14 Close Binaries, Mass-Luminosity Relation of Stars

V. B. Bhatia

 

1.  Learning Outcomes

 

After studying this module, you should be able to

  • sketch the equipotentials of effective gravitational field around the close binary system
  • locate the Lagrangian points in the equipotentials
  • define detached, semi-detached and contact binary systems
  • explain how matter is exchanged between the two components of the binary system
  • understand how an accretion disc is formed
  • define cataclysmic variable systems and recurrent novae
  • describe the nature of supernovae 1a
  • explain the formation of extra-galactic x-ray sources such as Hercules X-1 and Cygnus X-1
  • describe mass-luminosity relation
  • explain how dynamical parallaxes are determined

 

 

7.  Summary

  • A close binary system has five Lagrangian points where the effective gravitational field vanishes.
  • The inner Lagrangian point separates the two Roche lobes forming the figure of eight.
  • When both the Roche lobes are unfilled, the system is said to be detached.
  • When one Roche lobe is filled but the other is unfilled, the system is said to be semi- detached.
  • When both the Roche lobes are filled, the system is called a contact binary system.
  • If a contact binary system consists of a compact object and a normal star, matter can push past the inner Lagrangian point and can fall in the gravitational field of the compact object.
  • As it falls in the gravitational field, the matter gains kinetic energy.
  • When matter hits the surface of the compact object, kinetic energy gets converted into heat energy of the matter.
  • Since matter carries angular momentum, it does not fall on the surface of the compact object but forms an accretion disc around it.
  • When the compact object is a white dwarf star, the radiation from the accretion disc can explain recurrent novae.
  • By gaining matter from its companion, the white dwarf star can have mass exceeding Chandrasekhar limiting mass, which can lead to supernova explosion.
  • These supernovae are assigned class 1a. Since the exploding star has always mass equal to 1.4 solar mass, supernovae 1a always reach the same maximum brightness.
  • These supernovae can be used as standard candles for measuring cosmic distances.
  • When the compact object in the system is a neutron star, the matter in the accretion disc is so hot that it emits x-rays. This is a possible for model for x-ray sources of Hercules X-1 type.
  • When the compact object is a black hole, the source of x-rays can be modelled like Cygnus X-1.
  • Masses of stars determined by binary systems are used to establish a mass-luminosity relation, enabling the masses of stars to be estimated indirectly.

 

Suggested Readings

 

Major sources for the matter covered in this module are: Textbook of Astronomy and Astrophysics with Elements of Cosmology by V. B. Bhatia.

 

https://en.wikipedia.org/wiki/Lagrangian_point

https://www.space.com/30302-lagrange-points.html

https://imagine.gsfc.nasa.gov/science/objects/cataclysmic_variables.html

Oroszet.al. Ap, J., 2011

http://www.agnld.uni-potsdam.de/~shw/TSA/Application/X-Ray/Internet.html.

http://www.isthe.com/chongo/tech/astro/HR-temp-mass-table-bymass.html

https://www.nasa.gov/sites/default/files/images/138785main_image_feature_460_ys_full.jpg

https://en.wikipedia.org/wiki/Hercules_X-1

Discovery of a Periodic Pulsating Binary X-Ray Source in Hercules from UHURU: Tananbaum, H.; Gursky, H.; Kellogg, E.M.; Levinson, R.; Schreier, E.; Giacconi, R, 1972 ApJ…174L.143T

https://en.wikipedia.org/wiki/Cygnus_X-1

Cygnus X-1

http://www2.astro.psu.edu/users/rbc/a534/lec18.pdf