Dead Stars

A month ago, we looked at the varieties of stars that can be found in the universe. But stars have a limited amount of fuel, and when it runs out, stuff happens. Exactly what happens depends on the mass of the star, and some of them are among the weirdest and most interesting things in the universe.

The most common stellar remnant by far is a white dwarf. White dwarfs are what we get when a star stops fusing its atoms and its matter settles down. In a white dwarf, the gravity is so strong and the pressure is so high that it runs into a physical limit called electron degeneracy. You may have learned in chemistry class that atoms have electron orbitals, sometimes called electron shells, which can only hold a certain number of electrons each. This is an example of electron degeneracy. In a white dwarf, the atoms' outer layers of electrons are unbound, moving freely around the material, and they are degenerate because they have the maximum density allowed by the laws of physics. Because of their variety of temperatures, white dwarfs are not necessarily white, but can also be yellow, orange, red, and brown.

Once our sun goes through all of its phases, it will become a white dwarf, slowly cooling down until the end of time.

There are ways to increase a white dwarf's pressure beyond the electron degeneracy limit. One of them is for it to be made of denser material. Some white dwarfs are made of helium, which has two protons and two electrons, neither of which are bound to it. Other white dwarfs are made of various mixtures of carbon, oxygen, neon, and magnesium, each of which is more dense and has more bound electrons not contributing to degeneracy.

The other way to increase the pressure is for gravity to be so strong that the electrons combine with the protons, making neutrons. When this happens, there is no more electrical repulsion, and all of the matter collapses to the density of an atomic nucleus, where neutron degeneracy once again makes things stable. You can probably guess what neutron degeneracy is; if electron degeneracy is what we get when we have the maximum density of electrons, neutron degeneracy is what we get when we have the maximum density of neutrons. A stellar remnant made of neutron degenerate matter is called a neutron star.

White dwarfs do not turn into neutron stars. Instead, we start out with a very massive star, which has enough pressure to fuse its atoms beyond the elements mentioned above. The higher the element number, the faster the fusion happens, until it reaches core collapse, which causes a supernova and leaves behind a neutron star.

When neutron stars are young, they shoot high-energy gets of light and other radiation from their magnetic poles. They are also spinning, and their rotational poles are not lined up with their magnetic poles. This means their jets spiral around in a pair of cones. If Earth is in the path of one of these jets, the neutron star appears to pulsate in the night sky. Because of this, we call this kind of neutron stars pulsars. Most pulsars rotate once every few seconds, but some are as fast as a few milliseconds.

By Kevin Gill on Flickr

Some neutron stars have the strongest known magnetic fields in the uinverse, strong enough to deform atoms. These neutron stars are called magnetars.

If a relatively small supernova makes a neutron star, what happens if we turn up the mass? If we explode progressively heavier supergiant stars, we get heavier and heavier neutron stars, until suddenly . . . there is nothing. The star explodes, leaving only empty space behind. According to supernova theory and observational data, there is a mass gap between neutron stars around three times the mass of the sun and our next type of stellar remnant at five times the mass of the sun. This heavier next type is what I’m sure you have been waiting for this whole blog post: black holes.

An ancient philosophical question goes like this: what happens when an immovable object encounters and unstoppable force? Well it turns out that there is no such thing as an immovable object, but gravity can get strong enough to become an unstoppable force. If enough mass gets crammed into a small enough space, not even neutron degeneracy can prevent it from collapsing down to an infinitesimal point called a singularity. A certain distance away from the singularity, called the event horizon, gravity switches between weak enough to escape from and too strong for anything to resist. The event horizon is the black ball we picture when we think about black holes. Black holes are so mind-bendingly fascinating that they deserve a whole discussion to themselves.

These are all of the stellar remnant types we have evidence for (and as of last month, I might add with pride, we have pictures to back all of them up). However, there are still more which are theorized to exist, either presently unobserved or far in the future.

It may be that between neutron stars and black holes, there is another stopping-off point. Neutrons are made of quarks, so perhaps quark degeneracy can stop the formation of a black hole when neutron degeneracy is not enough. Such an object would, unsurprisingly, be called a quark star. It is unknown whether this is possible; the only hint we have is the small amounts of quark-gluon plasma made in particle accelerators under completely different conditions than we would expect in quark stars.

Remember how we left white dwarfs cooling off indefinitely? One day, many eons in the future, white dwarf stars will have cooled so much that they no longer give off any visible light. Then, they will be called black dwarfs. The time it will take for white dwarfs to cool down this much is orders of magnitude longer than the current age of the universe.

Yet even black dwarfs are not the end state of stellar remnants. To find out why, we have to talk about nuclear fission and fusion. Radioactive materials break apart into lighter elements, each with its own half-life, the time it takes for roughly half of the atoms to decay. This is natural nuclear fission. Fusion happens when atoms fuse together into heavier elements, releasing energy. Now you might notice that I said both fission and fusion release energy. This is only true when the product has less mass per nucleon (less energy density) than what we started out with. Iron has the lightest mass per nucleon of all, so the elements lighter than iron fuse, and the elements heavier than iron fission.

When we talk about radioactivity, we say that some atoms heavier than iron are radioactive, and some are stable. When we talk about fusion, we imagine we need the pressures and temperatures at the core of a star. These are both not entirely true. High temperatures and pressures raise the probability of fusion, but that probability never goes to zero. Similarly, the “stable” heavier-than-iron elements have an extremely long, but not infinite, half-life. For us humans, it is true enough to say fusion requires enormous temperatures and pressures, and many heavy elements are stable.

But if we look ahead in the future, and I mean so far ahead that it might as well be infinite, we get a different story. Given an infinite amount of time, anything with a static non-zero probability is guaranteed to happen, no matter how small that probability is. On a large enough timescale, black dwarfs will fuse their atoms together into iron, and any elements heavier than iron will break apart into iron. Long after even the biggest black holes have evaporated, iron stars will be the last objects left in the universe.

Mathematics: The Language of the Universe

Nature of Reality:
Quasi-Realism
Representational Realism
Existence and Natures
Knowledge of Reality
The Language of Reality

Toolbelt of Knowledge: Concepts
Algorithms
Equivalence
Emergence
Math
The Anthropic Principle
Substrate-Independence
Significance

In our discussions about the nature of reality, we have come to the view that reality is a thing unto itself, independent of perception, belief, or knowledge. Anything we perceive or think we know about reality is not reality itself, but only a representation we have constructed in our minds. A representation is true to the degree that its logic matches with the logic of the real thing it is describing. Today, we are going to talk about that logic, mathematics.

By WyrdWolf on Deviantart

A lot of people see math as something mysterious that they will never understand. But math is not supernatural. It is not hidden knowledge available only to an elite few. People who know math are not wizards or prophets, they are normal people just like you. I hope that after reading this discussion, you will be convinced that you can learn math too, if you so desire.

To start, let’s forget about numbers and just think about something physical, like air pressure. We know from centuries of experiments that, the pressure in a given volume is proportional to the number of molecules in the volume and the temperature. This may sound complicated, but all it means is if more air is added or the temperature is increased, the pressure increases.

Let’s look at the italicized statement. We have four physical quantities: pressure, volume, number of molecules, and temperature. Let’s shorten each of these to just their first letters: P, V, N, and T. “Is proportional to” means if you change what comes after it, then what comes before it changes by the same percentage. We can represent this by an equals sign and a constant, the letter k. Put this together, and we have,

It’s an equation! We have just done something marvelous; we have taken a fact about reality and written it as a mathematical statement. By doing this, we realize a profound truth: math is not just a tool to work with numbers and get answers to homework problems; it’s a language and a writing system. By becoming math-literate, we break into a higher level of understanding the universe.

Let’s try it again. This time we’ll start with an equation, and figure out what it means.

The first thing we need when trying to read this equation is what the letters mean. In normal languages, letters have mostly the same sounds wherever they appear. In math, it is not so; we must be told what each letter means every time. It is the organization, operations, and numbers that have consistent meaning. So here is what the letters in our new equation mean: capital T stands for temperature, small t stands for time, and k is a constant.

What operations does this equation have? The first thing we notice is d/d. This means, the rate at which the thing on top changes as the thing on the bottom changes. So for us, it would be the rate the temperature changes over time. Next, we notice a triangle before the T on the right. This triangle means the difference between two of what comes after it. So in our case, ΔT means the difference between the temperatures of two objects.

Putting all this together, we can read the equation. It says, “The rate at which temperature flows between two touching objects is proportional to the difference in temperature between the two objects.” This means if two touching objects have very different temperatures, heat will flow quickly between them, but if their temperatures are near each other, the heat will flow slowly.

There is one final piece to the equation, and that is the minus sign. This tells us that the temperatures are changing closer to one another, not running away to extremes. This makes sense. Cold things heat up when they touch hot things, and hot things cool down when they touch cold things. Heat always flows toward equilibrium.

The ability to read equations is only one small part of math. There is also geometry, group theory, set theory, vectors, tensors, and much more. All of these fields of study are called the same thing, math, so what do they all have in common? The answer is that mathematics is the set of all well-defined abstract ideas that follow the principle of non-contradiction. To create math, we must declare one or more axioms, statements that define an imaginary object.

Let’s take an example. "A circle is a shape where every point on its boundary is the same distance from its center." Based on this axiom, we can figure out all kinds of things about lines drawn through circles, intersecting circles, circles in curved space, and more. Everything in math is like this; we start with axioms, and then use logic on them to figure out all that we can about them.

Philosophers and scientists have often wondered at how well math is able to describe the universe. To some, it seems miraculous. However, based on everything we have talked about in the Nature of Reality series, I think it makes perfect sense. Here’s why:

1) A representation is true to the degree that its logic lines up with the logic of the part of reality it is meant to represent.
2) An idea is a representation.
3) Reality is well-defined and always follows the principle of non-contradiction.
4) Every idea that is well-defined and follows non-contradiction is mathematical.
Therefore, everything in reality can be truthfully represented by mathematical ideas.

If we accept the views of reality we have argued for on this blog, this is why Mathematics is the language of the universe.

Types of Stars in the Universe

On a clear, dark night, stars fill the expanse of the sky. These tiny dots of light twinkle and shine, as if the canopy between Heaven and Earth were pricked by a million needles and the holy light of God were shining through. Ever since our distant ancestors separated from the chimpanzees, we have gazed at the Milky Way with awe, imbuing it with images and meaning and stories. The stars are among the most wondrous things in existence.

With the dawn of science, we learned that the stars are other suns, each with its own set of planets. Stars come in many sizes and colors, depending on what they are made of and how far along they are in their life cycle. A star’s light comes from its surface temperature, as it radiates its heat energy away. The hotter the star, the brighter it shines, and the higher the peak frequency of its light. It is the same as why metals glow when they are heated. In order of increasing temperature, we get red, orange, yellow, white, and then blue. Because of the distribution of the light radiated, and the way our eyes work, we will never find a green or purple star.

A star forms when the gas (mostly hydrogen) in a region of space becomes dense enough that its gravity causes it to collapse together. As it shrinks, the tiny bits of angular momentum here and there build up, causing it to swirl around and form a protoplanetary disk. Most of the gas clumps in the center, forming the star, and the rest eventually becomes planets, moons, and asteroids. While this is happening, the star is called a protostar.

Once all of the dust has settled, the star officially begins its life, and is called a main sequence star. The mass of the star determines how hot it is, and therefore its color. From low to high, we have red dwarfs, orange dwarfs, yellow dwarfs, and blue . . . giants. A star massive enough to shine blue at birth is too big to be called a dwarf.

Our sun is a yellow dwarf, although it’s actually white, not yellow. The reason it looks yellow, orange, or red when it is low in the sky is because Earth’s atmosphere scatters the shorter wavelengths. this is also why the daytime sky is blue.

There are also brown dwarfs, but they are a little different. Brown dwarfs are objects that ride the fuzzy line between stars and gas giant planets, only hot enough to glow a faint dark red. They are a little over ten times the mass of Jupiter, and a hudredth the mass of the sun.

Stars don’t stay as they are forever. As they fuse up their hydrogen, they expand. A lot. As in, orders of magnitude. Once their hydrogen is spent, they contract until the helium in their cores begins to fuse. As the helium runs low, they expand again. The cycle goes on a few more times. When stars are in their expansion phase, they are called giants, supergiants, or hypergiants depending on their masses, and their color shifts toward the red end of the spectrum. Some stars, however, are so blue that they remain blue even at their largest.

These are all the types of stars that we know about that are around today. However, despite the nearly 14 billion years the universe has been around, it is very young compared to how old it will get. The smaller a star, the slower it fuses its fuel, so the longer every stage of its life lasts. In fact, red dwarf stars are so slow that none of them have used up all of their hydrogen yet. Here’s where things get interesting. It is predicted that red dwarfs don’t expand like other stars. Instead, they get hotter and brighter, turning into blue dwarfs. I find it just amazing that some trillion years in the future, a star type the universe has never seen before will start to appear.

But wait, you say. We can’t be done with stars yet! We haven’t talked about white dwarf stars or neutron stars. And you are correct. The reason we haven’t talked about them today is because they are dead stars, and dead stars are interesting enough that I wanted to give them their own discussion.