by Ken Hose
Globular Cluster M3 looks almost as stunning as M13 when viewed through a small telescope. You can’t see any color through the eyepiece, but properly exposed and processed photos show many light blue stars. Over 200 of these stars are variable stars of the type called RR Lyrae variables. These stars are very interesting because they have about the same average luminosity and there are two main types with periods averaging about 8 hours and 13 hours. This means that one can capture nearly a full period in one night’s observations.
I first became aware of the RR Lyrae variables when I happened across a video showing blinking light blue stars in M3. The video was made of a few frames taken over the period of one night. This really piqued my interest and I set out to image M3 myself. I took back-to-back images of M3 all night long with my 12.5” telescope and then I made my own video by combining four color images; one from the beginning, 2 from the middle, and one at the end of the night. The quality of the video was not great but I could easily see the light blue stars varying in brightness. (Check out my YouTube video. Right-click and choose the looping function.)
I was able to count about 70 blinking stars out of the 223 known RR Lyrae stars as documented by professionals. Not bad. The next thing I wanted to do is to capture a light curve to show how the stars vary in brightness over the night. From my images, I extracted the brightness by using a photometry program. There is nothing too complicated about this and any amateur with modest equipment can do this. I combined the results of 3 nights’ worth of observations to generate several light curves by making charts in Excel. See the included samples. The y-axis is the apparent magnitude and the x-axis is phase which can be thought of as time.
One really cool fact about RR Lyrae stars is that they all have about the same absolute magnitude regardless of where they are located in the universe. This allows us to use them as distance indicators, or “standard candles” as astronomers call them. Dimmer stars will be farther away and brighter ones will be closer. If we can work out the distance to one star, by parallax for example, we can then calculate the distance to all the other RR Lyrae stars based on their apparent magnitudes. This relationship is not perfect, as there are small variations in magnitude which depend on the abundances of elements other than hydrogen and helium in the stars. This causes the absolute magnitude to vary from about 0.4 to 0.8 in different galactic globular clusters. In M3 the absolute magnitude of the variables is about 0.58.
The so-called apparent magnitude is the brightness we measure here on earth and depends on distance to the star. My apparent magnitude measurements for the sample RR Lyrae stars above are 15.65 and 15.74 magnitudes (average ). The difference between the apparent and absolute magnitudes can be used to calculate the distance to the star. Astronomers refer to this difference as the distance modulus.
Before the distance can be calculated, the apparent magnitude needs to be corrected for absorption and scattering due to interstellar gas and dust. This correction can be worked out using photometric measurements at different wavelengths using photometric filters. M3 is located in the halo of our galaxy and the correction is minimal, or about 0.01 magnitudes. Stars located in the galactic plane, however, may have a correction as much as 1 magnitude or more because there is more gas and dust concentrated there. I looked up the correction factor for M3 in a reference book.
The average apparent magnitude of 13 of my light curve measurements is 15.69 which, coincidentally, is the same for the two sample stars above. So our distance modulus is 15.69 – 0.58 = 15.11 which gives a distance of 10,500 pc or about 34,300 light years. The accepted value is about 33,900 light years. I was a bit surprised that the results came so close to the accepted values. The error in my measurements is about +/- 0.05 magnitudes. This is another example of how backyard astronomers can do real science without professional equipment. Here is the Excel version of the distance formula: d = 10 X 10^(distance modulus/5) where the answer is in parsecs. One parsec is about 3.26 light years.