astronomy homeworks ( Astronomy of the Universe AST 101)
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Homework2notes.docx
Star formation and evolution.
Stars form in molecular clouds.
The core of the star is a plasma.
Hydrogen fusion begins and is sustained making a star.
Once a star begins to fuse hydrogen in the core it is referred to as being on the main sequence. A star on the main sequence remains the same size because the outward pressure from fusion is balanced by the inward pull of gravity … this places the star in equilibrium.
Be familiar with the proton-proton chain.
Once hydrogen fusion is no longer sustainable in the core, the fusion moves outward. This increases the outward pressure, causes the star to increase in size, and it is now considered to be in the giant phase. Remember that moving the location of the fusion does not change the mass of the star and initially does not change the size. This means that the force of gravity is unchanged.
As the star continues to get bigger, the mass is unchanged but the density decreases. This means that the gravitational field inside the star decreases and the star gets much bigger.
At this point, what is happening in the core of the star? Since there is no longer injection of energy into the core by the fusion, the temperature of the core decreases. This means that while the star is getting bigger the core is actually getting smaller.
Remember that the hydrogen fusion is releasing energy and generating helium. The energy is being released into the environment in the form of photons. The helium, which is heavier than its surroundings, is building up around the core of the star.
As the star progresses through the giant phase, more helium builds up around the core. As with the initial plasma core; the temperature, density, and pressure of the helium increase. This continues until the helium is at a high enough temperature to sustain fusion.
Helium fusion takes place via the triple-alpha process.
A helium four nucleus is referred to as an alpha particle. The triple alpha process combines three helium nuclei to make carbon-12.
Be sure to understand that lithium, beryllium, and boron are all present in the star but don’t contribute directly to the star’s evolution. This is why we are not concerned with them in this class.
When the helium begins to fuse, there is energy being injected into the core again so the core grows in size. Also, the star itself shrinks (this is beyond the scope of the class). Understand that the star getting smaller means that now the gravitational force outweighs the outward pressure from fusion. It will continue to collapse until these two forces balance (this is the equilibrium state), and its momentum will allow it to continue to shrink. This leads to the star oscillating back and forth about an equilibrium position. This is a variable star.
So far we have:
1) Stars form in molecular clouds
2) Plasma core is generated and hydrogen fusion begins
3) This is the main sequence
4) Hydrogen fusion moves away from the core
5) This is the giant phase
6) Helium builds up around the core
7) Helium fusion begins
8) Star gets smaller and becomes a variable star
9) Eventually the helium fusion will move outward
10) Similarly, now the carbon builds up around the core
Hertzsprung Russell Diagram
The horizontal axis is temperature (sometimes referred to as color). Cooler temperature is to the right and hotter temperature is to the left. This is surface temperature. The surface of a star (referred to as the photosphere) is the distance from the center where the star changes from being opaque to transparent. It appears to be a surface because external light would bounce back upon striking it.
The vertical axis is luminosity (brightness or intensity or magnitude). There are two different magnitudes to consider: absolute magnitude and apparent magnitude. Absolute magnitude is a physical property of the star while apparent magnitude is how bright it appears based on the observation location.
Magnitude should be thought of as a flux rate (the rate at which photons are being emitted or observed). The absolute magnitude is the rate at which photons leave the star. The apparent magnitude is the rate at which photons are observed at a given location.
When creating an HR diagram, the vertical axis should be the absolute magnitude and not the apparent magnitude.
A star forms in a molecular cloud. At this point it is collapsing due to gravity but there is no fusion. This means that a protostar (a star that is forming due to gravitational collapse) will have a low surface temperature and be relatively dim. This places it in the bottom right corner of the HR diagram.
Once fusion begins, the star is said to be on the main sequence. From *lots* of observations, the main sequence occupies a certain region of the HR diagram. The location on the main sequence is based on mass. Higher mass stars are further to the left while lower mass stars are further to the right.
The surface temperature is the rate at which energy leaves the surface per unit area. When hydrogen fusion leaves the core, the star enters the giant phase and gets considerably larger. The total energy output increases, but the surface temperature decreases.
This is because the rate at which energy is leaving the star per unit area has actually decreased (the increase in surface area is large compared with the increase in total energy output).
This means that when the hydrogen fusion leaves the core, the location of the star on the HR diagram moves up and to the right.
At some point on the HR diagram, the star begins moving downward and to the left. This means that the star is getting smaller. From previous discussion, we know that this means that the helium fusion has begun around the core. The point on the HR diagram where this takes place is called the helium flash.
Effectively the HR diagram is a visual representation of how the surface temperature and luminosity change as the star evolves.
Once carbon has built up around the core, low and high mass stars evolve differently. Low mass stars won’t generate a high enough temperature to cause the carbon to fuse.
Since the carbon won’t fuse, the star eventually becomes unstable because there’s not enough hydrogen and helium to continue the current fusion processes
In the above diagram, the hydrogen burning shell is the outer boundary of the red area. The outer boundary of the blue area (which is also the inner boundary of the red area) is the helium burning shell.
The red area is referred to as helium rich. The blue area is referred to as carbon rich.
At some point the lack of carbon fusion and the decreasing availability of hydrogen and helium make the low mass star unstable. This leads to a process known as a planetary nebula. Planetary nebulae have nothing to do directly with planets. The name stems from the fact that low under low magnification they look like planets.
The instability created causes the star to eject the outer 1/3 of its mass. This ejection forms a nebular region around the star. The 2/3 of the mass that remains becomes a white dwarf.
This ejection is considered to be an extreme stellar wind. Understand that the mass loss is occurring from the low density region of the star. This means that the remaining object is at a much higher average density than before.
The increase in average density causes the gravitational field inside the star to increase while the decrease in fusion causes the outward pressure to lessen. This combination causes the remaining object to shrink.
The result is an object called a white dwarf at the center with an expanding nebular cloud around it.
Understand that the outward flowing gas is three dimensional. When viewing the central region the line of sight passes through a much thinner sheet of gas. This makes it appear as though there is little or no gas in front of the white dwarf.
Recall that a scale up model of a hydrogen atom using a tennis ball as the proton would require the electron to be about two miles away. After the mass is ejected, the remaining object begins to shrink. This continues until the molecules are as tightly packed as possible.
Since fusion will no longer support the star from collapsing, the star continues to shrink until the individual molecules provide resistance against further collapse.
This should be thought of as a three dimensional grid where there are tennis balls placed four miles apart. This is because the individual electron orbital shells will not overlap. Because of this the object cannot shrink any further.
This situation is referred to as electron degeneracy. Basically this means that no two electrons can occupy the same space at the same time.
Finally, the resulting object is a white dwarf. It has its molecules packed as tightly as possible without overlapping the electron orbital shells. This is considered to be one of the final evolutionary steps of a low mass star (a star that is eight times the mass of our sun or less).
The final stage of evolution is that the white dwarf eventually stops giving off energy and becomes a black dwarf. Once the white dwarf quits releasing energy it is still there but not visible. This is referred to as a black dwarf.
Unlike with low mass stars, high mass stars are able to fuse carbon and heavier elements.
A better description is that the hydrogen burning shell is the outer boundary of the bronze area and that the bronze ring is the helium rich zone where the helium created by the hydrogen fusion is falling toward the core because it is heavier than its surroundings.
The product of the silicon fusion process is iron. Iron does not fuse in the core of a high mass star for two reasons. The first is that the temperature is not high enough, and the second is that iron fusion is endothermic while the other fusion processes are exothermic.
The result of these is that usually the star’s core is not hot enough for iron to fuse. If the star is very large and such a temperature is attained, the fact that iron fusion is endothermic causes the fusion to pull energy from its environment and the temperature drops.
After the iron builds up and the star begins to run out of fusion material, the star proceeds to becoming a supernova. As the amount of fusion decreases, so does the outward pressure. This causes the star to begin to collapse. Understand that the star is a giant ball of fluid, so when it begins to collapse there are pressure waves sent toward the core.
These pressure waves will not reach the core because they overlap and bunch up together. While this is happening, there are still more waves coming in behind them. This means that the inward pressure is increasing greatly.
Eventually the inward pressure will be high enough that it causes the core to collapse and rebound. The rebound is what creates the supernova and blows the star apart. This is the only observed time in the universe that temperatures and pressures are high enough so that fusion will create elements that are heavier than iron.
When a high mass star explodes, it does not always explode completely. Sometimes a supernova remnant (SNR) is left behind. In theory there are three possible remnants although current research suggests that only two are probable.
1) White dwarf – this is exactly the same type of object as the one that forms during a planetary nebula. This will be 1.44 times the mass of our sun or less
2) Neutron star – this is a heavier remnant between 1.44 and 3.0 times the mass of our sun.
3) Black hole – this is the heaviest remnant and is 3.0 times the mass of our sun or greater.
The type of remnant left behind is dependent on the mass of the remnant itself, not on the mass of the star.
Remember that a white dwarf is supported against gravitational collapse by electron degeneracy. This means that the electron orbital shells of the molecules do not overlap. By increasing the mass of the remnant (and thereby increasing the pressure at the center), the molecules at the center will have their electrons pushed into the nuclei. This causes electrons and protons to collide and form neutrons.
The result of this is that the neutrons are now pushed together and the density of the remnant is much higher. This is referred to as a neutron star (which is probably better named a neutron ball). As before, no two neutrons can occupy the same space at the same time. This means that a neutron star is supported against gravitational collapse by neutron degeneracy.
In order to learn more about neutron stars we need to talk about the Earth’s magnetic field first. The Earth’s magnetic field is generated in the core (remember that moving charges generate a magnetic field). This is due to three reasons:
1) The core of the Earth is molten. This allows for greater movement of charged particles.
2) The core of the Earth is conducting. Even though it is molten it will still conduct.
3) The Earth rotates at a quick rate. This basically acts as a stirring rod for the fluidic core.
The Earth has two major axes: rotational and magnetic
The rotational axis of the Earth is fixed. Basically this means that it rotates about the same axis continually. A result of this is that the Earth’s equator does not change location.
A consequence of the physics principle of conservation of angular momentum is that when a rotating body is placed into a smaller volume it will rotate faster.
Apply this to a neutron star. Remember that when a high mass star explodes, the remnant that is left behind will shrink. If its mass is between 1.44 and 3.0 times the mass of our sun, it will form a neutron star. This means that it has overcome electron degeneracy and is being supported against gravitational collapse by neutron degeneracy.
When the neutron star forms, it may have a very slow rotation rate. However, the fact that it is collapsing considerably increases that rotation rate due to conservation of angular momentum.
At this point several nuances need to be considered in detail.
1) In the process of forming the neutron star, would you expect every electron to run into a proton? No, especially not in the heavier nuclei. This is because of the distribution of protons throughout the nucleus. The result of this is that there are more neutrons than there were before, but there are also isolated protons and neutrons.
2) Will the rotational axis of the neutron star be fixed? Yes. This is because the internal pressure is so high that none of the particles are able to move relative to one another.
3) Will the magnetic axis of the neutron star be fixed? Yes. This is because each individual charged particle remains in the same place relative to one another and is in a cyclic rotation around the rotational axis.
The purpose of the Earth’s magnetic field is to act as a shield against high energy charged particles.
Most of the charged particles are diverted around the Earth. Some of them, however, congregate at the magnetic poles. This is referred to as the charged particles being captured in the upper atmosphere.
Once the atmosphere is saturated with these charged particles, they are released and fall toward the Earth. This is observed as the Northern and Southern Lights.
In similar fashion, charged particles that encounter a neutron star will also build up around the poles. Again, there will be a saturation level for the particles around then neutron star. This will cause them to be ejected from the poles, but the result is much different.
Since the neutron star is rotating very quickly, instead of falling toward the surface they are ejected outward like a slingshot. The material is ejected outward in jets along the magnetic field axis.
Will the magnetic axis and the rotational axis of the neutron star be aligned? The answer is no because the charge distribution is not symmetric about the rotational axis. This means that there will be an angle between the two axes.
Observers that are fixed will not see a continuous output of light from the neutron star’s jets, but they *may* see them in pulses. These are referred to as pulsars. The fastest pulsars have over 1,000 pulses per second, which means that the neutron star is rotating more than 1,000 times every second.
Would we expect for the majority of neutron stars to be pulsars? Yes, because we would expect the neutron star to be rotating quickly and have a strong magnetic field as a result.
