Through analysis of digital images, Christa and I wanted to construct our own H-R Diagram for the open star clusters NGC6939 and "Wild Duck", and the globular clusters Meisser 5 and Messier 12. We hypothesized that the open cluster's diagram will be more concentrated along the middle where the main sequence line exists; and that the globular cluster's diagram will be more varied and spread out.
We started by asking the Hands-On Universe network to send us images of the clusters that we selected, using both blue and visual filters. We found the brightness of all the stars in the image; and with a known star and its known magnitude, we were able to calculate the blue and visual magnitudes for each star. With that information we calculated the color index which therefore allows us to find the temperature. We then used the distance-luminosity formula to calculate each star's absolute magnitude.
The Graphical Analysis program allowed us to construct our very own H-R Diagram. We used the temperature as the "x" axis and the absolute magnitude as the "y" axis. Although the diagram does show that the globular clusters have a greater variation of star types than the open clusters, the populations don't line up in the expected way along the main sequence. There seems to be some sort of calibration problem which to date we have not been able to identify.
Introduction
Through every neighborhood the variety in people is amazing. There are differences in their age, skin color, hair color, habits, tendencies, and every aspect of a human imaginable. In our observed "Starry Neighborhoods" there are also countless variations from star to star in size, temperature, magnitude, color, and again, every aspect of a star imaginable. What we have done is taken four different star clusters (two open and two globular) and identified the differences in literally hundreds of stars. The end result is portrayed on our very own H-R Diagram.
Purpose
The purpose of our project is to determine the difference in the stellar populations of old globular clusters versus young open clusters, and to ultimately make an accurate representative H-R diagram of our results. By analyzing CCD images of representative star clusters, we intend to determine the temperature and absolute magnitude of many individual stars. By plotting absolute magnitude vs. temperature, the variations in star types can be compared.
Hypothesis
We hypothesize that the population of stars in the globular cluster will contain a wider variety of stars than the open cluster. We believe this because, as stars age and progress through their life cycle, their location on the H-R diagram changes. They progress through the main sequence line where they spend 90% of their life, the other 10% is spent either in the giant or white dwarf stages. The stars in the globular clusters have had the time to progress through the main sequence, therefore we expect to see a wider variety of stars in the globular cluster than in the open.
Background Report - click here
Materials
-reference books
-calculator
-Apple Macintosh Computer
-Graphical Analysis Program (from Vernier Software)
-HOU binder with practice labs
-digital telescope images
-Red Shift astronomy software
-Image Processing software
Procedure
1) Open desired images using HOU image processing software, go to data tools, click on find. This will find the counts on the first 20 stars. Repeat this until there are no more unmarked stars. Repeat for both B and V images.
2) Look at results window and find the difference between the x and y coordinates, of the same star. Go to manipulations, click on shift and shift one image to match the other such that the stars "line up". Record counts.
3) Plug each count into the formula:
magnitude of target star = magnitude of known star+log(count ratio)/log (2.512).
This will give the magnitude of each star.
4) Calculate the B magnitude - V magnitude. This number is the color index.
5) Look at the color index graph and look up each number to find the corresponding temperature.
6) Calculate absolute magnitude with the formula
M is absolute magnitude, m is apparent magnitude, d is the known distance. Solving for M gives
7) Go into Graphical Analysis and graph the temperature*(-1) on the x-axis and the absolute magnitude*(-1) on the y-axis. (Graphing the inverses allows the scale to decrease from the origin along both axes as is traditional in the H-R diagram.) This graph is your H-R diagram for one set of images.
8) Repeat all steps for second set of images.
9) Put both sets of data on one graph and this H-R diagram will illustrate the differences from one image to the next.
Data and Results
Links to data tables: Open Clusters M11 NGC 6939 Globular Clusters M5 M12
The most reliable data is plotted below. (ZAMS = "zero age main sequence".) M5 and NGC 6939 images both included standard stars with known magnitudes in both blue and visual, wheres we had to use more speculative methods to estimate blue magnitudes in the other images.
Conclusion
It's wonderful being right! The globular cluster, as predicted, was much more spread out on the H-R diagram than the open cluster. There were stars that appear to be entering the giant phase, and others appearing to be approaching the white dwarf stage. The majority of the stars are in one region. However, the location of the majority of the stars just doesn't seem right. They are located just above the expected position of the main sequence line. We believe that there could be an error in the calibration in some images related to standardization and/or the specific color filters used. Perhaps a follow-up project involving many clusters having standard stars with reliable known magnitudes in both blue and visual will produce results with a better fit to the ZAMS line.
Special Thanks
We would like to give special thanks to our wonderful Astronomy teacher, Mr.Sweet. Also we owe a debt of gratitude to the Hands On Universe network and Kitt Peak Observatory for their help; their images are what made our work possible.
Bibliography
1. Abell, Morrison, Wolff.Realm of the Universe, W.B. Saunders Co, 1988
2. Karkoschka.The Observer's Sky Atlas, Springer-Verlag, 1990
3. Seeds.Astronomy,Wadsworth Publishing Co, 1997
4. Seeds.Horizons,Wadsworth Publishing Co, 1993
5. HOU Curriculum Guide