Stellar Evolution A star begins as a very light dispensation of interstellar gases and dust particles over a distance of a few twelve lightyears. Although there is intensely low pressure existing between stars, this dispensation of gas exists instead of a real vacuum. If the density of gas becomes bigger than 0.1 particles per cubic centimeter, the interstellar gas grows uncertain. Any small alteration in density, and because it is impossible to have a perfectly even distribution in these clouds this is something that will naturally occur, and the area begins to contract. This happens because between about .1 and 1 particles per cubic centimeter, pressure gains an inverse relationship with density. This causes internal pressure to decrease with increasing density, which because of the higher external pressure, causes the density to continue to increase. This causes the gas in the interstellar medium to spontaneously collect into denser clouds. The denser clouds will contain molecular hydrogen (H2) and interstellar dust particles including carbon compounds, silicates, and small impure ice crystals. Also, within these clouds, there are 2 types of zones. There are H I zones, which contain neutral hydrogen and often have a temperature around 100 Kelvin (K), and there are H II zones, which contain ionized hydrogen and have a temperature around 10,000 K. The ionized hydrogen absorbs ultraviolet light from it is environment and retransmits it as visible and infrared light. These clouds, visible to the human eye, have been named nebulae. The density in these nebulae is usually about 10 atoms per cubic centimeter. In brighter nebulae, there exists densities of up to several thousand atoms per cubic centimeter. This is extremely large in comparison to densities outside the nebulae, which is slightly less than .1 atoms per cubic centimeter.
Groups of stars begin to form from these larger, denser clouds of gas and dust. Again, any deviation that occurs in these clouds will break the entire cloud into a number of condensed groups. If a grouping of gas has over a certain mass, gravity, instead of pressure variances, will then be strong enough to condense it. First, a high mass cloud will contract, then begin breaking apart and each individual mass will break apart and contract at different rates. The rate at which it contracts is dependent on the mass of each condensation, it is basically the acceleration due to the gravity of each condensing cloud. There is evidence of this in the grouping of stars into clusters and that all the stars are the same age in these clusters, as well as the large number of binary star systems that exist. The cloud can condense at an unimpeded free-fall rate until its own infrared radiation can’t escape. When this happens, the cloud dims and greatly slows in its condensation, as the infrared radiation provides and outward force and starts heating the new protostar. The protostar finally stops condensing, maintaining its size when inward gravitational pressure is balanced by outward gas and radiation pressure.
For a star around one solar mass (which is about 2x10^30 kilograms), it takes a few million years to move from a protostar to a main sequence star. The higher the mass of the protostar, the less time this takes; a star of twice this mass takes less than a million years to condense. And the lower the mass of the protostar, the more time it takes to condense and reach the main sequence; a star of half this mass can take over a hundred million years to condense.
Mentioned often in this paper is the term main sequence star. What is meant by a main sequence star is based on where it would be placed on a Hertzsprung-Russel diagram (the figure attached to the back of the essay). A Hertzsprung-Russel diagram is useful for charting the development of a star through time. The y axis charts increasing luminosity of the star, and the x axis charts decreasing temperature, color, or spectral type (which are all related). The path a star will follow, and it’s final outcome is determined primarily by the initial mass of the cloud it condensed from, although other minor influences include the charge of the star, it’s rotational velocity, and the percentage of hydrogen that was in it’s primary formation. But all stars will pass once through this main sequence, where the stars spend the majority of their life. Stars sit on a slope on the main sequence where the following formula holds true:
This is the Stefan-Boltzmann law, the relation of a star’s luminosity (L) to temperature (T), other factors are the star’s radius (R) and sigma, the Stefan-Boltzmann constant (5.6697 • 10-8 J s-1 m-2 K-4). This equation is an important tool to determine the radius of a star, since it’s luminosity and temperature is relatively easy to figure out.
A star’s size falls into the categories: Dwarf, subdwarf, main sequence, subgiants, giants, and supergiants. There are overlaps in this classification however, since the main sequence can include blue giants and brown dwarfs. There are relatively few subgiants and subdwarfs, since these are transitional stages that stars quickly pass through to get to and from the main sequence. Also, as stars during their formation move left along the Hertzsprung-Russel diagram, they pass through the red giant phase, and can be mislabeled as red giants. The main difference between these and red giants is that these protostars still have an abundance of hydrogen to be used.
In order to make the determinination of a star’s evolution possible, all of the features of a star must be known, including it’s temperature, mass, radius, distance, and internal constituents.

To determine the chemical composition of a star, an examination is made of the absorption or emission spectrum of the star, this spectrum is the groups of wavelengths that the star is most willing to absorb or emit. This spectrum is compared to the spectra of individual elements to determine which elements the star contains. When a star first forms, most of it is hydrogen, roughly 25% of it is helium, and somewhere less than 1 part per thousand will be heavier elements.
The distance a star is from earth is determined using many methods. The easiest is the parallax method, which uses the small angle theorem by measuring the change in a star’s location against the stellar background during the earth’s rotation around the sun.
Another method is called spectroscopic parallax. First the spectral type of the star is determined, and it’s location on a Hertzsprung-Russel Diagram is found, to determine the star’s absolute magnitude. With the star’s absolute magnitude, and apparent magnitude as measured on earth, the distance to the star can be determined using this formula: M = m + 5 – 5logr
Where M is the absolute magnitude of the star, m is the apparent magnitude, and r is the star’s distance away. This gives a measurement of the star in parsecs. The definition of a parsec is the distance from which the earth’s half-rotation around the sun would appear as one parallax second, which is about 3.26 light years.
A second way to measure the distance of the star using its spectrum is to measure how much the spectrum is shifted to the red end of the spectrum and comparing it to where the wavelengths should be on the spectrum. With a measurable change in wavelength, the velocity at which the star is moving away from earth can be determined. With the velocity of the star away, one can use Hubble’s distance relation to find the distance of the star: v = Hd
With H equal to somewhere between 50 and 100 km/s per megaparsec.
The mass of a lone star is more difficult to determine than other features, estimates can be made based on luminosity, temperature, and radius. The most accurate measurements of mass come from easily observed (visual) binary star systems. The total mass of the system can be determined by using Kepler’s laws of planetary motion: M (a) + M (b) = r³/p²
The distance of the stars from one another is r, and p is the period of the system’s orbit in years. If the stars are visual binaries, the stars individual masses can be determined through a ratio of their distances from the system’s center (the more massive star will be less accelerated by gravity, and will be closer to the center).
Like the evolution from protostar into star, less massive stars leave the main sequence slower and more massive stars leave the main sequence faster. Extremely low mass stars (that undergo hydrogen fusion) have lifespans of dozens of billions of years.
Protostars will only become stars if their mass is high enough to start hydrogen fusion, otherwise they will pass through the main sequence of stars and become bodies similar to our own Jupiter or Saturn. These objects are also often given the name brown giants. The mass necessary for a high enough pressure to start hydrogen fusion is about .08 solar masses. This series of steps in the hydrogen fusion process are seen here:
If a star has a mass of more than .08 solar masses, necessary for fusion to occur, but less than .3 solar masses, it can only produce helium 3, after which, it will simply continue to contract.
When the star’s core of hydrogen drops to about 1% of it’s former mass, the star begins to contract and increase in temperature. When all of the hydrogen is gone from the core, the reactions take place in an expanding shell of hydrogen around the core, as the helium inside the core grows. The core then heats and contracts as well. As the core contracts, the radius of the star expands quickly, causing the temperature of the star to drop accordingly. This state of a star is known as a red giant, as the decrease in temperature leads to a lowering of the frequency of light being emitted, closer to the red end of the spectrum. A star will reach this phase if it has over .3 solar masses. If it is between .3 and 1.4 solar masses, after expanding into a red giant star, it will slowly collapse into a white dwarf star, its fusion processes ended, and it will slowly cool. A white dwarf maintains its size when inward gravitational pressure is balanced by the degeneracy pressure of the electrons inside the star. 1.4 Solar masses is the dividing line between a white dwarf and a neutron star. If the mass of the star is greater than this 1.4 solar mass limit, the fusion process repeats with the newly formed heavy elements in the star’s core, primarily helium. This helium fusion process is called the triple alpha process, and is shown here:
When the star runs out of these other fusionble elements, the outside of the star will explode in a supernova. Meanwhile, gravitational pressure will force the electrons into the nuclei of the atoms in the star, the same electrons that had kept the star at a stable radius. The inside of the star will collapse much smaller than a white dwarf, to a radius of only a few kilometers. Their density becomes several billion kilograms per cubic centimeter. When the electrons and protons are forced into each other, a large amount of x-ray radiation is produced as well as neutrinos. This process combined with the explosion of the outer layer of the star will release more energy than the rest of the galaxy combined at this one time. With the decreased radius of the star comes a greatly increased rotational velocity. When a neutron star first forms, they can go through a rotation in a matter of milliseconds. It will eventually slow down, however, because of drag from its magnetic field. If a neutron star’s axis of rotation is greatly off from its magnetic poles, more than about 30 degrees, it is seen as a pulsar. This is because the neutron star still emits a large amount of radiation primarily from its magnetic poles, and its magnetic poles periodically pass into our view due to their misalignment with its axis of rotation. So earth witnesses very steady pulses of radiation from them.
A different occurrence than a supernova, there are also novae, which occur in binary star pairs. As mass from one star is accreted to the other star, a shell of hydrogen and other materials build up , and under enough pressure, a hydrogen fusion reaction occurs that blows the hydrogen shell off of the star. This, unlike a supernova, is a phenomenon repeatable by the same binary star system.
If the star has a mass of over 2.4 solar masses, it also supernovas, but after collapsing, inward gravitational pressure is so great that the star can’t find an equilibrium of pressures. The star will collapse to a high enough density that the escape velocity from it is greater than the speed of light, so no radiation can escape from it, giving it the name black hole. The density inside these black holes is considered to be infinite. Because of the tendency of massive black holes to never lose mass but rather absorb everything, one can say the true end phase of a star’s life has occurred when it is pulled into a black hole.

Resources:

Books:
Meadows, A .J. Stellar Evolution. London: Pergamon Press, 1967.
Shklovskii, Iosif S. Stars: Their Birth, Life, and Death. Moscow: Central Press for Literature in Physics and Mathematics, 1975.
Livio, Mario. Unsolved Problems in Stellar Evolution. Cambridge: The Cambridge University Press, 2000.
Websites:
http://www.wikipedia.org/wiki/Astronomy_and_astrophysics
Encyclopedia of Astronomy Terms http://imagine.gsfc.nasa.gov/docs/science/how_l1/spectral_what.html NASA’s Introduction to Spectral Analysis http://zebu.uoregon.edu/textbook/se.html Hypertext Book on Stellar Evolution @ The University of Oregon http://hyperphysics.phy-astr.gsu.edu/hbase/starlog/staspe.html#c1 Star Spectral Classifications @ Georgia State University http://oposite.stsci.edu/pubinfo/PR/96/22/pulsars.html How Pulsars Are Formed @ The Space Telescope Science Institute