The Point of My Research

June 2, 2014

I talked with my prof and got further information on what the point of the project is. It has to do with the Kepler space telescope. If you haven’t heard, two of its four wheels, which are used to point the telescope to a location, are broken, and so the telescope can’t maintain its sight to a position in the sky. Not only is there the fact that it is rotating around the Earth, the light from the sun has momentum. The light will push the telescope, and the irregularity of the telescope’s shape causes it to torque. The only way for the telescope to not be perturbed is to lie perpendicular to the sun. Unfortunately, that means that it can only observe in the plane of ecliptic, and it can’t maintain the same field of view throughout the year as the telescope has to maintain perpendicularity to the sun as the Earth orbits the sun. Nevertheless, useful science can be done. The telescope will observe certain fields of view, and when time is up, it will rotate again to another field of view that will maintain perpendicularity.

The point where my research comes in has to do with the way the above procedure means that the antenna is not facing the Earth properly. That means in order for them to continually observe an area in space, they will have to keep the information in the hard drive, and then send it back to Earth once the observation period is over. That means they have a limited amount of data they can store, and so the mission will have to be picky in which data they store. Looking for brown dwarfs to observe is supposed to help out Kepler in keeping . There are areas where not much brown dwarfs discovered, so what I am doing is helping that process out.

For now, I am just installing the astropy library for Python language. l will be looking at some picture of brown dwarfs, download them, and hopefully astropy can take those pictures and present them to me.

Source

http://keplerscience.arc.nasa.gov/K2/MissionConcept.shtml


Introduction to my Research: Brown Dwarfs

June 2, 2014

So, I got accepted into a summer research program. They are going to pay me and everything, yay! Which is why I thought I should blog about my research.

What I am doing this summer is basically sift through infrared data and looking for object called brown dwarfs and classifying them. Brown dwarfs are in a way objects that represent the transitions between planets and stars. They are much more massive than planets, enough to have fused deuterium (hydrogen, but with a neutron) for a short while, but they are not massive enough to fuse regular hydrogen. The mass may range from 13 to 80 Jupiters. After the short lived deuterium fusion phase, they just start cooling down. They tend to emit most of the light in the near infrared zone. Size wise, they are not too different from Jupiter because the interior pressure is governed by electron degeneracy. Basically, the pressure of electrons due to them not being able to occupy the same energy states is what holds the object from further collapse. In a pressure dominated by degenerate matter, adding more mass doesn’t cause an object to grow much.

How does one empirically distinguish a brown dwarf from a low mass star? There is a simple test called the Lithium test. If one can detect lithium, it is probably a brown dwarf. Stars are hot enough to be able to fuse lithium, unlike brown dwarfs, and lithium fuses at a similar temperature to hydrogen. That said, the highest mass brown dwarfs can burn lithium, so at the high end range of brown dwarf mass, they are indistinguishable from stars. Well, there is another way, but it is harder to do. Basically, measure the temperature and mass of a brown dwarf binary. The theory is that an object of certain mass will have a different temperature curve as it ages than one of a different mass. If an object is massive enough to be a star, the temperature will stabilize due to sustained fusion, if not it keeps cooling down.

Before we go on, I would like to address how we can know what compounds such a distant object have. We look at the spectrum of light from the object, and see which wavelengths are missing. Certain compounds absorbs light at certain specific frequencies because of the way the electrons are configurated energy wise. Electrons can only occupy certain energies, and so they will absorb only light of certain energies.  So, when you look at the spectrum of light coming off the planet, there will be chunks of light that will be missing corresponding to the energy absorbed. Imagine that the rainbow has various thin strips on it missing, that is what it is like.

Brown dwarfs come in two spectral type, the L type and the T type, with L being the hotter, more luminous type. The temperature itself is correlated with luminosity by the fourth power, so measuring luminosity gives you the temperature. The spectral types are related to what compounds one detects in the atmosphere. The L types have the temperature range of 1300 K to 2500 K. The hottest L type show vanadium oxide and titanium oxide absorption signatures in the spectra, and as the brown dwarf gets cooler, this transitions to a spectra with absorption due to metal hydride (FeH, MgH, CaH, etc) and Alkali metal compounds (NaI, KI, etc), while the metal oxide absorption disappears. The T type are objects below 1500 K, and the spectra contains absorptions from methane, water, ammonia, and CO. Does this mean that the transition of  spectra represents another good way to gauge the temperature of the object? Yes for early L and late T. Not so much for the transition between late L to early T. In that section, the temperature doesn’t change very much while the spectra changes. A point of note is that the temperature/spectra correlation works much better with optical than infrared.

There is a reasonable explanation for the transitions of spectra a brown dwarf undergoes. As the brown dwarf cools, the metal oxides condense and fall off deeper into the atmosphere. This uncovers the spectra from the alkali metals and hydride metals. As the temperature goes lower to the T type level, clouds become an important component. This explains the rapid change in spectra with the slower change in temperature as this transition of dusty atmosphere occurs around a short range around 1400 K.  At temperatures lower than 1400 K, the dust sinks and the metal hydrides condense while conditions are right for the reaction of CO+H2=H2O+CH4 occurs, meaning carbon monoxide with hydrogen reacts to for water and methane. This explains the methane absorption that dominates in the T brown dwarfs.

Finally, I would like to point out the model pointed out above for the brown dwarfs differs with metallicity. Metals in astronomy are all elements with higher atomic number than helium. Brown dwarfs are allowed to be more massive and hotter with less metal.

This is a basic summary of what we know about brown dwarfs. If you want to know more about them, you can of course go ahead and read what I linked below. There has also been some advances, like the discovery of below freezing brown dwarfs. And there are mysteries to be solved, like the fact that there are three scenarios for condensations and dusts that plays a key role in the late L to early T spectrum.

I have done all this preliminary reading. Hopefully I know what I will be doing. Granted, there will be some fumbling around as this is my first legit science project ever.

Source and reading materials

http://www.annualreviews.org/doi/abs/10.1146/annurev.astro.42.053102.134017?journalCode=astro

http://web.archive.org/web/20060928065124/http://www.carnegieinstitution.org/News4-3,2001.html (brown dwarf)

https://en.wikipedia.org/wiki/Brown_dwarf


A Little Something on Triton

May 28, 2014

Here is a video on Neptune’s largest moon Triton, with a cute Triton thumbnail. It is a great summary of the basic facts regarding this object:


Star Endings: Pair Instability and Photodisintegration

May 27, 2014

Population III Stars

For the third part in the series of posts on star deaths, we look at deaths at the most extreme ends. They happen to enormously massive stars that were only common during the beginning of the universe, called the population III stars. Population III stars are a class of hypothetical first generation, never observed stars, that are believed to be over a hundred times more massive than the sun, and have none or almost no metal ( in astronomy any element of higher atomic number than helium).  Now, why they are called population III instead of I, don’t ask me, but turns out it is all reversed. Population II is the metal poor stars, and population I is metal rich stars like the sun.

While stars of 100+ solar mass exists in today’s universe (as seen here), they are extremely rare. In terms of probability, there is the fact that this kind of massive stars are extremely short lived compared to other stars, less than 10 million years compared to billions of years like the sun. In terms of the time scale of the universe, that is a blink of an eye, so more likely than not, you will miss it. Physically, huge stars form more easily in metal poor condition. The presence of metals allow for further cooling of gas to takes place, which inhibits the formation of huge stars. The temperature is important because the hotter the gas, the higher the gas pressure is, which counteracts the force of gravity. So, cooler gas contracts further, which gets fragmented in the process, creating smaller stars. In that way, metallicity is once again shown to be a powerful factor in determining the life and times of a star.

So, considering the hypothetical/theoretical nature of these objects and events, should we take all of this with a grain of salt? Well, yes and no. We do believe the theories are correct because they have worked in other situations. At the same time, that doesn’t mean we know all the details, and those details do matter when formulating accurate theories. Furthermore, there are the issues of rotation. The way I think of it is, the general picture is likely to be right, but if new observations come that contradict certain aspects of the models, then of course, I change my mind. That said, these are issues that are already being probed, with the search of population III stars being a high priority, and hey look, pair instability supernovas are already looking very likely.

Pair Instability End

Pair instability happens to stars beyond 140 solar mass. The energy in the core is such that the photons in there create electron-positron pairs. This happens because other forms of energy can be transformed into matter, and due to conservation principles, of charge (+1 for positive charge, -1 for negative charge) and particle number(+1 for matter, -1 for antimatter). Enough energy is taken away in the process that gravity dominates and the core starts contracting. Now, pair instability does occur in lower mass stars, around 100 to 140 solar masses, but it isn’t  enough to cause a runaway nuclear explosion. Instead, it will increase nuclear reaction until gravity and pressure balances out. This pulsation goes on until a star loses enough mass so pair instability doesn’t happen. Otherwise, the collapse of the core causes an uncontrollable reaction of oxygen and silicon to begin. While turning a huge amount of mass into Nickel 56, the core bounces back from collapse. What ends up happening is an extremely energetic explosion that leaves no remnant of the star behind. The star has pretty much been completely obliterated. Well, I guess you count count the gas and dust left by the star as remnant if you want…

Photodisintegration End

At the 250 solar mass point, a star dies by photodisintegration instability. At the energy generated by this star, a significant portion of the photons gets used up splitting atoms apart. The core collapses without the energy needed to hold up the star from its own gravity, and a black hole forms. This is pretty much core collapse, as in previous post, but with a different reason for the instability to happen, so some of the detail from the previous post about degeneracy and black holes applies here. I am not exactly sure at which part of the chain of nuclear reactions this happens at, though.

I wish I could say that there have been this kind of supernova observed. As far as I can see, I haven’t found any article regarding any observation of this type of supernova. So, for now you can put this entirely in the hypothetical area in your mind.

Conclusion

With this, I conclude the three series of posts on how stars die. Now you know the general process of how stars die, with some of the gory details displayed. If they felt dense, I feel for you. Even I learned a lot on the nuances of these processes, and had one hell of a time researching a lot of these facts. Even so, if these posts have informed you and made you interested in astronomy, well then I am happy. If it made you want to vomit, I am okay with that too, just tell me what went wrong!

Sources and Reading Materials

http://www.universetoday.com/24776/what-were-the-first-stars/

Click to access Bromm02.pdf

http://scitation.aip.org/content/aip/magazine/physicstoday/article/64/4/10.1063/1.3580493

http://www.solstation.com/x-objects/first.htm

Click to access 0107037v2.pdf

Click to access 0905.0929v1.pdf

http://www.skyandtelescope.com/astronomy-news/a-super-duper-supernova/

http://news.nationalgeographic.com/news/2009/12/091202-biggest-star-explosion-supernova/

Click to access 52134.web.pdf

Click to access 0212469v1.pdf


The Power of Scientific Modeling

May 10, 2014

Scientific modeling is a powerful tool. Using the laws of physics, and computers if you want things to be much more convenient, you can predict how nature will behave and how it has behaved in the past. Recently, astronomers modeled the universe starting from 12 million years after the Big Bang, and let it run to present day, 13.7 billion years later. The result is what I would call beautiful. A great match between observation and theory. Here is a video by Nature journal explaining this:

As explained in the video, the simulated properties of the universe matches a lot with the properties of a real life universe, so we know that the laws of physics we have developed is in the ball park area of correctness. It is also explained that it is not perfect, and that is because even though we got a lot of it right, our knowledge of the universe is not perfect. That doesn’t mean science is wrong, it means it is incomplete, and we have to do more detective work in order to work out the rules of nature.

Here is another great match between data and models, this time between real life yearly average temperature and two models crunched by computers using the laws of physics. One of the models is temperature with human forcing of CO2, and the other one only includes natural factors. As you can see, real world data matches the one with human forcing, and it also “predicts” past temperatures very closely (shout out to badatronomy’s great post on climate change):

Another point of note is, all scientific models and measurements have uncertainties in them, but the data itself remains most of the time within the boundaries of the errors, so it is a good fit.

One of my favorites is the modeling of the ENSO without taking account of it. Meaning, you model the Earth with the ocean and atmosphere, plug in the laws of physics and various conditions, and ENSO will naturally occur in the simulation even though we don’t the exact mechanism for it. That is the predictive power of science.


Planet of the Day: Kepler 186f

April 18, 2014

Great news, they found a 1.1 Earth mass planet orbiting in the habitable zone of a red dwarf star. Now, it isn’t the first Earth sized planet, but this one is in the habitable zone. There are other Earth sized planets going around the star too, four of them. They are all closer to the star, and not in the habitable zone. That we have found all those planets around the star is pretty great, though. Here is a great graphic of the planets and a great visual of how the transit method of planet searching works from io9:

 

Notice how the system is very compact, and how far away the fifth planet, 186f is compared to the other 4. Another fact of note is that the fifth planet orbits around 0.3-0.4 AU away from the star, which is similar to where Mercury is, or around one third the distance of the Earth from the sun. While that is still a huge distance, in terms of distances in our solar system, the planets are really close together.

Don’t assume, though, that it may be anything like the Earth. We don’t know its mass, so we don’t know the density, which means we don’t know what it is made of. We don’t know if it has surface waters or thick atmosphere or life. We don’t know anything except its size and period of the orbit, and size of the orbit. It is just a candidate planet and a neat discover. For more information, just go and read the links.


Star Endings: Core Collapse End

April 9, 2014

Neutron Degeneracy End

Last post, I talked about how stars less than 10 solar masses ended as an electron degenerate objects called white dwarfs (with a caveat I will talk about later). But what happens when stars go over that mass? Stars above that mass creates a core that is above 1.44 solar mass. They can do this because the core temperature becomes high enough to fuse neon and oxygen into more massive elements.  There is a nice chart here to the processes in a 25 mass star. This is not as simple of a process as before. Elements like neon can’t just fuse directly. What happens instead is photodisintegration. High energy gamma ray hits an atom and spits out a helium nuclei and that is used to fuse with a larger element. So neon goes down to oxygen with photodisintegration, oxygen combines with oxygen to form silicon, and sulfur. And then the helium nuclei formed by photodisintegration combines with them until it goes to nickel 56 (28 proton + 28 neutron) and  iron 56 (26 proton + 30 neutron). As it does so, the cliched onion layer is formed in the core (note, the summary above is extremely simplified, as shell burning and all sorts of other fusions occur too):

(source: wikipedia)

At this point, a big problem ensues. Fusing iron and nickel 56 absorbs energy, instead of emitting it. Think about it this way. Let’s say photodisintegration happens on iron 56, which absorbs gamma ray and releases a helium nuclei, and the helium nuclei resulting from it is used to smash into an iron 56 and turn it to nickel 60. The gamma ray absorbed for the photodisintegration is greater than the gamma ray released after the fusion. This means that the energy needed to keep the core balanced against gravity is being taken away. Even worse, at these later stages, processes called electron capture occurs. This happens when a proton captures an electron and turns into a neutron. This takes away the electrons needed to maintain degeneracy pressure.  Those, combined with the loss of energy due to the domination of nuclear decays in which a lot of the energy is turned to neutrinos (ghost like particles, they can pass through matter unaffected and it is the product of nuclear decays and reactions), the core is teetering at the edge of collapse. Now the question is, how massive must the core be to overcome electron degeneracy?

For electron degenerate star cores, solar mass 1.4 is a special number. When there is no thermal pressure to counter act gravity, and the core is only being supported by electron degeneracy pressure, it is the mass in which the star collapses. This number is called the Chandrasekhar limit. Yet, the Pauli exclusion principle must hold. Two particles can’t be in the same quantum state (like space, energy, angular momentum, etc), and further collapsing the star would allow that to happen to electrons. So what nature does instead is electron capture, the electron goes on to combine with all the protons to form neutrons. Nature has avoided putting two particles in the same quantum state, and the core is now supported with neutron degeneracy pressure. This happens because two neutrons can’t be in the same quantum state, filling up all the lower energy levels, and this allows for a stronger opposing pressure that prevents further collapse.

What is left is an object composed of mostly neutrons, called the neutron star for obvious reasons. It is in an exotic, extremely dense state of matter, with all the 1.4 solar mass compressed into a ball the size of a city. Its gravitational force is such that if a 10 gram object were released a kilometer away, it would make an explosive impact of 10 tons of TNT (assuming I did my calculations right). This density is possible because an atom has a vast amount of empty space occupied by the electrons, unintuitively so. With the electron gone, all the neutrons can move a lot closer together, greatly reducing in size.

An important event that happens during core collapse is the supernova. While the collapse and electron capture is happening, the core heats up tremendously, and photodisintegration shreds the atoms in the core into helium nuclei. All three processes happen at the same time. Eventually all the matter coalesce together as if it were one giant atom of neutron. Meanwhile, during electron capture, a huge number of neutrinos are formed. Normally, they all pass through matter like ghosts, but there are so many of them, and due to the extreme conditions in the star, they still manage impart a tremendous amount of energy on the outer envelope. This causes the outer layer to explode, easily outshining an entire galaxy. This explosion is what you know as the supernova. During this explosion, the r-process causes the fusion of elements heavier than iron. The supernova, therefore, is not only a destructive process, but a creative one too, progenitors to all sorts of matter, without which we would only have mostly hydrogen and helium.

Supernovas are also very pretty. Here is a picture of a remnant called the Crab Nebula, which is glowing due to the high energy radiation from the neutron star exciting the electrons in the gas:

Eventually, that will fade as the gas is spread out, and all that will remain is the neutron star in the center, which is in a long process of cooling down.

The picture I painted above is very general. A star around 8 to 10 solar mass, for example, can undergo supernova even though the core is oxygen-neon-magnesium due to electron capture, and this happens along with an explosive oxygen flash, which while not the cause of the supernova (again, it is due to neutrinos), it is an additional important detail. It is not just the mass, but something called metallicity that affects the process. Before that, it is first important to talk about what happens when even neutron degeneracy can’t hold the gravitational force.

Black Hole End

If the core exceeds 2-3 solar mass, even neutron degeneracy can’t hold the gravity of its own mass. It is the Tolman-Oppenheimer-
Volkoff limit. As you can see, there is a huge uncertainty as to what that limit is. That is due to the uncertainties regarding the relationships between states in a neutron star. States are properties like volume, temperature, energy, pressure, etc that describes what is happening to the particles of an object on average. Whatever the limit is, once it is reached, neutron degeneracy pressure can’t hold the gravitational force of the object, and so the star remnant keeps collapsing. Hypothetically, nature might have yet another line of defense against total collapse by forming it into a quark star, made of even more fundamental subatomic particles. They haven’t found one yet, either because it doesn’t exist or the margin of the conditions needed to make it happen is very small, so I will just skip on this one and say there is no particle degeneracy left to hold up the star. The star starts collapsing even further. But wait, it can’t! The Pauli exclusion principle is supreme! Well, nature would rather cover up that awkward fact than to ever allow the principle to be violated. All the matter collapses into a black hole so we never get to see what really goes on! So, is the Pauli exclusion principle actually violated? Or is something else going on? Who knows. Personally, I think nature is a dirty cheater. The laws of physics is getting too extreme? Nope, nope, sorry, you don’t get to see it!

So, after the collapse and explosion, what remains is an object with a gravitational pull so strong that not even light can escape from it. The edge of the black hole is a surface of total blackness (well, it’s not really total blackness due to quantum mechanics, but I am not talking about that) called the event horizon. We don’t know anything inside it because nothing goes faster than the speed of light. If light at the event horizon were going away from the black hole, it would just be hanging there since that is the point in which the escape velocity is exactly the speed of light. Their existence has been confirmed indirectly by detecting objects and swirly gas moving as if an invisible object the mass of a star were pulling on them. Overall, they are very mysterious objects, the most extreme of the stellar corpses.

Now, this is where the concept of metallicity becomes extremely important. You might think metallicity means it is the amount of metals in the ordinary sense. But in astronomy, metal means any element higher than helium. Yes, this sounds ridiculous, but scientists are always in the business of taking words and make the meanings different for their own fields. Anyways, for massive stars, metallicity greatly affects how stars die. The lower the metallicity, the easier it is to have a black hole. That is due to metallicity affecting how much mass stars lose in the process, and the more mass loss there is, the less massive the star ends up as, which means the end product is less massive. There is also a process where the material expelled during a supernova falls back on top of a neutron star, turning it into a black hole. This type of process does not produce bright supernovas.

Wikipedia created a great table summarizing how metallicity and mass affects how a massive star end its life. It is basically a summary of this physics paper in table form. I want you to know though, that this is a year 2002 information, and some of the specifics may have changed. It does show the bigger picture of how things work, though, and that is what I believe is more important for this kind of article.

At the end there is an extreme where stars achieve mass that are in a way legendary, for they are extremely uncommon, and may have existed only for a short time in the early universe. If a star has low metallicity, it may go above 140 solar mass, and end in a process called pair instability, and at even higher mass, by photodisintegration. How do they work? That will be the subject of another post.

Sources and Further Reading Materials

Click to access nph-iarticle_query

Click to access 1102.5735v3.pdf

Click to access 0212469v1.pdf

http://www.uni.edu/morgans/astro/course/Notes/section2/new9.html

Click to access lecture12.11.pdf

http://www.opencourse.info/astronomy/introduction/19.stars_death_high-mass/

Click to access nph-iarticle_query

http://www.nasa.gov/audience/forstudents/k-4/stories/what-is-a-black-hole-k4.html#.U0TYCvldWl4

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/blkhol.html

http://io9.com/5710012/quark-stars-and-strange-matter-a-guide-to-the-weirdest-stars-in-the-universe


This Is Why You Should Never Read Science From Regular News Media

March 18, 2014

Because they screw it up and spew misinformed drivel like Salon does. If they would have done a modicum of research, they would have found out the discovery is the sign of a gravitational wave embedded in the cosmic microwave background. This is more about the evidence for Alan Gurth, Andrei Linde, etc’s inflationary model, which covers up some of the unsolved gaping hole left by the big bang theory. Yes, the article does talk about the fact that it confirms inflation, but they always mix the facts up with some misinformation. As of yet, there hasn’t been any direct observation of gravitational waves. Not that it matters much because gravitational waves have been confirmed by indirect observations before even this one.  For example, by observing two neutron stars orbiting close to each other, they have found behavior that matches those predicted by the existence of gravitational wave. Seriously, research! Or am I asking too much for a reporter these days?


Rare Snapshot of Rapidly Evolving Star

March 12, 2014

This is filler for my next post in star death, but thought I should show you something relevant to stellar evolution. This one is a yellow hypergiant, in fact, the largest yellow hypergiant discovered. Yellow hypergiants are one stage of a 25 plus solar mass star, and they are very rare. One of the great things about this one is that as decades went by, the swelling and cooling of the star was noticeable. That rarely happens over human lifetimes, as changes in stars happen over millions or billions of years. Another fascinating thing is that the star swelled so large that it is pretty much touching its smaller binary counterpart. I don’t know how exactly this will play out, but as the article says, it will probably affect how the star evolves in the future.


Star Endings: Electron Degeneracy End

February 19, 2014

Introduction

Welcome to my next series of posts, which is about all the way stars die. You see, depending on the mass of the star, they can have very different “endings”, sort to speak. So don’t believe anyone who tells you that the sun is going to explode or something like that. It won’t. Instead, something else is going to happen. There are a lot of caveats as to how this works, and as you will see in another post, mass is not the only factor in how a star ends up. Also, each endings have sub endings, the universe is quiet complicated after all. What I will not be going into is the details of the evolution of the stars. Just their deaths. The posts would be really long and meandering with those details included, so I will be very general instead. Believe me, there are a lot of ways stars evolve and the intricacies are enormous. Now that you know what you will be getting, let’s begin.

The Basic Working of a Star

In order to understand how all stars die, one has to understand the inner workings of a star. All stars are fueled by the fusion of atoms in its interior. During their main sequence phase (the relatively stable, long lived part of a star’s life), hydrogens are fused into helium. When it does so, a little bit of the mass of the atoms are converted into light, E=mc^2=pc, Einstein’s famous equation (Wait, pc? What the hell is that, you might be wondering. That may be a topic for another discussion, but the energy due to mass m turns into the energy due to momentum p of light). Incredibly, the sun loses millions of tons every second to this process. And in fact, the mass of the four protons used to produce helium are a little bit more than the mass of helium.

During that main sequence period, the thermal and radiation pressure from a star’s interior counterbalances the gravitational force trying to squeeze the star. So long as that hydrogen in the sun’s core keeps fusing, the truce is maintained, and the star keeps chugging along without agitation. But as we all know, resources don’t last forever. What happens when the hydrogen, or at least the really hot hydrogen in the center that are able to fuse runs out, and all that remains are useless helium and hydrogen? That is when all hell breaks loose, and the differing mass of the stars will send them into wildly different paths.

Electron Degeneracy Pressure

One fundamental concept I want to get to before going into what will be the remnants of the dead star is the concept of degenerate matter. Aside from being a really cool sounding word, it is the stuff stars will eventually be made of. They are highly compressed form of matter, squeezed to such an extent that quantum mechanical properties take over classical mechanics. In degenerate matter, pressure does not depend on temperature. What happens instead is that if you dump mass on it, instead of getting bigger, pressure increases and the whole thing becomes smaller and denser. They are strange kinds of matter indeed, and neither solid, liquid, gas, nor plasma quiet describes what this is. It is another state of matter.

What causes this phase of matter at extreme high pressure is the fact you can’t just keep squeezing things infinitely without running into a snag, which is the rules of quantum mechanics. In the case of electron degeneracy, it is the fact that electrons have to keep filling lower and lower energy levels. According to the Pauli Exclusion Principle, no electrons shall occupy the same quantum states. So for example, two electrons can’t be in the same energy unless their spin number is different (in quantum mechanics, spins are rotations that look like it exists, but really isn’t there, yeah, it is kind of confusing). Since there are only two spin numbers, positive and negative, if you try to squeeze one more electron into the energy level, the particles will resist the other electron from moving in. That creates the pressure needed to resist the compression.

Now, considering the extreme gravity of a ball of super high density stuff, the pressure needed to hold the degenerate matter must be enormous. The counteracting electron pressure is caused by the momentum of the electrons heavily affected by the uncertainty principle, which is the prime characteristic of quantum physics. The uncertainty principle says that you can’t measure position accurately without creating uncertainty with momentum and vice versa. So, since objects in degenerate matter are very tightly packed, the position becomes very certain, but the momentum becomes extremely uncertain. Which means that there is a probability that collectively, momentum will be high enough to resist the strong gravitational force that threatens to collapse the matter. Now you can see why increasing temperature does nothing. The force involved is too great for temperature to increase electron pressure in degenerate matter. Also, at that scale, the uncertainty principle is the dominant factor at play.

As you will see in a later post, even as electron degeneracy pressure fails, there will be a fail safe that particles will rely on to make sure the rules of quantum mechanics is respected. When even that fails, well, they commit the most dramatic suicide in the universe. At the point before 10 solar mass stars, though, electron degeneracy will prevail, and what remains after everything is over are hot corpses called white dwarves. These are extremely dense, exotic objects in which an object the size of planet Earth can have the mass of the sun, and it is what will remain after the end of these low massed stars.

Convection End

For stars below 0.5 solar mass, the action in the middle layer of the star, between the surface and the core, becomes extremely important. Take a look at the following diagram of the interior:

(source of image)

The circular arrows represent convective zones while the squiggly arrows represent the radiative zone. They represent the different ways in which energy moves outside. In radiative zone, light bounces around from atom to atom, taking on average over 170 thousand years to leave it. In the convection zone, the plasma moves by convection towards the top, being less dense due to the higher temperature at the bottom, and when it reaches the top, it releases the light energy. Now, notice how red dwarves, to the left of the diagram, consists almost entirely of convective zones? This means that even as the hydrogen is used up in its core, the convection ensures that fresh materials from the top reaches down to the bottom. Combined with having so much materials to work it, and the much slower pace of reaction compared to the more massive stars, red dwarves will get to live for trillions of years to come. Which means that the end of their lives has never been observed, and details on how they might die are mostly theoretical. Nevertheless, let’s speculate, shall we?

Red dwarves, after their extraordinarily long lives, are theorized to die quietly. Like all stars, they will grow brighterThe lower massed ones won’t expand into a red giant due to it not being opaque enough. Instead, they will grow brighter and brighter and change colors and probably reach yellow to white. Eventually though, the hydrogen will run out and all that will remain is helium. Unlike all other star deaths, there will be no fireworks accompanying the fuel shortage. Red dwarves aren’t massive and hot enough to fuse helium into carbon, and due to how the convection mixes up the materials, there won’t be any hydrogen shell to fuse around the helium. The gravitational force will overcome the outward pressure and the star will compress into a helium white dwarf. Or at least that is what is believed the future of a red dwarf star is.

Planetary Nebula End

Above 0.5 solar mass, stars will be able to go on further with the nuclear reactions. They will swell many times their size as their luminosity increases significantly while the star ekes out a reaction from the bits of hydrogen around the helium core when the core was compressing. Later the core will ignite its helium and turn it to a carbon/oxygen core. Finally, when the helium runs out, another compression of the core will ignite the helium shell around the core. As shell helium fusion turns on and off due to running out and then being repleted by the fusion of hydrogen above it, a thermal pulse causes a huge chunks of the hydrogen envelope of the star to be blown away. The star will blast away layers after layers of plasma over periods of tens of thousands of years, creating gas envelopes around the core, the materials speeding away. This is how the sun itself will die. The end result is this:

(source of image)

 The core that remains will shine extremely hot with ultraviolet, stripping off the electrons from the gas and  causing the gas to glow. This is the so called “planetary nebula“.  If it is going to go out, might as well die beautifully, right? Over time, the gas dissipates and all that will remain is the carbon/oxygen electron degenerate matter, the most common form of white dwarves. The stars with 8 to 10 solar masses will get the chance to fuse carbon and get an oxygen/neon/magnesium core. You might think that after this, there will be higher masses in which more opportunity to fuse atoms occur. Yes, they do, but in terms of electron degeneracy, this is where it stops.

Fate of the White Dwarves

Even after the fusion stops and all that remains is the white dwarf, the star will keep shining on gloriously for a long time. Degenerate matter is a perfect conductor of heat, and the glowing you see is the heat stored in it. It starts out tens of thousands of degree hot and over time cools down. Eventually, the white dwarf will seize to be visible, and a very long time after that, stop emitting heat. Such an object, the black dwarf, does not exist yet because the universe is not old enough to have it cooled down, but it is the most likely outcome.

Now, the electron degeneracy scenario might work for the stars less than 10 solar masses, but what happens to star around and above that? What happens when the core gets so massive that electron pressure is not enough to hold up the core? Will electrons get to occupy the same quantum state? No, as hinted previously, particles like electrons hate being in the same quantum state and it will do everything it can to avoid that. For these massive stars, the core collapse ending is what awaits them, and interestingly, the explosion of a white dwarf is possible through such a mechanism. This will be the subject of the next post.

Sources and further reading materials:

http://imagine.gsfc.nasa.gov/docs/science/know_l2/stars.html

http://ircamera.as.arizona.edu/astr_250/Lectures/Lec17_sml.htm

http://solar.physics.montana.edu/ypop/Spotlight/SunInfo/Radzone.html

http://solar.physics.montana.edu/ypop/Spotlight/SunInfo/Conzone.html

http://onlinelibrary.wiley.com/doi/10.1002/asna.200510440/pdf

Click to access 0004-637X_482_1_420.pdf

http://www.universetoday.com/18847/life-of-the-sun/

http://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_deathlow.html

http://www.universetoday.com/44836/unusual-massive-white-dwarf-stars-have-oxygen-atmospheres/