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The Stars A star’s a star, some matter in a ball Compelled to courses mathematical

The Stars A star’s a star, some matter in a ball Compelled to courses mathematical Amid the regimented, cold, inane, Where destined atoms are each moment slain” JRR Tolkien “Mythopoeia”. Star basics 101. Observations: The physical conditions for stardom are Mass > 2 x 10 29 kg (0.1 M  )

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The Stars A star’s a star, some matter in a ball Compelled to courses mathematical

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  1. The Stars A star’s a star, some matter in a ball Compelled to courses mathematical Amid the regimented, cold, inane, Where destined atoms are each moment slain” JRR Tolkien “Mythopoeia”

  2. Star basics 101 Observations: The physical conditions for stardom are Mass > 2 x 1029 kg (0.1 M) Radius > 7 x 107 m (0.1 R) Temperature > 3000 K (at surface) Star material is brought together by gravity – with the star formation process determining the final mass Mass-luminosity law: Mass ‘sets’ Luminosity L L and main sequence location ‘set’ Temperature T L and T + main sequence in HR diagram law ‘set’ radius R

  3. Star basics 101 Observations: Stars radiate energy into space Physics: The Second Law of Thermodynamics: Hot objects radiate energy into their cooler surroundings Question: If stars are very old, why have they not simply cooled-off?

  4. Observations of our Sun: Climate models, geology and the fossil record Sun’s energy output (luminosity) has been near constant for at least the last 3 to 4 billion years Therefore, the Sun must have ‘tapped’ a good energy supply that has kept it hot and luminous The internal energy supply replenishes the energy lost into space at its surface

  5. The question: where does the energy of a star (the Sun) come from? The answer: historically, many energy sources have been considered but we now know that stars are powered by nuclear fusion and the conversion of hydrogen (H) into helium (He)

  6. Sir Arthur Stanley Eddington (1882 - 1945) Stars and Atoms (1920) “I ask you to look both ways. For the road to a knowledge of the stars leads through the atom, and important knowledge of the atom has been reached through the stars” 1926

  7. Nuclear fusion Theory: 1938: nuclear fusion - conversion of four hydrogen atoms into one helium atom with the liberation of energy 4H  He + energy Theory built on many independent discoveries: 1920: Francis Aston experimental result mass (He atom) < mass (4 hydrogen atoms) mass difference = 0.007 mass of 4 H atoms Francis Aston (1877 – 1945)

  8. Proposition: 1926: A. Eddington suggests that the mass difference may appear as energy 1905: A. Einstein shows that E = mc2 Result: Enuclear = (Dm) c2 OOTETK Energy generated per second by fusion reactions Mass ‘converted’ into energy per second

  9. Some numbers Sun emits 4 x 1026 Watts of energy into space To produce Sun’s energy through fusion reactions, Einstein’s equation tells us: Dm = (4 x 1026)/(3 x 108)2 = 4x109 kg/sec Its luminosity matter converted into energy per second

  10. We have seen that… Stars generate energy by fusion reactions within their hot central cores Fusion reaction: 4H  He + energy Energy related to mass difference of 4H and He as found by Francis Aston at Cambridge Aston found: Dm = 0.007 x 4H Einstein gives us: Enuclear = (Dm) c2 Eddington speculates Enuclear powers stars

  11. A quick calculation How much matter has the Sun converted in to energy since it formed? Age = 4.5 billion years Dm = 4.5x109 x 3.16x107 x 4x109 = 5.7x1026 kg Seconds in a year 95 x Mass converted to energy by the Sun since it formed is equivalent to

  12. The equations of stellar structure (don’t write these down!) Computer modeling Can only solve the equations that describe the structure of a star numerically

  13. Results: detailed numerical models confirm once fusion reactions begin the star has ‘tapped’ a long-lived energy source and ‘sits’ on the MS Main sequence stars Stars converting 4H  He within their cores  • Hence:Here’s the reason why most stars (92% of total) are on the main sequence in the HRD: • The MS phase is the longest-lived phase because stars are mostly composed of hydrogen ---- Recall spectral analysis indicates that ~ 75% of star mass is hydrogen

  14. Computer models further reveal HR diagram features: Main sequence stars Stars converting hydrogen into helium Giant stars Stars converting helium into carbon White dwarf region Cooling-off region for low mass stars that have exhausted helium in their cores

  15. Energy generation and the Sun’s journey through HR diagram Main sequence Hydrogen  Helium Bright Red Giants Helium  Carbon Planetary Nebula Luminosity Sun Star formation (sets mass) White Dwarfs Cooling Dim Spectral type O B A F G K M Hot Cool No longer generating energy in their interiors

  16. Question: how long can the Sun ‘shine’ by Hydrogen fusion ? t = (amount of fuel available)/(rate of fuel consumption) t = (0.1)(0.007)M c2 / L (calculation assumes 10% of Sun’s H is converted to He) time during which H burning can take place in the Sun is t = 1010 years Solar System is 4.5 billion years old – the Sun is “middle aged”

  17. All good things come to an end Stars have a large, but limited supply of hydrogen hence a finite main sequence life time tms = main sequence life time = fuel available / rate of consumption = (constants) (M / L) (*)

  18. Recall: main sequence stars obey a ML law: L = constant M3.5 Combine the ML law with eqn(*), then, Important result: tms = constant / M2.5 The more massive a star is, the shorter is its main sequence life time

  19. The main sequence lifetime of a star of mass M is  Some example life times tms(yrs) = 6 x 1010 for M = 0.5 M tms(yrs) = 3 x 107 for M = 10 M M = 7.5M Textinct(dinosaurs) = 65 Myr

  20. Computer models reveal Brown dwarf: Not enough mass to be a star – a bit like a super massive Jupiter

  21. End gameswhere the core and the envelope part company M < 8 M: core  White Dwarf and cooling sequence envelope  Planetary Nebula envelope material slowly returned into space and ISM M > 8 M: core  Neutron star (Minitial < 40 M)  Black hole ? (Minitial > 40 M) envelope  explosive dispersion of star supernova remnant: most of star ejected into space and ISM at very high speed - to be incorporated into new stars

  22. The Ring Nebula (in Lyra) Composed of material that was once the outer layers of the star Expansion velocity is ~25 km/s Central White Dwarf

  23. Supernova: when stars go wild X-ray image of the Tycho SNR Observed by Tycho Brahe in 1572. Expansion speed of nebula is 5000 km/s • M > 8 M: • Final stages are rapid and violent. • Core collapses as it can no longer find an energy source through fusion reactions and this triggers the complete destruction of the star • The ‘explosion’ of a single massive star can briefly outshine an entire galaxy

  24. “To infinity and beyond” SN are the brightest standard candles known and The scale of the Universe is determined by studying supernova in distant galaxies The observable universe extends to a distance of order 10 billion parsecs 1600 galaxies visible in an area of just 10-3 of a square degree This implies 60 billion galaxies in the observable universe

  25. The remnants White dwarfs: Minitial < 8 M Highly compressed core of star Composed of carbon and helium Mass of Sun, but size of the Earth Supported by a quantum mechanical effect acting on electrons Neutron Star: 8 M < Minitial < 40 M Even more compressed than White dwarfs Mass of Sun, but 20 km diameter Supported by a quantum mechanical effect acting on neutrons Black hole: 40 M < Minitial The ultimate collapsed state Region cut-off from our universe Interior structure = ??? Pauli exclusion principle Wolfgang Pauli The ultimate black spot

  26. End phases of star evolution return material to the ISM – and new stars can form from this star-processed material

  27. Cosmic recycling Final stellar end stages (PN and SN) material that has been processed by nuclear reactions inside of stars is returned to the interstellar medium (ISM) In addition, the cosmologists tell us Only H and He produced in the early universe Hence - an incredible result All of the elements (C, N, O, etc..) that make up the Earth and enable life as we know it were formed inside of stars We are indeed all STAR CHILDREN

  28. Peace and love man Big Bang Hydrogen + helium Star formation ISM time Z enhancement End phase (PN + SN) Definition: Z elements (metals): all elements other than hydrogen and helium WD, NS, BH Result: ISM becomes increasingly metal rich with time

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