Star Formation and Evolution Low and Medium Mass Stars Four Components of the Interstellar Medium Component Temperature Density (K) (atoms/cm 3 ) HI Clouds 50 150 1 1000 Intercloud Medium 10 3-10 4 0.01 Gas HI and ions of other elements partially ionized Coronal Gas 10 5-10 6 10-4 10-3 highly Ionized Molecular 20 50 10 Clouds 3-10 5 molecules 1
Phenomena Resisting Gravitational Collapse of a Cloud Fragment Rotation: In the rotating cloud s frame of reference, there is a centrifugal force pulling the cloud material outward. Thermal Motion: The random motions of atoms and molecules exert a pressure that resists collapse. Magnetic Fields: Ionized atoms falling inward are deflected by the magnetic field which thus opposes gravity. Neutral atoms collide with the ions, so their fall is also obstructed. The magnetic field thus exerts a pressure opposing collapse. Turbulence: irregular motions, including whirlpools of gas, oppose collapse. Phenomena that Produce Shock Waves can Cause Gravitational Collapse of Cloud Fragments Supernova Explosions Stellar Wind from a Hot, young Star Radiation Pressure from a Hot, young Star Cloud Collisions Spiral Arms of the Galaxy Overview of Star Formation Collapsing cloud fragment Protostar (converts gravitational energy to heat and light) Main Sequence Star (generates light and heat by fusion of H to He) As material surrounding the young star falls toward it, it is channeled along magnetic field lines and heated by the conversion of gravitational energy into heat and light. After crashing onto the surface near the magnetic poles, much of it is ejected and focused by the magnetic field and the pressure of the accretion disk to form a jet of ionized gas emerging from each pole. 2
Properties of an Ideal Gas An ideal gas is a gas of particles that don t stick to one another when they collide. The material in a main sequence star is so hot that, even in the core where the density is more than 100 times the density of water, it behaves like an ideal gas. When the atomic nuclei collide (and fusion doesn t occur), they just bounce without sticking. Because of this, you must understand the following properties of an ideal gas in order to understand the behavior of a main sequence star. A. Ideal Gas Equation of State: The pressure P (the force on a square meter of surface), number of particles per unit volume n, and absolute temperature T are related by the formula PV = NkT. k is a constant. B. Virial Theorem: When a star contracts, its gravitational potential energy decreases; half of the lost GPE increases the star s temperature and half is converted into electromagnetic energy. C. When an isolated gaseous region expands, its temperature drops. D. When an isolated gaseous region contracts, its temperature rises. E. The average kinetic energy of the particles of a gas is proportional to its temperature. Hydrostatic Equilibrium When all of the forces on an object cancel each other so that the net force is zero, and the object (according to Newton s first law of motion) is not accelerated, the object is said to be in equilibrium. When the net force on the parts of a fluid (gas or liquid) is zero, the fluid is said to be in hydrostatic equilibrium. A main sequence star is approximately in a state of hydrostatic equilibrium. If we imagine it to be divided into shells that fit together to form a continuous sphere, the net force on each shell is approximately zero. The white arrows in the figure represent the outward pressure force on the shell. The green arrows represent the force of gravity on the shell lldue to all of the mass inside id it. If something causes the pressure to drop, the force of gravity is then greater than the pressure force. The shell accelerates inward. If something causes the pressure to rise, the pressure force is then greater than the force of gravity. The shell accelerates outward. 3
Principles Responsible for the Stability of a Main Sequence Star A. The rate of energy production by fusion in the star s core increases with temperature. B. The absolute temperature is proportional to the average kinetic energy of the particles of the gas. C. When the star expands, its gravitational energy increases. The law of conservation of energy and the virial theorem require that this increase be compensated for by a decrease of some other energy. In this case, the average kinetic energy of the atoms decreases and photons are absorbed. Since temperature is proportional p to the average kinetic energy of the nuclei, the expansion of the star is accompanied by cooling. D. When the star contracts, its gravitational energy decreases. In this case, the average kinetic energy of the atoms increases and photons are emitted. Therefore, the star heats up. The Stability of a Main Sequence Star As we ve seen on the surface of the Sun, a star is in continual turmoil. Pressure, temperature, and volume of a star are continually fluctuating. Why doesn t the star collapse or explode? Consider a shell of material in the core. Suppose that the shell is initially in hydrostatic equilibrium and there is a random increase in the rate of energy production in the shell. The increased energy production rate increases the temperature of the shell. Since the pressure is proportional to the temperature, this results in a pressure increase. Because of the increased pressure, the shell is no longer in hydrostatic equilibrium. The outward pressure force is greater than the inward force of gravity, so the shell expands. The expansion of the shell causes its temperature to drop. The lower temperature slows the rate of energy production. As a result of the lower pressure, the shell contracts. The contraction causes the temperature to increase, which causes the rate of energy production to increase. 4
Why is there a mass-luminosity relation? A protostar contracts until it is in hydrostatic equilibrium. The pressure force on any shell is then balanced by the force of gravity on that shell. The higher the mass of the star, the stronger the force of gravity and the higher the pressure required for hydrostatic equilibrium. Since pressure is proportional to temperature, the higher pressure needed by high mass stars implies that they also have higher temperatures and therefore a higher rate of energy production (luminosity). The observed mass luminosity relation is approximately given by L M 3.5. The amount of mass converted into energy is proportional to M. The lifetime of a star is therefore related to mass by E M 1 t =. L 3.5 2. 5 M M If we use solar mass units and accept the value 10 10 years as the main sequence lifetime of the Sun, then 10 10 t = years. Example: the lifetime of a 16 solar mass 2.5 M star is 10 10 10 10 7 t = = 10 years 2.5 5 16 4 Why is the main sequence a band rather than a line? NkT For an ideal gas, PV = NkT. Solving this for P, we get P =. V Every time 4 protons fuse to form 1 helium nucleus, the number N of nuclei in the core decreases without an immediate change in V and with little immediate change in T. Therefore the pressure decreases and the outward pressure force no longer balances the inward force of gravity. Since the gravitational force is now greater than the pressure force, the core of the star contracts. This contraction heats up the core and increases the rate of energy production and therefore the luminosity of the star. The star moves upward away from the zero age main sequence. The increased luminosity of the core increases the pressure on the rest of the star. This causes it to expand and cool. Thus, the star moves to the right away from the zero age main sequence. ity Luminosi Schematic HR Diagram Temperature 5
Hydrogen Fusion in Main Sequence Stars A star spends about 90% of its life as a main sequence star. This phase of its life is characterized by the production of energy by the fusion of 1 H 1 into 2 He 4. Stars with masses between 0.08 and 1.1 times the mass of the Sun do this by means of the proton proton chain, which was described in the lecture on the Sun. Although stars more massive than this also fuse hydrogen by this means, most of their energy is due to a more complicated process called the CNO cycle. The net effect of one round of the CNO cycle is to covert 4 protons into one helium nucleus, but there are a number of intermediate steps that involve the use of 6 C 12 nuclei as a catalyst. Proton - Proton Chain H + H H + e + ν 1 1 2 + 1 1 1 e H+ H He +γ 2 1 3 1 1 2 He + He He + H + H 3 3 4 1 1 2 2 2 1 1 CNO Cycle C+ H N+γ 12 1 13 6 1 7 N C+ e + +ν 13 13 7 6 e C+ H N+γ 13 1 14 6 1 7 N+ H O+γ 14 1 15 7 1 8 rate = ct 20 rate = ct 4 O N+ e + +ν 15 15 8 7 e N+ H He+ C 15 1 4 12 7 1 2 6 Laws of Stellar Structure Hydrostatic Equilibrium Energy Transport Conservation of Mass Conservation of Energy Limits of the Main Sequence Upper Limit: High mass stars (300 solar masses). Lower Limit: Low Mass Stars (0.08 solar masses). Brown Dwarfs: No Fusion (M < 0.08 solar masses. 6
Why do heavier elements fuse at higher temperatures? The electrostatic force that two charged particles exert on each other is called the Coulomb force and is given by the following equation kq1q F = 2 2 d k is a constant, q 1 and q 2 are the charges, and d is the distance between them. For fusion to occur, the particles must get very close to each other. However, the closer they get, the more strongly they repel each other. They must collide at very high speeds in order to get close enough for the strong nuclear force to bind them. Since the average speed of a particle of an ideal gas is proportional to the square root of the temperature, fusion will only occur at high temperatures. A combination of high stellar core temperatures and quantum mechanical tunneling makes fusion possible in stellar cores. The heavier elements have more nuclear charge than the light elements. Since the Coulomb force is proportional to the product of the charges, fusion of the heavier elements requires higher temperatures. Energy Production in Stars Proton-proton chain (M 1.1 M Sun ) This is the main source of a star s energy for spectral classes cooler than F0 It dominates at core temperatures between 3 10 6 and about 2 10 7 K CNO cycle (M > 1.1 M Sun ) Same result as the PP chain, but carbon acts as a catalyst; i.e., it facilitates the fusion of H to He but doesn t get used up. This produces energy faster than the PP chain in spectral classes hotter than F0. It dominates at core temperatures greater than about 2 10 7 K Triple α process 3 2 He 4 6 C 12 + energy Requires core temperatures 10 8 K Carbon fusion T core 6 10 8 K Neon fusion T core 1.5 10 9 K Oxygen fusion T core 2 10 9 K core Silicon fusion T core 3 10 9 K Only stars with main sequence masses greater than 20 solar masses will undergo silicon fusion. The most tightly-bound element is 26 Fe 56. It can release energy by neither fusion nor fission. 7
What causes a star to become a red giant? As hydrogen fuses, the helium nuclei fall toward the center of the star and accumulate there to form a helium core. Inert He As more He rains down into the (not hot core, the conversion of gravitational energy into heat and light increases its temperature and pressure. The hot He core heats up the hydrogen in a shell outside the region that was the core of the main sequence star. This shell becomes hot enough for H fusion to begin. H fusion H and He envelope (not hot enough for fusion) He enough for the triple α process) Eventually, the combination of radiation pressure and thermal pressure from the shell causes the star s envelope to expand and cool. The star becomes a red giant. The temperature of the core is high enough to cause the H shell to fuse rapidly, resulting in a dramatic increase in the star s luminosity. The Pauli Exclusion Principle Electrons, neutrons, protons, and neutrinos are examples of fermions. They are particles with an odd multiple of one-half the fundamental unit of angular momentum. The Pauli exclusion principle is a physical law obeyed by all fermions. In a bound sample of fermions of a given type, no two particles can have both the same energy and the same spin orientation. The condition in which all of the electrons in an object are in their lowest possible energy states is called electron degeneracy. 8
generate De Energy Diagrams for Degenerate and Non-degenerate Electron Gases An electron bound to an atom can only have one of a set of discrete energies. This is also true for electrons bound inside a star. If the electron density is low, as it is in a normal star, most energy levels are empty and an electron can easily acquire enough energy to jump to a higher energy level. Under these conditions, the electron gas is called non-degenerate. Its pressure is proportional to its temperature (PV = NkT) If the electron density is greater than about 10 9 kilograms per cubic meter, there will be electrons in all of the lowest levels. Under these conditions, the electron gas is called degenerate. Only the few electrons with the highest energies can easily acquire enough energy to jump to higher energy levels. For most electrons, the nearby levels are already filled with electrons. on-degenerate N The Properties of Degenerate Matter In order to compress it, we must change the energy of large numbers of electrons. However, only a few electrons (those in the highest occupied levels) can have their energies changed by small amounts. Therefore, the degenerate matter resists compression; it is extremely rigid. It easily conducts both heat and electricity. In contrast to an ordinary gas, its pressure depends only on its density not on its temperature. The free electrons in a metal form a degenerate electron gas; that s why a metal is a good conductor of both electricity and heat. 9
The Triple Alpha Process and the Helium Flash 4 2He is called the alpha particle, and the fusion of three helium-4 nuclei to produce a carbon nucleus is called the triple alpha process. The triple alpha process actually takes place in two steps 4 4 8 8 4 12 He + He Be +γ Be + He C +γ 2 2 4 4 2 6 In stars with masses between 0.4 and 4 solar masses, the helium core becomes degenerate before the temperature is high enough to ignite helium. This results in an explosion called the helium flash. Helium ignition temperature increase without increase of pressure (the gas is degenerate) increase of helium fusion rate throughout the core further temperature t increase without tincrease of pressure further increase of helium fusion rate throughout the core After a few minutes, the temperature is so high that the core becomes non-degenerate. Although the peak luminosity may be as high as 10 14 times that of the Sun, all of the energy is absorbed by the red giant s envelope. This, combined with the short duration of the event, makes the helium flash virtually unobservable. White Dwarfs When gravity compresses a star so much that a mass comparable to the mass of the Sun is squeezed into a volume comparable to the mass of Earth, the density is about 10 9 kilograms per cubic meter. This compact object, supported by electron degeneracy pressure, is called a white dwarf. Estimate of the density of a white dwarf = 6 30 R 7000km 7 10 m, M M 2 10 kg 4 volume = π ( 7 10 m) 3 = 1.4 10 m 3 6 21 3 density mass volume 4 volume = πr 3 = 3 30 2.0 10 kg density = = 1.4 10 kg / m 21 3 1.4 10 m 9 3 A cubic inch of this material would weigh about 10 tons! 10
White Dwarfs in Globular Cluster M4 M4 is 7000 light years away. The image on the right is the HST image of the small region indicated in the groundbased image on the left. Circles are drawn around the white dwarfs. Globular clusters are old, so they are expected to contain many white dwarfs. Of M4 s 100,000 or so stars, about 40,000 are expected to be white dwarfs. Low Mass Star Low mass stars are called red dwarfs Masses between 0.08 and 0.4 solar masses The lifetime of a 0.4 solar mass star is about 100 10 9 years. White Dwarf Black Dwarf A low mass star is convective throughout its entire volume. The helium created by fusion is mixed with the material in the rest of the star. Because of this, it never has a dense helium core surrounded by a shell in which hydrogen is undergoing fusion, which is the condition that results in a red giant. Consequently, these stars never become red giants. They will gradually cool to become black dwarfs composed mainly of a mixture of H and He. 11
HST Near Infrared Image of a Red Dwarf The white streak is a result of overexposure of GL 105A. Gliese 105C 27 light years away in constellation Cetus. GL 105C is 25,000 times fainter than GL 105A. The temperature of GL 105C may be as low as 2600 K. Mass is about 0.08 to 0.09 times the mass of the sun. Since this is an infrared image, the colors you see are false colors. Medium Mass Star Red Giant Masses between 0.4 and 8 solar masses. The envelope of the red giant becomes unstable (thermal pulses)and is expelled. The nebula that results is called a planetary nebula. Fluorescence occurs only if the temperature of the star inside the expelled material is least 25,000 K. Eventually, a star will be incapable of generating energy by nuclear fusion. If its mass is then less than the Chandrasekhar limit (1.4 M ) the star will be a hot white dwarf that slowly cools by emitting electromagnetic radiation. WhiteDwarf + Planetary Nebula Black Dwarf These white dwarfs are composed primarily of carbon and oxygen. The carbon and oxygen are ionized and embedded in a degenerate gas of electrons. When the temperature is low enough, the carbon and oxygen crystallize. 12
A Planetary Nebula The hot relic of the dying star s interior emits ultraviolet radiation, which causes fluorescence of the expelled envelope. NGC 2392 is 5000 light years away in Gemini. 13