12 Masses of Stars

V. B. Bhatia

 

1.  Learning Outcomes

 

After studying this module, you should be able to

  • relate masses of stars to binary groups
  • understand that a binary group can be a visual group, spectroscopic group or eclipsing group
  • describe the nature of a visual binary group
  • calculate the masses of visual binary group using Kepler’s laws
  • explain how the masses of both the components can be found if both are visible
  • describe how spectroscopic binary stars are recognized from the behaviour of their spectral lines
  • recognize the orbital elements of a binary star
  • derive relation between the orbital elements and the masses of the binary stars

 

2.  Introduction

 

So far, we have dealt with the properties of stars like their surface temperature, luminosity and nature of spectra.  Based on their spectral properties, stars have been classified in seven major classes.  A chance observation of correlation of luminosity with the surface temperature of stars led to the development of H. R. Diagram and luminosity classification of stars. H. R. Diagram and its variant colour-magnitude diagram have been of immense use to astronomers and astrophysicists in learning about the evolution of stars. Several times it has been said in these modules that the mass of a star is an important parameter in determining the rate at which it evolves.  It is, therefore, time that we learnt how the masses of stars are actually determined. The next few modules are devoted to this topic.  We shall find that not all star masses can be determined directly.  Those stars whose masses can be found directly are used to establish the relationship between mass and luminosity, called the mass – luminosity relation.  Masses of most stars are then found indirectly using this relation.

 

 

5.  Summary

  • Mass of a star is an important parameter which determines the rate at which it evolves.
  • Most stars exist in binary groups and groups of three or more stars.
  • Application of Kepler’s laws to the binary groups is the source of stellar masses.
  • Binary groups can be visual, spectroscopic or eclipsing binary groups.
  • Visual binaries are accessible to observation with telescopes.
  • Spectroscopic binaries reveal themselves through an oscillating set of spectral lines.
  • Eclipsing binaries are recognized when one component eclipses the other and gets eclipsed in turn.
  • The more massive component of the group is called the primary, while the less massive is called the companion.
  • Since the centre of mass (or barycenter) of a binary system moves in a straight line in the sky, the two components move around this moving centre and execute serpentine motions in the sky.
  • The orbit of a binary system is an ellipse. The plane of the ellipse is generally inclined to the plane of the sky. The orbit projected on the plane of the sky is also an ellipse, but the primary in not at the focus.
  • Kepler’s third law can be applied directly to the visible system. If both the components are visible, mass of individual member of the group can be found.
  • By studying the behaviour of oscillating lines of a spectroscopic binary system, we can plot the velocity curve of the binary system.
  • Analyses of velocity curves leads to the determination of the orbital elements of the system, which lead to the determination of stellar masses.
  • Since the inclination of the orbit to the plane of the sky is not generally known, we can place only a lower limit on the combined mass of the two stars.
  • The masses of only a small fraction of stars can be found by analyzing binary systems. These masses can, however, be used to establish a mass-luminosity relation, which can be used for finding masses of most stars.

 

Know More

 

The basic source of the material on binary stars is Textbook of Astronomy and Astrophysics with Elements of Cosmology by V. B. Bhatia. This material has been supplemented by the following web sources:

  • https://en.wikipedia.org/wiki/Visual_binary
  • http://www.ast.cam.ac.uk/~pettini/STARS/Lecture04.pdf
  • http://www.atnf.csiro.au/outreach/education/senior/astrophysics/binary_types.html
  • http://burro.astr.cwru.edu/Academics/Astr221/StarProp/speclipse.html
  • http://www.astro.caltech.edu/~george/ay20/Ay20–Lec4x.pdf
  • https://en.wikipedia.org/wiki/Orbital_elements
  • https://commons.wikimedia.org/wiki/File:WZ_Cephei_binary.png
  • https://commons.wikimedia.org/wiki/File:Eta_carinae_orbit.png
  • https://en.wikipedia.org/wiki/Alpha_Centauri#/media/File:Alpha,_Beta_and_Proxima_Centauri_(1).jpg
  • http://spiff.rit.edu/classes/phys440/lectures/reduced/reduced.html