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Lecture 19: Compact Objects

Sirius B. Objectives: how mass determines final state of star examine basic properties of compact stellar remnants distinguish between white dwarfs , neutron stars and black holes importance of novae and type Ia supernovae. Lecture 19: Compact Objects.

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Lecture 19: Compact Objects

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  1. Sirius B • Objectives: • how mass determines final state of star • examine basic properties of compact stellar remnants • distinguish between white dwarfs, neutron stars and black holes • importance of novae and type Ia supernovae Lecture 19: Compact Objects • end-points of stellar evolution determined by initial mass: •  brown dwarfs (no H fusion) •  M-S lifetime > age of Universe! •  white dwarfs ( mass loss on AGB v effective !) •  neutron stars (via supernovae) •  black holes (via supernovae or GRBs) • White dwarf properties: • supported by electron degeneracy pressure • mixture of C and O • what is the maximum M of a white dwarf ? Additional reading: Kaufmann (chap. 22 - 24), Zeilik (chap. 17 - 18) PHYS1005 – 2003/4

  2. Chandrasekhar Limit : • recall from Lecture 17, WD core is supported by e- degeneracy pressure: • which leads to: • and since H/S equilibrium requires: • then as core M increases, Pc required increases faster than Pd unless R decreases • however, as then eventually particles  relativistic, and then • which leads to: • and now as M increases, Pd cannot increase sufficiently to maintain H/S equilibrium •  gravity wins ! •  there is a maximum M of a WD = 1.4 MO • called the Chandrasekhar Limit PHYS1005 – 2003/4

  3. Neutron star properties: • consist mostly of neutrons (volume 1015 smaller than Sun) • supported by neutron degeneracy pressure • discovered in 1967 by Hewish & Bell as radio pulsars • e.g. Crab pulsar, P = 0.033 s • i.e. it spins 30 times per sec • magnetic fields ~ 108 – 1011 T • 6 amazing NS facts: • surface gravity ~ 200 billion g • drop 1gm from 1m  hits surface at 2000 km/s (with KE ≡ 1 ton of TNT!) • entire lifetime’s energy needed to climb 1mm hill • falling from great distance, reach ~2/3 c • in free-fall, your feet accelerate 76 million g faster than your head as you hit surface • 1cm3 at B=1011 T has enough electromagnetic energy to power the UK grid for 5,000 yrs • they too have maximum M ( ≈ 3 MO) PHYS1005 – 2003/4

  4. Measured Masses of compact objects: PHYS1005 – 2003/4

  5. Black Hole properties: • escape velocity given by K.E. = P.E. : • so and v = c when • which is known as the Schwarzschild radius • this is correct even under General Relativity • inside RS even light cannot escape, thus nothing can (and hence RS represents the Event Horizon of the BH) • all mass concentrated at a single point, the singularity (why so called?) • only properties of mass, charge, spin remain (i.e. much simpler than ordinary stars !) • but how do we detect BHs if even light cannot escape ?! • use accretion of matter in binary systems • one star accretes matter from its companion • releases large L from small volume  very hot  X-rays, γ-rays • detect them from space as X-ray sources PHYS1005 – 2003/4

  6. PHYS1005 – 2003/4

  7. PHYS1005 – 2003/4

  8. Accretion Power: • compact object (mass M, radius R) accretes mass m from its companion  energy released is simply GMm / R • maximum energy obtainable from m is mc2 • so fraction of rest mass converted  energy is • which for WD (0.6 MO, 0.01 RO) is • and for NS (1.4 MO, R = 10 km) • i.e. >20x more efficient than fusion ! • BH is slightly more complicated calculation as: • no solid surface (never get K.E. out) • only get E down to last stable orbit (at 3RS) • so • and since RS = 2GM / c2, then PHYS1005 – 2003/4

  9. BH/NS X-ray source properties: • BH/NS both efficient X-ray emitters when accreting • so how can they be distinguished ? • X-ray pulses  NS • need hot spot on surface • X-ray bursts  NS • accreted H burns  He  He flash • measure mass M: • if >3MO BH ! • quiescent X-ray sources very important here as X-ray irradiated disc makes it impossible to see the mass donor • e.g. V404 Cyg has K = 255 km/s in 6.5 day orbital period • mass donor very low M, so treat like planet orbiting massive compact object i.e. use Kepler 3 from Lecture 10: • and since K = 2πr / P, then M1 = PK3 / 2πG • or M1 = (6.5 x 24 x 3600) x 255,0003 / 2πG = 11.1 MO(verify !) PHYS1005 – 2003/4

  10. Novae and Type Ia Supernovae: • SNe so far are type II – from massive stars • distinguished from type I by their light curves and spectra (details in textbooks) • Type Ia have no H in their spectra • likely complete detonation of CO white dwarf • how ? • only in binary systems ! • WD originally heavier star • but transfers some mass onto companion during RG phase • then companion evolves  RG branch • transfers matter back onto WD  UV, X-rays • accreted H undergoes nuclear burning  nova explosion (also useful as local distance indicator) • or possibly supernova if WD taken over Chandrasekhar limit ! • a type Ia supernova • important for cosmology as all must occur only when WD reaches particular M all of same brightness ! i.e. perfect standard candle ! PHYS1005 – 2003/4

  11. X-ray pulsations in Her X-1 and Cen X-3 observed by Uhuru satellite in 1970s PHYS1005 – 2003/4

  12. PHYS1005 – 2003/4

  13. PHYS1005 – 2003/4

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