13 Masses of Stars (Contd.)

V. B. Bhatia

 

1.  Learning Outcomes

 

After studying this module, you should be able to

  • describe how masses of both the components of a spectroscopic binary system may be found
  • explain the meaning of mass function of a binary group
  • describe the nature of an eclipsing binary group
  • understand the variety of light curves
  • explain how the masses and radii of stars of an eclipsing binary group can be extracted from their light curves

 

2.  Introduction

 

In Module 17 we started discussing the determination of stellar masses. Recall that the mass of a star is an important attribute because it determines the way the star will evolve. Recall also that the source of information of stellar masses is the study of binary stars. A binary system may be a visual binary system, a spectroscopic binary system or an eclipsing binary system.  Usually the information we get is about the mass of either the more massive component or the combined mass of the two components.  However, by a lucky chance, if a system is a visual binary as well as a spectroscopic or an eclipsing binary system, then it is possible to get information about the masses of both the components of the system.

 

In the last module, we dealt with the visual binaries. We also learnt how the velocity curve of a spectroscopic binary system may be extracted from the data collected about the system and orbital elements of the system may be found, leading to an upper limit on the combined mass of the system.  In this module, we learn how, under favourable circumstances, the masses of both the components of a spectroscopic binary group may be gleaned from the observational data.

 

We also describe the variety of light curves of eclipsing binary systems and explain how the light curves may be used to estimate sizes and masses of the stars belonging to these groups.

 

5.  Summary

  • When velocity curves of both the components of the spectroscopic binary group can be deciphered, masses of both the components can be estimated.
  • Since the inclination of the orbit to the plane of the sky is an unknown quantity, we calculate only the mass function of the binary system.
  • From the eclipses caused by the two components to each other, we get the light curve of an eclipsing binary system.
  • Light curves show a lot of variety depending on the luminosities of the two components, the sizes of the two components, distances of the two components from the CM and the inclination of their orbits to the plane of the sky.
  • Analyses of light curves lead to information on sizes, luminosities, separation and masses of the components of the eclipsing binary system.
  • If the eclipsing binary system is also a spectroscopic binary system, we can get the inclination of the orbit and hence individual masses of the components, rather than the mass function.

 

Suggested Readings

 

The basic material for this module is taken from Textbook of Astronomy and Astrophysics with Elements of Cosmology by V. B. Bhatia. This material has been supplemented by the following web sources:

  • http://www.eso.org/public/images/eso1311a/
  • http://www.astro.caltech.edu/~george/ay20/Ay20-Lec4x.pdf
  • http://spiff.rit.edu/classes/phys230/lectures/mass/mass.html
  • http://www.astro.sunysb.edu/metchev/PHY521/lecture26.pdf
  • www.astro.umass.edu/~snell/lectures228/lecture7.odp
  • http://astronomy.nju.edu.cn/~lixd/GA/AT4/AT417/HTML/AT41708.htm