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White Star, Black Hole. Frank Hsia-San Shu Taichung First Senior High School 26 February 2005 1905 = Einstein ’ s Miracle Year. Surface & Interior of Sun. Pressure at Center of Sun. Pressure at center of Sun = weight of column of material per unit area above center - PowerPoint PPT Presentation

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  • White Star, Black HoleFrank Hsia-San ShuTaichung First Senior High School26 February 20051905 = Einsteins Miracle Year

  • Surface & Interior of Sun

  • Pressure at Center of Sun

    Pressure at center of Sun = weight of column of material per unit area above center

    Central pressure 50 times larger:

  • Visualizing Central Pressure of Sun

  • Solar Plasma electrons positive ions (nuclei)

    A lot of space between individual particles, unlike the case if unionized atoms were pressed up against each other at mean density of Sun, where most of volume is occupied by the fuzzy electronic shells of the atoms.Electrons and nuclei therefore behave as freely moving particles, i.e., as an ideal gas satisfyingP = nkT , where P = pressure, n = number density, k = Boltzmanns constant, T = temperature on Kelvin scale.For the central values, P = and n = we get T = K at the center of the Sun.

  • 3-D Random Walk of Photons Out of Sun

  • Radiative Transfer in the Sun

    X-rays free flight optical photons random walk photosphere Slow photon diffusion from interior to surface is what regulates energy leakage to the rate

  • Source of Energy Output of SunEvery second, the Sun radiates more energy than lies under the sands of all Arabia.When will the Sun (and the other stars) run out of energy?If the Sun shone by burning fossil fuel, and it were entirely made of coal or oil, it could last only about 10 thousand years. This is far too short shorter than how long humans have been on Earth (7 million years), much shorter than how long life has existed on Earth (3.5 billion years).More powerful energy sources:Chemical reaction with greatest release of energy per kg: H+H = H H

    For Sun, this reaction could last about 25 thousand years, still far too short.Nuclear reaction: p D + other things p For Sun, this reaction (and others like it) could sustain Sun for 10 billion years. Long enough.

  • Nuclear EnergyNet reaction: 4HHe (fusion reaction).Mass deficit: Energy release: Implication: If Sun were 100% H, fusion reaction of H into He (hydrogen burning) would provide store of energy sufficient to last 100 billion years at present rate of solar usage: Since the Sun is actually only 70% H and since only inner 13% of mass (core) is hot enough to burn H during the so-called main-sequence stage, the main-sequence lifetime of the Sun = 9 billion years (see Problem Set 4).The Sun, with an age of 4.5 billion years, is half way through its main-sequence life. What it will turn into after another 4.5 billion years is one of the more interesting stories of astronomy.

  • Need for High Temperatures

  • Stability of Solar Thermonuclear Reactor

  • Summary of Interior of Sun

  • From Main Sequence to Subgiant

  • Horizontal Branch Star

  • Planetary Nebula to White Dwarf

  • Some Planetary Nebulae

  • Motion of Sirius A & B

  • Theory of White DwarfsR. H. Fowler (1889-1944) proposes white dwarfs, made of element of mean atomic number Z and atomic weight A, are supported against self-gravity by electron degeneracy pressure mass-radius relationship such that Ras M:

    For M = R is somewhat smaller than the radius of the Earth.S. Chandrasekhar (1910-1995) includes effect of special relativity, finds R 0 as M finite value (Chandrasekhars limit).Controversy between Eddington and Chandrasekhar. Chandrasekhar leaves England for United States, settles in University of Chicago. Gave moving tribute in 1982 to commemorate 100th anniversary of Eddingtons birth. Awarded Nobel Prize in Physics in 1984.

  • Difference Between Chocolate Cakes and White Dwarfs 0.4 kg 0.8 kg

    0.4 M 0.8 M

    As M, c, and P increases less quickly when density . Radius 0 when M where

  • Mass-Radius Relationship of Cold Bodies Jupiter White Dwarfs

    planets

    moons

    asteroids

  • Jupiter Is Close to BeingLargest Cold Object in Universe

  • Similarity Between Cooling Ember and White Dwarf

    Cooling White Ember Dwarf

    Radiates energy, Radiates energy, becomes cooler. becomes cooler.

  • Path to Yet More Compact ObjectsIf M were to exceed 1.4 solar masses, would R of a WD really shrink to zero?As rises, electron degeneracy-energy becomes greater and eventually can make up the mass difference between a proton and a neutron.Electrons get squashed inside protons, and ions of a WD star become converted to neutrons.As rises even more, neutrons become degenerate and are able to exert pressure at zero T.The balance of neutron degeneracy pressure and self-gravity gives rise to a new state of possible equilibrium, a neutron star.

  • Eta Carina A Pre-Supernova

  • Supernova 1987A and its Precursor Star in the LMC

  • Crab Nebula = SN1054

  • Crab Pulsar

  • Pulsars Blink Like Rotating Lighthouses

  • Neutron StarsOn average, neutrons stars are smaller than white dwarfs by a factor Actually, by about 103.Therefore, mean density is higher by factor of ; i.e., instead of .At such densities (nuclear densities), matter is very incompressible, with the pressure rising rapidly as the density increases.Rate of rise of pressure with density = square of speed of sound. Speed of sound cannot exceed speed of light limit to how much matter, even nuclear matter, can resist gravity

  • Cosmic Scale

  • Atoms Are Mostly Empty Space

  • Stellar Processing Determines Relative Abundances of the Elements

  • Summary of Dying StarsRed Supergiant:Dust grains form in cool outer input of atmosphere and expelled by small ISM radiation pressure. solidsPlanetary Nebula: Shell of gas and dust illuminated glowing and excited by hot central star, shell of which is exposed core of red ionized supergiant destined to become WD. gasSupernova Remnant:Ejecta of processed matter from neutron high-mass star which impacts with ISM star or and forms supernova remnant that is a black source of cosmic rays. hole

  • Idea of Black HoleConsider the escape speed from the surface of a body of mass M and radius R: m M R (See Problem Set 3.)

    For a neutron star of mass and radius , we get

    which is 63% the speed of light c!The above calculation motivates us to ask a question first asked by Pierre Laplace (1749-1827): For given M, what R would yield an escape speed equal to c? Answer:

    This is the correct answer, but the reasoning is incorrect on two counts.First, Newtonian mechanics giving the equation for a marginally bound orbit,

    does not apply to photons of zero rest mass m and speed c.Second, Newtonian concepts about gravity do not apply to a situation where the gravitational field of a body is so strong that even light finds it difficult to escape its clutches.Two mistakes combine to give the right looking answer! Correct derivation based on Einsteins theory of general relativity first given by Karl Schwarzschild (1873-1916).

  • Event Horizon of Black Hole

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