# II.7 Measuring the Distances to the Galaxies by means of Cepheid variables.

## 1. What's a Cepheid variable ?

It's a star whose brightness varies with a period of a few. This period depends on the average brightness of the star.

### Research:

1. Locate the Cepheus constellation on a skymap, then in the sky.
2. Do you have legends in your country about that constellation? Do you know who was Cepheus and his legend in Greek mythology?
3. What are the reasons of the brightness variation of this kind of stars?

## 2. Brightness chart of Delta Cephei:

 Days 0 1 1,5 2 3 4 5 6 7 8 9 10 11 12 13 m 4,12 4,28 4,30 4,20 3,55 3,80 4,00 4,20 4,30 3,95 3,55 3,85 4,10 4,28 4,30

### Research:

1. From these data, draw the graph of brightness of Delta Cephei.
2. What is the period, measured on the graph, of Delta Cephei?
3. The ordinate in this graph is the apparent visual magnitude.
Look for the relations between brightness, luminosity, apparent visual magnitude and absolute visual magnitude.
4. How distant is Delta Cephei? How could that distance be measured?

### Suggestion:

• How can the brightness of a star be measured?
• Is it possible to receive a rough result about brightness variation of one Cepheid, in order that groups can work and find the period from a real observation document?

## 3. Relation between period and luminosity:

Values: Cepheids in the Small Magellanic Cloud (SMC):

 Days 2 3 5 10 20 50 100 M -2,2 -2,2 -2,5 -3,2 -4,0 -5,0 -6,2

### Research:

1. How has the distance to the Small Magellanic Cloud been measured?
2. Can we consider that all the stars in this small galaxy are at the same distance from us?
3. Calculate the absolute magnitude of Delta Cephei (using graph no 2) and then the distance to Delta Cephei.

## 4. Observation of a Cepheid variable in another galaxy :

### Suggestion:

1. Observe directly a Cepheid variable in another galaxy.
2. Obtain the rough graph of the variation of its brightness.

and then:

Measure the period of this star and compute the distance of this star, and thus, of its galaxy.

## 5. A few solutions:

 2.2 5,37 days 2.3 brightness = luminosity / 4Pi*d2, d being the distance of the star. compared magnitudes of two stars: m1 - m2 = -2.5 log E1 / E2 absolute magnitude at a distance of 10 parsecs: M - m = -5 log d+5 2.4 950 light years 3.2 Yes, as the size of the Small Magellanic Cloud is small in comparison with the distance between that galaxy and us (distance: 165 000 light years, diameter: 14 040 light years, i.e. 8,8%). 3.3 about -2,8: its average apparent magnitude being about 4, we get a distance of 230 pc or 750 light years.

Author: Frederic DAHRINGER, CLEA.