Variable Stars

Instructions:  Read the small summary below and then follow the requirements section below.  Note that you are going to have to do some research in order to answer all of the questions. You may find an introductory astronomy text very useful. 

     The brightness of stars is not a constant.  The Sun for example, has been slowly brightening since it was born 4.6 billion years ago.  Itis now about 30% more luminous than it was at birth.  It will continue to slowly brighten for the next 5 billion years, after which it will run out of hydrogen to fuse in its core and begin to die, first by becoming a red giant, much more luminous than it is now, and scorching the Earth in the process.  In addition to this slow brightening, the Sun varies slightly (a fraction of a percent) depending on how many sunspotsor flares are present on the side we see.  It is also suspected that the Sun varies over periods of decades or centuries, but this remains to be confirmed and the mechanism by which this may happen is not understood. 

     An astronomer living next to another star would hardly be able to detect any short term change in the Sun.  By contrast, the brightness of many stars varies by large amounts, sometimes over a period of hours!  Most of these "variable stars" are unstable, dying stars (most are red giants) that swell and shrink repeatedly over periods of days to a few years.

     In this lab, we will see three types of variable stars simulated and measure their brightness changes.  We will graph the brightness of the star vs. time.  This is called the "light curve".  We will then use this information to estimate properties of the variable stars. 

Eclipsing Binaries

One type of variable star is not truly variable at all.  It is called an "eclipsing variable".  The brightness appears to change because one star of a multiple star system passes in front of the other and blocks part of the total light from the system as seen from Earth.  Algol

(Beta Persei) is a great example of such a variable star.  The system lies at a distance of about 100 light years and consists of a white, B8 main sequence star 100 times as luminous as the Sun and 2.6 million miles in diameter(!); and a yelow-orange K subgiant star about 3 times as luminous as the Sun and about 3 million miles in diameter.  The two stars orbit each other about 7 million miles from each other in only 2.7 days!  When the brighter, slightly smaller star covers the fainter, larger star, the total brightness of the system drops by about 10% (which is barely perceptable to a trained eye, yet easily noticed by a detector similar to the one in your cell phone or digital camera).  However, when the fainter star covers most of the brighter star, the total brightness drops by 79%.  At mid-eclipse, Algol is less than 1/3 as bright as it usually is!!  This light change can be easily noticed by Astronomy 12 students!   The total eclipse lasts for about 10 hours, but most of the action takes place in the central 6 hours.

Cepheid Variables

Perhaps the most famous type of variable star is a pulsating red supergiant called a Cepheid variable - named after delta Cephei a 2nd magnitude star in the constellation Cepheus the King (adjacent to Casseopea the Queen).  These variable stars are so famous because of their usefulness in measuring their distances.  They pulsate in brightness (and in size) like clockwork and the period of their pulsation depends upon their luminosity.  Thus, if you time the period of the pulsation, then you can determine the luminosity using the "period-luminosity relationship".  If you compare the luminosity to the measured brightness, then you can calculate the distance to the star.  They become very important when they are seen in other galaxies using large telescopes.  They allow us to measure the distance to those other galaxies! 

Supernovae

A supernova is a star that blows up.  Actually the inner core collapses but the outer core and top layers are blown into space.  They are fantastically luminous.  There are two different types of supernovae.  Type I is a white dwarf explodes and Type II is a red supergiant that explodes.   A supernova can release as much energy in a few seconds as the Sun will in its entire 10 billion year lifetime!  A supernova brightens very suddenly and very dramatically and then fades slowly over weeks, months, and even years. The shape of the light curve tells astronomers which type of supernova it is. 

Requirements

1.  The three tables of your observations.  These would be presented in your Observations section of your formal lab report if you decide to write one.  

2.  Answers to questions below.

3.  If you decide to write a formal lab report for this lab, you are also required to answer all of the extra credit questions below.  Use them to help with your Results section. 

Questions.

1.  What is the magnitude system?  How much is 5 magnitudes in brightness?  1 magnitude?  Which is brighter, a 3rd magnitude star or a 4th magnitude star?  How faint of a star can the average person see on a dark night?

2.  A)  Make a graph of the brightness of the eclipsing binary vs. time in minutes.

     B)  Make a graph of the brightness of the Cepheid variable vs time in days.

     C)  Make a graph of the brightness of the Supernova vs time in days.

To answer the following questions, find information about the famous eclipsing binary Algol in Perseus. 

3.  Sketch how the binary would look during its different orbital phases if we could see it clearly enough.

4.  Highlight the part of the eclipsing binary orbit that you saw in the lab.

5.  Extra Credit: When you compare the brightness and sizes of the stars in Algol, what is so unusual about them?

6.  Extra Credit: How did the stars get that way?

To answer the following questions find information about Cepheid variables.

7.  Obtain a detailed graph of the period-luminosity relationship for Cepheid variables and provide it here.

8.  Estimate the period of pulsation for the Cepheid that you observed (refer to your graph of its light curve).

9.  Use the answers to questions 8 and 7 to determine the luminosity of the Cepheid variable. 

10. Extra Credit: use the measured brightness of the Cepheid variable that you saw and the answer to question 9 to calculate the distance to the star.  You may have to refer to an introductory astronomy text to do this.

11.  How are the distances to nearby stars usually measured?  Why are Cepheids useful? 

To answer the following questions, find information about supernovae, especially the differences between Type I and Type II supernovae.

12.  Sketch the light curves for typical Type I and Type II supernovae.

13.  Extra Credit: Why are the two curves different?

14.  Which type of supernova did you observe?

15.  What is the luminosity of the supernova that you observed?

16.  Extra Credit:  Calculate the distance to the supernova.  Why is this type of supernova important?

17.  The location of the simulated supernova that you saw in class was at the location of the famous Crab Supernova.  What is the crab nebula?  When did this star explode?  Which type is it?