Chapter 9: Structure and Formation of Stars
Highlights
1. Interstellar medium
2. Nebula: emission nebula, reflection nebula
3. Interstellar reddening
4. Infrared satellite images: Infrared Cirrus: a faint wispy network of dust and cloud
5. Molecular clouds: Shockwave
6. An Association is a group of stars
7. A Protostar
8. Evolutionary track: Birth line
9. T: Tauri Stars: Herbig-Haro objects
10. Bipolar flow
11. Bok Globules: EGGs Evaporating gaseous globules
The space between stars is called interstellar medium. This space or medium is not completely devoid of matter. The space is filled with hydrogen 75% and helium 25%, traces of carbon, nitrogen, oxygen, calcium, sodium, molecular hydrogen and silicates. The matter is non-uniformly distributed, presence of hot , low density gas currents circulating in the medium and generating twisted complex tangle of cool, dense clouds like the puff of a cigarette smoke.
NEBULA: The interstellar medium is seen as patches of dust and clouds of gas. Such cloud is known as Nebula. In the presence of hot stars nearby, the gases in the nebula are ionized. Energy from hot stars absorbed. This produces an emission spectrum and the nebula is called emission nebula. This spectrum contains three visible lines of hydrogen blending into pink color of the nebula. In some cases, nearby star light is reflected off the dense clouds of nebula resulting in the blue color of the nebula. This is called reflection nebula made by reflection of star spectrum. Tiny dust grains scatter blue light more than red light. Sometimes the starlight from distant stars are blocked by the nebula or dense gas clouds.
Many times,the starlight from hot stars passing through the gas clouds are scattered. Blue light is more scattered out than red light. This results in the reddening of the interstellar medium, known as interstellar reddening.
The infrared images of the interstellar medium shows presence of dusty clouds all over the space. These false color images in the infrared show structures similar to CIRRUS clouds and so these are called infrared cirrus. Generally speaking, the slow moving dusty clouds being very cold help produce formation of hydrogen and other compounds. Infrared images have indicated the presence of vast amount of giant molecular clouds in some parts of the sky. If there exists hot stars nearby, they produce shockwaves that pass through the giant molecular clouds, compressing the gas to form denser clouds. The shockwaves may happen to pass a number of times, fragmenting the gas clouds into
smaller and denser structure. This fragmentation favors production of group of early stage stars called Association. This is similar to the rain drops produced in a thunder cloud. The compression of dense gas by shockwaves produces fragmentation, gravitational force triggers free fall contraction of gas clouds resulting in a cocoon of early star called a Protostar. Such a proto star is covered with dense cloud of gas as in a cocoon. The free fall contraction due to gravitational pull slows down due to production of immense heat and dense material. The heat energy generated blows away the outer shell of cocoon.
Contraction of the protostar continues, ionizing the gas atoms into electrons and positively charged ions, generating immense heat that triggers nuclear reaction in the core eventually. The star is born. The time it takes for a protostar to contract and become main sequence star depends on the mass its mass. More massive stars contracts faster and genertes more heat energy driving the cocoon of dust faster and reaching the main sequence earlier than less massive star. Sun took 30 million years to reach ms.
15 Solar mass star will take 160,000 years and 0.2 solar mass star will take 1 billion years to reach main sequence (ms).
When the contracting protostar is visible by blowing out the dust cloudy envelope, it has reached the ms and the lower edge of ms is called birth line. Main sequence is NOT a line but a band.
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As a typical case, a fragment of 1-solar mass gas clouds may form a protostar from 50 to more than 1000K collapsing dust heating it up. Exact process is poorly understood, complex collapsing process of dust particles. Dust clouds hide the protostar, its probable color is luminous red, a few thousand times larger than sun - red giant on H-R digram. Then makes a free-fall like fast contraction, constantly heating up, not enough temperature to start nuclear reaction. Free fall stops, slow intense contraction starts temperature rising to begin nuclear reaction. During contraction, gravitational energy due to collapsing dust clouds converts into heat energy, half of it radiates out and the rest increases the internal temperature. Climbing internal temperature ionizes gas into free electrons and atomic nuclei. Center gets hot enough to begin nuclear reaction, protostar halts contraction, having blown away its cocoon of gas and dust, it becomes a new star or a main sequence star. Length of time in evolutionary track depends
on mass. More massive 15 solar mass takes 160,000 yrs reach main sequence 1-solar mass takes 30 million yrs and 0.2 solar mass takes 1 billion yrs. This is of course a theoretical model.
We now look for observational evidence.
Difficult to observe protostar obscured by clouds of gas cocoon, it spends about 0.1% of its total life
as protostar. The birth line is when it first becomes visible on a line at the main sequence. So, early evolution of protostar is hidden from our direct observation. Dust absorbs light from protostar and radiates infrared radiation. This is detected as a bright source by Infrared Astronomy Satellite. T-Tauri stars or variable stars T in Taurus constellation, seemed to be just clearing cocoon of surrounding dust and debris. These stars vary in brightness, their gas particles flowing away like strong solar winds, sources of infrared radiation,
an indication of presence of debris & dust, and the object like a rotating disk. NGC2264 contains large number of T Tauri stars,
some are so young that they are yet to reach the main sequence line, now present on the right side of main sequence birth line in H-R diagram. There is evidence from such star forming objects, of blasting gas away in two shooting jets in opposite directions, called BIPOLAR FLOW.
There is also evidence of spinning disk of gas around a forming star, additionally gas falling
into the disk, result of the interaction between the magnetic field of interstellar cloud and the rotating disk is blowing up of gas & dust outward along axis of rotation. Rotating disk and bipolar outward flow of two jet streams of gas dust are common events in the star formation. Many times, the entire region is a site of active star formation as in Eagle Nebula seen by Hubble's telescope.
BOK GLOBULES are objects, observed as dark patches of dust cloud 1 ly wide, 10-100 solar mass silhouetted against the background of bright nebula. The star forming objects are common near the region of Bok Globules. Astronomers call them EVAPORATING GASEOUS GLOBULES or EGGs.
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12. Nuclear energy and nuclear force: strong force and weak force
13. Nuclear fission and Nuclear fusion reactions
14. Hydrogen fusion: must overcome Coulomb barrier
15. Proton: proton chain and CNO cycle
16. Heavy element fusion: triple alpha process
17. Pressure-temperature thermostat
18. Stellar Structure: laws of mass and energy
19. Conservation of mass and conservation of energy
20. Hydrostatic equilibrium
Most of us are familiar with electric force. The electric force is attractive for opposite signs of charges and repulsive for like charges. The nucleons are found in the nucleus of the atom. Nuclear forces are present among all combination of protons and neutrons inside the nucleus. Electrons in outer orbits are ignored while we study nuclear forces inside the nucleus. In nuclear physics, there is no distinction between protons (positive) and neutrons (electrically neutral). The common name of proton and neutron is nucleon.
There are two types of nuclear force: strong force (interaction) and weak force (interaction). The strong nuclear force is the most powerful of all natural and fundamental forces. The two familiar nuclear reactions due to strong nuclear force are: (a) nuclear fission and (b) nuclear fusion. Both the nuclear forces are significantly strong for very short. Nuclear fission is a process in that a heavy nucleus such as Uranium splits into lighter nuclei and gives off large amount of heat energy. Nuclear fusion is a process in which the two or more lighter nuclei may combine to produce larger more compact nucleus and give off large amount of energy. In both situations, mass loss produces the heat energy predicted by Einstein's famous mass energy relation
E = mc2
An example of nuclear fusion is 4 hydrogen nuclei combine to produce a helium nucleus giving off a large amount of energy. COULOMB barrier is referred to as the electrically repulsive force among the positively charged protons. The nuclear force being much stronger at short distance can easily overcome the repulsive Coulomb force among the protons. There is no Coulomb force with neutrons. The strong attractive nuclear force is the same among proton and proton as among proton and neutron or neutron and neutron at short range. Strong attractive force results into strong and violent collisions. At the center of the star, the gas is hot and dense, the nuclei are ideally very close to each other for nuclear reactions to occur. Four protons combine to produce a Helium nucleus consisting of two neutrons and two protons. The excess energy appears in the form of gamma rays, neutrino and positron.
A second type of nuclear fusion takes place in massive large stars ( > 1.1 solar mass) with the help of carbon nuclei and hydrogen, going through transformation into nitrogen, then oxygen and finally emerging as He nucleus and the same initial carbon nucleus. This process is called CNO cycle and it requires intense energy and extreme temperatures ( > 16 million degrees) at the core of a massive star. There can be nuclear reaction with heavier nuclei. At sun's core hydrogen nuclei are burnt first. When hydrogen is exhausted, then the immense heat at the core ignites the second nuclear reaction involving heavier elements such as helium and helium nuclei forming beryllium nuclei. Beryllium nuclei in its turn combine with other He nuclei to produce carbon nuclei. This process that involves 3 helium nuclei to produce a carbon is called TRIPLE ALPHA PROCESS.
TRIPLE ALPHA PROCESS.
Alpha is the name of helium nucleus. The pressure temperature thermostat is extremely useful concept for understanding the mechanism of star formation.
It is a constant battle between the heat and radiation energy pushing the inwardly collapsing dense gas under gravitation. The two are always playing against each other as in a thermostatic control of constant temperature device like a freezer.
Helium "Burning"
TRIPLE-ALPHA PROCESS
4He2 + 4He2 => 8Be4
8Be4 + 4He2 => 12C6 + g
Other Reaction Processes
12C6 + 4He2 => 16O8 + g
14N6 + 4He2 => 18O8 + e+ + g
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At 600 million degrees, carbon nuclei fuses in a complex chain of nuclear reactions known as heavy-element fusion. This produces aluminum, magnesium, silicon and iron. This process is complicated by the fact that nuclei can react by adding a proton, neutron or helium nucleus, also combining directly with other nuclei. Unstable nuclei decay by ejecting electron, positron or helium nucleus.
Thermonuclear fusion - fusion of small mass nuclei, primarily hydrogen nuclei, to form more massive nuclei, primarily helium, with resulting direct conversion of mass into energy by E = mc2
Mathematical form: 41H1 => 4He2 + g + n
1H1 = hydrogen nucleus, i.e., proton
4He2 = helium nucleus, i.e., 2 protons + 2 neutrons
g = gamma-ray photon
n = neutrinos
Hydrogen "Burning"
Proton-Proton Chain
1H1 + 1H1 => 2H1 + e+ + n
2H1 + 1H1 => 3He2 + n
3He2 + 3He2 => 4He2 + 21H1
Carbon-Nitrogen-Oxygen Cycle
12C6 + 1H1 => 13N7* + n
...
15N7 + 1H1 => 12C6 + 4He2
Four conservation laws:
1. The conservation of mass law states that sum of the masses of the layers around the star is equal to mass of the star.
Mass conservation - total mass equals sum of layers of shell masses
2. The conservation law of energy - Energy Generation: Sun would cool at a much faster rate, fast enough to be measurable, if Sun emitted radiant energy only. Yet it stays at about the same temperature for a long time. Sun is not cooling significantly. Consequently, Sun has energy source that replaces energy loss in luminosity, thus keeping interior hot. Amount of energy flowing out of the top surface of a layer of the star must equal to the amount of energy coming in at the bottom of the surface of the layer plus whatever the energy generated within the layer.
Energy conservation means, luminosity equals sum of energy generation in each layer plus the energy entering the layer.
Also related is the idea of Thermal Equilibrium
Thermal equilibrium means, amount of energy produced inside equals amount radiated away as luminosity
3. Law of Hydrostatic equilibrium - weight of overlaying layers balanced by pressure forces of hot gases pushing out.
Mathematically, weight of gas = outward pressure of hot gas
Results: star neither expands nor contracts in their main life.
It is a self-regulating mechanism.
If too much energy is produced, Sun heats up and expands
If too little energy is produced, Sun cools down and contracts
Hydrostatic equilibrium means, weight of overlying layer is balanced by outward pressure of hot gases flowing outward from below
4. Law of Energy Transport: Energy transport means, movement by various physical processes of energy from deep interior to the surface. Energy moves from hot (high-energy density) region to cool (low-energy densty) region. The law states that the energy must move from warmer region to the colder region by three processes e.g., conduction, convection and radiation. Energy liberated in deep interior is in form of relatively few high-energy gamma-ray photons
Radiative transport - energy moves outward by absorption and re-emission by matter, degrading the photon energy to a large number of low-energy visible photons. This happens from the core to the bottom of the photosphere.
Because solar gases are almost totally ionized, behavior of nuclei and free electrons is simple, its behavior is predicted by ideal gas laws.
Opacity of the gas means the resistance it offers to the flow of radiation. This strongly depends on temperature.
Opacity - resistence offered by matter to the movement of radiation through it
transparent <=> opaque
Convective transport - hot gases rise, cooling, and sinking back down to be re-heated and rise again; cyclic movement of matter as in the photosphere of the sun
Why Stars Evolve?
1869, Homer Lane, American meteorologist, wrote first paper on physical conditions inside Sun
Stars are self-gravitating, self-luminous spheres of hot gas. Life cycle of star is a battle with gravity (self-gravitation) to keep from squeezing star out of existence; three forces can counter gravity
Kinetic pressure of hot gases (star must cool)
Repulsion from Pauli exclusion principle for electrons
Repulsion from Pauli exclusion principle for neutrons
Sun, model for stellar structure
Sun is model for processes undergoing in other distant stars
Physical laws operating inside Sun and presumably other stars can be inferred from the knowledge of the sun
Stellar Evolutionary Models
Mathematical model calculated as means of studying evolution of stars.
Stellar model obtained by solving equations of stellar structure
Structure equations describe mass, pressure, temperature, and luminosity from center to surface
Stellar models suggest physical processes going on inside real stars. Sequence of stellar models calculated for different times in star's life show evolutionary tracks in H-R diagram
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MORE NOTES OF THE CHAPTER
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Where did All These Stars Come From?
Today we will become entangled in a Cosmic "Who Did it" - a mystery that has as its goal
the understanding of the formation of the stars themselves. Nature has provided us with
the following clues:
· Dust lanes in the milky way
· Dust in the presence of clusters of young blue stars
· Bright emission Nebulae
· Dark nebulae
· Interstellar Medium
· Radio emissions from dark clouds
Birth of Stars
· Stars born in giant molecular clouds composed of gas and dust (interstellar matter),
which lie along spiral arms of our Galaxy
· Giant molecular clouds
Diameter: 60 to 300 light years
Gas density: 102 to 106 particles/cm3
Mass: 105 to 106 Msun of gas and dust
· Collapse of giant molecular clouds initiated by
Self-gravitation in growing density
Squeezing by spiral-density waves or supernova shocks
Shock Compression Of Clouds
· Shock Front
· Giant Molecular Cloud
· Interstellar shock wave strikes cloud
· Fragmentation process begins in cloud
· Star formation begins in cloud
Cloud fragments into smaller, denser bodies of 103 to 105 Msun
These collapse into groups of young stars
Examples of birthplaces of stars
Eagle nebula
Orion nebula
Omega nebula
Star Formation in Orion Nebula
If gravitational force unchecked, gravity would squeeze star down to nothing as star contracts
Force opposing gravity
Gas pressure
Radiation pressure
Interstellar magnetic fields
Gas pressure holding up weight of overlying layers decreases due to loss of energy as star radiates in visible and infrared
Radiation from developing star hidden by surrounding gas and dust
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Stellar - Pre-Main-Sequence Evolution
Birth of Stars
Stars born in giant molecular clouds composed of gas and dust (interstellar matter), which lie along spiral arms of our Galaxy
Giant molecular clouds
Diameter: 60 to 300 light years
Gas density: 102 to 106 particles/cm3
Mass: 105 to 106 Msun of gas and dust
Collapse of giant molecular cloud initiated by
Self-gravitation in growing density
Squeezing by spiral-density waves or supernova shocks
Cloud fragments into smaller, denser bodies of 103 to 105 Msun
These collapse into groups of young star forming objects called "ASSOCIATION."
If gravitational force unchecked, gravity would squeeze star down to nothing as star contracts
Force opposing gravity is
Gas pressure
Radiation pressure
Interstellar magnetic fields
Gas pressure holding up weight of overlying layers decreases due to loss of energy as star radiates in visible and infrared
Radiation from developing star hidden by surrounding gas and dust cloud in a Cocoon
Examples of birthplaces of stars
Eagle nebula
Orion nebula
Young star cluster
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CONSTITUENTS OF INTERSTELLAR MEDIUM
Interstellar Medium gas
Interstellar Medium dust
Interstellar Medium molecules
Result of the solution of differential equation formed by applying laws of physics- stellar model
Solar Interior Model:
Protostar contracts from interstellar medium
Burns hydrogen on main sequence
Contracts, initiates helium burning as red giant
"Ash" of one nuclear-burning phase provides fuel for next burning phase
High-mass stars alternately contract/ignite new sources of thermonuclear burning
Shed outer layers and die
Low-mass stars as white dwarfs
High-mass stars as neutron stars
Extreme high-mass stars as black holes
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Stellar Evolution:
- Main-Sequence Evolution: When a protostar begins to fuse hydrogen, it stops contracting and becomes stable. We may say it has reached the line of main sequence stars at the lower edge of the band. These stable stars are located in the main sequence band. They are 90% of all stars in the known universe. More massive star must be more luminous.
Main Sequence
Contraction from interstellar medium leads star to zero-age main sequence where hydrogen burning is initiated
Main sequence is composed of those stars and only those which are in hydrogen-burning phase of life. Mass luminosity relation is linked with Hydrostatic Equilibrium.
It states that the outward pressure generated by the hot energetic gas is balanced by the weight og the mass due to inward gravitational pull. Also, this relates to understanding of Pressure-Temperature Thermostat that regulates energy production in the core of a star. In that, if the energy production by nuclear reaction slows down, the internal temperature falls down, the decreased outward pressure resulting from low temperature gives in to the inward contraction of gravitation. Gravitational contraction takes over squeezing and raising the temperature higher and increasing the nuclear reaction (hydrogen burning, four nuclei becoming one nucleus) that counters the contraction of gravitational force. On the other hand increasing outward pressure of nuclear energy expands the star, it cools a little bit due to expansion, nuclear reaction slows down and makes room for force of gravity to take over.
So, stars on main sequence are stable but not uneventful. Sun at its birth 5 billion years ago was 70% luminous than now. It will be 200% luminous after 5 billion years in giant stage of its life. Earth temperature will increase by at least 34 degrees F. Long before, the ice-cap in the polar region will melt and this will bring disaster effect on earth's climate.
An average star spends 90% of its life on the main sequence.
Stars remain on main sequence most of their lives for two reasons:
Large yield of energy per gram for hydrogen fusion
Vast amount of hydrogen available
Time star spends on main sequence is proportional to mass divided by luminosity
Now, Luminosity L = M3.5
Tmain sequence is proportional to (Mass/Luminosity). That is,
Time spent T = M/L = M/M3.5 = 1/M2.5
Mass loss at various periods of star's life may significantly alter course of subsequent evolution, since evolution is controlled by star's mass. More massive star like 25 solar mass will die in 7 million years and low mass red dwarfs (0.1 solar mass) may live 300 billion years.
Star replaces radiated energy through hydrogen "burning" and other thermonuclear fusion processes
Hydrogen burning:
Low-mass hydrogen nuclei fuse at very high temperatures, > 106 K,
41H1 => 4He2 + energy
End product heavier helium nuclei
Plus energy by converting mass into energy according to Einstein's equation E = mc2
Hydrogen burning phase defines main-sequence phase of star's life (about 90% of total life span)
SOME KEY POINTS:
The birth of stars from Interstellar Medium
Formation of stars from the interstellar dust cloud and gas
Nuclear energy of stars
Nuclear binding energy
Hydrogen Fusion
Heavy element Fusion
Stellar Evolution (and Structure)
About Main Sequence Stars
Life expectancy of Stars
The Orion Nebula
KEY WORDS
INTERSTELLAR MEDIUM
NEBULA
EMISSION NEBULA
REFLECTION NEBULA
INTERSTELLAR REDDENING
INFRARED CIRRUS
MOLECULAR CLOUD
SHOCK WAVE
ASSOCIATION (of stars)
PORTOSTAR
EVOLUTIONARY TRACK
BIRTH LINE
T TAURI STAR
HERBIG HARO OBJECT
BIPOLAR FLOW
BOK GLOBULE
STRONG NUCLEAR FORCE
WEAK NUCLEAR FORCE
NUCLEAR FISSION
NUCLEAR FUSION
COULOMB BARRIER
PROTON-PROTON CHAIN
CNO CYCLE
NEUTRINO
TRIPLE ALPHA PROCESS
CONSERVATION OF ENERGY
HYDROSTATIC EQUILIBRIUM
ENERGY TRANSPORT
OPACITY
STELLAR MODEL
BROWN DWARF
ZERO AGE MAIN SEQUENCE (ZAMS)
Protostar eventually becomes a star.
In the H-R diagram the luminosity versus temperature change as protostar progresses toward real star is shown by a line that is called EVOLUTIONARY TRACK.
Evolutionary track is not actual movement of star.
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Nuclear binding energy: four known forces in the world. Nuclear power plants generate
energy by nuclear fission. Stars make energy by nuclear fusion much harder to control on
earth. In it, lighter nuclei form tighter association releasing a large amount of energy.
Coulomb barrier the repulsive electric force among like charges are easily overcome by much powerful nuclear force called Strong Interaction in nuclear reaction. Proton-proton chain produce helium nuclei, releasing large energy in nuclear fusion. In CNO cycle, carbon pass through stage of its own isotope and then nitrogen and oxygen
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Pressure-temperature thermostat:
STELLAR STRUCTURE:
laws of mass and energy
hydrostatic equilibrium
energy transport processes
stellar models
main sequence stars
mass-luminosity relation
life of main sequence stars
life expectancies of stars
Orion nebula
Updated 08/01/02