0.003 mag) along the 110° length of Stripe 82.

Although a detailed study is beyond the scope of the present work, we identified a strong systematic deviation in the u passband (Δu

22 mag) at the faint end, beyond the magnitude limit set in our sample (u < 20.6). One likely cause of the systematic offset is a Malmquist-type bias in the calibration catalog, because faint sources near the detection limit can either be detected or missed, due to the existence of large Poisson errors. Since the calibration catalog took the average of the source magnitudes from individual images, the mean magnitude could therefore be biased toward brighter source measurements. We avoided the photometry zero-point issue by requiring σu < 0.03 mag small photometric errors also make the photometric metallicity estimates more reliable.

We have not made use of the main SDSS photometric database in this work. The 95% completeness limit in the u bandpass of the main survey is 22.0 mag, but the σu = 0.03 mag limit corresponds to u ≈ 18.7 mag, on the order of 2 mag shallower than for the Stripe 82 catalog. At this limiting magnitude, use of the main SDSS database would allow exploration of heliocentric distances only up to

2.2 kpc for the construction of an unbiased [Fe/H] sample at [Fe/H] < −1.2, which is an insufficient volume to probe the halo MDF.

To summarize, in the following analysis we used the selection criteria listed below.

The above selection restricts the photometric sample to 0.2 gr 0.5 (see Figure 11). The total numbers of objects that passed the above selection criteria are 2523 from the calibration catalog and 2626 from the co-added catalog. The median r magnitudes are 18.7 mag and 19.1 mag for the calibration and the co-added catalogs, respectively, with a

0.3 mag dispersion. The standard SDSS star–galaxy separation based on the difference between point-spread function (PSF) and model magnitudes is robust to r

21.5 (Lupton et al. 2002 Scranton et al. 2002), so the contamination by galaxies in our sample should be negligible (see also Annis et al. 2011 Bovy et al. 2012a).

3.2. Contamination by Distant Giants and Thick Disk Stars

Our calibration is valid for main-sequence stars only, and we have explicitly assumed that the great majority of stars in the sample are in their main-sequence phase of evolution. However, there certainly exist distant background giants and subgiants along each line of sight, and their distances can be greatly underestimated if a photometric parallax relation for main-sequence stars is blindly applied. Unfortunately, ugriz photometry alone is not sufficient to reliably discriminate giants from dwarfs, unlike horizontal-branch stars (Ivezić et al. 2007), and therefore some level of contamination by giants in our sample is unavoidable.

We evaluated the level of expected giant and subgiant contamination using cluster photometry for both M13 ([Fe/H] = −1.6 see Figure 11) and M92 ([Fe/H] = −2.4) (An et al. 2008). In order to carry this out, we applied cuts based on χ and sharp parameters in DAOPHOT (Stetson 1987) as in An et al. (2008). Based on the large extent of these clusters on the SDSS CCD chips, we opted not to apply cuts based on the distance from the cluster centers.

We assumed that the number density of the halo follows a power-law profile with an index of −2.8 and a halo ellipticity of 0.6 (e.g., Jurić et al. 2008). Using this model, along with the photometry for each cluster, we simulated color–magnitude diagrams for each line of sight in Stripe 82, and applied the same mass–metallicity–luminosity cuts to the sample as in the previous section. We integrated the number of giants out to 30 kpc from the Sun, beyond which the giant contamination is negligible, because either those distant giants are too faint to be included in our sample or they do not satisfy our selection criteria. Each object was tagged as either a (sub)giant or a dwarf, depending on the location on the original cluster color–magnitude diagram, and the number of giants included in the sample was counted. From the above calculation we found that the contamination rates are at about the 10%–15% level from the M13 photometry, and the 15%–20% level when using the M92 photometry. M92 is more metal-poor than M13, so more cluster giants fall in the color range (0.2 gr 0.5), which is implicitly set by our sample selection criteria. This results in a slightly higher contamination rate from the M92 photometry.

More than any other parameters (e.g., shape parameters of the halo) in the model, we found that the assumed fraction of giants is the dominating factor that determines the total contamination rate in our sample. Note that our estimate for giant contamination in the sample is higher than what Jurić et al. (2008) estimated (

4%). Jurić et al. (2008) obtained an estimate of the fraction of giants to be about 5% from M13, using the SDSS pipeline Photo values in this crowded region, over a color range similar to that in our analysis, and concluded that the bias in the number density of the halo is about 4% arising from the misidentification of giants as main-sequence dwarfs.

Giant contamination in our sample produces an overall shift of the photometric metallicity estimates toward higher values. Figure 14 shows the fiducial sequences on the ug versus gr diagram for a number of clusters that were used in our color calibration. The black lines shown are fiducial sequences, with the dotted lines indicating a giant sequence. For M67, only a main sequence was detected in SDSS (giants are too bright to be included An et al. 2008). The overlaid gray lines in each panel show our calibrated models at [Fe/H] = −3.0 (left most), −2.4, −1.6, −0.8, and 0.0 (right most), respectively. At a given gr, giants have redder ug colors than the main sequence, which leads to an overestimated photometric metallicity if they are misidentified as dwarfs. The size of a bias in the photometric metallicity can be as large as 0.5–1 dex, but fortunately this only applies for a limited number of stars along each line of sight.

Figure 14. Fiducial sequences of the calibration cluster sample (black lines) in the ug vs. gr plane. The solid black lines represent a dwarf sequence dotted lines show the giant sequence. Overlaid gray lines are calibrated models at [Fe/H] = −3.0 (left), −2.4, −1.6, −0.8, and 0.0 (right), respectively. At a given gr, giants have redder ug colors than the main sequence, leading to an overestimated photometric metallicity. Values in parentheses next to the cluster name indicate the cluster metal abundance in [Fe/H].

On the other hand, contamination by thick-disk stars in our sample is negligible. We performed a set of Galactic simulations to check the overall fraction of thick-disk interlopers in our sample along various lines of sight, using artificial star test results in Section 2.5. To simulate a dispersion in the underlying [Fe/H] distribution, we combined artificial stars at the central [Fe/H] (≈−0.7 for the thick disk and ≈ − 1.6 for the halo) with those at ±1σ values (±0.2 and ±0.4 dex for the thick disk and the halo, respectively), taking normalizations from a Gaussian distribution. We adopted the Galactic structural parameters in Jurić et al. (2008).

The fraction of thick-disk stars, of course, is varying at different Galactic latitudes, so we computed the fraction of thick-disk stars along Stripe 82. We found that the average fraction is negligible (0.4% of the entire sample) below photometric [Fe/H] = −1.0 (see also Bovy et al. 2012b). This is because our sample selection, based on mass, metallicity, and distance, is strongly biased against stars with [Fe/H] > −1.2. If all the stars below solar metallicity are included in this estimate, the fraction becomes

3.4%. However, only stars with photometric metallicities less than [Fe/H] = −1 are concerned in the following discussions, and we can safely assume that the thick-disk contamination is negligible.

Ultraviolet Space Astronomy

IX Extragalactic Objects

The external galaxies, like our own, are gigantic clusterings of stars (as many as 10 11 to 10 12 ) and associated interstellar material. There is a wide variety of shapes and stellar content among external galaxies: many are spiral galaxies resembling our own, whereas others are spherical or elliptical and are devoid of obvious spiral patterns.

As in the case of our galaxy, UV observations are expected mainly to reveal the hot stellar component. However, an advantage in observing other galaxies is that the spatial distribution of the hot stellar population is seen at a glance, whereas this is much more difficult to determine for our own galaxy, which we view from within. The variations in this distribution from one galaxy to the next, and in comparison with the distribution of cooler stars and of interstellar material in these galaxies, provide information on star formation rates and history and on the overall evolution of galaxies. The ability to detect and measure hot stars in the presence of a much larger number of cool stars, by means of UV observations, is even more important in studies of external galaxies than our own, since in the former individual stars often are not individually resolved and hence problems due to image overlap and confusion are more severe. Ultraviolet observations also provide more sensitive measurements of the interstellar material in observations of starlight extinction or reflection.

Some galaxies, notably the Seyfert galaxies and quasi-stellar objects (quasars), exhibit highly energetic activity in their central regions, which far transcends that which can be associated with even the most massive individual stars. The total luminosity of an active galactic nucleus can greatly exceed the total luminosity of the remainder of the galaxy quasars are, in fact, by far the most luminous objects in the universe. Observations of these objects in the UV can add to the store of knowledge that is needed to acquire an understanding of these objects.

Photometric and spectrophotometric measurements of a number of external galaxies were obtained with OAO-2 and subsequently were supplemented by more sensitive observations with IUE. Ultraviolet images of the Magellanic Clouds and a number of other galaxies have been obtained in sounding rocket flights, the Apollo 16 mission (see Fig. 24 ), Astro space shuttle flights of the Goddard Space Flight Center's UIT (see Fig. 25 ), and other UV-imaging space experiments. The HUT on the Astro space shuttle flights has been used to obtain far-UV spectra of quasars and other extragalactic objects at wavelengths as short as 92 nm.

FIGURE 24 . Comparison of far-UV and visible imagery of the Large Magellanic Cloud, the nearest external galaxy. (a) Image in the wavelength range 1250–1600 Å (10 min) obtained with the Naval Research Laboratory S201 camera on Apollo 16. (b) Visible-light image, to the same scale. (Lick Observatory photograph.)

FIGURE 25 . Comparison of far-UV images (top), taken with the UIT on the Astro-2 shuttle mission, and ground-based visible images (bottom) of three spiral galaxies. (Courtesy of T. Stecher, NASA GSFC).

These observations are being greatly extended using imaging and spectroscopic instruments on the HST, in particular the STIS, and with the recently launched FUSE. Among other things, these new instruments have provided measurements of the gas and dust in external galaxies and in intergalactic space.

One of the most important objectives of the HST is to determine more accurately the distance scale of the universe it can do this by observing galaxies at much greater distances with the same degree of detail as nearer galaxies are presently observed with ground-based telescopes. Ultraviolet observations are an important aspect of these studies, because the most luminous hot stars are useful distance indicators, and these are much brighter in the UV than in the visible. Also, for very distant objects, the redshift due to the expansion of the universe allows observations of wavelengths below the 91.2 nm short-wavelength limit for nearby objects, set by the absorption due to local interstellar atomic hydrogen.

Stellar Structure and Evolution

VI.C Evolution of 25 M⊙ Stars

The high-mass stars evolve similarly to the stars of 5 M during main-sequence and immediate post-main-sequence evolution, except that the fraction of the mass contained in the convective core is larger, and the very highest mass stars may lose mass even on the main sequence. The 25-M star evolves toward the red giant region, but helium burning at the center occurs when Teff is still in the range 10 4 to 2 × 10 4 K, and carbon burning starts soon afterward. The star expands to become a red giant with L/L = 2 × 10 5 and Teff = 4500 K. A sequence of several new nuclear burning phases now occurs in the core, rapidly enough that little concurrent change occurs in the surface characteristics. Carbon burns at about 9 × 10 8 K, neon burns at 1.75 × 10 9 K, oxygen burns at 2.3 × 10 9 K, and silicon burns at 4 × 10 9 K. A central core of about 1.5 M, composed of iron and nickel, builds up, surrounded by layers that are silicon rich, oxygen rich, and helium rich, respectively. Outside these layers is the envelope, still with its original composition. The layers are separated by active shell sources. The temperature at the center reaches 7 × 10 9 K and the density is 3 × 10 9 g cm −3 (see Fig. 5 ). However, the sequence of nuclear reactions that has built the elements up to the iron peak group in the core can proceed no further. These elements have been produced with a net release of energy at every step, a total of 8 × 10 18 ergs g −1 of hydrogen converted to iron. However, to build up to still heavier elements, a net input of energy is required. Furthermore, the Coulomb barrier for the production of these elements by reactions involving charged particles becomes very high. Instead, an entirely different process occurs in the core. The temperature, and along with it the average photon energy, becomes so high that the photons can react with the iron, breaking it up into helium nuclei and neutrons. This process requires a net input of energy, which must ultimately come from the thermal energy of the gas. The pressure therefore does not rise fast enough to compensate for the increasing force of gravity and the core begins a catastrophic gravitational collapse. On a time scale of less than 1 sec, the central density rises to 10 14 g cm −3 and the temperature rises to 3 × 10 10 K. As the density increases, the degenerate free electrons are captured by the nuclei, reducing the electron pressure and further contributing to collapse. At the same time, there is very rapid energy loss from neutrinos. The point is reached where most of the matter is in the form of free neutrons, and when the density becomes high enough, their degenerate pressure increases rapidly enough to stop the collapse. At that point a good fraction of the original iron core has collapsed to a size of 10 6 cm and has formed a neutron star, nearly in hydrostatic equilibrium, with a shock front on its outer edge through which material from the outer parts of the star is falling and becoming decelerated. The core collapse is thought to be the precursor to the event known as a supernova of type II.

The question of what happens after core collapse is one of the most interesting in astrophysics. Can at least part of the gravitational energy released during the collapse be transferred to the envelope and result in its expansion and ejection in the form of a supernova? Present indications are that it is possible and that the shock will propagate outward into the envelope. A large fraction of the gravitational energy is released in the form of neutrinos, produced during the neutronization of the core. Most of these neutrinos simply escape, but the deposition of a small fraction of their energy and momentum in the layers just outside the neutron star is crucial to the ejection process. Assuming that the shock does propagate outward, it passes through the various shells and results in further nuclear processing, including production of a wide variety of elements up to and including the iron peak. It also accelerates most of the material outside the original iron core outward to escape velocities. When the shock reaches the surface of the red giant star, the outermost material is accelerated to 10,000 km sec −1 , and the deeper layers reach comparable but somewhat smaller velocities. Luminosity, velocity, and Teff as a function of time in numerical simulations of such an outburst agree well with observations. The enormous luminosity arises, in the earlier stages, from the rapid release of the thermal energy of the envelope. At later times, most of the observed radiation is generated by the radioactive decay of the 56 Ni that is produced mainly by explosive silicon burning in the supernova shock. Supernova observations are best fit with total explosion energies of about 10 51 erg. The Crab Nebula ( Fig. 14 ) is consistent with this energy and an expansion velocity of 10,000 km sec −1 . Another good test of the theory of stellar evolution is the calculation of the relative abundances of the elements between oxygen and iron in the ejected supernova envelope. Integration of the yields of these elements over the range of stellar masses that produce supernovae gives values that are consistent with solar abundance ratios.

FIGURE 14 . Crab Nebula in Taurus (M1, NGC 1952) in red light, the remnant of the supernova explosion in AD 1054 (Shane 120-in. reflector). (Lick Observatory photograph.)

From original burst, fraction of stellar mass still surviving on Main sequence - Astronomy

Stars are formed within molecular clouds, vast aggregations of molecules residing in the galactic disks. These clouds that often contain the mass of a million stars, are much denser and colder than the surrounding interstellar gas. Stars are born out of the collapse of small condensation areas that are scattered throughout the much larger volume of a molecular cloud. The collapse can occur due to random density fluctuations or be externally triggered, e.g., by shockwaves from supernovae or galaxy collisions. Soon after the collapse begins, a small pressure-supported protostar at the very center of the collapse flow develops. During the main collapse phase, the central protostar is surrounded by an inward flow of gas and dust. As the protostar evolves both the temperature and the density increase inside. Finally, the central core of the protostar heats up so much that nuclear "burning" is initiated and the star begins its energy production through nuclear fusion.

Star formation is a process complicated by the details of cloud fractionation, rotation, turbulence, and magnetic fields. While the formation of low-mass stars (below 8 solar masses) is thought to be understood and proceeding through an accretion disk, the mechanism to form more massive stars is not quite understood as well. Due to the larger radiation pressure of their emissions, the accretion disk would be blown away. The current model assumes, consistent with observations, the formation of a directed jet, transporting a small fraction of material but clearing a cavity through which most of the radiation can escape without interaction with the accretion disk (Bannerjee and Pudritz 2007). In this way, low-mass and high-mass stars could be formed in a similar manner. Other models assume coalescence of two or more light stars or competitive accretion of a low- and a high-mass star feeding from the same molecular cloud (Bonnel et al. 1997 Bonnel and Bate 2006).

The galactic mass distribution of the newborn stars is known as the initial mass function. To sustain nuclear burning in their interiors, stars must have at least 8% of the mass of the Sun. During their formation, stars with a smaller mass do not release sufficient gravitational binding energy to heat the gas to temperatures required for igniting nuclear fusion. These are called brown dwarfs. The lower-mass stars between about 8 and 40% of the mass of our Sun are called red dwarfs, because of their small size and their low surface temperature. At the other end of the mass range stars more than 100 times as massive as the Sun are highly unstable due to spontaneous pair production of electrons and positron from plasma interactions and therefore do not exist in our Universe. During their enormous life spans, stars produce energy through nuclear fusion and shine continuously over millions to billions of years. Lower-mass stars consume their fuel very quietly and survive for several billion years. Massive stars, on the other hand, burn out in a few millions of years.

Stars undergo drastic changes during their evolution. One of the best methods for charting the course of stellar evolution is the Hertzsprung–Russell (HR) diagram shown in Fig. 8, a particular type of graph developed in the early twentieth century by the astronomers Hertzsprung and Russell. In this diagram, the luminosity or energy output of a star is plotted on the vertical axis, and the surface temperature of the star on the horizontal axis. For historical reasons, the surface temperatures along the horizontal axis are plotted backward, so that they increase toward the left. In the HR diagram the various stars are then plotted according to their luminosity and surface temperature. As one can see, the stars are not distributed randomly in the HR diagram, but are rather grouped in certain areas.

Most of the stars line up along a well-defined band on the HR diagram known as the main sequence and are therefore also called main-sequence stars. This trend is no coincidence. Stars that lie along the main sequence have the proper internal configurations to support fusion of hydrogen to helium. Since stars spend most of their lifetime in this hydrogen burning state, most stars in the HR diagram are lying on the main-sequence band. Our Sun is also a typical main-sequence star.

After the hydrogen supply in the core of the star is exhausted and converted to helium, the central temperature is too low to fuse helium into heavier elements. Therefore, the core lacks an energy source and cannot support anymore the overlying bulk of the star. Through the gravitational pressure, the size of the core shrinks and the temperature of the central region increases accordingly. The heat released by the core increases steadily the luminosity of the star. Paradoxically, even though the helium core is shrinking, the radius of the star, determined by the outer hydrogen layer, increases by factors of 100 to 1,000. Through this expansion, the surface temperature drops by as much as 50% and the star becomes redder. Therefore, these stars are called red giants and are found in the HR diagram in the upper right corner.

When the core temperature of the red giant reaches about one hundred million degrees, a new sequence of nuclear reactions called helium burning begins in the core where helium nuclei fuse to carbon and oxygen. Our Sun has lived for 4.5 billion years and has already burnt half of its hydrogen in the core. After about another 5 billion years our Sun will also become a red giant and will thereby increase its size so much that the radius of the Sun will reach about the Earth's orbit.

The further evolution of a star and the nature of its stellar death depend on the initial mass. If the initial mass of a star is less than about 8 solar masses, it is burning He in an unstable way (see also Sect. 4.3) and the resulting pulsations lead to the loss of huge quantities of hot gases toward the end of its life. This cloud moving away from the star is called a planetary nebula. The central small and hot core of the star that is left over is a white dwarf and consists of the ashes of helium burning, i.e., carbon and oxygen. Even though the surface temperature of the white dwarf is still very hot its luminosity is small, because nuclear fusion has ceased. Therefore, the white dwarfs are found in the lower left corner of the HR diagram.

If the initial mass of a star is more than about 8 solar masses further burning phases will take place. These are called advanced burning phases and consist of carbon, neon, oxygen, and silicon burning, being named after the nuclei mainly destroyed in that phase. In these subsequent burning phases, heavier and heavier nuclei are built up, and the ashes of the preceding burning phases provide the fuel for the subsequent burning phases. However, in the outer and therefore cooler and less dense regions of the star the previous burning phases are still continuing. This leads to shell burning with distinct adjacent shells of different chemical compositions, in which different burning phases prevail. In the outermost shell of the star still hydrogen is burnt into helium (hydrogen burning), in the next shell helium to carbon and oxygen (helium burning), and finally, in the fully evolved star, there follow still carbon, oxygen, neon, and silicon burning shells (Fig. 9). In the core of the star significant amounts of iron are accumulating through silicon burning. A detailed discussion of the nuclear burning phases is given in Sects. 4.2 through 4.4.

A detailed introduction to stellar evolution is given in the following books: Clayton (1984), Hansen and Kawaler (1994), Kippenhahn and Weigert (1994), Phillips (1994), Tayler (1994). Books and reviews discussing stellar nucleosynthesis are Rolfs and Rodney (1988), Arnett (1996), Thielemann et al. (2001b). Tables of nuclear reaction rates and cross sections can be found in Rauscher and Thielemann (2000).

The endpoint in the evolution of stars with more than 8 solar masses is a type II supernova. One should not confuse novae with supernovae and even the two types (i.e., type I and type II) of supernovae are quite different. It will become evident in the following that the sites of these explosive events are only loosely related, despite the similarity in the name. There is a major difference in the underlying mechanism between type I (SN I) and type II supernovae (SN II). The confusing choice of names is, once again, historical. Astronomy is guided by observations and early astronomers did not have the equipment to investigate the objects in any detail. Obviously, even today, it is impossible to view the events in binary systems directly. Much more detail can be seen in light curves (i.e., brightness as a function of time) and spectra.

Historically, the comparatively frequent novae (see Sect. 5.2) were named first. Subsequently, much brighter eruptions of light were observed in the sky. Since they are brighter by more than a factor of 10 6 , they were appropriately termed supernovae. The light curve of a supernova is somewhat different from that of a nova: its rise time is only a few hours instead of days and it exponentially decays after having reached its peak. Closer investigations showed that several classes of supernovae can be found, according to features in their spectra: type I do not show hydrogen lines, whereas they are found in type II eruptions. This indicates whether the exploding object has an extended hydrogen envelope (such as massive stars). A more detailed classification scheme is shown in Table 2. Type Ia supernovae are further discussed in Sect. 5.3, while the unique scenario producing all other types (SNIb,c SNII) is shortly introduced in the following.

When the stellar core becomes dominated by iron, the fusion into heavier elements does not lead to the release of energy, but rather requires absorption of energy. (See, e.g., Fig. 7.13 in Chap. 7, Vol. 1, showing the cross section of the stability valley of nuclei with iron at its lowest point.) Therefore, the core lacks an energy source and is unable to support itself against gravity anymore leading to a collapse of the star. In a single second the innermost regions are compressed to nuclear densities of about 10 12 kg/m 3 and temperatures of about 10 11 K. The iron nuclei, which have been synthesized just before in silicon burning are broken up again into protons and neutrons through the high-energy thermal radiation. The innermost regions are compressed so much that the core density becomes sufficiently high for electrons and protons to combine, producing neutrons and neutrinos. As the collapse continues, this giant ball of neutrons generally reaches a state of maximum density, and then bounces back. The bounce drives an extraordinarily powerful shock wave outward through the outer parts of the star. Investigations within the last 3 decades have made it clear that this prompt shock will not have enough energy to explode the remaining outer layers of the star. Only with the additional supply of energy through neutrino heating can the shock wave be supported to blow apart the star completely. This powerful explosion can explain supernovae of type II, but also of type Ib,c. At the center of the supernova explosion, the dense core of neutrons may be left behind as a neutron star. Alternatively, if the remaining core becomes heavier than a few solar masses through partial fallback of material, it can even collapse into a black hole. The dual explosion mechanism with prompt shock and delayed explosion by neutrinos is still not understood well. A proper treatment of the neutrino transport requires detailed three-dimensional hydrodynamic simulations, which are currently beyond the capability of modern computers and thus one has to refrain to approximations whose merits are debatable. For an overview, see, e.g., Janka et al. (2007).

The physics of the remaining compact objects after stellar death, e.g., white dwarfs, neutron stars, and black holes are discussed by Shapiro and Teukolsky (1983).

For nuclear reactions to take place in the interiors of stars, a temperature of at least 10 million degrees is necessary. This high temperature is needed because nuclei have positive charge and therefore repel each other through the Coulomb potential. The typical kinetic energy of nuclei in stellar interior range from between a few keV to a few 100 keV being much smaller than the typical height of a few MeV of the Coulomb barrier between reaction partners. Therefore, nuclear reactions in stars proceed mainly by barrier penetration exploiting the quantum mechanical tunnel effect. The cross sections decrease exponentially with the kinetic energies of the nuclei because of the decreasing penetration probability through the Coulomb barrier. The dependence on the relative kinetic energy E between interacting nuclei can be represented most simply by a formula in which a factor proportional to the inverse of the relative kinetic energy 1/E and the barrier penetration factor G(E) is factored out from the cross section: &sigma(E) = (1/E) G(E) S(E). This leaves a function S(E) called the astrophysical S-factor that varies smoothly with the kinetic energy E of the interacting nuclei in the absence of resonances. Neutron-induced reactions would not have to overcome the Coulomb barrier. However, neutrons are not very abundant in stellar interiors. They still play a major role for the nucleosynthesis of heavy nuclei through the so-called s- and r-processes, to be discussed in Sect. 4.5.

The reaction rate, expressed as the number of reactions per volume and per time, is proportional to the astrophysical S-factor. At the temperatures and densities relevant to the stellar environments the interacting nuclei have a Maxwell distribution of speeds. This distribution has also to be taken into account when determining the reaction rate. An introduction to astrophysical S-factors and reaction rates can be found in many textbooks on nuclear astrophysics, e.g., Arnett (1996), Rolfs and Rodney (1988), Iliadis (2007), Boyd (2008).

Nuclear burning in late hydrostatic phases (see, e.g., silicon burning) and in different explosive scenarios proceeds at high temperatures and densities. This leads to equilibrium between forward and reverse reactions, e.g., capture and photodisintegration. It gives rise to equilibrium abundances depending only on the supply of free neutrons and protons and on certain nuclear properties. High temperatures favor the creation of light nuclei because photodisintegration processes dominate. High densities lead to heavy nuclei, and intermediate conditions yield the highest abundances for nuclei with high binding energies. Such an equilibrium can be established within a group of nuclear species where individual reactions link different groups. This is called quasi-statistical equilibrium (QSE). The full nuclear statistical equilibrium (NSE) is reached when all nuclei are equilibrated.

In the following, the different burning stages will be described one by one, starting with hydrogen burning, being the first burning stage of every star.

In hydrogen burning, occurring in the cores of main-sequence stars like our Sun, ordinary hydrogen nuclei (i.e., protons) are burnt through a chain or cycle of nuclear reactions into 4 He nuclei. In this stellar plasma there are two processes burning hydrogen: the proton–proton chain (pp-chain) (Fig. 10).

The pp-chain proceeds through a sequence of two-body reactions. The first reaction in the pp-chain is the exothermic fusion of two protons p into the deuteron d consisting of a proton p and a neutron n through the reaction

For this reaction to take place a proton p must be converted into a neutron n through p &rarr n + e + + &nu, releasing a positron e + and a neutrino &nu. Such a conversion can only proceed through the weak interaction (see Sect. 3.1). Therefore, the rate of the reaction in Eq. (2) is very low, which makes the reaction the bottleneck of the pp-chain.

Once the deuteron d is formed, it very rapidly undergoes the reaction

There are two alternatives for the next step, leading to a branching of the pp-chain into the ppI- and ppII-chain. In the ppI-chain, occurring in 86% of the cases, two 3 He nuclei fuse to a final 4 He nucleus while two protons are released:

In the ppII-chain, occurring in 14% of the cases, a 3 He nucleus fuses with a 4 He nucleus creating a 7 Be nucleus and thereby releasing a photon, &gamma:

In almost all cases, this reaction is followed by the capture of an electron and emission of a neutrino &nu, thereby converting a 7 Be nucleus into 7 Li. This is followed by the capture of another proton, creating two 4 He nuclei:

Another branching into the ppIII-chain occurs in a very small percentage of cases with a total probability of only 0.02%. In this chain, reaction (5) is followed by the following sequence of reactions:

The net reaction of all three pp-chains

leads to a transformation of four protons into a 4 He nucleus releasing two positrons e + , two neutrinos &nu and a total energy of 26.73 MeV. A fraction of this energy is carried away by the neutrinos, which leave the star practically unhindered due to their negligible interaction with the solar material.

Fusion of hydrogen into helium may also be achieved through another sequence called CNO-cycle (Fig. 11), which is notably different from the pp-chain:

In this sequence the C, N, and O nuclei only act as "catalysts" and the net reaction of the CNO-cycle is again given by Eq. (8).

For main-sequence stars lighter than about 2 solar masses, the pp-chain dominates in hydrogen burning, whereas the CNO-cycle is favored over the pp-chain in stars that are more than twice as massive as the Sun.

In our Sun the pp-chain dominates over the CNO-cycle, producing about 98% of the total energy. A prerequisite for CNO-cycles is, of course, the existence of the elements C, N, O in the stellar plasma. Stars formed early in the Galaxy (first-generation stars) contain only primordial elements and thus are not able to burn hydrogen through a CNO-cycle at all.

The Sun's temperature in the core is about 1.5 × 10 7 K, whereas the surface temperature is only about 5,600 K. The Sun has already lived for 4.6 billion years, and will have enough hydrogen supply to live for about another 5 billion years. This leads to a long lifetime of about 10 billion years before its fuel is exhausted.

How can information be obtained from the Sun's core, where hydrogen burning takes place? The photons reaching us from the Sun are emitted from the solar surface. They have changed their energy enormously by many scattering processes on their way from the hot solar core to the relatively cool surface of the Sun. Therefore, in the visible region only the solar surface and not the solar interior can be observed. One possibility to obtain information about the Sun's core is helioseismology, i.e., by observing the vibration modes of the Sun. It was confirmed through helioseismology that our standard solar model is correct (Fiorentini and Ricci 2000 Bahcall et al. 2001a Christensen-Dalsgaard 2001).

Another possibility is to observe the neutrinos that are set free in nuclear reactions of the pp-chain and CNO-cycle and reach the surface practically unhindered. Presently four neutrino detectors measuring solar neutrinos exist: HOMESTAKE (USA), GALLEX (Italy), (SUPER)KAMIOKANDE (Japan), and SNO (Canada). All these neutrino detectors are underground in order to shield out the cosmic rays that would give unwanted background signals in the neutrino detectors. The existing solar neutrino detectors measure only about 1/3 to 1/2 of the electron neutrino flux compared to the value calculated from the standard solar model (Bahcall 2000). This discrepancy is called the solar neutrino problem (Bahcall 1989, 1999). Possible problems both with the neutrino measurements and with our standard solar model have been ruled out. Recently, at SNO it was possible to observe not only the solar electron neutrinos, but also the &mu- and &tau-neutrinos in the same experiment (Heger 2001 SNO Collaboration et al. 2002a, b). The measured total neutrino flux agrees with the value expected from the standard solar model. The solution to the solar neutrino problem implies some new physics by the introduction of the so-called neutrino oscillations Neutrino oscillations (see Sec. 8.2 in Chap. 10, Vol. 1). Through such oscillations, the electron neutrinos &nu emitted in the solar core by the nuclear reactions given in Eqs. (2), (6), and (7) can change into other types of neutrinos. Thus, mainly &mu-neutrinos emerge on their way from the core of the Sun to the detector. Experiments measuring electron neutrinos thus show a smaller flux than initially emitted in the solar core (Bahcall 2001 Bahcall et al. 2001b Fiorentini et al. 2001). This physical picture is the culmination of about 40 years of solar neutrino detection and research.

Recently, these findings have been combined with the results of the so-called atmospheric neutrino anomaly, where &mu-neutrinos generated in pion decays oscillate over into, mainly, &tau-neutrinos. In addition, terrestrial experiments performed with neutrino fluxes (produced either at nuclear power plants or with accelerators) provide substantial information on the mixing pattern among the different neutrino species. Searches for possible oscillations into further light neutrino flavors, which would be of clear cosmological significance, have not yet provided a clear answer to the question of their existence. (See Sect. 8.2 in Chap. 10, Vol. 1).

The fusion of protons into helium continues until the star has exhausted its hydrogen. When this happens, the star undergoes a gravitational collapse and the temperature rises to about a few times 10 8 K in the core of the star, which makes the fusion of helium into heavier nuclei possible. In the first reaction of helium burning, the fusion of two 4 He nuclei creates the 8 Be nucleus. However, the 8 Be nucleus has an extremely short mean life of only 10 -16 s, before it decays back again to two 4 He nuclei. This process is in equilibrium, where the rate of production equals the rate of destruction of the 8 Be nucleus:

The 8 Be just produced can, however, capture another 4 He nucleus creating the 12 C nucleus through the reaction

The reactions (10) and (11) are called the triple-&alpha reaction, because three 4 He nuclei or &alpha particles are necessary for the creation of 12 C. This reaction can only create carbon in appreciable amounts because of the existence of a resonance in 12 C at the relevant energy for helium burning. Through this resonance, reaction (11) is enhanced by many orders of magnitude.

In helium burning, about half of the carbon nuclei produced are converted to oxygen nuclei 16 O by the capture of another 4 He nucleus:

Further captures of helium nuclei 4 He by oxygen nuclei 16 O occur only to a much lesser extent and therefore helium burning comes to an end after the creation of 12 C and 16 O.

Carbon and oxygen are the two most important elements for carbon-based life. Carbon is needed for the complex nuclei of the DNA and proteins, whereas oxygen is needed even for water. Interestingly enough, these two elements are extremely fine-tuned with respect to the nuclear force. If the strength of this force were 0.5% larger or smaller, the average abundance of carbon or oxygen in our Universe would be reduced by more than two orders of magnitude. This would make the existence of carbon-based life in our Universe very improbable (Oberhummer et al. 2000 Schlattl et al. 2004).

Outside the stellar core burning helium, hydrogen burning continues in a shell around the core. If the initial mass of a star is less than about 8 solar masses no more burning phases will take place after helium burning and nuclear burning stops. A white dwarf with a surrounding expanding planetary nebula will be the endpoint of the star's life. Charbonnel et al. (1999) and Marigo (2001) review the chemical yields in light and intermediate-mass stars between 0.8 and 8 solar masses.

Two interesting effects happen in helium burning of low-mass stars. Firstly, stars with less than about 2 solar masses undergo a core He flash instead of igniting stable He burning after the H burning phase. This is because the cores of lower-mass stars are more dense than those of higher-mass stars. For stars with less than about 2 solar masses, the contracted He core is so dense that it cannot be described as an ideal gas. Rather, it is a degenerate gas, in which pressure is only depending on density but not on temperature. Once the triple-&alpha reaction, being very efficient at high density, is ignited, a thermonuclear runaway ensues because the rising temperature does not raise the pressure and therefore does not cause an expansion of the burning zone. Thus, the usual self-regulation mechanism of hydrostatic burning is not working anymore and He burning proceeds quickly to high temperature. Very high temperatures lift the degeneracy of the gas and its equation-of-state becomes temperature dependent again very suddenly. This causes an explosive expansion of the outer core, also ejecting the outer layers of the star as a planetary nebula.

The second phenomenon occurs in stars between 2 and 8 solar masses, the so-called Asymptotic Giant Branch (AGB) stars. Regular He burning takes place in the core of these stars in their red giant phase. With the exhaustion of He in the center of the star, the burning zone moves outward and becomes a burning shell. Thus, there are two shells burning, a H-burning shell and a He-burning shell. The He-burning shell is very thin and does not generate sufficient energy to balance the mass layers on top of it through radiation pressure. This squashes the shell more and more. Because of the nonlinear dependence on density of the triple-&alpha rate, which is actually two reactions one after another, the energy release will considerably increase but still not be enough to expand and self-regulate the shell against the pressure from the surrounding layers. Further contraction enhances the triple-&alpha rate nonlinearly and so on. Although the gas is not degenerate, a similar thermonuclear runaway as in the degenerate case occurs. When a critical temperature is reached, enough energy is released to expand the shell explosively against its surroundings. This rapid expansion, the He-shell flash, is so strong that it also blows out the H-burning shell. Due to the expansion, the density drops and the triple-&alpha reaction ceases. Quickly, the star contracts again, the outer material settles, and first the H-burning shell and then the He-burning shell is ignited again. This sets the stage for another such cycle. AGB stars undergo a large number of such pulses, where the thermonuclear runaway phase with the flash lasts only a few hundred years whereas the time between pulses is a hundred to a thousand times longer. Oscillations and vibrations are induced into the stellar plasma by these pulses, leading to increased mass loss from the surface of the star. AGB stars have strong stellar winds, which considerably decrease their total mass during their evolution. The shell flashes have another important impact: they cause large convection zones, mixing the plasma constituents across large distances within the star. This is important for the production of the s-process nuclei (see Sect. 4.5.1).

He-shell flashes only occur in low-mass stars because they are caused by thin He-burning shells and the size of the shells scale with the stellar mass.

In a massive star with more than 8 solar masses, the next stage after helium burning is carbon burning. This starts when the carbon/oxygen core has shrunk so that the temperature at its center has reached about 5 × 10 8 K. Then two carbon nuclei fuse together creating 20 Ne or 23 Na nuclei:

The next stage is neon burning starting at 10 9 K, in which photons first disintegrate 20 Ne and liberate 4 He, which in turn reacts with the undissociated 20 Ne to build up 24 Mg and further nuclei:

Oxygen burning occurs when the temperature reaches 2 × 10 9 K, the most important reaction being the one producing 28 Si:

The final stage is reached at a temperature of 5 × 10 9 K, when silicon burning begins. At this high temperature, a series of reactions takes place beginning with the photodisintegration of 28 Si:

Then the released 4 He nuclei build up heavier nuclei by successive capture reactions

and so on. At such high temperatures, capture and photodisintegration reactions are in equilibrium. In this so-called nuclear statistical equilibrium (NSE) the knowledge of individual reactions or reaction rates is not important anymore to calculate the abundances. The produced abundances only depend on the temperature and density of the plasma and the nuclear binding energies (Iliadis 2007 Boyd 2008). The result of this series of photodisintegration and capture reactions is the steady buildup of heavier elements up to the elements grouped around iron (Hix and Thielemann 1998), with 56 Ni preferentially produced because it is the nucleus with the highest binding energy and having equal number of protons and neutrons.

T he sequence of stellar burning is terminated when the core of the star is largely composed of elements in the mass region of nickel and iron, because no more energy is to be gained from further nuclear reactions. As soon as the energy produced is not enough to maintain the hydrostatic equilibrium, the core cannot support the outer layers anymore, and it begins to collapse due to its gravitation, leading to a core-collapse supernova (see Sect. 4.1.3).

In a core-collapse supernova explosive nucleosynthesis also takes place through the outward proceeding shock wave (Thielemann et al. 2001a), modifying the elemental abundance pattern of the outer layers of the pre-supernova star. This explosive burning of the C-, Ne-, O-, and Si-layers in the star mainly leads to modifications of the abundances in the region from Ca to Fe (Rauscher et al. 2002). Photodisintegration of heavy nuclei also leads to the production of proton-rich stable nuclides, the so-called p-nuclides (see also Sect. 4.5.2). The strong neutrino emission caused by the formation of a neutron star in the core collapse influences nucleosynthesis in the deepest, barely ejected layers of the star as well as in the outer layers (Sects. 4.5.2 and 4.5.3).

Nucleosynthesis of massive stars is reviewed by Rauscher et al. (2002), Woosley and Heger (2007). An overview of stellar nucleosynthesis including hydrogen, helium, neon, silicon, and explosive burning as well as the basics of the s- and r-process are given by Rauscher and Thielemann (2001). Explosive burning and the s- and r-processes are also introduced below.

As it has been seen in the preceding sections, stellar burning phases only lead to the production of nuclei up to Fe. A review by National Research Council of the National Academies identified 11 key questions to be addressed in science in the next decade (Turner et al. 2003). Ranked three on the list is "How were the elements from Fe to U produced?" Although the ground to answer this question has been laid by Burbidge et al. (1957), Cameron (1957) and much progress has been made since then, there remain a number of problems regarding the astrophysical sites of certain nucleosynthesis processes and also concerning the properties of certain, highly unstable nuclei in such processes. In the following subsections, a brief summary is given of the current knowledge of how elements beyond Fe were synthesized.

Due to the lack of a Coulomb barrier, the most likely process for the formation of elements heavier than those grouped around iron is neutron capture. If a supply of neutrons is available, they can accrete by sequential neutron captures on a "seed nucleus" in the region of iron to build up neutron-richer nuclei. As the neutron number of the nucleus increases, it will become unstable to &beta - decay, transforming a neutron into a proton in the nucleus, and emitting an electron and an antineutrino. Successive neutron captures, interspersed by &beta - decays build up many, but not all of the heavier stable nuclei.

There are two basic timescales in this scenario of heavy-element nucleosynthesis by neutron captures: (1) the &beta-decay lifetimes, and (2) the time intervals between successive captures that are inversely proportional to the neutron capture reaction rates and the neutron flux. If the rate of neutron capture is slow compared to the relevant &beta decays, the synthesis path will follow the bottom of the stability valley very closely. On the other hand, if the rate of neutron capture is faster than the relevant &beta - decays, highly neutron-rich nuclei will be formed. After the neutron flux has ceased, those nuclei will be transformed to stable nuclei by a series of &beta - decays. The above two processes are called s- and r-process, respectively, according to their slow or rapid rate of neutron capture. The observed abundances of nuclei in the solar system, especially in the regions of closed-shell nuclei, suggest that the s- and r-processes contributed more or less equally to the formation of the elements above the iron region (see Fig. 12).

Two important reactions provide neutrons for the s-process:

The reaction on 13 C is much more efficient in releasing neutrons because it is strongly exothermic, as opposed to the second reaction. However, 13 C normally does not occur in He-burning zones whereas 22 Ne does. This proved to be a longstanding problem in complete stellar simulations of s-process nucleosynthesis.

Early observations (see Burbidge et al. 1957) had already found Tc on the surface of AGB stars. Since Tc isotopes are short lived compared to the age of such a star, they had to be produced in that star and brought up to the surface. Only in recent years, sophisticated stellar models were able to follow the complicated convection and nucleosynthesis processes inside AGB stars with sufficient accuracy to confirm them as the production sites. He-shell flashes (see Sect. 4.3) and the mixing brought about by them turned out to be the key (Busso et al. 2001 Boothroyd 2006). Such a flash can mix down protons from the unburnt outer layer of the star, which can then be used to produce 13 C by proton capture on 12 C and subsequent &beta-decay of the resulting 13 N. With this 13 C neutrons can be very sufficiently released even during the interpulse phase. Additionally, the reaction on 22 Ne can release further neutrons during the high temperature phase of the flash itself. Thus, the nuclides in the stellar plasma are irradiated with neutrons in bursts over millennia. The large convection zones appearing in the flash phase bring up the newly synthesized material to the surface.

In the manner described above, AGB stars produce the majority of the s-process nuclei, the so-called main component. It was known for a long time that there must be a second site of s-processing, producing light s-nuclei. Because they exhibit smaller abundances than those of the main component, this was called the weak component. Such a weak s-process is found in massive stars (i.e., stars with more than 8 solar masses), where capture of 4 He by 22 Ne is the main neutron source. Massive stars reach higher temperatures than AGB stars already in their late evolution stages, which help to release neutrons. Even more neutrons can be released during explosive burning, when the temperature rises due to the supernova shock wave passing through the outer layers of the star. Because of the inefficiency of the 22 Ne neutron release and the short timescale, this mechanism cannot proceed much beyond Fe in massive stars.

For nucleosynthesis of the heavy elements through the s-process in both AGB and massive stars, there already must be nuclei present in the iron region, which were produced in previous generations of stars. Thus, the s-process will be stronger in stars formed more recently than in older stars containing less heavy elements.

Since the buildup of nuclei in the s- (and r-) process follows the neutron-rich side of the stability valley (see, e.g., Fig. 13 in Chap. 7, Vol. 1), 32 proton-rich isotopes cannot be produced in either process. These so-called p-nuclides occur naturally but with abundances many orders of magnitude lower than the other nuclides. The hypothetical process synthesizing these nuclides was termed p-process and several models have been suggested. The commonly favored one is photodisintegration of preexisting nuclei in the Ne/O shells of massive stars. When a supernova shockfront is passing through these layers, the high temperatures of 2𠄴 GK enable photodisintegration, starting with &gamma-induced emission of several neutrons, leading to proton-rich nuclei. The photodisintegration path can branch when proton or &alpha emission becomes more favorable than neutron emission in such proton-rich nuclei. The bulk of p-nuclides can be explained in such a model but some problems remain (Rauscher et al. 2002 Arnould and Goriely 2003 Boyd 2008). Especially the production of the light p-isotopes, in particular 92,94 Mo and 96,98 Ru, is not understood. Among the p-nuclei they have by far the highest abundance but cannot be produced concurrently with the others. It remains an open question whether the stellar models have to be revised or an additional production mechanism has to be invoked for these light p-nuclei.

The neutrino flux of a core-collapse supernova is high enough to contribute to the nucleosynthesis of certain rare elements and isotopes, even in the outer layers of the star. In this so-called &nu-process, inelastic scattering of a neutrino leads to formation of an excited daughter nuclide, which then decays by particle emission. This process can contribute significantly to the production of light ( 11 B, 19 F) and heavy ( 138 La, 180 Ta) nuclides (Woosley and Weaver 1995 Heger et al. 2005).

In addition to s-process nucleosynthesis, about half of the nuclides beyond Fe are produced through rapid neutron captures on short timescales in the r-process. The site of the r-process is controversial. Mostly favored are core-collapse supernovae where appropriate r-process conditions are thought to be found close to the region of neutron star formation. These innermost layers, which are barely ejected, move outward within a strong neutrino flux, driving the material to become very neutron rich. With a high neutron density, neutron captures can proceed much faster than &beta-decays and produce very neutron-rich nuclei far from stability. Through simultaneously occurring captures, photodisintegrations with neutron emission, and &beta-decays, heavier elements are synthesized within a few seconds. When the ejected material cools down, those highly unstable nuclei decay back to stability, thus supplying the needed fraction of heavy elements. While the s-process is confined to the region up to Bi, the r-process is thought to also reach the region of fissionable nuclei and produce natural, long-lived elements such as U. The endpoint of the r-process path is highly debated since it depends on fission barriers of very neutron-rich, heavy nuclei, for which there is no consensus among theoretical models yet.

The conditions in those innermost regions of a core-collapse supernova are closely linked to the working of the explosion mechanism. Since the latter is not yet fully understood, it is not yet clear whether the required conditions can actually be established. Therefore, a number of alternative scenarios are still discussed, such as jet outflows from asymmetrically exploding stars. The search for the site of the r-process remains a major focus of research.

Recently, an additional nucleosynthesis process in the deep layers of the exploding star has been suggested (Fröhlich et al. 2006). It was discovered that the combined flux of neutrinos and antineutrinos from the emerging, hot neutron star initially creates very proton-rich conditions before the matter becomes neutron rich at later times and/or larger radii. The high temperature and density environment gives rise to rapid proton captures, thus synthesizing nuclei beyond Fe but on the proton-rich side of stability. A small number of neutrons are required to speed up the matter flow to heavier elements and these are produced by antineutrino captures on protons. The &nup-process could perhaps explain the surprisingly high abundance of Sr, Y, and Zr found in very old stars (Travaglio et al. 2004 Frebel et al. 2005). Again, the details of this so-called &nup-process (including the question of how efficiently it can produce elements beyond Fe) depend strongly on the conditions in the deep layers of the exploding star and the explosion mechanism. Among the suggested alternative scenarios are wind outflows from the accretion disks around black holes formed by core collapse of very massive stars (Surman et al. 2006). These are also thought to be the cause of so-called &gamma-ray bursts, which are the most energetic phenomena observed in our Universe today (MacFadyan and Woosley 1999 Mészáros 2006).

The light and fragile elements lithium, beryllium, and boron (LiBeB) are not primarily produced in primordial or stellar nucleosynthesis. In fact, the abundance curve in Fig. 13 shows a huge dip (almost a gap, actually) for the mass numbers 8�, reflecting the scarcity of LiBeB-nuclei in the solar system. Only the nuclide 7 Li can be produced both in primordial (see Sect. 3) and in stellar nucleosynthesis (see Sect. 4.2), whereas the nuclides 6 Li, 9 Be, 10 B, and 11 B are almost pure spallation products of heavier elements.

The high-energetic galactic cosmic rays (GCRs) originate probably from supernovae (Erlykin and Wolfendale 2001). GCRs consist mainly of fast-moving bare hydrogen and helium nuclei and, to a lesser amount, of carbon, nitrogen, and oxygen nuclei (CNO)-nuclei. Hydrogen and helium nuclei of interstellar clouds can spall the CNO-nuclei in flight of the fast GCRs. Therefore, the GCRs are by about a million times enriched in LiBeB-nuclei compared to the solar system abundance.

The most plausible origin of the main bulk of LiBeB-nuclei is that hydrogen and helium nuclei of GCRs hit and spall CNO-nuclei contained in interstellar clouds. However, this process alone seems unable to produce LiBeB at the observed level. Therefore, another production site of LiBeB-nuclei has been proposed. This invokes in-flight fragmentation of carbon and oxygen nuclei by collision with hydrogen and helium nuclei in interstellar clouds. The sites of this process are mainly the surroundings of massive stars, which are able to furnish freshly synthesized carbon and oxygen nuclei and accelerate them via shock waves. Finally, spallation through neutrinos in supernova explosions also produces the nuclides 7 Li and 11 B (Hartmann et al. 1999).

A review of nucleosynthesis by spallation is given by Vangioni-Flam et al. (2000). *****



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Massive stars fuse heavier elements in their cores than lower mass stars. This leads to the creation of heavier elements up to iron. Iron robs critical energy from the core, causing it to collapse. The shock wave, together with a huge swarm of neutrinos, blast through the star’s outer layers, causing it to explode. The resulting supernova creates even more heavy elements, scattering them through space. Also, happily, we’re in no danger from a nearby supernova.

Table of Contents
Massive Stars Fuse Heavier Elements Up To Iron 1:15
Iron Uses High Amounts of Energy, Thus Making Stars Collapse 3:58
The Resulting Supernova Creates Even Heavier Elements 10:00
Relax, Something Else Will Kill You 9:04

Blowing Bubbles [credit: NASA/CXC/April Jubett]
The Sizes of Stars [credit: ESO/M. Kornmesser]
Red giants [credit: Wikimedia Commons]
Alpha Orionis [credit: A. Dupree (CfA), NASA, ESA]
Sun and VY Canis Majoris [credit: Wikimedia Commons]
Witch Head Nebula and Rigel [credit: Rogelio Bernal Andreo]
Layers of a massive star,_8M%2B).png [credit: Wikimedia Commons]
NASA's Swift Reveals New Phenomenon in a Neutron Star [credit: NASA's Goddard Space Flight Center]
What is a black hole? [credit: NASA/CXC/M.Weiss]
The Death of Stars [credit: ESA/Hubble]
Giant Mosaic of the Crab Nebula [credit: NASA, ESA, J. Hester (Arizona State University)]
Hubble and Chandra spot a celestial bauble [credit: NASA, ESA, the Hubble Heritage Team (STScI/AURA), and NASA/CXC/SAO/J. Hughes]
Vela Supernova Remnant [credit: Marco Lorenzi]
Spica [credit: Phil Plait]
Cassiopeia A [credit: Oliver Krause (Steward Observatory) George H. Rieke (Steward Observatory) Stephan M. Birkmann (Max-Planck-Institut fur Astronomie) Emeric Le Floc'h (Steward Observatory) Karl D. Gordon (Steward Observatory) Eiichi Egami (Steward Observatory) John Bieging (Steward Observatory) John P. Hughes (Rutgers University) Erick Young (Steward Observatory) Joannah L. Hinz (Steward Observatory) Sascha P. Quanz (Max-Planck-Institut fur Astronomie) Dean C. Hines (Space Science Institute)]
Sloshing Supernova [credit: NASA's Goddard Space Flight Center Video and images courtesy of NASA/JPL-Caltech]
Star Burst [credit: NASA's Goddard Space Flight Center Video courtesy of ESA/Hubble/L. Calcada]

Stars are in a constant struggle between gravity, trying to collapse them, and their internal heat trying to inflate them. For most of a star's life, these two forces are at an uneasy truce.

For a star like the sun, the balance tips in its twilight years. For a brief, glorious moment, it expands, but then blows away its outer layers, leaving behind the gravitationally, compressed core. It goes out with a whimper. Well, a whimper from a two octillion ton, barely constrained, nuclear powered fireball.

But, more massive stars aren't quite as resigned to their fate. When they go out, they go out with a Bang! A very, very, big bang.

In the core of a star, pressure and temperature are high enough that atomic nuclei can get squeezed together and fuse. This releases energy and creates heavier elements. Hydrogen fusion makes helium. Helium fusion makes carbon. And each heavier element, in general, takes higher temperatures and higher pressures to fuse.

Lower mass stars, like the sun, stop at carbon. Once that builds up in the core, the stars fate is sealed. But, if the star has more than about eight times the sun's mass, it can create temperatures in its core in excess of 500,000,000 degrees Celsius, and then carbon will fuse.

There are actually a lot of steps in this process, but in the end you get carbon, fusing into neon, magnesium and some sodium. What happens next hearkens back to what we found goes on in the sun's core as it ages. Fuse an element. Create a heavier one. Then that heavier one builds up until the core contracts and heats up enough to start fusing it.

So carbon fusion makes neon, magnesium, and sodium, and those accumulate. The core heats up, and when it reaches about a billion degrees, neon will fuse. Neon fusion creates more magnesium, as well as some oxygen. These build up in the core, it shrinks, heats up to about 1.5 billion degrees, and then oxygen fuses, creating silicon. Then that builds up until the temperature hits about 2 to 3 billion degrees, where upon, silicon can fuse.

Among a pile of other elements, silicon fusion creates iron, and that's trouble. Big, big trouble. Once silicon fusion starts, the star is a ticking time-bomb.

But, before we light that fuse, let's take a step back. What's happening to the outer layers of the star? What do we see if we're outside, looking back at it? Because the star was born massive, it spent its hydrogen-fusing days as a blue, main sequence star. Stars like this are extremely luminous, and can be seen for tremendous distances.

Like the sun, though, a massive star changes when hydrogen fusion stops. Its core contracts, and then helium fusion begins. It swells up, just as the sun will, but instead of becoming a red giant, it generates so much energy, it becomes a red super giant.

These are incredibly huge stars. Some, over a billion kilometers across. And they are luminous. For example, Betelgeuse in Orion is a red super giant and one of the brightest stars in the sky, despite being over 600 light years away. From that distance, you'd need a descent telescope to see the sun, at all. And that's nothing compared to VY Canis Majoris, the largest known star, which is a staggering 2 billion kilometers across. We even have a special term for it--a hyper giant.

As the core switches back and forth from one fusion reaction to the next, the outer layers respond by contracting and expanding. So a red super giant can shrink and become a blue super giant. Rigel, another star in Orion, is a blue super giant, putting out over 100,000 times as much energy as the sun.

OK, let's go back to the core. It now looks like an onion, with multiple layers. Iron is building up in the centers, surrounded by fusing silicon, outside that is a layer of fusing oxygen, then neon, then carbon, then helium, then finally hydrogen.

You might think massive stars would last longer because they have more fuel than lower mass stars. But the cores of these monsters are far hotter, and fuse elements at far higher rates, running out of fuel more quickly.

A star like the sun can happily fuse hydrogen into helium for over ten billion years. But a star twice as massive as the sun, runs out of hydrogen in just two billion years. A star with eight times the Sun's mass runs out in only a hundred million years or so. And each step in the fusion process happens faster and faster than the one before it.

In an extreme case, like for a star twenty times the mass of the sun, it'll fuse helium for about a million years, carbon for about a thousand, and neon fusion will use up all its fuel in a single year. Oxygen lasts for a few months. Silicon fuses at a ridiculously high rate. The star will go through its entire supply in, get this, a day. Yes! One day. The vast majority of a star's life is spent fusing hydrogen. The rest happens in the metaphorical blink of an eye.

Silicon fuses into a bunch of different elements, including iron. That inert iron builds up in the core, just like all those elements did before. And just like before, the iron core shrinks and heats up. But there's a huge difference here.

In all the previous fusion stages, energy is created. That energy transforms into heat and that helps support the soul-crushing amount of stellar mass above the core. But iron is different. When it fuses it actually sucks up energy instead of creating it. Instead of providing energy for the star, it removes it. This accelerates the shrinking, compressing the core, heating it even more.

Even worse, at these temperatures and pressures, the iron nuclei suck up electrons that are whizzing around, which are also helping support the core. It's a double whammy. Both major means for support for the star are removed in an instant. Silicon fusing into iron is happening so fast, this literally takes a fraction of a second once it gets started.

The core gets its legs kicked out from under it. It doesn't shrink it collapses. The gravity of the core is so mind-bogglingly strong that the outer parts crash down on the inner parts at a significant fraction of the speed of light. This slams down on the central core, collapsing from several hundred kilometers across, down to a couple of dozen kilometers across, in just a few thousandths of a second. The star is doomed, because all hell is about to break loose.

Now, at this point, one of two things can happen. If the star has less than about twenty times the sun's mass, the core collapse stops when it's still twenty or so kilometers wide. It forms what's called a neutron star, which I'll cover in the next episode.

If the star is more massive than this, then the collapse cannot be stopped by any force in the universe. The core collapses all the way down down to a point. The gravity becomes so intense that not even light can escape. A black hole is born.

We'll cover black holes in a future episode as well, but for now, what happens when the core collapses and suddenly stops?

The core of the star, whether it's a neutron star or a black hole, is now extremely small with terrifyingly strong gravity. It pulls on the star's matter above it. HARD! This stuff comes crashing down at fantastic speed, and gets hugely compressed, furiously heating up.

At the same time, two things happen in the core. While this stuff is falling in, a monster shock wave created by the collapse of the core moves outward, and slams into the incoming material. The explosive energy is so insane, it slows down that material substantially. The second event is that the complicated quantum physics brewing in the core, generates vast numbers of subatomic particles called neutrinos. The total energy carried by these little neutrinos is almost beyond reason.

In a fraction of a second, they carry away one hundred times as much energy as the sun will produce over its entire lifetime! That's an incredible amount of energy!

Now, these little beasties are seriously elusive, and hate to interact with normal matter. One single neutrino could pass through trillions kilometers of lead without even noticing. But, so many are created in the core collapse, and material barrelling down on the core so dense, that a huge number of them are absorbed. This vast wave of neutrinos slams into the oncoming material, like a bullet train hitting a slice of warm butter. The material stops its in-fall, reverses course and blasts outward.

The star explodes. It explodes. (Explosion sound)

This is called a supernova, and it is one of the most violent and terrifying events the universe can offer. An entire star tears itself to shreds, and the expanding gas blasts outward at 10% the speed of light. The energy released is so huge, they can be seen literally half way across the universe. They outshine all the stars in the rest of the galaxy combined.

The expanding material, called the supernova remnant, forms fantastic shapes. The most famous is the Crab Nebula, from a star we saw blow up in the year 1054. The tendrils formed as the material expands into the gas and dust that surrounded the progenitor star.

As remnants expand and age, they become more tenuous. Some have bright rims as they push into material in between the stars. Others form complex webs of filaments.

I'm often asked if there are any stars near enough to hurt us when they explode. The quick answer is no. Even though supernovae are super violent, space is big. A supernova would have to be a least 100 light years from us before we start feeling any real effects.

The nearest star that might explode in this way is Spica, in Virgo, and it's well over 100 light years away. I say, might explode, because it's at the lower mass limit for going supernova. It might not explode at all. Betelgeuse will certainly explode some day, but it's too far away to hurt us. We're pretty safe from this particular threat.

I'll note, that after all this, there is another kind of supernova involving white dwarfs, which we'll cover in our episode about binary stars. Happily, we're probably safe from them too. Breathe easy.

As terrifying and dangerous as supernovae are, there's a very important aspect to them that you need to know. Supernovae are capable of great destruction, but they also are critical for our own existence. When the star explodes, the gas gets so hot, and is compressed so violently by the blast, that it undergoes fusion, what astronomers call explosive nucleosynthesis, literally creating heavier elements explosively.

New elements are produced in quantities that dwarf the Earth's mass. Calcium, phosphorous, nickel, more iron. All made in the hellish forage of the supernova heat, and flung outward into the universe. It takes millennia or longer, but this material mixes with the other gas and dust clouds floating in space. Sometimes, these clouds will be actively forming stars. Sometimes the collapse of the cloud to form stars may actually be triggered by the supernova slamming into it. Either way, the heavy elements created in the supernova will become part of the next generation of stars and planets.

Supernovae are how the majority of heavy elements in the universe are created and scattered. The calcium in your bones, the iron in your blood, the phosphorus in your DNA. All created in the heart of the titanic death of a star. That star blew up more than five billion years ago, but parts of it go on--in you.

Today you learned that massive stars fuse heavier elements in their cores than lower mass stars. This leads to the creation of heavier elements up to iron. Iron robs critical energy from the core, causing it to collapse. The shock wave, together with the huge storm of neutrinos, blast through the stars outer layers causing it to explode.

The resulting supernova creates even more heavy elements, scattering them through space. Also, happily, we're in no danger from a supernovae.

Crash Course Astronomy is produced in association with PBS Digital Studios. They have a YouTube channel with great videos. Go, just go over there. Check their videos out, they're fantastic. This episode was written by me, Phil Plait. The script was edited by Blake de Pastino, and our consultant is Dr. Michelle Thaller. It was directed by Nicholas Jenkins, edited by Nicole Sweeney, the sound designer is Michael Aranda, and the graphics team, as always, is Thought Café.

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​I am currently a Lyman Spitzer Fellow at Princeton University. I was a Burke Fellow at the California Institute of Technology (2018-2021).

I received my PhD degree in Astronomy at the University of Texas at Austin in 2018, under the supervision of Prof. Pawan Kumar.

I received my bachelor's degree in physics from Yuanpei College, Peking University (PKU) in 2013. The Yuanpei Program, named after PKU&rsquos most revered president, Mr. Cai Yuanpei, allows students to freely choose their field of study. I got interested in astrophysics from a coincidental discussion on cosmic rays with Prof. Zhuo Li, who later became my undergrad advisor.


My research goal is to understand underlying physics behind various high-energy transient phenomena, including fast radio bursts (FRBs), tidal disruption events (TDEs), and compact object mergers . I have also worked on gamma-ray bursts, formation history of binary black holes, accretion disks, pre-supernova mass loss, and hyper-velocity stars. Based on my expertise in plasma physics, special/general relativity, hydrodynamics, radiative transfer, and stellar evolution, I have developed analytical and numerical methods to recognize the mechanisms responsible for the diverse observational behaviors of these transient sources.

I enjoy interactions with other researchers on various topics. Many of my projects were

done together with my fellow postdocs as well as students. Below I describe a selection of my works. Interesting predictions from my research and observational tests are summarized in a table at the end.


Emission Mechanism: In Lu, Kumar & Zhang (2020), we propose that FRBs are generated by Alfven waves propagating in the neutron star (NS) magnetosphere to large distances where they become charge starved, and charge clumps are accelerated by an electric field and coherently generate curvature emission in the radio band.

Figure to the Right : Alfven waves launched from the magnetic foot points propagate along the field lines to distances much larger than the NS radius where the charge density is too low to sustain the current associated with the wave. As a result of charge starvation, a strong electric field component parallel to the background B-field develops, and charge clumps are accelerated to high Lorentz factors and coherently produce curvature emission in the radio band. The FRB emission is narrowly beamed into the region spanned by the orange arrow. The Alfven waves launched far from the poles are trapped by field lines that do not extend to large distances, and a pair fireball is formed which emits hard X-rays visible from a large fraction of the sky. This model provides a unified picture for faint bursts like FRB 200428 as well as the bright events seen at cosmological distances.

mv2.jpg/v1/fill/w_175,h_239,al_c,q_80,usm_0.66_1.00_0.01,blur_2/Alfven_waves_v6.jpg" />

Figure to the Right : Sudden magnetic energy release excite horizontal shear mode oscillations in the crust. The shear waves propagate along the crust, and the horizontal shear oscillation is well coupled to the magnetospheric B-field lines which are anchored on the NS surface. Thus, a large fraction of the shear-wave energy to be transmitted into the magnetosphere as Alfven waves.

mv2.jpg/v1/fill/w_110,h_147,al_c,q_80,usm_0.66_1.00_0.01,blur_2/seismic_waves_v2.jpg" />


​Main-sequence stars are shredded by tidal forces when they get sufficiently close to a supermassive black hole (BH) . After disruption, the star is stretched into a long thin stream (of aspect ratio

1000) in highly eccentric orbits (1-e

0.01) which undergo general relativistic precession . Such precession causes the stream to self-intersect and the shocked gas expanding from the intersection point will eventually form an accretion disk, which powers multi-wavelength emission. A few dozen of these tidal disruption event (TDE) candidates have been found in recent surveys designed to find variable sources in the optical/UV and soft X-rays.

Global numerical simulation of the hydrodynamic

evolution of the thin fallback stream is prohibitively

expensive. In Lu & Bonnerot (2020), we made a key

simplification of the problem by first calculating the

location where the stream self-intersects according to

general relativistic geodesic motion and then performing

hydrodynamic simulations of the stream collision

process in a local corotating frame near the intersection

point. The two stages are joint together by a Lorentz

transformation. We found that the self-crossing shock redistributes energy and angular momentum of the gas in the fall-back stream. For sufficiently deeply penetrating orbits (Rp >

15Rg), the shocks at the intersection are able to unbind a large fraction (up to 50%) of the fallback gas. We call the unbound gas the &ldquocollision-induced outflow&rdquo or CIO. We found that the CIO covers a large fraction of the sky viewed from the BH and is able to reprocess the hard (EUV/soft X-ray) photons from the disk into the optical band. This provides an explanation of the bright optical emission seen in many TDEs. Viewing angle effects then cause the X-ray luminosity to vary by orders of magnitude from one event to another. The CIO carries a large kinetic energy of 1e50-1e52 erg and can generate radio emission at the level of ASASSN-14li when it drives a shock into the surrounding medium on parsec scales.

mv2.png/v1/fill/w_196,h_151,al_c,usm_0.66_1.00_0.01,blur_2/edgeon_disk.png" />


The LIGO-Virgo Collaboration recently reported a puzzling event, GW190814 , with component masses of 23 and 2.6 Msun. In Lu, Beniamini & Bonnerot (2021), we propose a 2nd-generation merger scenario where the secondary of GW190814 was from a previous binary neutron star (bNS) coalescence and the remnant was able to merge again with the 23 Msun BH tertiary. This occurs when the remnant (most likely a low-mass BH) receives a kick of about 100 km/s in the direction of the "loss cone" shaped like a flying saucer, as shown in the figure below. This model was motivated by the relatively small rate (1 to 23 per Gpc^3 per yr) inferred from GW190814 and the secondary mass being close to the total masses of known bNS systems. We show that about 1% of the bNS coalescence occurring in triple systems should give rise to 2nd-generation mergers, provided that a massive BH tertiary is located at a separation less than a few AU. Since the total bNS coalescence rate is of the order 10^3 per Gpc^3 per yr, this model requires that at least 10% bNS mergers occur in triple systems. Since the typical delay time for the 2nd-generation merger is about a Hubble time, these bNS mergers in triples occurred in the distant past when the Universe was less metal-enriched. Low-metallicity (< 0.1 solar) is also favored for the formation of the 23 Msun BH.

This model has a number of testable predictions, one of which is that the secondary of GW190814-like events should have dimensionless spin of about 0.7. Our work provides a strong motivation for future studies of triple massive star evolution.

mv2.png/v1/fill/w_180,h_160,al_c,usm_0.66_1.00_0.01,blur_2/schematic_figure_v1.png" />


The classical problem of a relativistic jet interacting with the circum-stellar medium (CSM) requires expensive 2D simulations (for the axisymmetric case). In Lu, Beniamini & McDowell (2020), we present a simplified model by assuming that the shocked CSM and jet material are in an infinitely thin surface, so the original 2D problem is effectively reduced to 1D. From general conservation laws, we derive the equation of motion for each fluid element on this surface, taking into account the deceleration along the surface normal due to newly swept-up mass and lateral expansion due to pressure gradient in the tangential direction. The pressure and energy density of the shocked CSM are given by the jump conditions at the forward shock. The method is implemented with a finite-differencing method, in a new (C++) code Jedi (for &ldquojet dynamics&rdquo). In a few seconds on a single CPU core, the code solves the jet evolution from ultra-relativistic initial conditions to non-relativistic speeds, as well as the synchrotron flux at arbitrary viewing angles and frequencies including self-absorption. It has been demonstrated in a number of test cases that our method provides a good approximation for the hydrodynamics and afterglow emission for a wide variety of jet structures and CSM density profiles.

The following figures show the lightcurves at 10^15 Hz (left panel) and 10^9 Hz (right panel) for different viewing angles (1 to 90 degrees). The solid lines include the contributions from both the forward and the counter jets, and the dashed lines are only for the counter jet (which moves away from the observer). The dotted lines are for the same initial conditions but without including the effect of lateral expansion.

mv2.jpg/v1/fill/w_192,h_133,al_c,q_80,usm_0.66_1.00_0.01,blur_2/LC_PLjet_narrow_nu15.jpg" />

mv2.jpg/v1/fill/w_192,h_133,al_c,q_80,usm_0.66_1.00_0.01,blur_2/LC_PLjet_narrow_nu9.jpg" />

The following figure shows the hydrodynamic evolution of a power-law structured jet, with a jet core size , and energy per solid angle and four-speed beyond the jet core. The jet core has Lorentz factor 300, isotropic energy 10^52 erg, and half opening angle 0.03 rad (1.7 degree). The CSM has uniform density of 0.01 cm^-3. The jet is axisymmetric with its axis is along the x direction. The length unit is the deceleration radius. The colored lines shows the location of the jet surface at different times which are in units of the deceleration time. The black dots show the numerical grid points and the black lines are their trajectories (lateral expansion is clearly seen).

Watch the video: Mortiis - Stjernefødt (November 2022).