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Scenario 4 - Detection of binary stars: the case study of Sirius

Classification of Sirius as an astrometric binary star

I. General Information
Two stars can appear to be very close together in the sky, either because they both happen to be seen in almost the same direction while they are actually considerable distance apart, or because they really are close together in space. Double stars of the first type are called optical binaries. There are in fact very few examples. Most stars that look double are indeed physically bound: they are true binary stars, or double stars. Each star moves in an ellipse around the other, as the planets do around the Sun.


 
Photos of Kruger (visual) Binary star taken in 1908, 1915 and 1920

Repeated measurements of the positions of certain stars have permitted the discovery of irregularities in their proper motions indicating the presence of an invisible companion, either so faint or so close that its image cannot be separated from that of the principal star. Thus in 1844 F. W. Bessell discovered that Sirius shows a non-linear proper motion, whose oscillations resemble those of a visual binary star: he deduced that the proper motion of Sirius is affected by the gravitational interaction with a second star whose luminosity is low. Sirius , has a magnitude of 8.7 while the magnitude of Sirius is -1.4. The diagram of the right shows the paths of Sirius and Sirius , plotted with respect of an absolute reference system.

 

Duration:
Theory:    1x45 min
Observational Activities:  2x45 min

Vocabulary:
Visual binary stars, astrometric binary stars, oscillation

Tools and Materials:
Network of Robotic Telescopes, PC with broadband connection, Paper sheet, Pencil, Ruler

Aims and Objectives:
The users should:

  • be able to prepare and make astronomical observations
    be able to use celestial coordinates
  • be able to detect a binary star through examining the light curves of eclipsing binary systems and more precisely the variations of the apparent visual magnitude
  • be able to Analyze the shapes of the light curves of eclipsing binary stars so that  find certain physical parameters of the atmospheres of the system of stars. When there is a total eclipse, we can determine the ratio of the effective temperatures of the two components it is also possible, in the case of certain pairs, to deduce the diameters of the stars.
  • be able to detect binary stars by using various techniques
  • be able to understand the scientific methodology
  • be able to distinguish and classify the binary stars according to the three classes i.e. visual binary stars, astrometric binary stars and spectroscopic binary stars

Users’ Misconceptions:
Binary stars orbit around a common point called centre of mass

II. Educational Phase
Stimulation:
1x45 min

  • Presentation of selected photos and/or videos of the Sirius binary star
  • Short discussion on the Sirius case i.e. Sirius’ non-linear proper motion, whose oscillations resemble those of a visual binary star. Factors affect the Motion of Sirius. Draw up a list on a blackboard with a proposed method of detecting the binary feature of Sirius
  • Draw up a list on a blackboard with the proposed method of detecting other binary systems

Experimental Activities:
First phase (1x45 min)
The users of the D-Space service must:

  • select a  Robotic Telescope among the Network of Robotic Telescopes
  • check the meteorological status for the site where the selected Robotic Telescope is located 
  •  fill in the celestial coordinates of Sirius and the proper time of observation

Second phase (1x45 min)

The users of the D-Space service must:

  • take the Sirius image from the Database Library
  • study and understand the analysis methods followed in the theory
  • detect the existence of a binary star using various techniques i.e. periodic variations of apparent luminosity, observing their orbits (a star moves in an ellipse around the other, as the planets do around the Sun)

Observation - Discussion:
Discussion of the theoretical issues arising from the observational (experimental) activities
This is facilitated with the assistance of the website's theory tutorial and links

  • Theory and observation (experiment) comparison

Consolidation:
Questions, exercises and tasks aiming at consolidation of the acquired knowledge

Exercises:
Parameters measured from observation of binary stars

Analysis of the shapes of the Light curves of eclipsing binary stars allows us to find out certain physical parameters of the atmospheres of the stars of the system. When there is a total eclipse, we can determine the ratio of the effective temperatures of the two components; it is also possible, in the case of certain pairs, to deduce the diameters of the stars. This determination requires the knowledge not only of the Light curve, but also of the spectra of the two components, which allows us to establish the variation of their radial velocities; the diameters can then be determined as absolute values. It has been possible to calculate diameters in this way for only a small number of stars, but such measurements are important because, along with interferometry, they provide a way to measure directly the diameter of stars.