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Calculate the net force acting on a particle

Mass transfer in a binary system. Calculate the net force acting on a particle . Gravitational potential in the corotating frame. Mass Transfer in Binary Stars. In a binary system, each star controls a finite region of space, bounded by the Roche Lobes (or Roche surfaces ).

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Calculate the net force acting on a particle

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  1. Mass transfer in a binary system Calculate the net force acting on a particle

  2. Gravitational potential in the corotating frame

  3. Mass Transfer in Binary Stars In a binary system, each star controls a finite region of space, bounded by the Roche Lobes (or Roche surfaces). Lagrange points = points of stability, where matter can remain without being pulled towards one of the stars. Matter can flow over from one star to another through the Inner Lagrange Point L1.

  4. How the matter from a star can be brought to L1 point? Two mechanisms of mass transfer in a binary system Accretion through Roche lobe outflow Accretion from stellar wind

  5. Accretion from a stellar wind

  6. Star overflows its Roche lobe

  7. Formation of an Accretion Disk The rotation of the binary systems implies that gas flowing through the L1 point will have relatively high specific angular momentum - too much to directly accrete onto a compact companion star.

  8. Initial ring of gas spreads into the disk due to diffusion. To be able to accrete on the star, matter should lose angular momentum as a result of viscous friction Friction leads to heating of the disk and intense radiation!!

  9. White dwarf binaries Neutron star binaries Black hole binaries Accreting binary systems

  10. Nova Explosions: a mechanism Hydrogen accreted through the accretion disk accumulates on the surface of the WD • Very hot, dense layer of non-fusing hydrogen on the WD surface Nova Cygni 1975 • Explosive onset of H fusion • Nova explosion

  11. Accreting neutron stars and black holes Black holes and neutron stars can be part of a binary system. Matter gets pulled off from the companion star, forming an accretion disk. => Strong X-ray source! Infalling matter heats up to billions K. Accretion is a very efficient process of energy release.

  12. The Universe in X-ray and gamma-ray eyes Giacconi: Nobel prize 2002

  13. Accretion onto a neutron star

  14. X-ray pulsar: an accreting neutron star Compare with a radio pulsar

  15. Pulsars are slowing down with time. Millisecond pulsars: how can an old neutron star rotate at a rate 1000/sec?

  16. Accretion onto black holes There is no hard surface. Will there be any radiation from the infalling matter??

  17. Cygnus X1 – first black hole

  18. Measurement of binary system parameters gave M ~ 7 Msun

  19. High-Mass X-ray binary: accretion from a wind Cygnus X1

  20. Low-Mass X-ray binary: accretion through Roche-lobe overflow

  21. Binary systems If we can calculate the total mass and measure the mass of a normal star independently, we can find the mass of an unseen companion a – in AU P – in years M1+M2 – in solar masses

  22. Low-mass X-ray binaries are best candidates because the mass of a red dwarf is much less than a black-hole mass

  23. Black-Hole vs. Neutron-Star Binaries Black Holes: Accreted matter disappears beyond the event horizon without a trace. Neutron Stars: Accreted matter produces an X-ray flash as it impacts on the neutron star surface.

  24. Soft X-ray transients (X-ray Novae)

  25. Black Hole X-Ray Binaries Accretion disks around black holes Strong X-ray sources Rapidly, erratically variable (with flickering on time scales of less than a second) Sometimes: Quasi-periodic oscillations (QPOs) Sometimes: Radio-emitting jets

  26. Radio Jet Signatures The radio jets of the Galactic black-hole candidate GRS 1915+105 V ~ 0.9 c

  27. Gamma-ray bursts Discovered in 1968 by Vela spy satellites Occur ~ 3 times a day at random positions in the sky

  28. Variability on a less than 1 ms timescale – must be a very small object R < ct ~ 100 km

  29. GRBs are distributed isotropically on the sky There is a deficiency of weak bursts – are we looking over the edge of their distribution? Compton gamma-ray observatory discovered two puzzles:

  30. GRB distribution Gamma-ray sky

  31. Breakthrough: in 1997 when BeppoSAX satellite was able to detect the burst position at 1 arcmin resolution and coordinate with optical telescopes within 1 hour after the burst An X-ray image of the gamma-ray burst GRB 970228, obtained by the team of Italian and Dutch scientists at 5:00 AM on Friday 28th February, 1997, using the BeppoSAX satellite.

  32. Discovery of the optical and radio counterparts of GRBs Spectral lines with redshift from 0.8 to almost 4! • GRBs are at the edge of the observable universe • They must be the most powerful explosions in the • universe: ~ 1 solar mass is converted into gamma-rays • in a second!

  33. Gamma-ray burst models Hypernova??

  34. Known types of supernovae Type II: hydrogen lines; collapse of a massive star Type I: no hydrogen lines Fig. 10-18, p. 202

  35. Hard to imagine a supernova without ejection of a star shell

  36. Colliding neutron stars

  37. Continuing cycle of stellar evolution

  38. Our Earth and our bodies are made of atoms that were synthesized in previous generations of stars

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