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Color Magnitude Diagram of Cluster M67 - by Tim Hunter:

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Tim Hunter is a classmate of mine, and owner/operator of two fine observatories in Arizona - the 3 Towers Observatory and the Grasslands Observatory. His project on M67 is similar to mine but special in that instead of using provided data he decided to use his own. His project highlights how he captured his own science images and used them to create a color magnitude diagram of M67.

Abstract
Introduction
Equipment and Observations
Results
Discussion
Conclusion
References

Abstract 

Color magnitude diagrams (CMD’s) of the open cluster M67 (NGC2682) were constructed from data obtained with a Meade LX200 12-inch telescope at the 3towers Observatory in Tucson, Arizona, and from data obtained with the 24-inch f/5 telescope at the Grasslands Observatory near Sonoita, Arizona.  The CMD’s plots V magnitudes versus B-V color indices and R magnitudes versus B-R color indices for selected stars in the cluster.  The diagrams obtained generally fit published data.

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Introduction 

M67 is a well studied open cluster (Gilliland, Nissen, Sanders, Sandquist).  It was discovered by Messier in 1780, though there is evidence that it was observed earlier by Johann Gottfried Kohler (Archinal, 2003).  M67 is visible to the unaided eye at a dark sky site.  Archinal and Hynes (2003) consider M67 to be an unusual cluster in many respects.  It lies far from the Galactic plane, and it is fairly large and spread out.  One could conclude it is either close by and still near the Galactic disk where it formed, or it is quite old and has traveled around the Galaxy many times.  If it is old and has traveled around the Galaxy, it has probably been perturbed into an orbit above the Galactic disk far from where most open clusters are found.  This has allowed M67 to age gracefully without much disturbance.   

The present project consists of the construction of color magnitude diagrams (CMD’s) for  M67 using amateur observatories and imaging equipment.  The CMD’s and their accompanying data are compared with professional data, and their limitations discussed.  Also, the CMD’s and their data are used to make reasonable inferences about M67’s distance and age.  Is M67 close and young, or is it far away and old?

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Equipment and Observations 

The 3towers Observatory is located in the Catalina foothills five miles north of the center of Tucson, Arizona, at an altitude of 2600 feet (792 meters).  It contains a Meade 12-inch LX200 telescope, an Apogee AP7 CCD camera (thin, back-illuminated SITe 512 x 512 24 micron chip), and an ISIS FW-1 filter wheel with Johnson-Cousins R, V, B, I, and Clear parfocal filters (Hunter, #1).  The CCD field of view is 21.7 arcminutes, having 2.5 arcseconds per pixel.   

Images of M67 and two Landolt Standard Fields were obtained on 23 March 2004, a clear night with slight haze in the Eastern sky with no visible haze near the location of M67 or the standard stars used for the project.  A series of five bias, and five 60-second dark images were taken just prior to imaging M67.  The CCD camera operated at a temperature of -350 C for all images.  The bias and dark images were each median combined to produce master dark and master bias frames.  The images of M67 consisted of 60-second exposures through V, B, and R Johnson-Cousins photometric filters.  An example of one of the images is shown in figure 1:

Flat frames for each color were obtained after the individual color frames of M67 were taken.  The LX200 Meade telescope has considerable “mirror flop”, and the most accurate flat images are obtained by placing a translucent plastic cover over the corrector plate and exposing the sky for several minutes at the exact location of the telescope used for the data images.  The images of M67 were taken with the object having an air mass of 1.07 for the B and R images and 1.10 for the V image.   

Two Landolt Standard Star fields were imaged.  They were chosen from the WIYN CCD database of Standard Fields (Smith, 1998).  The fields were the one’s closest to M67, and they had an air mass of 1.44 and 1.30 at the time of their observations.  They were centered at RA = 08:53:45, Dec = - 00:34:30 and RA = 09:21:32, Dec = 02:47:00, respectively.  Figure 2 and 3 illustrate V images from these fields:

The M67 data image in each color and the Landolt Standard Star images were calibrated by MaxIm DL/CCD using the master bias, master dark, and flat images for each color (Diffraction Ltd, 2003).  The calibration used auto dark frame scaling and was applied to the flat images.  MaxIm DL/CCD was chosen for the calibration, because it was the software used to control the Apogee AP7 CCD camera (Apogee, 2004). 

The photometric zero points in each case were obtained by equal weighting of the five Standard Stars in each field.  Mira Pro 7.0 (Axiom, 2004) was used to use measure these standard fields as well as the V, B, and R data images of M67.  The aperture photometry tool was set to the Mira default settings, using a target radius of 7 pixels with sky background annulus radii set to 20 and 25 pixels for all measurements.  The full width half maximum (FWHM) for the V M67 image was 2.4 pixels.  

A color image of M67 was created using the separate images in B, V, and R.  One hundred nine stars in this image were labeled for ease of identification during photometric measurement of the separate color images.  The stars chosen for labeling and subsequent photometric analysis were predicted by Sanders (1977; 1989) to have a greater than 50% probability of being members of M67.  Figure 4 illustrates these stars:

A total of 109 stars were originally selected for measurement.  Twenty-four of these stars are either double or sufficiently close to other stars that more than one star was included in the photometry aperture.  These stars were eliminated from measurement, and a total of 85 M67 stars were then measured on the individual V, B, and R images.  The Guide Star Catalog (GSC) and the Sanders (1977) listings for these stars are shown in Sheet 1 of the Excel attachment 3towersM67ColorMagDiag.xls.

The photometric zero points chosen for the Mira Pro 7.0 measurements of the M67 images were linearly extrapolated from the photometric zero points for the Landolt Standard fields and are as follows: 

M67 V (air mass 1.10) – 18.864; M67 B (air mass 1.07) – 18.731; M67 R (air mass 1.07) – 18.766. 

Note: the Landolt Standard field photometric zero point for B actually decreased from 18.675 at air mass 1.44 to 18.471 at air mass 1.3!  This is hard to explain, and it is assumed that when the B image of the Landolt Standard field at air mass 1.3 was being exposed, an unnoticed cirrus cloud passed over the field reducing the photometric limiting magnitude.  A photometric zero point for B for M67 at air mass 1.07 was extrapolated from the relationships between the photometric zero points for B, V, and R at the Landolt Standard field at air mass 1.44.

Air mass corrections were calculated for V and R, using the following formulae (V illustrated):

mV- V =  + x1V + x3V ´ 1.3,  for Landolt Standard Field at air mass 1.3

mV-V = + x1V + x3V ´ 1.44,  for Landolt Standard Field at air mass 1.44

x1V = constant offset term; x3V = air mass correction term 

In the case of each color, V, B, or R, there are two equations and two unknowns.  Solving these equations for V and R gave air mass corrections of 0.166 for V and 0.164 for R.  No air mass correction could be obtained for B, because the data points for B values of the Landolt field at air mass 1.3 are suspect.  This term was set at 0.25.  This value was selected from examining a number of references listing air mass correction values for Kitt Peak National Observatory near Tucson (Everett, 2001; Romanishin; Walker).  It represents a best guess estimate for the actual air mass correction for the 3towers site which has nearly the same desert conditions as Kitt Peak, though it is at a lower altitude.   

Initial review of the CMD’s produced from the data on these 85 stars gave a somewhat sparse graph making recognition of a definite cluster trend difficult (see below Results).  As a consequence, photometric data was then gathered on another 265 stars in the M67 field.  This was closely examined, and 223 of the 265 stars were carefully selected for measurement based on their probability of being members of M67 (Sanders, 1977).   

Next, data from the Grasslands Observatory was examined.  On 19 March 2004, four days before the formal initiation of this project, M67 was imaged at the Grasslands Observatory through V, B, and R filters using the 24-inch f/5 telescope at the observatory (Hunter, #2).  A Finger Lakes Instrumentation Dream Machine CCD (1024 x 1024, 24 micron thin, back-illuminated SITe chip) was used with a CFW-1 Color Filter Wheel containing Johnson-Cousins photometric filters (Finger Lakes).  Exposures were 60-seconds V, 90-seconds B, and 30-seconds R.  The CCD field of view was 28 arcminutes, having 1.8 arcseconds per pixel.  The FWHM for the M67 V image was 2.7 pixels.  The air mass for M67 was 1.1. 

The R image was discarded for photometry due to partial cloud cover when the image was taken.  The images were calibrated using standard Bias, Dark, and Flat Field images routinely used at the Grasslands Observatory.  Unfortunately, no Landolt Standard fields were obtained with the M67 images.  The results for the selected 85 stars measured at the 3towers Observatory was used to characterize the photometric zero points for the Grasslands V and B images.  The Grasslands CCD camera operated at a temperature of -350 C for all images, and the software controlling the camera and the software techniques used for the photometric data measurements was the same as used for the 3towers Observatory data.

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Results

The raw Mira Pro 7.0 data for this project for the stars in M67 is contained in the attached Excel files, 3towersMiraRawData.xls and GrasslandsMiraRawData.cvs.  These data sheets include information on the net counts, errors, and signal to noise ratios for the individual star measurements. 

3towers Observatory Results

The instrumental and corrected photometric results for this project are shown in the attached Excel file 3towersM67ColorMagDiag.xlsSheet 1 delineates the original 85 stars measured, the Sanders (1989) star number for each star, and the Guide Star Catalog (GSC) listing for each measured star.  The instrumental and corrected V, B, and R magnitudes for each star are shown as are calculated B-V and B-R color indices for each star.  Column H calculates the difference between the V magnitudes of Sanders (1989) for each star versus the V magnitudes obtained for this project.  The average difference between the Sanders and Hunter V magnitudes is 0.23.  Figure 5 represents the color magnitude diagram of M67 for these 85 stars showing V magnitude versus B-V color index.

Sheet 2 shows data for the additional 265 stars from the M67 field.  These stars were selected at random, while sheet 3 shows data for 223 stars specifically selected because they meet Sanders 1977 criteria for a greater than 50% probability of being members of M67.  When the data for these stars is combined with the data for the 85 stars originally selected and measured, new color magnitude diagrams were produced showing V magnitude versus B-V color index  (figure 6) and R magnitude versus B-R color index (figure 7).

Grasslands Observatory Results

The Finger Lakes Instrumentation CCD camera at the Grasslands Observatory has 4 times the area of the Apogee AP7 camera at the 3towers Observatory.   Five hundred twenty-four stars were measured on the Grasslands images.  The photometric results for this data is shown in the attached file, GrasslandsM67Data.xls.   The instrumental photometric V and B zero points for the Grasslands data were determined by taking the corrected magnitudes for Hunter stars 1-8 in the 3towers Observatory data and using them as standard stars for the Grasslands data.  This produced a V photometric zero point of 20.728 and a B photometric zero point of 20.621.  The instrumental magnitudes of the 524 stars measured were corrected using an air mass correction in V of 0.12 magnitudes and B of 0.20 magnitudes based on the fact the Grasslands Observatory is at an altitude of 5000 feet (~1525 meters) being not much lower than the altitude of Kitt Peak Observatory.  Figure 8 shows a composite color image of M67 from the individual V, B, and R images, and figure 9 shows a color magnitude diagram of V magnitude versus B-V indices for the Grasslands data.  

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Discussion

The color magnitude diagrams derived for M67 are in general agreement with those published in the professional literature.  Figures 10-12 show color magnitude diagrams of M67 from three different professional sources:

M67 is an old cluster with many of its stars having left the main sequence.  Even the limited color magnitude diagrams produced for this project show a main sequence turnoff and a giant branch.  The lower end of the main sequence is not shown in the 3towers data, but it is evident in the Grasslands data, though the Grasslands data does not go nearly as faint as the data from Gilliland. 

The color diagrams and the photometric values in this project are limited by a number of factors.  The main sequence is not well represented as there are too few stars for a complete diagram.  The effective limiting V magnitude for the 3towers Observatory data is 15, while many of the main sequence stars in M67 are below this magnitude.  Gilliland (1991), for example, plots stars down to 22nd magnitude.  The magnitude limitations herein are a reflection of the relatively small size of the 3towers Observatory telescope, the relatively short exposure times, and the limitations of the suburban skies (visual limiting magnitude overhead 5.5) at the 3towers Observatory.   The Grasslands Observatory data goes fainter to magnitude 17, but its values are tied to those from the 3towers Observatory as no Landolt Standard fields were taken with the Grasslands data.  

Table 2 shows the 3towers photometric V magnitude counts for selected stars representing magnitudes 10.5-15.  These demonstrate good counts for the brighter stars, but it apparent that stars fainter than 14th magnitude suffer from low counts, and their expected accuracy can not be better than 0.02 magnitudes. 

Nevertheless, for 85 selected stars, the 3towers Observatory V magnitudes differ from Sanders (1989) only by an average of 0.23 magnitudes.  Sanders’ magnitudes are a combination of his own work and the work of others, some of which includes photographic data.  It should also be noted that there are seven stars (Hunter #’s 21, 26, 46, 72, 87, 99, and 102) that differ from those of Sanders by more than 0.5 magnitudes.  The reason for this is unknown.  It does not seem to be correlated with the B-V indices of the individual stars.  Stars #72 (Sanders 963; GSC 814:2317) and #102 (Sanders 770; GSC 813:2212) differ from Sanders’ results by more than a magnitude!  Close inspection of the data images obtained at the 3towers Observatory and the identification chart published by Sanders in 1977 shows there was no misidentification of the two stars.  Visual inspection of the V image of M67 shows these two stars were definitely brighter than the respective V magnitudes of 14.46 and 14.64 listed by Sanders.  These stars have respective B-V indices of 0.502 and 0.587 and are otherwise unremarkable.  They may have been mistakenly measured in the past, or they may be variable stars.  An interesting future project would be to monitor these and other selected M67 stars for variability. 

This project could have been improved by taking longer M67 data exposures and by using data from the larger telescope at the Grasslands Observatory obtained in a more systematic fashion with Landolt Standard fields.  This would have permitted photometry on fainter stars.  The exposures were limited to 60-seconds at the 3towers Observatory to insure there would be little guiding error.  The Meade LX-200 telescope at the 3towers Observatory does not have precise tracking, and exposures longer than 60-seconds frequently show significant trailing.  Shorter exposures could have been added together, but this introduces potential problems for data reduction and calibration with the Landolt Standard field sequences.  If longer exposures were to be used on either the 12-inch Meade LX-200 telescope at the 3towers Observatory or the 24-inch f/5 telescope at the Grasslands Observatory, the brightest stars in M67 would become saturated.  Thus, a wide range of photometric magnitude measurements for M67 requires a series of differing exposures for the cluster. 

Another limitation of the project as presented herein lies in the lack of thorough standardization of the 3towers Observatory telescope/CCD system with the sky conditions and the lack of Landolt Standard fields for the Grasslands Observatory data.  One or more Landolt Standard fields should have been imaged throughout the evening over a wide range of air masses from the Zenith, if possible, to at least air mass 2 (Zenith Angle 600 ).  This would have insured much better air mass correction for the V, B, and R sequences, and if the Landolt Standard field data had been examined as it was obtained, the problem experienced with the B Standard field images as discussed above might have been obviated.  A future project for both observatories is to perform such a standardization routine for one or more Landolt fields over a sequence of two to three nights.  This data could then be collated and serve as a baseline for future photometric endeavors.  Proper calibration of photometric data with Landolt Standard fields that are imaged on the same night a data set is taken will still be requisite for the most accurate photometry. 

Two goals of this project were to produce a rough estimate for the distance modulus of M67 and estimate M67’s age.  Examination of the CMD’s for V versus B-V (figures 5 and 6) show the main sequence turnoff point for the cluster roughly occurs between V magnitudes 12.0-13.0 at a color index of 0.5-0.7.  A representative main sequence star in M67 near the turnoff point has a V magnitude of 12.5 and a B-V index of 0.6.  Such a star with a B-V color index of 0.58 is a G0 star with an absolute magnitude MV of 4.2 (Ostlie, 1996).  If this star is representative of the top of the main sequence in M67, then a calculated distance modulus of M67 is 12.5-4.2, or 8.3, which is equivalent to a distance of 457 parsecs.  Sandquist (2004) derived a distance modulus for M67 of 9.72, and Sanders (1989) lists a distance modulus of 9.5.  The present estimate is off by more than a magnitude because of its very simplistic approach, but it provides evidence that M67 is not nearby. 

Estimating the age of M67 requires the use of sophisticated isochrones, an endeavor beyond the scope of this project.   Nevertheless, plunging ahead and again using the purported G0 star at the top of the M67 main sequence, such is star is noted to be slightly more massive than the Sun (Mstar/MassSun = 1.05).  It will have a slightly shorter life on the main sequence than the Sun, whose lifespan on the main sequence is estimated to be 1010 years.  The Sun is currently nearly 5 x 109 years old.  A G0 star near the end of the main sequence should be at least this old.  To be conservative, an age of 5 billion years will be estimated for M67.  This value compares favorably with the most recent age estimates of M67 of 4-5 billions years (Archinal, 2004; Sandquist, 2004).  Previous professional estimates had placed its age as somewhat greater.  Clearly, M67 is quite old for an open cluster.  Its age is measured in gigayears, not in millions or hundreds of millions of years. 

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Conclusion

The color magnitudes diagrams of M67 obtained for this project are limited but are a reasonable representation of M67’s characteristics.  They support the widely held professional believe that M67 is an unusual very old open cluster. 

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References 

Apogee Instruments, Inc., Auburn, CA. 

Axiom Research, Tucson, AZ. 

Archinal BA, Hynes SJ. Star Clusters.  Willmann-Bell, Inc., 2003, Richmond, VA. 

Diffraction Ltd., Ottawa, ON, K2G 5W3, Canada. 

Everett ME, Howell SB.  A technique for ultrahigh-precision CCD photometry. Pub Astron Soc Pac 2001; 113: 1428-1435.   

Finger Lakes Instrumentation, LLC, Lima, NY 14485, USA. http://www.fli-cam.com.  

Gilliland RL, Brown TM, Duncan DK, Suntzeff NB, Lockwood GW, Thompson DT, Schild RE, Jeffrey WA, Penprase BE. Time-resolved CCD photometry of an ensemble of stars in the open cluster M67. Astron J 1991; 101, #2: 541-561.

Hunter TB.  The 3towers Observatory: http://www.3towers.com/3towersObserv.htm

Hunter TB.  The Grasslands Observatory: http://www.3towers.com

Kaler JB. Stars and Their Spectra. An Introduction to the Spectral Sequence.  Cambridge University Press, 1989, Cambridge, page 265.

Nissen PE, Twarog BA, Crawford DL. UvbyH-beta photometry of main-sequence stars in M67.  AA 1987: 93: 634-646. 

Ostlie DA, Carroll BW. An Introduction to Modern Stellar Astrophysics. Addison-Wesley Publishing Co., Inc., 1996, Reading, MA, pages A13-14. 

Romanishin W. An Introduction to Astronomical Photometry Using CCDs. 2000, University of Oklahoma, Norman, OK.   

Sanders WL. Membership of the open cluster M67. Astron Astrophys Suppl 1977; 27: 89-116. 

Sanders WL. UBV photometry of M67 members. Rev Mexicana Astron Astrof 1989; 17: 31-35. 

Sandquist EL. A high relative precision color-magnitude diagram of M67. MNRAS 2004; 347: 101-118. 

Smith PS. Standard star fields suitable for UBVRI photometric calibration of the WIYN CCD imager.  September 1998; at: http://www.noao.edu/wiyn/obsprog/images/atlasinfo.html

Walker EN. CCD photometry. at: http://www.britastro.com/vss/ccd_photometry.htm.

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