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H-R Diagrams of M13 and M28


Hertzsprung-Russell Diagrams of Globular Clusters M13 and M28 Sankalp Raju UC Davis COSMOS Cluster 9: Introduction to Astrophysics July 30, 2010

H-R Diagrams of M13 and M28 Abstract This paper creates and analyzes the H-R diagrams for globular clusters M13 and M28 to


determine their respective ages. After aligning and adding a World Coordinate System to each image, Source Extractor was used to identify objects in every photograph. A source code in Python was then written to check for matches, measure the magnitude of objects, and print the final H-R diagram itself. Unfortunately, neither clusters age could be determined since the H-R diagram of M28 was incomprehensible and M13 lacked enough data. If given more time, improvements could have certainly been made to make accurate estimates of their ages.

H-R Diagrams of M13 and M28 Introduction For thousands of years, individuals have attempted to understand the stages of a stars life by observing specific stars in the night sky. Through the independent research of Ejnar Hertzsprung and Henry Norris Russell, astronomers recognized that stars


occupied specific regions in a temperature vs. luminosity plot, which further helped them discover distinct characteristics of galaxies and clusters. Thus, the Hertzsprung-Russell diagram (H-R diagram) revolutionized astronomers perception of a star clusters life. An H-R diagram has two axes, similar to that of a graph on a Cartesian coordinate plane. The x-axis always represents a measurement of temperature such as spectral classification or color index. Spectral classification is a method for labeling individual stars according to the amount of hydrogen found in their spectra. Today, spectral classification is synonymous with temperature thanks to Annie Jump Cannons simplification of the system (Thakar, n.d.). Although the temperature or spectral classification is most commonly found in the x-axis of an H-R diagram, the color index is also frequently used. The color index is a numerical system for describing the color of a star. To calculate a stars color index, one must measure the magnitude of two colors using filters that only allow specific wavelengths of light to pass, such as blue (B) and green (V). The difference between these two measurements (B-V) results in a single numerical value that describes the color of a star. In the case of blue and green filters, smaller values represent bluer, hotter stars while larger values denote redder, cooler stars (Thompson, 2003). The y-axis of an H-R diagram represents either the apparent brightness or the intrinsic luminosity of a star. An objects absolute magnitude is a measurement of

H-R Diagrams of M13 and M28 intrinsic brightness irrespective of distance. In other words, the absolute magnitude of


any object is equal to its apparent magnitude if it were 10 Parsecs away from the observer (Smail, 1998. Therefore, most H-R diagrams have brightness on the y-axis and the temperature along the x-axis (Ball, 2004). One might assume that an H-R diagram of a galaxy would appear random. On the contrary, almost ninety percent of all stars form an orderly diagonal band spanning from the bottom right of the H-R diagram to its top left (Figure 1). Astronomers named this narrow band the main sequence since all stars spend most of their lives fusing hydrogen into helium. Although the main sequence is the most prominent feature in an H-R diagram, there are distinct outliers in the top right and bottom left corners. Almost all giants and supergiants, stars that have expanded due to a lack of hydrogen at high enough temperatures, can be found in the upper right corner of the diagram; they are enormous, bright stars that are slightly cooler and red. One can also find white dwarves, stars on the verge of dying, on the lower left corner of an H-R diagram since they retain heat but hardly emit any light (Thompson, 2003). This paper will analyze the

Figure 1. Sample H-R Diagram. The narrow band down across the diagram is known as the main sequence. (Kochava, 2009)

characteristics of the globular clusters M28 and M13 through the use of multiple H-R diagrams. Globular clusters are a collection of older stars that orbit a center of mass. As a result, the density of stars is far greater around the center of the cluster as opposed to its

H-R Diagrams of M13 and M28


outskirts (Smail, 1998). Charles Messiers discovery of M28 in 1774 was quite distinctive since it was only the second globular cluster identified to contain a pulsar, a neutron star emitting electromagnetic radiation. M13, on the other hand, is known as the "great globular cluster in the constellation of Hercules" since it contains hundreds of thousands of stars (Fromment, 2007). This paper will measure the luminosity and colors of several hundred stars in M28 and M13, analyze their HR diagrams, and use the information to estimate the age of these clusters.

Data Jim Misti captured the four images of M28 used in this paper (red, blue, green, luminance) and two images of M13 (blue, green) on August 29, 2005 at Misti Mountain Observatory, Arizona. Misti took three minute exposures for the blue, red, and green images in M28, and one minute exposures for the blue and green images in M13 using a Ritchey-Chretien 32" telescope and a SBIG STL-11000 CCD camera. Each pixel in a CCD camera detects the number of photons it receives and displays an image accordingly. A longer exposure results in a brighter image--crucial for capturing distant and weak star clusters such as M28 and M13 (Richmond, n.d.). Since M28 is a relatively fainter star cluster and requires a longer exposure to collect a noticeable amount of photons, the exposure time for the unfiltered luminance image was eight minutes (Figure 2).

Figure 2. M28 Blue Filter. This black and white image was taken by a CCD camera through a blue filter. (Misti, 2005)

H-R Diagrams of M13 and M28 Using software such as CCDSoft, CCDSharp, MaxIM DL, and Photoshop CS, Misti subtracted and divided all the photographs by the dark frames and flat fields,


respectively. As a result, no further processing was necessary to calibrate the images. The images were then placed under a single folder, extracted, and aligned using CCD Soft so that an overlap amongst the photographs would not blur the final image. Because a CCD camera can only detect the number of photons and not the type of photon, all of the raw data taken by Misti were black and white images. To create a final colored image, CCD Soft "color combined" the aligned images and displayed a single photograph of M28 and M13. The color combine application balances the ratio of the green, red, and blue filters to digitally color a single, final image.

Analysis The aligned photographs were not only combined to create a single colored image, but were also used to introduce a coordinate system that enabled specific stars to be identified. Using astrometric stars--stars with well-known positions in the sky--a program known as CCD Soft added the World Coordinate System, or WCS, in each aligned image. Before CCD Soft could construct a coordinate series for each object, one had to input both the right ascension and declination of the star cluster. Adding the WCS in every photograph made it possible to identify the same star with itself in multiple different images. A program known as Source Extractor (SExtractor) helped distinguish stars in M28 and M13 from noise. By adjusting parameters such as detection threshold, analysis threshold, and deblending contrast, one could choose to detect fewer or more objects

H-R Diagrams of M13 and M28 based on their brightness and pixel size. In M28, SExtractor detected approximately


5,526 objects in the blue filtered image alone by specifying the detection threshold to 1.7, the analysis threshold to 5, and deblending contrast to 0.005. On the other hand, SExtractor only detected 2,435 objects in the blue filter of M13 under the same parameters. SExtractor applied these parameters to all the aligned images since they were stored in the same folder. Although SExtractor occasionally misidentified objects that were clearly noise or meaningless background objects, it also recognized the significant stars both distant from and close to the center of the globular clusters. After SExtractor determined the significant objects in each image saved as an .FIT file, it cataloged all the data into an .SRC file. SExtractor not only listed all the recognized objects in .SRC files, but also added eight columns of characteristics for each individual star. Characteristics included the x position, y position, magnitude, flag, and star/galaxy classification. Since excess objects were present in all photographs, SExtractor distinguished a varying number of individual ,,stars in each image. Thus, it was critical to match and store the common, more reliable objects and discard any noise or background stars. With the aid of

Figure 3. Identified Objects in M28. The purple dots represent the objects SExtractor identified from the image. (Misti, 2005)

Robin OConnells source code, Python immediately discarded mismatched stars. The source code initially imported data from the .SRC file and read the characteristics specified. Python would only store stars if there were objects within two

H-R Diagrams of M13 and M28 pixels of the expected position in another filtered image; otherwise, they were thrown


away. After comparing objects in four different filters, the original count of 5,526 stars in M28 drastically reduced to merely 463 stars. Because M13 only had two filters and is richer, the 2,435 objects were only reduced to 956 stars. Once all the matched stars were identified, they were plotted to make an H-R diagram. Python kept track of all the stars magnitude in each individual filtered image to create an accurate representation of an H-R diagram. On the x-axis, the magnitudes of stars from the green filters were subtracted from those of the blue filters. The y-axis represented the magnitude of the stars from the green filter. Plotting the stars in this manner produced HR diagrams shown in Figure 4 and Figure 5.

Figure 4. H-R Diagram of M28. Each red dot represents a star's color index and magnitude.

H-R Diagrams of M13 and M28


Figure 5. H-R Diagram of M13. Each red dot represents a star's color index and magnitude.

As one might notice, the H-R diagram for M28 is fairly sporadic and no conclusions can be made about the globular cluster since the diagram lacks a definite correlation to analyze (Figure 4). The cause for M28s irregular behavior is essentially due to the excess noise present in the images. The globular cluster takes up a small part of Mistis photographs and is predominantly surrounded by background and foreground stars. Because SExtractor also identifies the stars encompassing M28, no trend of the actual cluster can be discerned. There would have been several possibilities for solving this problem if more time was available. By adjusting the code in Python, it would have been possible to limit SExtractor to only identify objects in a specific square area--namely the globular cluster

H-R Diagrams of M13 and M28 itself. Additionally, keeping track of the flags might also be useful if one wanted to remove extraneous objects and record brighter, obvious stars.


Figure 6. Comparison of H-R Diagrams. The H-R diagram of M13 produced in this paper (right) is compared to that of a scientific journal (left). (Stetson, 1998).

Unlike M28 and its inconsistent H-R diagram, M13 has distinct features that can be easily discerned (Figure 5). The horizontal branch can be found on the left of the image, though it isnt very horizontal at all. As opposed to M28, this papers H-R diagram of M13 is very accurate when compared to that of a scientific journal. An important step in maintaining this precision was the calibration of the image with the aid of outside sources. Once a specific stars true B-V magnitude was obtained, SExtractors magnitudes were scaled to match its values. As a result, objects in the graph are fairly near their true values: if one observes closely, the "horizontal" branch of M13 in both HR diagrams breaks off at approximately 14.5 (G). An interesting question that arose when analyzing the two images was why SExtractor and Python only displayed a middle fourth of the ,,true H-R diagram. To

H-R Diagrams of M13 and M28 resolve this issue, it is important to understand both the capabilities and limitations of


SExtractor. Because the stars below the graph were dimmer, it was harder for SExtractor to detect them based on its settings. If one were to modify the parameters, however, SExtractor would not only pick up the dimmer stars, but also identify background objects and noise that would only detract from the precision of the H-R diagram. SExtractor also failed to identify the brighter stars in M13, which is quite non-intuitive. Because luminous stars tend to be bigger, gravity brings them towards the center of the globular cluster together. As a result, SExtractor was unable to discern individual stars in the center of the globular cluster since was comparable to one giant mass of light. It was impossible to estimate the age of the globular cluster since M13s H-R diagram did not display the turn-off point. Better equipment or data would have been an easy fix for this problem but were unavailable at the time.

Conclusion Although the H-R diagrams for M28 and M13 were unsuccessful in relaying information on their age, reasons for their failure were noted and could have been fixed if given enough time, recourses, or data. Nevertheless, this paper was quite successful in constructing an accurate H-R diagram in the case of M13, albeit incomplete. While this paper was specifically directed at analyzing M13 and M28, an H-R diagram can be used for any group of stars. Although this paper is a small example of it, H-R diagrams are truly necessary in analyzing a star clusters life and characteristics.

H-R Diagrams of M13 and M28 References


Ball, L. (2004). Colour of stars. Retrieved from Australia Telescope Outreach and Education website: education/senior/astrophysics/photometry_colour.html Harrison, T. (2008). The Hertzsprung-Russell diagram. Retrieved from Newman, P., & Gibb, M. (n.d.). Background: Life cycles of stars. Retrieved September 27, 2004, from xray_spectra/background-lifecycles.html Poulsen, M. (n.d.). Hercules Globular cluster (Messier 13). Retrieved from ESO Projects website: cas-projects/denmark_m13_2/ Richmond, M. (n.d.). The Hertzsprung-Russell (HR) diagram. Retrieved from Richmond, M. (n.d.). Introduction to CCDs. Retrieved from classes/phys445/lectures/ccd1/ccd1.html Smail, I. (1998). HR diagram for a Globular cluster. Retrieved from Thakar, A. (n.d.). The H-R diagram. Retrieved from SkyServer website: Thompson, T. (2003, April 15). Hertzsprung-Russell diagram and stellar evolution. Retrieved from

H-R Diagrams of M13 and M28 Acknowledgements This paper would not have been possible without the help of Chris Faasnacht, Vera Margoniner, Chris Taylor, Jim Johnson, Mounika Kandalam, Anuraag Dulapalli, Robin OConnell, and many other fellow peers.



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