Dancing With Stars

Introduction Image
  1. In the sky, two out of every three stars are in the ‘Binary System’. For example, Alpha Centauri had a companion called Proxima Centauri.
  2. Stars occur in many different combinations of binaries; some have 4 to 5 in binary.
  3. binary stars come in two basic classes → A] Wide Binaries: They are in the large distance and long period orbits. The members of these binaries evolve separately as a single star. B] Close Binaries → Here, one star affects the evolution of another. These binaries are formed by the fragmentation of a single protostar clump.
  4. The force of gravity and the principle of conservation of linear and angular momentum govern the orbits of a pair of binary.
  5. Two stars Orbit one another in the elliptical path around a common center of mass. They move in a mutually opposite direction. The period of orbit is same for both.
  6. For a star in binary, speed of orbit is directly proportional to the size of orbital path.
  7. The sun moves in a tiny orbit around the center of mass; its speed equals 30 miles per hour.
  8. The square of the period of orbit (P) is directly proportional to the cube of the size of the orbit (a³) divided by the total mass of stars (M).
  9. For two stars in a binary system, each reaches out to gravitationally dominate some region beyond its surface (Fig- 1).
  10. Beyond the ‘Roche Lobe’, the matter belongs to none of the stars there; the matter is thrown away at 90 degrees if the matter reaches Lagrangian point.
  11. Two stars in a Closed Binary System born at the same time but are non-identical.
  12. Mass of the star- in binary- is directly proportional to the size of the Roche lobe. Therefore, the force of gravitation is directly proportional to the size of the Roche lobe.
  13. Massive stars expand till they feel their Roche lobes completely.
  14. As the star passes its Roche lobe it transfers the mass to its smaller companion star and expands again. Thus, with the same Roche lobe, it gets smaller and smaller (Fig- 2).
  15. The mass-losing continues until all the envelope of the big star vanishes; it remains with a small core and evolves as a white dwarf. However, a potentially massive star will turn to a neutron star or a black hole.
  16. For the stars which are too close → 1) even a small mass-loss can cause a huge reduction in Roche lobe. Therefore, the two stars arrive at the same point of evolution and try to transfer the mass to each other. Yet, as no star accepts this matter, due to the reduced Rosh lobe, the matter then shoots off the system and generates a flat common ‘Excretion disc’. Do not confuse the excretion disc to the ‘Accretion disk’!
  17. However, in the above scenarios, a star with initially smaller mass remains in the main sequence until the massive star evolves completely.
  18. In case of the more compact stars → the mass-transfer from star A to star B will create the luminosity at a certain rate. This luminosity may reach at such a strong level that it can resist the infall of matter by exerting the pressure. The luminosity reaches beyond the Eddington limit, thus, the matter forms the sphere around the two stars forming the common envelope. Now, the stars Orbit into that envelope, but soon, due to an increase in the friction and heat on the inner walls, the envelope is ejected just as the planetary nebulae.
Figure- 1
Figure- 2






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Rohan Gharate

Rohan Gharate


I am a high school student and an excellent astrophysics enthusiast