Part 1 : HR Diagram

In this exercise we will explore the HR diagram. We will look at M15 and be able to calculate certain values such as the age of the cluster and the distance away. We will also mark the various evolutionary stages of the stars we are looking at. Chapter 15 of the book may aid you some in identifying the different components of clusters.

Section 1: M15

M15 is a globular cluster. Globular clusters are clusters of stars that reside on the outskirts of our galaxy (sort of like suburbs). As we will see soon, they are very old, and very far away.

Attached is a HR diagram for the M15 cluster. The data points are REAL data!

References for the data:

Brighter Objects: Buonanno, R. et al, 1983, Positions, Magnitudes, and Colors for Stars in the Globular Cluster M15, Astron. Astrophys. Suppl. Ser., 51, 83

Dimmer Objects: Sandage, A. & Katem, B., 1977, Faint Photometry in M15: the Intrinsic Width of the Main Sequence, the Luminosity Function, and the Density Gradient of Faint Field Stars, Ap. J., 215, 62

NOTE: You will notice a discontinuity between these two data sets. This is due to different calibrations of the telescopes they are using. This is a common problem in Astronomy, and as you can see, it can lead to great problems at times although here we are not too badly affected.

1) Using the HR Diagram attached, circle and label the following:

a) Main sequence (this is the part on the bottom that goes up and to the left note that is stops when it stops going continuously up and to the left)

b) Turn off point (this is the part where the main sequence stops going up and to the left and starts to go up and to the right)

c) Red giant branch (goes up and to the right)

d) Horizontal branch (use chapter 17 page 542 of the text book to help you here)

2) Lets imagine a star exactly like our sun was that is inside the cluster. What would you expect its B-V value to be if as viewed from earth it is 0.68 (hint, how if at all does color change with distance)? Using that find where on the H-R a main sequence star like our sun would be in this cluster. Mark the position on the chart above and note its V value below.

3) Lets imagine a star exactly like our sun was a little bit further away from us than the cluster. How would its V value change (remember that smaller numbers of magnitudes are brighter than bigger magnitudes)? Note, I am not asking for how much, just in what direction on the chart. Draw in a possible value for the sun if it were a little bit further away from us than the cluster and label it SUN FURTHER AWAY.

4) Now we will examine the distance to this cluster. To do this recall that the Absolute Magnitude of the sun is +5.0. The Absolute Magnitude represents the brightness of an object from 10 parsec away. The factor brighter or dimmer that the sun would be in this cluster would be a measure of how much closer or further this cluster is than 10 parsecs. Since light spreads out as the square of distance, each factor of 4 brighter or dimmer an object is corresponds to a distance factor of 2. 9 would be 3, ect.

First, what is the difference in magnitudes from your answer for the V value for a star like our sun in question 2 and the suns Absolute Magnitude (which is +5.0)? We will set this value equal to X. That is X = V value of sun in cluster 5

The distance to the cluster is then:

Distance = 10 parsecs * 10X/5

What is the distance to this cluster? Be sure to show work, use proper scientific notation, and to use 2 significant digits. Also note that if you get an answer like 107.6 then you have to split that into 100.6 * 107 and plug in 100.6 on the calculator, so in this case you would get 3.98 * 107 seeing as 100.6 = 3.98

5) Now we go for the age. This one is a bit trickier. However we are aided by the fact that the stars in the cluster are all about the same age. Since the lifetime of a star depends on its mass, to determine the age of a cluster, we just need to look at the mass of star which is just starting to stop being a Main Sequence Star. That is we need to know the V magnitude of the turn off point. The expected lifetime of that star is the age of the cluster. So, for normal stars the lifetime is

(if Y = V magnitude of turn off point V magnitude of the sun if it was in the cluster):

Lifetime = 10 billion * 10(4Y/15)

However, for this cluster the stars are sooooooooo old that they have almost no metals. That makes the properties of the stars far different. The age of this type of cluster is 4 times more than what the equation above gives you. So, what is the correct age of this globular cluster (i.e. it is 40 billion * 10(4Y/15))? Show work! Use 2 significant digits, and answer in terms of billions of years. Hint, first find the value for Y by using the turn off point that you marked in question 1b, and you found V for the sun in question 2 and yes, Y will be negative.