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Mass and the Properties of Main Sequence Stars

Mass and the Properties of Main Sequence Stars. M ass is the most important properties of the main-sequence stars. It determine their luminosity, surface temperature, radius, and lifetime.

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Mass and the Properties of Main Sequence Stars

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  1. Mass and the Properties of Main Sequence Stars Mass is the most important properties of the main-sequence stars. It determine their luminosity, surface temperature, radius, and lifetime. • Nuclear fusion requires high temperatures and densities in the core, and the star’s internal conditions are determined by the equilibrium condition between the inward pull of gravity and the outward push of pressure. • In a star that has high mass, the greater weight of its overlying layers means the star must sustain a higher nuclear fusion rate to generate the additional pressure needed to maintain gravitational equilibrium. • The higher nuclear fusion rate makes the star more luminous. • The high luminosity requires a star to have either high temperature or large size, or both. • The higher luminosity also means that it will run out of fuel faster than less massive stars. ~10 Rsun ~3 Rsun 1 Rsun 0.1 Rsun

  2. The Lifetime of Main-Sequence Stars • The lifetime of a star is determined by how fast it burns its supply of hydrogen…This hydrogen burning rate can be inferred from the luminosity of the star. • The Mass-Luminosity Relation • Once we have observationally determined the luminosity and mass of many main sequence stars, we find that the higher the mass M of a star is, the higher is its luminosity (L). • L/L⊙ = (M/M⊙)3.5 Note: The Mass-Luminosity relation applies to main-sequence stars only! For example, • A 10 M⊙star is roughly (103.5 ~ ) 3,000 brighter, or burning its hydrogen times 3,000 faster. • We know that the lifetime of the Sun is about 10 billion years. • The more massive star would have a lifetime of about 10 × 10 billion years ÷ 3,000 ~ 30 million years.

  3. Giant and Supergiants Giants and supergiants are stars nearing the ends of their lives. • Giants and supergiants do not follow the relationship between surface temperature and luminosity for hydrogen-burning, main-sequence stars. • The supply of hydrogen fuel in the core of the giants is running out, and they respond to this fuel shortage by releasing fusion energy at a furious rate. Thus, in order to radiate away this huge amount of energy, the surface of a dying star must expand to an enormous size (Chapter 12) • Because giants and supergiants are so bright, we can see them even if they are not especially close to us. • Many of the brightest stars visible to the naked eye are giants or supergiants. • They are often identifiable by the reddish color produced by their cool surfaces. • Giants and supergiants are considerably rarer than main-sequence stars. When we look at the sky, most of the stars we see are main sequence stars. • Betelgeus: M2 I Betelgeuse and R Doradus

  4. For example, Sirius B(DA2) is a white dwarf with a diameter of 12,000 km and a mass of ~ 1 solar mass. Its surface temperature of 25,000 K makes it brighter than the main star (A1, 9,900 K) in this Chandra X-ray image. Sirius White Dwarf White dwarfs are the exposed core of the dead low-mass main-sequence stars, supported against gravity by electron degenerate pressure (Chapter 12). • Properties • Hot surface (not long after the formation), comparable or higher than the surface of the Sun. • Low luminosity (0.0001L⊙ to 0.1L⊙ ) • High mass: comparable to the Sun • White dwarfs have high surface temperature and low luminosity:  Small size – comparable to the size of the Earth. • White dwarfs are small in size, but high in mass: • Very high density

  5. Note that the sizes in this figure are not to scale! • Orbit of Mars • Orbit of Mercury Summary of Sizes of Stars – From Supergiants to White Dwarfs Supergiant ~ 100 – 1000 Rsun Giant ~ 10 – 100 Rsun Main-Sequence Star ~ 0.1 – 10 Rsun White Dwarf ~ 0.01 Rsun About the size of Earth!

  6. Properties of Stars • Classifying Stars • Star Clusters • Open and Globular Clusters • Dating the Age of the Universe by Globular Clusters

  7. Star Clusters The Pleiades • Most stars are formed from giant clouds of gas with enough material to form many stars. When we look into the sky, we often find clusters of stars. There are two types of clusters: • Open Clusters • Found in the disk of the galaxy. • Contains a few thousand stars. • Span about 30 light-years. • Globular Clusters • Found in the halo of the galaxy. • Up to one million stars. • Spans about 60 to 150 light-years. Because • Stars in the same cluster lie at about the same distance from Earth • Stars in the same cluster are formed roughly at the same time. They are useful as a cosmic clock…

  8. HR Diagram of Star Cluster Pleiades is an open cluster that contains thousands of stars… • The H-R diagram of Pleiades shows that most of the stars fall in the main sequence curve. • However, it is missing the O and B type stars. • The high-luminosity end of the curve moves away from the main-sequence curve… If the stars in Pleiades were all formed at the same time, then higher mass stars would move off the main sequence curve first. Therefore, the theoretical lifespan of the most massive star of the cluster remaining in the main sequence tells us about the age of the cluster. H-R Diagram of Pleiades

  9. Dating the Age of Star Clusters • When a star cluster is born, it contains stars spanning the entire range of the H-R diagram. • As the cluster ages, the high-luminosity, hot, blue stars move away from the main sequence curve first. • The point where the curve of the H-R diagram deviates from the main sequence curve (the main-sequence turn-off point) indicates the age of the cluster. Evolution of the H-R Diagram of Star Cluster 100 million years 10 billion years New-born Luminosity Luminosity Luminosity Main sequence curve Temperature Temperature Temperature Time

  10. Examples of H-R Diagram of Star Clusters We have only being plotting the H-R diagrams for about 100 years. Therefore, we do not have a time sequence of H-R diagrams to show the evolution of any cluster. However, if we plot the H-R diagrams of several star clusters with different age, we should see the evolutionary effect…

  11. Dating the Age of the Universe with Globular Cluster • The age of the oldest star cluster should give us an lower limit of the age of the universe, since no star can form before the universe was born! • Most of the open clusters are relatively young. Very few are older than 5 billion years. • The age of some of the oldest globular cluster, such as M5 below, is about 13 billion years. Therefore, the age of the universe must be more than 13 billion years. H-R Diagram of M4 Age: ~ 10 billion years. Image of M5, in Constellation Serpentis, with apparent brightness magnitude of mv = 12

  12. Chapter 12 Star Stuff • Star Formation • Evolution of Low-Mass Stars • Evolution of High-Mass Stars

  13. From Clouds to Protostar Molecule cloud glows in the infrared, but is dark in the visible light image! Stars form in cold(10-30 K), dense (although still very low density compared with the density we are used to) molecule clouds composed of mostly hydrogen and helium. • The low temperature allows the formation of hydrogen molecule H2 – hence molecule clouds. • Low temperature and ‘high density’ allow gravity to compress the clouds without resistance from thermal pressure. • Because of the low density, the gas can radiate away its thermal radiation quickly. The temperature of the gas remain low (~ 100 K), and emits in the infrared wavelengths. • As the cloud undergoes gravitational contraction, density increases, making it increasingly difficult for radiation to escape. • The gas heats up as the density increases, eventually forms a dense, hot protostar!

  14. Disks and Jets The random motion of the molecule can contain a net angular momentum, as the cloud contract, • this angular momentum is conserved, and results in the fast rotation of the protostar and the subsequent formation of a disk and jets • Details of how the jets are formed is still unknown. Magnetic field probably plays an important role! Image of jet and disk of a protostar!

  15. Jet in Neutron Stars • Similar to the core of the low-mass stars, electrons degeneracy pressure will resist the gravitational pressure. However, because of the high mass, it cannot hold off the gravitational collapse like in the case of the white dwarfs. • As gravity overcomes electron degeneracy pressure, and the core collapse rapidly, the electrons and protons recombine to form neutrons, and releasing neutrinos and energy at the same time  Supernova explosion. • Eventually the neutron degeneracy pressure will balance the gravitational pressure (if the star is not too massive) to form a neutron star. • The estimated of the neutron stars are about 10 km in diameter, with a mass of about 1 M⊙ Too small to be directly observed! • However, the strong gravity of the neutron stars pull surrounding materials in, forming an rapidly rotating accretion disk. The high speed collisions between the materials and the neutron stars generate strong X-ray, as the image of crab nebula from Chandra X-ray Observatory has shown. Conbined Hubble’s visible (red) and Chandra’s X-ray (blue) images.

  16. More Example of Astronomical Jets Jets are found in many different spatial scales. In this composite picture of x-ray (blue) picture from Chandra X-ray Observatory, visible (white) image from Hubble Space Telescope, and radio (red) image from the Very Large Array radio telescope, jets (seen in radio emission in red) are ejected from a supermassive black hole in galaxy cluster MS 0735.6+7421 in constellation Camelopardus. http://chandra.harvard.edu/photo/2006/ms0735/

  17. Examples of Star Forming Molecular Clouds and EGGs The Eagle Nebula is a star forming region in the constellation Serpens. • Evaporating Gaseous Globules (EGGs) are dense regions of molecular hydrogen (H2) clouds that have gravitationally collapsed to form stars. • UV radiation from hot bright star (off the image) evaporates the outer layer of the dense H2 cloud, revealing the denser regions that are forming stars. EGGs in Eagle Nebula in constellation Serpens http://antwrp.gsfc.nasa.gov/apod/ap061022.html

  18. Star-Forming Region in W5 This picture of the star forming region W5 in constellation Cassiopeia was obtained by the Spitzer Space Telescope. The insert at the lower-left-hand corner is the same region taken in the visible wavelength. Dusts and dense H2 cloud blocks visible radiation, and the region looks dark in the visible image. • Infrared radiation are emitted by the cold and dense H2 clouds. • Additionally, infrared radiation can propagates through the gas and dust, allowing us to see inside the clouds. http://www.spitzer.caltech.edu/Media/releases/ssc2005-23/index.shtml

  19. Star Forming Region in NGC 2467 This picture of NGC 2467 shows stars at different stages in star formation process. • The bright stars on the left of the image are stars that have already formed and the winds probably have dispersed the planetary nebulae around them. • The star at the lower left is emerging from its planetary nebula. • The deep dark lanes near the center are dense regions that are probably forming new stars inside. • The bright walls of gas on the right are gases been evaporated by some newly-formed hot stars. http://antwrp.gsfc.nasa.gov/apod/ap050131.html

  20. The Mass Limits of Main Sequence Stars • Usually a single group of molecular clouds can give birth to a star cluster containing thousands of stars. The mass distribution of the stars is such that there are a whole lot more low mass stars than high mass stars. • Upper limit of stellar mass: ~ 100 Msun • The core temperature becomes so high that radiation pressure (pressure exerted by photons) upsets the equilibrium between the thermal pressureand the gravitational pull. The star becomes unstable… • No star with mass greater than 100 Msun has been observed. • Lower limit of stellar mass: ~ 0.08 Msun • The core temperature of objects with mass less than 0.08 Msun is not hot enough to trigger hydrogen burning. • Jupiter is 0.001 Msu

  21. Brown Dwarfs Brown dwarfs are objects that does not have enough mass to maitain core hydrogen fusion, with mass less than 0.08 Msun. • Brown dwarfs are supported by electron degenerate pressure (like white dwarfs). • Brown dwarfs and large planets are similar in size • Distinction between brown dwarfs and planets is fussy: • Support mechanism? • Deuterium fusion (>13 Mjupiter)?

  22. The Origin of Degenerate Pressure1. Fermions and Bosons. • In quantum physics, particles are divided into two types: fermions and bosons. In quantum physics, one of the intrinsic properties of particles are called spin. Spin is associate with the angular momentum of the particle around its center of mass. In quantum physics, spin can only have values equal to multiple of 1/2, such as ½, 1, 1 ½ , 2, …it is a quantized quanty. • Fermions are particles with half-integer spin, such as • Electrons, • Protons, • Neutrons • Bosons are particles with integer spin, such as • Deuterium: isotope of hydrogen, containing one proton and one neutron in its nuclei. • Helium-4 (superconductivity). • Photons

  23. The Origin of Degenerate Pressure2. Pauli’s Exclusion Principle and Heisenberg’s Uncertainty Principle • Degenerate pressure arises from two fundamental laws of quantum physics: • Pauli’s Exclusion Principle for the fermions: • No two particles (fermions) can occupy the same quantum mechanical state simultaneously. • Heisenberg’s Uncertainty Principle: • The product of the uncertainty in the position of a particle and its momentum is always greater than the Planck constant • x p ≥ h • where x is the uncertainty in the position of the particle, p is the uncertainty in the momentum of the particle, and h = 6.626  10-27 gm cm2/sec is the Planck’s constant.

  24. Pauli’s Exclusion Principle Under normal conditions, electrons in atoms can occupy a large number of energy states, like students in a mostly-empty class room: there are more seats available than people. In this situation, we do not need to worry about the exclusion principle. • When atoms are compressed, like in a white dwarf where thermal pressure is no longer able to resist the gravitational force of the matter, the number of available energy states is reduced, similar to a packed classroom…in which only one person is allowed in each seat (the exclusion principle). • The reduced number of energy level available in the compressed atoms is equivalent to confined space allowed for the electrons, or small x in the uncertainty principle.

  25. Uncertainty Principle and Degenerate Pressure According to Heisenberg’s Uncertain Principle, x p ≥ h very small x requires that p ≥ h / x be very large. • Very large uncertainty in the momentum of the electrons means that their velocity varies over a very large range (recall the definition of momentum: p = mv) • A very large range in the possible range of velocity of a large collection of particles is equivalent to saying that this collection of particles have a very high temperature (Recall the definition of temperature in Chapter 5.) • High ‘temperature’ means high pressure!

  26. Important Properties of Degenerate Pressure Degenerate pressure becomes appreciable only when the atoms are compressed by a tremendous pressure. This is because the Planck constant is a very small number… and h = 6.626  10-27 gm cm2/sec • Thermal pressure depends on the temperature. A gas cloud at a temperature of 0 K does not posses any thermal pressure. However, degenerate pressure does not depend on temperature. The temperature of the white dwarfs can be at absolute zero, its electron degenerate pressure will be the same as it is at 25,000 K. • There are different kind of degenerate pressure: • Electron degenerate pressure (in white dwarfs and brown dwarfs – chapter 12). • Neutron degenerate pressure (in Neutron Stars – Chapter 13).

  27. Star Formation • Evolution of Low-Mass Stars • Evolution of High-Mass Stars

  28. Evolution of Low Mass Stars – I • Low Mass Stars: M < 8 – 10 M⊙ • Evolutionary History for a typical low-mass star like the Sun • During the main-sequence phase, helium produced by the proton-proton chain (hydrogen burning) accumulates at the core. As a main sequence star exhausts its core hydrogen supply, its energy output is reduced. • Without the thermal pressure of the hydrogen fusion, gravitation contraction continue, and the core temperature rises. • Because the temperature required to start helium burning is much higher (~ 100 million degrees), there isn’t enough thermal pressure at the core to resist the gravitational contraction (just yet). • The core temperature rises, as well as the outer layer of the star where there are still substantial supply of hydrogen, triggering shell hydrogen burning, at a much higher temperature than the core temperature in the main sequence stars. • The high temperature shell hydrogen burning produces more energy than the same star in its main sequence core hydrogen burning stage Higher luminosity. • The high thermal pressure of the shell hydrogen burning push the envelop of the star outward, much larger than its size at the main sequence stage giant. • The large surface area of the giant cools off fast red giant. • From sub giant to red giant: few hundred million years.

  29. Structure of Red Giants • Inert Helium core  Most of the mass of the star is concentrated at the helium core. • The electron degeneracy pressureof the inert helium core balance the gravitational contraction. • Hydrogen-burning shell. • Hydrogen envelop.

  30. Evolution of Low-Mass Star – II The time it takes to reach the red giant state depends on the mass of the star • For star with lower mass then the Sun, it takes longer. • As the shell hydrogen fusion stops, the helium core of the low mass stars may never a temperature high enough for helium fusion to start. • As fusion stops, the gravitational collapse continue, eventually stopped by the electron degenerate pressure of the helium core. • The star become a helium white dwarf. • For star more massive than the Sun, it takes less than 10 billion years. • As the shell hydrogen fusion exhausts its fuel, gravitational collapse continue. However, the high mass of the star means that the core temperature can reach 100 million degrees, sufficient for helium fusion to start.

  31. Evolution of Low-Mass Star– III Triple alpha process in helium burning stars • Helium fusion converts three helium atoms into one carbon, and generating energy. • Theoretical model suggests that before core helium fusion phase, the star is supported by the electron degenerate pressure of the helium core. This degenerate pressure does not increase with the increasing core temperature as the star contracts. • However, once helium fusion starts, it releases a large amount of energy in a short time, causing the star to expand rapidly. This is referred to as the Helium Flash.

  32. Evolution of Low-Mass Star – IV After helium flash, the star settles into a helium burning stage, the energy of the star decreases… • The helium burning stars are smaller, hotter, and less luminous than the star in the red giant state. • The helium core of the low-mass stars fuse helium into carbon at about the same rate. Therefore, they appears on the HR diagram as a horizontal line. • This state is represented in the HR diagram as the horizontal branch. • Low-mass stars spend about 100 million years in this stage.

  33. Evolution of Low-Mass Star – V The helium fuel in the core eventually runs out, and core fusion ceases. • The carbon core will begin to contract due to gravity. • The increased temperature due to the contraction will cause shell helium burning around the carbon core. • Further out, a shell hydrogen burning continue on top of the helium shell – double-shell buring, ~ 1 million years. • Both shells contract with the carbon core, driving the increase in temperature and fusion rate. • The star expands further, becomes larger and more luminous than its red giant phase. • Fusion of carbon requires high temperature, ~ 600 million degrees. This is unlikely to happen for low-mass stars. Click to start animation

  34. The end of Low-Mass Stars:Planetary Nebulae • As the star’s luminosity and radius increase, its wind will grow stronger as well. The star ejects its outer layer to form the beautiful planetary nebula. • The exposed core will be hot for a long time, emitting UV radiations. • The UV radiation will ionize the gas in the expanding shell, making it grows brightly.

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