Exercise

To determine the age, we will make a HR diagram for M67 using the data from Part 1 and 2.

Generally, the HR Diagram plots luminosity, or an absolute magnitude, as a function of temperature. Luminosity is difficult to determine though. However, if we assume the stars of interest are all part of the same cluster, then we can assume that they are all the same distance away. This is a good approximation, and it allows us to plot apparent magnitude instead of luminosity on the HR Diagram. 

Make the HR Diagram for M67 using the apparent magnitudes and temperatures for the stars in the finder chart. You should use the V magnitudes. Label the axes of your HR Diagram, and indicate where the main sequence, giant branch, and main sequence turn off point are located on it.

Once you have the HR Diagram, answer the questions below.

  1. What is the Main Sequence turn off age of the cluster?
  2. What assumptions did you make to determine the turn off age?
  3. If the reference star has an absolute magnitude of Mv=5.01, find the distance to the cluster. You can calculate it using the equation on the background section or using this simulation.
  4. Using the distance you found in Question 3, find the absolute magnitudes of the three hottest stars in M67. 
  5. Use the HR-Diagram Explorer  to determine the luminosities and radii of the three hottest stars. You will need the absolute magnitudes from Question 4.
  6. What are the luminosity classes of the three hottest stars in Question 5?

Age of a Globular Cluster

We will now determine the main sequence turn off age of M67. The main sequence turn off age tells us how old the cluster is. The mass of a star sets the luminosity, the temperature, the size, and how fast it will evolve off of the main sequence. This is fortunate because stars of the same mass will evolve at the same rate. Listed below are the main sequence life times of stars. 

Spectral Class Luminosity Time on Main Sequence
O 104 Lsun < 107 years
B 103 Lsun 108 < t < 109 years
A 101 Lsun 109 years 
G 100 Lsun 1010 years 
K 10-1 Lsun 1011 years 


You can also calculate the age for main sequence stars directly from the mass and luminosity

tage = tsun (Lsun*M)/(L*Msun), and

L ~ M3

where tsun = 15 Gyr.