Draft version October 7, 2017 Preprint typeset using LATEX style emulateapj v. 01/23/15
CREATING A COLOR MAGNITUDE DIAGRAM OF M53 Wyatt Griffith Draft version October 7, 2017
ABSTRACT A color magnitude diagram of M53 was generated using magnitudes that were measured with photometry programs. IRAF and DAOPHOT were used to measure the instrumental magnitudes of all the stars in 50 different images of M53. The images were then aligned using DAOMATCH and DAOMASTER so that the measured magnitudes could be attributed to a particular star and averaged across all the images. These average instrumental magnitudes were compared to known magnitudes for a set of standard stars such that they could be converted into absolute magnitudes. The magnitudes were then sorted into B, V, and I magnitudes and plotted against each other to create a color magnitude diagram. 1. INTRODUCTION
2. METHODS
M53 is a globular cluster in the Coma Berenicies constellation. It lives about 18 Kpc away from the solar system (about the same from the galactic center) and is estimated to be 12.6 billion years old.(6) Observations of M53 were made over the course of a week from March 5th to March 9th at the MDM Observatory on Kitt Peak. The 2.4 m Hiltner telescope was used for all of these observations using B, V, and I filters. Below is a colorized image of M53 taken during the observational trip and colorized afterwards using Fits Liberator and Adobe Photoshop.
There were several steps necessary to create a color magnitude diagram of M53. First a program needed to be taught how to select stars within an image such that it could measure their magnitudes. After all of the magnitudes in all the images have been measured, they needed to be attributed to specific stars such that an average magnitude could be calculated for any given star. This was done by aligning the images with DAOMATCH and DAOMASTER.(4) Once the images were aligned and the instrumental magnitudes for each star had been averaged across all of the images, they were converted into absolute magnitudes and plotted in a color magnitude diagram. 2.1. Photometry
Fig. 1.— Colorized Image of M53 (1)
In order to measure the magnitude of a star, the computer needs to understand what constitutes a star. This is done by measuring the PSF (Point Spread Function) of a variety of stars in each image and feeding that information into some files that are executed by a program. The PSF of a star basically denotes how light falls off from the center of a star. This was done within IRAF/NOAO/Obsutil using psfmeasure, which lets the user select a bunch of stars at once, and provides an average PSF of the stars selected, as well as an opportunity to remove outliers from this average.(3) When doing this, PSFs ranging from about 5.1 to 6.1 worked the best in latter steps even though some average PSFs that were measured ranged from 6.1 to 7.1. In those instances subtracting 1 from the average PSF allowed that next step to work. Once the average PSF was measured for a given image, that value (which is technically a full width, half max) can be used to calculate the FI and PS. These three values need to be changed in the DAOPHOT.opt, phot.opt, and allstar.opt files saved within the images folder associated with the image whose values were measured. Once those values were changed, DAOPHOT was ready to run and measure the magnitudes of all the stars it could detect in each image.(5) This involved typing “daophot” into the command line and entering other commands when prompted. The first command tells DAOPHOT to look for 100 stars with magnitudes less than 17. This step would produce 100 potential stars if fed PSFs within the acceptable range. If the PSF entered
2 into the .opt files was too high, DAOPHOT would only find 20 or 50 potential stars which would not be enough to continue the process. Once DAOPHOT has selected 100 potential stars, the user has to manually look at each star to verify that it is indeed a star. It will present the stars one at a time as ascii representations of their PSF. For each image that is presented, the user must select yes or no based on whether or into it looked like a star. Stars were generally round central objects with no extraneous brightness. Common things that got misidentified as stars by DAOPHOT include cosmic rays, extended objects, and stars that don’t have a clean profile. After all of the potential stars have been looked at, the program has a good idea of what counts as a star. Next, a program called allstar.scr must be run to go through the image and find all the stars that fit the parameters provided by DAOPHOT and measure their instrumental magnitude. This information gets output into a file with; the stars name within the program, its x and y coordinates, its magnitude, and the standard deviation in that magnitude. This process is repeated for each image. Most of the images that were analyzed were taken with a V filter so an effort was made to do a couple with B and I filters so that a diagram with colors and magnitudes could be made.
2.3. Plotting After the photometry has been done and the stars have been aligned it was time to condense all of the information into one file, convert instrumental magnitudes into absolute magnitudes, and plot the data in gnuplot. The information from each filter were combined in excel such that the column headers were; star name, x position, y position, and the B, V, and I magnitudes along with their standard deviations. These magnitudes were all instrumental magnitudes so the instrumental magnitudes for standard stars needed to be compared to their well known absolute magnitudes for this data to be useful to anyone else. This was done by downloading the magnitudes and positions of about 100 standard stars in M53 from The Canadian Astronomy Data Center, using DAOMATCH and DAOMASTER to align those stars with the data taken with the Hiltner Telescope, finding a conversion factor between the instrumental magnitudes and the absolute magnitudes, and converting those magnitudes.(2) After this was completed, the data was finally ready to be plotted. The plots include; a color magnitude diagram of M53, various plots showing magnitudes vs error, and a plot showing the positions of the stars that were measured. All of the plots were generated in gnuplot and are presented in the results section.
2.2. Alignment 3. RESULTS
The primary result of this project was creating a color magnitude diagram for M53. This was done by plotting the V magnitudes vs the (B - I) magnitudes, see Fig. 2 for the diagram.
13 Color Magnitude Diagram 14 15 16 V
Once all of the files containing all of the magnitudes and positions of stars have been generated, they need to be aligned with each other such that stars on one image can be correlated with stars on another image, and average magnitudes for stars that appear in multiple images can be made. This is done roughly using DAOMATCH first, then more precisely with DAOMASTER. DAOMATCH is run by; entering one image as a reference, entering the name of the output file, and then entering all of the images to be matched with the reference image one at a time. This was repeated three times, once for each filter and was involved very little adjustments as the images were fairly well aligned to begin with. After DAOMATCH is finished, DAOMASTER needs to be run to better align the images and output a useful file. DAOMASTER will take the output from DAOMATCH as its input as well as a few redundant parameters. These parameters are; the number of frames you would like a star to show up in for it to count as a star, the fraction of frames that need to have a star for that star to count, and the number of frames again. There are some more parameters about the maximum sigma and degrees of freedom and then DAOMASTER asks for a critical match up radius. The critical match up radius tells DAOMASTER within how many pixels two stars from different images have be in order to count as the same star. The user begins by selecting 5 for the critical radius which causes DAOMASTER to output how many stars it has found. The user must lower the critical radius by 1, until it is 1 and the number of stars detected stabilizes. Once the number of stars present in all of the images has stabilized, the user presses 0 to stop. Lastly DAOMASTER will ask what files the user would like outputted. For these purposes the important file was an updated position and magnitude file that contains the new coordinates for each star and the average magnitude across all the images of a given filter.
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Fig. 2.— Color Magnitude Diagram of M53 using V vs ( B - I )
In creating this diagram it is interesting to note how much standard deviation was involved with each magnitude. Fig. 3 shows the B magnitudes vs the standard deviation in those magnitudes.
3 0.06 Sigma in B 0.05
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0.04 600 Star Positions 0.03 400 0.02 Y Position
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Fig. 3.— B Magnitudes vs B Sigma
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Fig. 4 shows the V magnitudes vs the standard deviation in those magnitudes.
4. DISCUSSION
0.02 Sigma in V
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Fig. 4.— V Magnitudes vs V Sigma
Fig. 5 shows the I magnitudes vs the standard deviation in those magnitudes.
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Fig. 6.— Positions of Stars used for Photometry
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Fig. 5.— I Magnitudes vs I Sigma
Fig. 6 is a plot of the x and y positions of all the stars used for photometry. This is useful in ensuring that the resulting data comes from all portions of the cluster, not one isolated region.
The color magnitude diagram that was created does indeed look like a color magnitude diagram. There is a visible red giant branch as well as a horizontal branch. The red giant branch begins around (1, 15) where the stars evolve off of the main sequence and ends at about (3, 14) where the helium flash occurs, sending stars to the horizontal branch. Stars on the red giant branch are fusing a shell of hydrogen which surrounds a core of helium that is not hot enough to fuse. This core is degenerate so once the temperature in the core is sufficient for helium fusion, the entire core begins fusion at once. This is the aforementioned helium flash which dramatically changes a stars composition and sends it to the horizontal branch without stopping anywhere in between. This is why there is an increased density of stars in Fig. 2 at about (0, 17) with no stars connecting them to the top of the red giant branch at (3, 14). Once on the horizontal branch, stars begin fusing a core of helium and are still fusing a shell of hydrogen. These stars gently drift along the horizontal branch to the right until the helium core runs out and helium fusion in the shell begins. At this time the star begins going up the asymptotic giant branch. There is a small asymptotic giant branch in Fig. 2 located around (1, 15) and (2, 14) but there are not a lot of stars in M53 that are on this stage of stellar evolution. There are a few stars that don’t seem to fit into any of these categories but they are likely foreground and/or background stars that are not part of the cluster but occupy the same visual space in the sky. It is interesting to note that the standard deviation was much lower and less noisy for the V magnitudes than it was for the B or I magnitudes. This is probably because there were significantly more V images used than B or I images which resulted in better averages and thus better standard deviations.
4 REFERENCES [1]All observations were taken at the 2.4 m Hiltner Telescope at MDM Observatory Kitt Peak AZ by Nathanial Paust between March 5th and March 9th 2017 using BLANK second exposures in B, V, and I. [2]Government of Canada. National Research Council Canada. National science infrastructure (NRC Herzberg, Programs in Astronomy and Astrophysics) - National Research Council Canada. Government of Canada. National Research Council Canada. N.p., n.d. Web. 10 May 2017.
[3]NOAO. IRAF. IRAF Project Home Page. N.p., 22 Mar. 2012. Web. 10 May 2017. [4]Stetson, Peter. DAOMATCH, DAOMASTER. DAOMATCH and DAOMASTER packages for DAOPHOT. N.p., n.d. Web. 10 May 2017. [5]Stetson, Peter B. DAOPHOT - A computer program for crowded-field stellar photometry. Publications of the Astronomical Society of the Pacific 99 (1987): 191. Web. [6]”Messier 53.” Wikipedia. Wikimedia Foundation, 05 May 2017. Web. 10 May 2017.