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.

5. Two mechanisms of mass transfer in a binary system
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

6. Accretion from a stellar wind

7. Star overflows its Roche lobe

8. 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.
                                                                                                                      

9. 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!!

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

11. 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

12. 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.

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

14. Accretion onto a neutron star
Figure 11.8: Sometimes the X-ray pulses from Hercules X-1 are on, and sometimes they are off. A graph of X-ray intensity versus time looks like the light curve of an eclipsing binary. (Insets: J. Trümper, Max-Planck Institute) (b) In Hercules X-1 matter flows from a star into an accretion disk around a neutron star producing X rays, which heat the near side of the star to 20,000 K compared with only 7000 K on the far side. X rays turn off when the neutron star is eclipsed behind the star.

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

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

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

18. Cygnus X1 – first black hole

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

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

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

22. Binary systems a – in AU P – in years M1+M2 – in solar masses
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

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

25. 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.

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

27. 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

28. Radio Jet Signatures
The radio jets of the Galactic black-hole candidate GRS
V ~ 0.9 c

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

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

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

33. GRB distribution
Gamma-ray sky

35. 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 , obtained by the team of Italian and Dutch scientists at 5:00 AM on Friday 28th February, 1997, using the BeppoSAX satellite.

36. 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!

37. Gamma-ray burst models
Hypernova??

38. Known types of supernovae
Type II: hydrogen lines; collapse of a massive star
Type I: no hydrogen lines
Figure 10.18: Type I supernovae decline rapidly at first and then more slowly, but type II supernovae pause for about 100 days before beginning a steep decline. Supernova 1987A was odd in that it did not rise directly to maximum brightness. These light curves have been adjusted to the same maximum brightness. Generally, type II supernovae are about 2 magnitudes fainter than type I.
Fig , p. 202

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

40. Colliding neutron stars

42. Continuing cycle of stellar evolution

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