Project SEE: Investigating Variable Stars
By Noreen Grice
On a clear dark night, far away from bright city lights, thousands of stars are visible. Long ago, ancient observers imagined that stars were all the same but we now know that stars are actually different sizes and different distances from Earth.
A Greek astronomer named Hipparchos (who lived around 160-127 BC) created a way to describe the brightness of stars that he could see at night. Hipparchos called the very brightest stars, 1st magnitude, the next fainter stars 2nd magnitude stars and yet fainter stars 3rd, 4th and 5th magnitude stars. The very faintest stars that he could see were called sixth magnitude stars. For comparison, a 1st magnitude star is 100 times brighter than a 6th magnitude star.
To help you remember which magnitude means bright and which means faint, consider a running race. If there are six runners, the winner will be in first place (like first magnitude) and the last person to cross the finish line will be in 6th place (like a faint 6th magnitude star).
Over time, astronomers built instruments like binoculars and telescopes to help them see stars even fainter than 6th magnitude. The star magnitude system was then expanded to include stars that were fainter than Hipparchos could have seen and also to include objects like the Sun and Moon, which are much brighter than a 1st magnitude star.
Some stars are called variable stars because they appear to change their brightness, getting dimmer and brighter over time.
One type of variable star is called an intrinsic variable. The star itself actually grows and shrinks making it appear fainter and brighter. This happens when the star is in a point of its life where it is struggling to balance external gravity pushing in and internal pressure pushing out.
Many amateur astronomers around the world enjoy observing variable stars. They view the stars with the unaided eye or with binoculars or a telescope. They might take a photograph of the star with a few nearby stars, or simply record their personal observations with hand written notes. Some of these people submit their observations to groups like the American Association of Variable Stars Observers, so that other people can use the observations to study the variable stars further.
Variable stars can be studied by comparing their changes in brightness to the constant brightness of nearby non-variable stars. By tracking and graphing changes in brightness over time, it is possible to estimate the brightness cycle, or period, of variable stars.
Each time the variable star is observed, its magnitude is compared to a nearby non-variable star. In this activity, you will estimate (interpolate) the magnitude of a variable star over the course of twelve observations and then graph the changes in the star’s magnitude to estimate the period of that variable star.
1. You will find three observation pages (Braille: 1 / 2 / 3. Print: 1 / 2 /3) with twelve nights of observations. Each page has a reference magnitude chart on the top of the page and four nights of observation.
Study the star magnitude chart at the very top of the page so that you will be familiar with the different star magnitudes. The brightest star is first magnitude and appears the largest. Each subsequent magnitude appears fainter and smaller until you reach sixth magnitude, which is the faintest star visible to the unaided eye. To observe stars fainter than sixth magnitude requires optical aid such as binoculars or a telescope.
2. Scan the star fields on the first page. The star fields show the same stars each night and represent a very small area of the night sky. Each star on the first night’s observations is labeled either
star-a, star-b, star-c, star-d, or star-e. One these stars is a variable star. Compare the labeled stars from night #1 to the same stars in nights 2-4. The variable star changes its magnitude each night. Which star is the variable star?
3. Once you have identified the variable star, return to the first night’s star field. Compare each star to the magnitude chart at the top of the observation page. Make a list and record each star’s magnitude.
Star Magnitude (on Night #1)
4. After you have identified the magnitude for all of the stars in the night #1 star field, examine the variable star on nights #2-12.
Sometimes the magnitude of the variable star will not exactly match a whole magnitude on the chart. For example, the variable star might fit between a 4th and 5th magnitude and in that case would be recorded as a 4.5 magnitude star. Here is a fun part of science where you make your very best guess (interpolation) of the magnitude of the variable star.
Record the changing magnitude of the variable star on a new list, night by night. Since the other stars will not change their magnitude, you only need to track the changes in the variable star. Remember to compare the magnitude of the variable star to other nearby stars to estimate the variable’s changing magnitude.
Night # Variable Star Magnitude
Analyzing The Results
1. With a list of the variable star’s magnitude each night, you can make a graph called a light curve. You will plot the twelve observation nights on the x-axis (from night #1 to night #12) and plot the star magnitude scale on the y-axis (starting with faint 6th magnitude at the bottom and ending with bright 1st magnitude at the top) as indicated on the accompanying graph paper (Braille / Print).
Place a very thick piece of cardboard or corkboard under the graph paper. Use a pushpin (or push through metal paper fasteners and open the “wings” under the paper) to mark the positions of the variable star’s magnitude each night.
2. Once you have plotted the data points for the variable star’s changing magnitude on the graph, use a piece of string to connect the points from night to night. Tie the string to the first point on the graph and then just “loop de loop” the string around the pushpins or metal fasteners. Do you notice a pattern?
3. Remember that a variable star gets brighter and fainter in cycles. When the star is the brightest it can be, it is at maximum magnitude. When the star is as faint as it can be, it is at minimum magnitude.
What is the maximum and minimum magnitude of the variable star?
4. If you measure the time it takes for the variable to go from maximum magnitude to the very next maximum magnitude, you can establish the period of the star. Based on your light curve, how long is the period of this variable star?
Here is an example (Braille / print) of what the variable star light curve should look like.
Something Else to try:
Imagine that you observe a star to be a variable star and are told that is it not an intrinsic variable. What might cause the star to vary its magnitude?
The apparent change in the brightness of a star sometimes occurs because the visible star is really two stars orbiting each other; when one star eclipses the other, light is reduced but when both stars are side by side, we see their combined light. We call these star systems, eclipsing binary stars.
Here is a list of a star’s changing magnitude over the course of twelve nights. Use a new sheet of graph paper and plot the data just as you had for the intrinsic variable star.
Night # Eclipsing Variable Star Magnitude
Again use a string to connect the data points. How is the shape of this light curve different from the intrinsic variable star?
The light curve of an eclipsing binary star shows two dips, or drops in magnitude. The largest dip, called primary eclipse, happens when the larger star eclipses the small star and the most light is lost. The second, smaller, dip is called secondary eclipse and it occurs when the smaller star blocks a portion of the light from the larger star and some light is lost. When both stars are side by side, we see their combined light and that causes maximum magnitude.
According to the light curve, what is the brightest (maximum) magnitude of this star system?
If you measure from the brightest magnitude point (before a primary eclipse) to the next brightest magnitude (before the next primary eclipse) you can estimate the orbital period - how long it takes for the stars to orbit each other. According to your light curve (which should look like this: Braille / print), what is the orbital period of this eclipsing star system?