LAB 08 - RR Lyrae Variable Stars

LAB 08 - RR Lyrae Variable Stars

RR Lyrae variable stars (named after the prototype star RR Lyrae) are pulsating stars that regularly change brightness.  RR Lyrae stars have a mean absolute magnitude of 0.75 (M=0.75).  This makes RR Lyrae stars useful as standard candles to measure distances out to about 760,000 parsecs (about 2.5 million light years).  In the early 20^th century, astronomer Harlow Shapley observed RR Lyrae variable stars in several globular clusters that orbit our Milky Way Galaxy.  These observations provided a rough estimate of the distance to each globular cluster which led to the discovery that our sun is not at the center of the galaxy.   In this lab, you are going to use data from RR Lyrae variable stars to determine the distance to the globular cluster M15.

YOU MUST WATCH THIS VIDEO IF YOU WANT TO KNOW HOW TO DO THIS LAB:

The picture below shows the light curve for a typical RR Lyrae star.  The vertical axis represents magnitudes (note that smaller number means bright and large number means dim).  The light curve shows that the brightness of the variable star changes over time.  The top solid line intersecting the highest point on the light curve, indicates that this star has a magnitude of 14.25 when it is brightest. The bottom solid line intersects the lowest point on the light curve.  Here, the star is dimmest at apparent magnitude 15.05.    

Using these values, we can calculate the average apparent magnitude of the RR Lyrae variable star as (15.05 + 14.25)/2 = 14.65.  Using this value as m = 14.65, and given that the absolute magnitude of RR Lyrae variables is always M = 0.75, we can use the distance formula to calculate the distance to the star:

According to our calculations, the distance to this star is 6025.59 parsecs.  However, in order to get a better estimate of the distance to the whole cluster, it is advisable to use several variable stars, determine the distance to each, and then average the results to get the distance to the globular cluster.  

Below, you will see the light curves from the RR Lyrae variable star v24 located in globular cluster M15.  These are typical light curves in blue, visible, red, and infrared light that can be collected from a variable star.  

In this particular lab, you will be presented with the visible light curves from six different RR Lyrae variable stars in M15. 

Here is the sheet with all six light curves: RR Lyrae Variable Star Light Curves.pdf 

• For each light curve, you will determine the brightest magnitude and the dimmest magnitude (bright is up and dim is down). Then, you will average these values to get the average apparent magnitude for each star. 
• Next, you will calculate the overall average magnitude for this collection of stars. 
• It is this value for apparent magnitude (m) that you will use along with the absolute magnitude for RR Lyrae variable stars (M=0.75) in the distance formula:

• The basic assumption employed in this method is that all the stars in M15 are roughly the same distance from us so we can use an average apparent magnitude to calculate the distance.