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After the big bang, large regions of highly dense interstellar gas and dust began to accumulate, condense and form galaxies. Within these galaxies, smaller rotating molecular clouds, composed predominantly of hydrogen and helium, began to form, and within these clouds stars were born. Our sun is one of the many stars in our galaxy. With mass 2x1023 kg, radius 696000 km and luminosity 3.86x1026 Watts, it is composed of 70% Hydrogen, 28% Helium and 2% metals (elements that are not hydrogen or helium). Stars of similar masses have similar stellar evolutions so the life of stars like our sun, starting from their birth in molecular clouds, is extremely interesting for astronomers.
Molecular clouds have large densities (300 molecules/cm3) and extremely low temperatures (10-30 K), allowing the combining of atoms to form molecules1, and are subject to two forces: an inward gravitational attraction and an outwards gas/thermal pressure1. When the inward gravitational forces become larger than the outwards pressure forces the central regions, which are subject to higher gravitational attraction, are forced to contract2. This results in the collapse of the cloud and an increase in its temperature (change in gravitational potential energy (Î”Egp) increases particle kinetic energy (KE) allowing more particle collisions and the release of thermal energy in the form of photons1). In order to contract, the cloud needs to remain cool as increasing thermal pressure would impede stellar formation. The release of thermal energy by photons keeps the cloud at the desired temperature, allowing it to continue contracting1.
When the cloud is compressed sufficiently so that its mean density is extremely light, the action of gravitational forces causes the homogeneous medium to break up into several condensations3. This fragmentation of molecular clouds demonstrates why stars often form in clusters. The individual clouds continue contracting until they reach the 'hydrostatic equilibrium line'2. The growing densities of the clouds inhibit the escape of photons and thus the release of thermal energy.1 This causes a rise in temperature which increases the gas pressure of the cloud. Thus, fast contraction ceases as the centres of each cloud fragmentation become protostars, contracting very slowly.
A protostar is a new star before it begins to produce any nuclear energy in its core and establish a state of hydrostatic equilibrium. This state is achieved when its "inward gravitation attraction exactly balances the outward pressure forces at every point within the star"4. Due to the conservation of the initial cloud's angular momentum, an accretion disk of gas and dust forms around the protostar5. Material from the disk can accrete onto the star, increasing the rate of protostar contraction. Gravitational attraction causes matter to be pulled towards the protostar's centre and as a result, its central regions contract more rapidly, forming a core. Once the core forms, it accretes matter from the surrounding envelope. The changing gravitational potential energy of this matter produces heat, causing the dust grains and gas to radiate infrared wavelengths4. As the star continues to contract, its "self gravitation"4 increases, so the internal pressures increase to develop hydrostatic equilibrium. The star is now a very luminous pre-main sequence star.
Now in a state of hydrostatic equilibrium, the star's thermal energy content roughly equals its gravitational binding energy6. At the star's centre, the gas pressure increases to counter balance the star's increasing weight due to the accretion of mass from the accretion disk. The pre-main sequence star slowly collapses until there is enough energy in the core to ignite thermonuclear reactions, making it a "real star".
The star has now become a main sequence star. The majority of known stars, including our sun, lie on the main sequence line of the Hertzsprung-Russell diagram which is a plot of stellar luminosity versus temperature, with the main sequence shown as a diagonal line running from the bottom right to the top left hand corner. Stars spend on average 80% of their lives in the main sequence stage burning hydrogen to helium in their cores.
Thermonuclear reactions provide the long term energy sources for stars.4 Main sequence stars fuse hydrogen to helium in their cores via two main reactions: the Proton-Proton (p-p) chain and the Carbon Nitrogen Oxygen (CNO) cycle. The presence of each reaction is determined by stellar mass; the p-p chain dominates in low mass stars (< 1.5 solar masses), while the CNO cycle is more prominent in high mass stars (> 1.5 solar masses) with large core temperatures (> 1.8 x107 K). In our sun, both reactions take place however, the p-p chain is more important and occurs 91% of the time3. In the p-p chain reaction 4hydrogen nuclei fuse together to form 1 helium nucleus:
1H +1H -> 2H +e++ v
2H + 1H -> 3He +g
3He + 3He -> 4He + 1H + 1H
The CNO cycle still contains 4 hydrogen combining to produce 1 helium however it is a six stage process and requires the use of carbon as a catalyst:
12C + 1H -> 13N + g
13N -> 13C + e+ + g
13C + 1H -> 14N + g
14N + 1H -> 15O + g
15O -> 15N + e+ + v
15N + 1H -> 12C + 4He
It is possible to note carbon's role as a catalyst by observing that the cycle starts with the reaction of a carbon and a hydrogen nucleus and ends with the release of an identical carbon nucleus, thus not being used up in the process. This process dominates in hotter main sequence stars as the coulombic barriers of carbon and nitrogen are greater than that of protons and helium nuclei4 and thus lots of heat is required to overcome the electrostatic/coulomb repulsive forces on the nuclei. Similarly, the CNO cycle dominates in high mass stars as more massive stars have a larger gravitational pull towards the core and therefore they generate the high temperatures which the cycle requires.
Over time, as the hydrogen abundance in the core decreases, core temperature and density increase to maintain the same rate of nuclear fusion4 however, the central density of the star stays relatively constant. A star like our sun has enough hydrogen in its core to fuel it for 10 billion years5 however, only 10% of this hydrogen is used for energy generation during the main sequence phase of the star's lifetime2. As stars fuse hydrogen to helium their temperature increases, they expand slightly and due to the greater energy flow to the surface, they increase in luminosity causing them to move up the main sequence.
Low mass stars like our sun remain on the main sequence, burning hydrogen, for approximately 10 billion years. However, once the helium content in the core reaches 12%, hydrogen fusion stops. As no energy is being produced in the core there is no longer the outwards radiation pressure to maintain hydrostatic equilibrium with the gravitational forces and the star collapses. The change in gravitational potential energy of the atoms due to the cloud's contraction gives rise to an increase in their kinetic energy, thus producing thermal energy. This heats up a hydrogen shell surrounding the core causing it to start fusion again. As this hydrogen burning shell develops, the star's contraction rate slows and the shell increases in thickness. "This fusion is terminated when thermal instability arises in the shell. The shell narrows, the core "collapses" and the surrounding envelope rapidly expands"6 to form a Red Giant.
A Red Giant has all its mass concentrated in a core of a few Earth radii at temperatures of approximately 50 million K. This high density causes the electrons in the core to become degenerate ("occupy the same cell in phase space"7) producing a degenerate gas pressure which stops the red giant core from collapsing although no nuclear reactions are taking place8. The expansion of the star's envelope as it evolves from a main sequence star to a red giant means a decrease in surface temperature and an increase in opacity. Opacity is "the phenomenon of not permitting the passage of electromagnetic radiation"9 and so convection carries the star's energy outwards through the expanding envelope. This causes the star to be very luminous, evident in its placement on the Hertzsprung-Russel diagram.
Figure - The Hertzsprung - Russell diagram
Although the outer layers of the giant are expanding, the core of the star continues to contract. After a short phase of core contraction, the core temperature becomes high enough to ignite helium fusion. This is called the Helium Flash and helium fuses to form carbon in the Triple Alpha Process.
4He + 4He -> 8Be +g
8Be + 4He -> 12C +g
As the helium core is degenerate, increasing temperature due to its fusion does not cause an increase in gas pressure and therefore the core does not expand. The increasing temperature does however increase the rate at which the triple alpha process takes place. Eventually, the energy released by the helium flash raises the core temperature to a point (approximately 350 K) where the electrons in the gas are no longer degenerate and the thermal pressure becomes strong enough to "push against gravity"10 resulting in an expansion of the core. The fusion stops in the core but continues in the surrounding layer, causing it to expand into a red giant again and move up the asymptotic giant branch8. This branch is occupied by stars with a helium-filled core surrounded by a helium-fusion shell which is enclosed by a hydrogen-fusing shell11.
The more massive the star, the greater the core temperature produced by gravitational contraction before degeneracy sets in and the heavier elements it can fuse. In high mass stars, the core eventually gets hot enough so that the triple alpha process can fuse from carbon to neon to oxygen to magnesium to silicon and sulfur all the way up to iron. However, no matter how massive the star, the heaviest element that can be produced during fusion is iron. These elements are then thrown back into the interstellar medium by the supernova explosions of the more massive stars and without the triple-Alpha reaction, there would be only hydrogen and helium gas in the universe resulting in no solid planets and no life. Unfortunately for our sun and similar stars, carbon is the furthest element they can fuse as they will never achieve a high enough temperature to ignite carbon fusion.
As the contraction of the core does not produce enough energy for the burning of carbon, it contracts to a highly compressed state increasing the rate of helium burning in the process. The star then pulsates8 until the helium is exhausted from the core causing it to collapse and eject its outer layers. The envelope of outer layers separates from the core as a thin shell, expanding and cooling. This is called a planetary nebula and exists as a "halo" around the leftover core of the star. For stars less than 1.4 solar masses (the Chandrasekhar limit) the remaining core becomes a white dwarf composed of predominantly carbon and oxygen. White dwarfs cannot have masses greater than 1.4 solar masses as the degeneracy pressure of masses greater than this is insufficient to prevent further collapse.
White dwarfs are so dense that the atoms become completely ionized (degenerate) inhibiting the random movement of electrons and preventing further collapse. White dwarfs shine solely due to the left over kinetic energy of atomic nuclei in their interior as thermonuclear reactions do not take place in their cores. The motion of these nuclei eventually ceases, causing the white dwarf to cool and become a black dwarf.
The study of stellar formation offers great insight into the formation and structure of the universe. By studying the formation of stars of similar size to our sun, we further our understanding of our sun which in turn aids in an understanding of our solar system and thus planet Earth. Stellar formation is both a significant and a truly amazing topic of research.
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