Compact Stars: A Pretty Stellar Story

Stellar Remnants

If I were to immediately define “stellar remnants,” I would be beginning at the end. Instead, let’s begin at the beginning: the life cycle of a star, or stellar evolution.

Credit: http://www.schoolsobservatory.org.uk/astro/stars/lifecycle

After formation in a nebula, stars begin to live via nuclear fusion in their core. But eventually, the atoms needed for nuclear fusion -- hydrogen -- run out, and the death of the star begins. This death involves the fusion of new elements, resulting in either a large supernova explosion or a planetary nebula. After either comes our subject: compact stars, or stellar remnants.

Stellar remnants are the final stage of the star life cycle and are made up of the final material leftover at the death of a star. This material can take the form of a white dwarf, a neutron star, or a black hole, based upon its mass (see the Chandrasekhar limit).

Credit: https://www.spaceanswers.com/deep-space/five-amazing-facts-about-white-dwarfs/

A white dwarf, or degenerate dwarf, shown in the above image, is the result of the death of an average sized star. That is, someday our own Sun will become a white dwarf. It is very bright and very hot (as seen above), and composed mostly of helium, carbon, and oxygen. White dwarfs are also called degenerate dwarfs because they are made up of degenerate matter. Degenerate matter exists due to the Pauli Exclusion Principle, which states that electrons cannot occupy the same space. Therefore, electrons are forced to make up the energy state of an atom, and end up filling all energy levels of the atom, making it degenerate. This degeneracy halts the collapse of the white dwarf and its ability to perform nuclear fusion. Afterwards, white dwarfs continue to contract due to the force of gravity, which is why it is so hot! However, this heat is released by the white dwarf shining over time, and the white dwarf is not hot enough to replace that energy with nuclear reactions. Thus over time white dwarfs cool down and become black dwarfs, but this can take trillions of years -- longer than the current age of the Universe -- and so none exist today. White dwarfs are also capable of becoming supernovae if they consume a nearby star, often one that's part of a binary system. This can happen due to the white dwarf's extreme gravitational pull due to its large density -- a density so large that only a teaspoon of white dwarf matter would weigh 5.5 tons -- as much as an elephant here on Earth~

Credit: http://www.nbcnews.com/id/20360861/ns/technology_and_science-space/t/astronomers-spot-nearest-neutron-star/

The above image displays an artist's rendition of a neutron star -- actual images neutron stars are difficult to capture due to their small size. A neutron star occurs when the mass of the dying star exceeds the Chandrasekhar limit. Electron degeneracy can’t support the star’s mass, so collapses both protons and electrons into neutrons (hence the name!). Neutron stars are special in a couple of ways, and their existence actually affects human beings directly. Due to their high spin rate and electromagnetic radiation, the pulsing light emission of neutron stars can be seen from earth. The first observation of this was in 1967 by a woman named Jocelyn Bell. Though she suspected something complex was happening, her thesis advisor didn’t recognize the pulses (now known as Pulsars) and mistook the light as attempted contact from alien civilization. The pulses of light are actually electromagnetic radiation. Some neutron stars are the most magnetic objects in the Universe -- these especially magnetic stars are called Magnetars. Magnetars are so strong because the star's collapse and subsequent compression of magnetic field lines trap radiation in all but breaks at the magnetic poles. Like Earth, these magnetic poles are not directly aligned with the physical North and South poles.

Credit: http://www.pbs.org/wgbh/nova/next/physics/black-holes-could-turn-you-into-a-hologram-and-you-wouldnt-even-notice/

Pictured above is perhaps the most (subjectively) mythic of stellar systems -- the black hole. Black holes are the results of the death of the largest stars discussed in this article, and as a result have an immense density. They can be difficult to discover because black holes can’t be seen. However, we are able to see the accretion disks surrounding black holes. These are made up of a spiral of hot gas from a nearby star being pulled towards the black hole by its gravity, and can be seen at X-ray wavelengths. The binary star system of the star and the black hole is called an X-ray binary. The incredible density of the black hole contributes to such a large gravitational pull that the speed needed to escape is faster than the speed of light -- thus, not even light can escape a black hole. This impossibility of escape means that very little exploration of black holes can be done, but what is observed from the outside is strange enough to increase curiosity. For example, around the Event Horizon of a black hole time appears to slow. If you were to sit at the event horizon of a black hole, you would be able to use it as a time machine to see back through the entire evolution of the universe. You could even witness the future! Black holes are also infinitely dense, and because of this, the surrounding spacetime continuum is flexible. So flexible, in fact, that black holes can bend light from distant objects into a circle, which is called an Einstein ring.

TL;DR -- Even post mortem, stars continue to do some pretty fascinating things. We still have a lot to explore!

Hawking Radiation and evaporation of black holes

                Many theorize that there is nothing within a Black Hole, or more clearly no temperature or light. Within the Event Horizon, the point within a black hole where not even light can escape; the gravitational forces are so strong that anything passing the Event Horizon, including light, will never be able to escape. This theory that nothing can escape a black hole is theoretically sound because there is nothing faster than the speed of light. The only way matter could escape the gravitational pull beyond the event horizon would be if it were faster than the speed of light. While scientist have not been able to see a Black Hole close enough to determine whether or not it gives off blackbody radiation, Stephen  Hawking believes that a Black Hole can give off radiation and energy. This theory is known as Hawking Radiation. Hawking Radiation as well helps with the theory that Black Holes can evaporate by giving off energy.

Image credit: https://qph.ec.quoracdn.net/main-qimg-527e8a63b6a99759434c841f1f8bf28b-c?convert_to_webp=true

What is Hawking Radiation?

                 Due to the principles of Quantum Mechanics allows some form of energy to escape the event horizon and the black hole[1]. While classical mechanics does not allow this idea of energy escape.  If a black hole gives off a blackbody radiation what is creating this energy when everything that a black hole absorbs cannot escape? The energy that the black hole is giving off is radiating right before the event horizon. This energy is in the form of particles and antiparticle know as Virtual Particles. Their interaction with each other create this energy. 

Image credit: http://casa.colorado.edu/~ajsh/hawk.html

What do the Virtual Particles do and how they relate to Hawking radiation and energy?

                While Hawking Radiation is not proved to be correct, Stephen Hawking theorized that this energy escapes the Event Horizon as Virtual Particles. Virtual Particles are these theoretical particles move at such a fast speed that they cannot be seen, or virtually nonexistent. A virtual particle is composed of both a particle and an antiparticle the two separate, but then are attracted to each other and collide annihilating both. Virtual Particles in every section of space, only existing and annihilating at such a speed they cannot be seen.  This phenomenon occurs at such a fast rate that they cannot be seen, everywhere except on the event horizon of a black hole. On the Event Horizon, this separation can be seen because of the gravitational pull of the event horizon. While one particle is pulled within the black hole and disappears, the other is shot out of the event horizon.

Image credit: http://ircamera.as.arizona.edu/Astr2016/text/extplaydice.htm

 Evaporation of a black hole

              Only occurring after all matter surrounding the black hole has been absorbed. Virtual particles directly cause black holes to lose mass. This separation of Virtual particles causes a loss of a minutely small amount of energy due to the kinetic energy used when the particles separate. This loss of kinetic energy is because the particle and antiparticle are attracted to each other, for them to separate the black hole must use energy to separate them and thus lose mass. The idea of particles tunneling can also describe the loss of energy in a black hole. The Heisenberg uncertainty principle determines that the wavelength of a particle is an uncertainty. Because momentum and position cannot be precise for a particle, this uncertainty allows particles to exist inside or near the event horizon. The particle can then tunnel out of the black hole and cause it to lose a minute amount of mass.  While the energy loss is not even significant, over a long period this loss of energy will become significant, and the black hole would shrink and evaporate. This shrinking and evaporation of the Black hole cause it to become hotter as mass is inversely proportional to mass in a black hole as well decreases entropy.  This process would take over the life of the universe to take place, but it would evaporate.

 Conclusion

 For us to prove or disprove the idea of Hawking radiation and evaporation of black holes in nature rather than just in a laboratory could only be possible with the existence of micro black holes. The reason why they could be observed and help prove this theory is because they are so small that they could potentially evaporate right now.

In case you want to hear the same relative idea but through the voice of Morgan Freeman, click on this video below.

https://www.youtube.com/watch?v=1wHdtP0U6JA

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[1].Hamilton, Andrew. "Hawking Radiation." casa.colorado.edu. Last modified April 19, 1998. Accessed November 8, 2016. http://casa.colorado.edu/~ajsh/hawk.html.

Sources used:

Hamilton, Andrew. "Hawking Radiation." casa.colorado.edu. Last modified April 19, 1998. Accessed November 8, 2016. http://casa.colorado.edu/~ajsh/hawk.html.

Baez, John. "Hawking Radiation." math.ucr, University of California Riverside, 1994, math.ucr.edu/ 

     home/baez/physics/Relativity/BlackHoles/hawking.html. Accessed 1997. 

Stellar Parallax: An Astronomical Ruler

Stellar Parallax: An Astronomical Ruler

Image Credit: Gaia UK - https://gaia.ac.uk/science/parallax

Stellar parallax is an idea that has been around for thousands of years. To understand what it actually describes, we must first understand the word parallax. Parallax is the idea of an apparent shift in position of an object relative to surrounding objects based on the location of the moving observer. An example of this is a close road sign seen while driving as compared to the trees in the distance. The sign appears to move across the trees, despite the fact that its position remains constant. 

Now how can we use this phenomenon to our advantage? Clearly the intrinsic property that drives parallax is distance. Thus, when we see an object "shift" relative to another, we can conclude that the object that shifted is the closer one. This is the idea that the Greeks had when they considered stellar parallax. Stellar parallax is just what is sounds like, parallax of the stars. These Ancient Greek astronomers were considering the question of the center of the universe, and thought that if there Earth were moving around the Sun, they should observe some amount of stellar parallax. Of course, they were right about this theory, but ultimately were unable to make any observations of stellar parallax and ended up throwing away the heliocentric model and settled on the geocentric model.

Since then, our ability to observe far-away objects has obviously seen massive improvements. Thus, we have actually been able to record instances of stellar parallax, however small. The first measurement of such was taken in 1838 by Friedrich Bessel [1]. Clearly, it took quite awhile for stellar parallax to actually be proven through observation, but we knew that it should exist once we accepted Copernicus' heliocentric model. 

Stellar parallax made a large contribution to understanding the relative positions of stars in our galaxy. Modern technology has also made taking parallax measurements far easier and more accurate. The Hipparcos satellite (meant to represent "high precision parallax collecting satellite", also an homage to the Greek astronomer Hipparchus) has been the primary source of parallax measurements in recent decades. Since its launch in 1989, it has published position data on close to four million stars. This has given us a much greater model of what our galaxy looks like. [2] Pictured below is the Hipparcos satellite. 

Image credit - Hipparcos Wikipedia - https://en.wikipedia.org/wiki/File:Hipparcos-testing-estec.jpg

To use parallax to calculate distance, we have a simple equation: d = 1/p where d is the distance to the star measured in parsecs, and p is the parallax angle measured in arcseconds. The quantity 'p' can be visualized better in the schematic below. 

Image Credit - Las Cumbras Observatory - https://lco.global/spacebook/parallax-and-distance-measurement/

To use this equation, there are a few things we must know beforehand; the distance from the earth to the sun (1 AU, known with high accuracy), and the distance to the 'fixed' stars that we measure parallax against. We approximate this distance to be infinite, since we observe no parallax shift from them. In reality, there is a parallax shift in these stars, just not one that we can observe with our technology. An important thing to note about this equation is that it makes use of the small angle approximation. This approximation says that sin(θ) ≈ θ. In this case, the small angle is the parallax angle. One can imagine that the angle made by something multiple lightyears away from us would be quite small. Thus, the approximation is valid and our equation works. 

Another example of parallax (unfortunately not stellar) that I personally identify with is found in sailing. An adage that many sailors are familiar with is the one of "making trees" on another boat. This phrase comes from the idea that, when you are sailing faster than another boat during a race, it often appears as through trees are emerging from the front of their sail. This is due to parallax - since the opposing boat is closer to you than the trees in the distance, it appears as though the boat is actually moving backwards, when in reality you are just moving faster than them. So, parallax proves to be a useful tool in other parts of life outside of astronomy. 

I found a video that showcased this idea starting at 14:50 and ending around 15:05. In this case, the observer boat was "making trees" (well, making buildings, really) on the boats it was filming. This is a short instance of making trees, so it does not quite do justice to how useful it really is. However, I can say with confidence that parallax has helped me determine important details about wind strength and positioning on various courses that I've sailed on. 

https://youtu.be/mXOPvQz-JtY?t=14m50s

References

[1] Zeilik, Michael A.; Gregory, Stephan A. (1998). Introductory Astronomy & Astrophysics (4th ed.). Saunders College Publishing. ISBN 0-03-006228-4..

[2] https://en.wikipedia.org/wiki/Hipparcos

[3] https://lco.global/spacebook/parallax-and-distance-measurement/

Stellar Magnitude

Austin Lee

Stellar Magnitude

                 Stellar Magnitude was created by the Greek astronomer Hipparchus to rank their brightness. First magnitude is the brightest, second magnitude is the second brightest, and so on. It is logarithmic; brightness increases by a fixed 2.5 times with each magnitude. It is measured on a logarithmic scale and not a linear scale because the human eye perceives stimuli logarithmically, meaning that perception increases by a fixed factor. This trait is called Fechner’s Law.

                   Because the Greeks believed the stars were all located on the same sphere around the earth, this was an easy way to classify stars for them. But because we have learned this is not the actual structure of the universe, modern astronomy amends the concept of magnitude to fit our model. We divide magnitude into two groups: apparent magnitude, which is a star’s perceived brightness from any viewpoint, and absolute magnitude, which is the intrinsic brightness of a star that never changes, measured at 10 parsecs from the star. The absolute magnitude and apparent magnitude can vary greatly depending on the distance of the star from Earth. Vega is used as a reference scale for magnitude, marked at 0, and brightness increases in the negatives. Our sun on the scale has a very bright apparent magnitude of -26.74 because it is obviously the closest star to us, but only an absolute magnitude of 4.83, which is average.

 

Chart courtesy of http://www.astronomynotes.com/starprop/s4.htm

            As per the graph, the faintest naked eye star is a little past 5 on the apparent brightness scale. At 2, stars become hard to see in small cities. At 3, they are still barely visible in small cities but densely lit urban areas need binoculars to see the star. By 4, only the suburbs can see the star.

            By comparing the absolute magnitude (M) and apparent magnitude (m) of a star, we can determine our distance from the star. The difference between them (m-M) is called the distance modulus. A distance modulus of 0 means the star is 10 parsecs away, and a negatively increasing distance modulus means it is closer, and a positively increasing distance modulus means it is further away. 

Life Expectancy along the Main Sequence

Along the main sequence of a Hertzsprung-Russel Diagram, stars will spend their lives undergoing hydrogen nuclear reactions in their core, until they run out of hydrogen to fuse and they evolve off of the main sequence. You might think that a larger star will live longer; it has a bigger core, which means that it has more fuel to burn, right? In fact, the opposite is true. You see, a larger star, in order to counteract the effect of gravitational contraction, must create a larger outward pushing thermal pressure. A larger thermal pressure is created by a star undergoing more fusion reactions, which then leads to a higher core temperature, i.e. more thermal pressure. Since we know the mass and lifetime of our own Sun, 10 billion years, we can compare the lifetime of other stars.

Source: https://en.wikipedia.org/wiki/Main_sequence#/media/File:HRDiagram.png

Our Sun lies right about in the middle of the H-R diagram shown above. As mentioned before, the Sun has a life expectancy of 10 billion years, which is the time it takes for the Sun to use up all its hydrogen in its core (about 10% of the total mass of the core). If you took, for example, a sun that had a mass of 10M_sun, it has 10 times as much fuel as the Sun, but according to the H-R diagram uses its fuel 10,000 times faster (it is 10,000 times more luminous). Since luminosity if the energy generated per second, the total energy available divided by the luminosity is equivalent to the lifetime of the star. Therefore, it will live only a thousandth as long as our Sun will, 10 million years. The opposite is true for small suns. For a sun which is a tenth as massive as our sun, it will have a tenth as much fuel, but is a hundredth as luminous. This means it will live 10 times as long as our sun, 100 billion years.

Lifetime also has interesting implications for our continuing search for extraterrestrial life in our universe. The first life on Earth appeared about 1.2 billion years after Earth was formed, and if we use that as a guideline, there are a lot of stars in our universe that do not even live long enough to have a planetary system which can support life. Because of this, our search is narrowed down from the beginning; we can only look at longer living stars such as G, K, and M types even before we begin looking for planets in the habitable zone of the star.

As you can see, life expectancy has the opposite effect that you would respect. Large stars evolve off of the main sequence much faster than smaller stars do. In fact, we still have not seen some of the lower mass classes of stars experience star death, because their life expectancy far exceeds the 14 billion years the universe has been in existence.

The Sun and its Energy

Sun and its energy

The Sun is the center of our Solar System, and it provides energy for life on Earth, which is significant for us. Here I have a blog for you to learn some things about the structure of the Sun and its radiation transport.

https://www.cliffsnotes.com/study-guides/astronomy/the-sun-a-representative-star/properties-of-the-sun

The structure of the Sun/Radiation transport within the Sun

https://www.youtube.com/watch?v=bLnTwHCKs18

Core: Solar energy is produced at the center of the Sun, where temperatures reach 15 *10^6 K. The core is a significant zone that we need to pay more attention about it. It is in the core that nuclear fusion takes place. Nuclear fusion is a process that four hydrogen nuclei combine into one helium nucleus and release enormous amounts of energy described as Einstein's equation E=mc^2

Radiative Zone: Energy from the core slowly rises in the Radiative Zone. In this zone, the energy is transported by the photons from core to the convection zone. In this process, the photons travel at the speed of light. The paths they take through the Radiative Zone zigzag so much that This process will take about 170 thousand years. 
As the zone is very hot, the photons and electrons will be separated. And during the way out, the photons bounce into the free electrons and change directions for many times, that is the reason why it takes so long time for the photons to get out.

Here is a video that describes the process of energy's travel in the Radiative Zone.

https://www.youtube.com/watch?v=cGY8L8cb-g0

Convection Zone: At the bottom of Convection Zone, the solar plasma absorbs photons. This absorption makes it become ready to convect. In the convection process, the energy is transported upward by rising hot plasma. We know that the hotter gas has relatively lower density while the cool gas have relatively higher density. This difference in density makes it possible for the plasma to rise.

http://ircamera.as.arizona.edu/NatSci102/NatSci102/lectures/suninterior.htm

Here is a video with an experiment that describes the process of energy's travel in the Convection Zone.

https://www.youtube.com/watch?v=6w8u9YzZXNM

Photosphere: The Photosphere is the visible surface of the Sun, where the temperature is about 6000 K. This is the part that gives off light that we can see from here on Earth.

Chromosphere: The chromosphere is a thin layer of gas above the photosphere. The temperature at the surface of Chromosphere is about 4,300K while the temperature at the top of the Chromosphere can reach more than 10,000 K. This suddenly increase of temperature is a very odd behavior of the Sun.

Corona: The Corona's a gas layer above the Chromosphere and it is just as thin as the Chromosphere. The Corona is the outmost layer of the sun and extends about 1.8 Sun's radius from Chromosphere.  The temperature of Corona is 1,000,000 K. It is invisible for most times, but it is visible during a total solar eclipse when the Sun's surface is completely hidden by the Moon. here is a picture of solar eclipse.

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

Solar Wind: The solar wind is the stream of charged particles, or plasma, released from the upper atmosphere of the sun. When charged particles from the sun are blown to the atmosphere of the sun, they will cause the electrons in the atoms to move to a higher-energy state. And when the electrons drop back to the low-energy state,  they will release photons, in the other word, light. This process produces beautiful aurora. The solar wind was very powerful in the past compare with today's. In the past after the juvian lanets just formed,  the solar wind was so powerful that it was able to blow away the gaseous compnents of the solar nubela.

Sources:

http://futurism.com/how-the-sun-works/
http://earthsky.org/earth/what-causes-the-aurora-borealis-or-northern-lights

Why Does the Sun Shine?

Ethan vanderWilden, AS151, Professor McGrath, 11/3/16

A Shining Star:

Why Does the Sun Shine?

Why does the Sun shine? Well, that seems like a pretty important question. Let’s think; if the Sun didn’t shine, it would be very very cold. Also, it probably wouldn’t “be” anything because we certainly would not even be alive. The Sun’s shining gives us light and heat, two things that humans have been depending on for their entire existence.

Look at all the light and heat!!!

http://www.nasa.gov/sites/default/files/images/480273main_20100904-limb.jpg

There have been multiple explanations for why the Sun shines, all having to do with some form of potential energy being converted into a type of kinetic energy called radiative energy. Have you ever heard of sunlight? Well that is basically radiation from the Sun, which is radiative energy being given off by the Sun.

One explanation for why the Sun shines is that chemical potential energy is being converted into radiative energy. This means that the Sun is essentially burning some fuel source, similar to a car converting gas into kinetic energy to get the vehicle moving. However, this explanation has been exemplified as false. If we look at the mass of the Sun, and convert that mass into all of the energy that it could yield from being burned as fuel, the Sun could only shine (aka give off radiative energy) for about 9000 years. However, our solar system has existed for close to 4.5 billion years, so this cannot be the answer.

            

The ideas of converting either chemical or potential energy into radiative energy for the reason that the Sun shines are incorrect

(In order left to right, link sends you to page) 1 2 3 4

Another explanation is that gravitational potential energy is being converted into radiative energy. This means that the Sun is collapsing in on itself, and just as when someone jumps off of a diving board, they gain speed, the Sun would produce more kinetic energy. Similar to the chemical energy theory, if we look at the mass and radius of the Sun, and look at the amount of gravitational potential energy that could be converted into radiative energy, the Sun could only shine for around 30 million years. While this is certainly an improvement, it still struggles to account for the 4.5 billion year existence of our solar system. However, while gravitational contraction does not account for the Sun shining now, in the early stages of our Sun's history, gravitational contraction led to enough energy produced to heat the Sun's core to a temperature where nuclear fusion can occur.

The explanation of mass-energy conversion into radiative energy seems popular and accepted. Here, using Einstein’s E=mc^2, mass is converted into energy. The Sun has enough mass so that its nuclear potential energy could support the Sun shining for 10 billion years. This is well within our range of the solar system existing for the past 4.5 billion years. Now that this method is accepted, the question is: how does the process work (aka HOW does the Sun shine)?

Here, four Hydrogen atoms become one Helium atom, with gamma rays as a byproduct
https://en.wikipedia.org/wiki/Nuclear_fusion

Within the 10-15 million degree (Kelvin) core of the Sun, a process known as fusion occurs. Fusion can only happen under circumstances of high temperatures (greater than 10 million kelvin) and high densities, both of which exist in the core of the sun. At high speeds, the nuclei from Hydrogen atoms come close enough together for a force known as the “Strong Force” to bind the two atoms together. Through this binding of Hydrogen, fusion leads to the formation of Helium atoms. During this process of four Hydrogen atoms becoming one Helium atom, a total of 0.7% of the initial mass of the four atoms is “lost” due to two energy carrying gamma rays being given off. This 0.7% of the mass Hydrogen atoms is the radiative energy that we’ve been talking about! Without gamma rays, the Earth would be a cold, dark place...if it even were a place. These fusion reactions are also responsible for some of the generation of heavier elements present in our Universe, which are essential for future planets to live as these elements are eventually recycled back into the Universe. Inside of the Sun's core, fusion is the essential function that keeps our solar system functioning and alive.