Ding, Anthony - COSMOS - UC Davis

H-R diagram of M29 1
Studying the Hertzsprung - Russell Diagram of the Open Cluster M29
Anthony Ding
UC Davis COSMOS
Cluster 9: Astrophysics
July 26, 2009

H-R diagram of M29 2
Abstract
The goal of this study is to plot and study the H-R diagram of the open cluster M29. The
H-R diagram can have different values plotted on the x and y axes; in this study, the x-
axis represents the B-V value and the y-axis represents the V magnitude. Data used in
this study was collected by a 25-cm diameter Cassegrain telescope through a B filter and
a V filter. The raw data was cleaned, processed, and combined in CCDSoft and the
resulting images were plugged into SExtractor to obtain a list of all the stars in the images.
The stars were then plotted with Microsoft Excel to obtain an H-R diagram. The method
used to procure a rough estimate of the age of M29 is discussed in detail and, using the
diagram, the age of M29 is estimated to roughly 10-100 million years old. If more studies
and analyses are performed, much more information can be plucked from the H-R
diagram of M29.

H-R diagram of M29 3
Studying the Hertzsprung-Russell Diagram of the Open Cluster M29
Thousands of years ago, astronomers were interested only in counting the number
of stars in the night sky. Today, they are interested in categorizing them and learning
more about the lives of stars. The Hertzsprung-Russell diagram, which was developed in
the early 1900s, organizes groups of stars in such a way that a pattern immediately
becomes obvious to the eye (Spence and Garrison 1993). The diagram is plotted with a
star’s temperature on the x-axis, and its luminosity on its y-axis. The temperature
decreases going right, and the luminosity increases going up. This set-up allows scientists
to compare the brightness’s and luminosities of two or more stars by plotting them on the
diagram. Because a star’s luminosity can also be represented by its magnitude, it is
possible to graph the magnitude in place of the luminosity on the y-axis. In addition, the
temperature of a star corresponds to its color and spectral type, and both color and
spectral type can be inserted in place of the temperature.
Generally, stars plotted on an H-R diagram are the same distance away from the
Earth so that their magnitudes are comparable. Stars have two types of magnitudes,
apparent, and absolute. A stars apparent magnitude describes its magnitude as it looks to
the eye, disregarding its distance. A star’s absolute magnitude describes a star’s
magnitude at a set distance, 10 parsecs, or 100,000 km (Scheider and Arny 2009). In
order to convert from apparent magnitude to absolute magnitude, the distance from the
star to the Earth must be known. Therefore, it is much easier to convert the magnitude if
all the stars are the same distance away from Earth because only one distance has to be
used, as opposed to hundreds of distances if the stars are at different distances from Earth.

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This is why star clusters, in which all the stars are the same distance away from the Earth,
are ideal stellar objects to plot on H-R diagrams.
There are two possible type of star clusters, open, also known as galactic, star
clusters and globular star clusters (Schneider and Arny 2009). The major difference
between the two is that an open cluster is relatively young with well-dispersed stars and
an unsymmetrical shape, while globular clusters are relatively old with concentrated stars
and spherical shape. M29, also known as NGC 6913, is an open cluster located in the
constellation Cygnus. Open clusters are born through the condensation of a single gas
cloud (Schneider and Arny 2009). This means that in addition to being roughly the same
age, the stars in an open cluster will be the same distance from Earth and have the same
chemical composition (Frommert and Kronberg 2007). Because many of the properties of
stars in an open cluster are the same, plotting the stars on an H-R diagram is very useful
for comparing the properties that aren’t the same.
When you plot an open cluster on an H-R diagram, you get a characteristic line
starting from the top left, flattening out in the middle, and ending in the bottom right.
This sequence of stars is called the main sequence (Schneider and Arny 2009). In general,
stars in the main sequence are newly formed and burn through a process of nuclear fusion,
where hydrogen nuclei are fused to create a helium nuclei; in fact, our sun is one such
main sequence star. Stars spend most of their lives in the main sequence. As their fuel
burns out, the stars will eventually branch out of the main sequence. Stars that are in the
middle of their lifetimes can be found in the Red Giant branch, where they will
eventually burn out completely and turn into a white dwarf star (Iben 1966). In addition,
some stars may take an alternate path and branch off into what is known as the Horizontal

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branch; stars in the Horizontal branch are remnants of past Red Giant branch stars
(Catelan 2009). The location of stars in these branches can then be analyzed to determine
the age of the star cluster. The determination of a star’s age can lead to further knowledge
of stellar evolution: a study of the lifetime and evolution of a star.
Data
The data used in this study was collected from a Takahashi Cassegrain Reflecting
telescope with a 25-cm diameter lens. Images were captured by a SBig ST8 SE chargecoupled
device, or CCD, with a quantum efficiency of 60%, meaning that 60% of the
light photons that hit the CCD were recorded. All data was taken in 15 second exposures
on July 9 th and July 13 th at the Placerville Rotary Community Observatory. A total of 24
exposures were taken, 12 with a B filter and 12 with a V filter. The B filter lets in light
closer to the blue wavelength and the V filter lets in lights closer to the green and yellow
wavelengths. The raw data was then uploaded to a computer and processed with
CCDSoft, image processing software for CCD images and data reduction.
Analysis
To begin the process of data reduction, five dark exposures were taken at varying
exposure times and CCDSoft was used to divide the dark exposures to make them all
express an exposure time of 15 seconds, the exposure time of our data. Next, we median
combined the dark exposures to create a master dark image. The CCD is not perfect, and
sometimes, it records cosmic rays or ‘ghost’ photons which are not really there. To clean
up the image, counts due to cosmic ray hits and extra photons must be correctly identified
and removed. To do this, the dark images are combined to determine the location of
incorrect counts. After creating the master dark image, we subtracted it from the original

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images to obtain clean images. Separately, the blue filter images and visual filter images
were then aligned and combined to create a total of two images.
Image of M29 through B filter
Image of M29 through V filter
After that, we created a list of objects in the images using CCDSoft, and then transferred
the list and the images to a different piece of software, SExtractor. Through SExtractor,
we were able to obtain an SRC file with data on the entire list of identified objects in the
images, including their coordinates and magnitudes. We were then able to access the data
by opening the file with Microsoft Excel.
After the SRC file was extracted from the image, we isolated the x and y
coordinates and the magnitudes for both the B and V images. We then located certain
stars in the B and V images with CCDSoft and matched their coordinates in the SRC files
to find the magnitude of specific stars. However, there is a constant difference between
the star’s true magnitude, and the magnitude given to us by CCDSoft and SExtractor due
to differences in equipment, viewing conditions, and filters among others. Because of this
constant difference, we needed to use an outside article (Boeche, Munari, Tomasella, and
Barbon 2004) that listed the true magnitudes of the stars. Knowing the true magnitudes of
the stars for the B and V images, we were able to determine the difference between the
true magnitude values and the values in our Excel file. After finding the difference

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several times, we averaged the difference to come up with a constant. The average B
constant of 12.793 and the average V constant of 10.61655 were then added to the B and
V magnitudes to come up with new magnitudes for the two. Because the H-R diagram is
plotted with the V magnitude on the y-axis and the B-V value on the x-axis, the last thing
to calculate was the B-V values. After obtaining the V and B-V values, the data points
were graphed as a scatter plot in Excel.

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Conclusion
Although it is a little bit off, the H-R diagram of M29 represents the typical H-R
diagram of a cluster of stars. The line of data points stretching from the bottom left to the
middle is what is known as the main sequence, where most of the stars are. The almost
vertical line branching out of the main sequence is known as the Red Giant branch. With
knowledge about these two branches, it is possible to estimate the age of M29. In order to
do this, it is necessary to locate a star just about to leave the main sequence and just about
to enter the Red Giant branch. In other words, we need to find the “turning point”. Once
we find the star, we need to convert that star’s B-V value into its temperature, and then
into its spectral type. Knowing its spectral type, we can then match the star up with a
table that compares a star’s spectral type to its average lifetime in the main sequence.
This estimated age is correct because the lifetime given is the lifetime in the main
sequence, and the star chosen is one just about to leave the main sequence. And since all
stars are born at the same time in a star cluster, we can say that the age of the star is
roughly equal to the age of the cluster. In the case of M29, the turn-off point is within an
approximate range of -0.09 to 0.1. Using a chart that matches temperature B-V values to
temperature (Sloan Digital Sky Survey n.d.), we know that this corresponds to a
temperature range of about 11,000K to 9,000K. Using another chart, we know that the
particular stars in the turning point range are spectral type B stars (Nave 2009). This tells
us that the star, and thus the cluster, is around 10 million to 100 million years old (Wilcox
2005). The actual estimated age of M29, using much more accurate data, is 10 milion
years old (Frommert and Kronberg 2007). The large range of 10 million to 100 million
calculated with the data from this paper is due to the fact that open clusters are spread out,

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meaning that taking an image of an open cluster will inherently contain stars in front of
and behind the cluster that are not part of the actual cluster, meaning, if more accurate
data could be obtained, the age of M29 could potentially be measured to a more
reasonable degree of accuracy. Besides calculating a star cluster’s age, it is also possible
to determine the cluster’s distance from Earth using the H-R diagram. While this study
was only aimed at producing an H-R diagram for M29, an open cluster, it is possible to
create an H-R diagram for any grouping of stars, yielding a much larger volume of data
and information of the vast numbers of stars in space.

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References
Boeche, C., Munari, U., Tomasella, L., & Barbon, R. (2004). Kinematics and binaries in
young stellar aggregates. II. NGC 6913=M29. Astronomy and Astrophysics, 415,
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Catelan, M. (2009). The ages of stars: The horizontal branch. The Ages of Stars,
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Frommert, H., & Kronberg, C. (2007, August 27). Open Star Clusters. Retrieved July 10,
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Iben, I. J. (1966). Stellar Evolution.VI. Evolution from the Main Sequence to the Red-
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