11 H. R. Diagram – Colour- Magnitude Diagram

V. B. Bhatia

 

1.  Learning Outcomes

 

After studying this module, you should be able to

  • recognize the colour-magnitude diagrams of star clusters
  • note the turn-off points in CM diagrams
  • understand the evolutionary track of a star on the CM diagram
  • calculate the life-time of star on the Main Sequence
  • explain the connection between the turn-off point and the age of a cluster
  • Describe the nature of blue stragglers

 

2.  Introduction

 

In the last few modules we have been discussing H. R. Diagrams and its importance for the astronomer. We found that all the characteristics of a star can be found once the position of the star is known on the H. R. Diagram.  If, for example, a star is located on the giant branch then we know it surface temperature, spectral class, mass, radius and the kind of nuclear reactions that are going on in the core of the star. That is why when a new star is discovered, the attempt is to determine its location of the H. R. Diagram.

 

Since a star of a given spectral class could be a dwarf, giant or a supergiant, we had to find some way to supplement the spectral classification with a classification which would allow us to describe more comprehensively the class of a star. This supplementary classification is called the luminosity classification which we discussed in the last module. The luminosity classification classifies the stars as: I – Bright Supergiants; II – Normal Supergiants; III – Giants; IV – Subgiants; V – Main Sequence; VI – Subdwarfs and VII (or suffix wd) – White Dwarfs. When we include luminosity classification, a star of spectral class G2 on the main sequence is designated as G2 V.

 

We also found that it is easier to find accurately the colour of a star than determining its surface temperature. Moreover, the colour is found to follow faithfully the surface temperature of stars, as we have discussed in earlier modules. Therefore, astronomers find it easier to draw a colour- magnitude diagram rather than the usual H.R. Diagram.  It turns out that such diagrams for stellar clusters lead to the determination of the ages of clusters. Since the stars of a cluster can be reasonably assumed to have been born together, the stars can differ only in their mass and, to a small extent, chemical composition. The last two characteristics of the stars of a cluster allow us to estimate the ages of clusters, which is the subject of discussion in this module.

 

3.  Colour- Magnitude Diagrams of Stellar Clusters 

 

Figures 16.1 to 16.4 show the colour–magnitude (CM) diagrams of stellar clusters such as Pleiades, Praesepe (M44), M92, and M67.

Fig. 16.1. Colour-Magnitude Diagrams of Pleiades and Praesepe clusters. The turn-off point is shown by an orange dot. (Source: http://www.astronomy.ohio- state.edu/~pogge/Ast162/Unit3/tests.html)

 

In the case of Pleiades cluster, all the stars appear to lie on the Main Sequence. In the case of Praesepe and other clusters most of the stars again lie on the Main Sequence, but an important point to notice is that a few stars have turned to the right from the main Sequence towards the giant branch.  The point at which the stars turn to the right from the Main Sequence is called the turn-off point.  In the following figures these points are indicated by orange dots.

Fig. 16.2.  Colour-Magnitude diagram of open cluster Praesepe (M44). The turn-off is shown by an orange dot. Notice that the y-axis has apparent magnitude. As explained below, each star of the cluster has the same distance modulus; therefore, the apparent magnitude has to be adjusted by a fixed amount to get the absolute magnitude. This adjustment does not affect the shape of the diagram. The stars in the pink strip are giants. The presence of the blue star is important; we shall discuss it later. (Source: http://www.starobserver.eu/openclusters/m44.html)

 

Fig. 16.3.  Colour Magnitude diagram of globular cluster M92.  Note the turn off point at around colour 0.4. The overlying curves are called the isochrones. They will be discussed below.  (Source: http://www.pnas.org/ content/94/13/6579/F2.expansion.html)

 

Fig. 16.4.  H. R. Diagram of clusters M67 and NGC188. (Source: https://en.wikipedia.org/wiki/Messier_67#/media/File:Open_cluster_HR_diagram_ages.gif)

 

7.  Summary

  • Stars of a cluster can be assumed to have been born at the same time, so they have the same age. However, stars can differ in their masses. There can be small differences in chemical composition, too.
  • Stars of different masses have different life-times on the Main Sequence.
  • After residing on the main sequence, the stars evolve away from the Main Sequence towards the giant branch.
  • High mass stars evolve faster than the low mass stars.
  • The turn-off point in the colour-magnitude diagram of a cluster gives the mass of the stars that have started evolving away.
  • Since the time spent by these stars on the Main Sequence is known, the turn-off point determines the age of the cluster.
  • A few stars are found on the Main Sequence above the turn-off point. These stars are called blue stragglers, because they are not expected at that position.
  • It is thought that these stars were initially less massive than the stars at the turn-off point, but accreted mass from their binary companions and found themselves above the turn-off point.
  • The open or galactic clusters are much younger than the globular cluster populating the central bulge of the galaxy. Their ages vary from a few million to a few billion years.
  • The ages of globular clusters are in the range 12 – 14 billion years, uncomfortably close the age of the universe itself.
  • Efforts are being made to determine the ages of clusters more precisely to avoid conflict with the age of the universe.

 

Know More

 

The basic material is from Astronomy and Astrophysics with Elements of Cosmology, V. B. Bhatia, Narosa Publishing House, New Delhi, which has been substantially augmented by material from the following sources:

 

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit3/tests.html

http://www.starobserver.eu/openclusters/m44.html

http://www.pnas.org/content/94/13/6579/F2.expansion.html

https://en.wikipedia.org/wiki/Messier_67#/media/File:Open_cluster_HR_diagram_ages.gif

http://sci.esa.int/education/36828-stellar-processes-and-evolution/?fbodylongid=1742

Australia Telescope Outreach and Education

https://www.wikiwand.com/en/Red-giant_branch

http://abyss.uoregon.edu/~js/ast122/lectures/lec15.html

https://ned.ipac.caltech.edu/level5/March03/Vandenberg/Vandenberg3.html

http://rml3.com/a20p/mainseqfitting.htm

http://www.astro.caltech.edu/~george/ay1/lec_pdf/Ay1_Lec09.pdf

http://burro.cwru.edu/academics/Astr221/LifeCycle/clusters.html

https://www.e-education.psu.edu/astro801/content/l7_p6.html

http://applet-magic.com/virialth.htm

http://coolcosmos.ipac.caltech.edu/cosmic_classroom/cosmic_reference/molecular_clouds.html