Age and Distance of the Open Cluster NGC 6819

Brett Ragozzine and Kyle Uckert

2008 June 11

 

Abstract

Optical BV photometry was obtained on the open cluster NGC 6819 from the data archives of the Canadian Astronomy Data Centre (CADC).  The data were taken with the CFH12k Mosaic camera on the Canada-France-Hawaii Telescope (CFHT).  A color-magnitude diagram (CMD) shows stars down to a limiting magnitude of V ~ 22 to determine both the age of the cluster by the Main Sequence turn off and the distance to the cluster using spectroscopic parallax.  This magnitude is sufficiently faint to show many stars on the Main Sequence.  The age of NGC 6819 is estimated here to be ~ 2.5 ± 0.5 Gyr.  This agrees with the estimate made by Kalirai et al. (2001) of 2.5 Gyr.  The distance to NGC 6819 is calculated to be 2.16 ± 0.57 kpc and is comparable to several published results.

1. Introduction

   Open clusters are collections of hundreds or thousands of stars that have formed from the same giant molecular cloud (Carroll & Ostlie).  Performing a thought experiment of the members of an open cluster, we could conclude that the least massive members might still be approaching the Main Sequence of the Hertzsprung-Russell (HR) diagram, stars of slightly more mass reside on the Main Sequence, and the most massive stars have long since reached the Main Sequence and began their way along the giant branches of the HR diagram.  The two purposes of this project are to 1) calculate the age of open cluster NGC 6819 by calculating the brightness in V on a color-magnitude diagram (CMD) and 2) calculate the distance to this cluster through spectroscopic parallax.

   Having been created from the same molecular cloud at approximately the same time, these stars have similar ages, composition, and distance from us.  This provides an opportunity to study a group of stars that formed with nearly the same initial conditions, with the exception of their individual masses.  Plotting the stars of a cluster on a CMD, which is similar to the HR diagram, creates a visual line of stars on the Main Sequence.  The point on the CMD where the cluster members turn off from the Main Sequence gives insight into the age of the cluster (Sandage 1957).  The distance to NGC 6819 is then measured by calculating the distance modulus, the difference between the apparent and absolute magnitudes, m and M, in the following equation.

m – M = 5 log10 ( distance / 10 pc )

  The distance to NGC 6819 is taken from Students for the Exploration and Development of Space (SEDS) to calculate the absolute magnitude needed to estimate the age.  To separately calculate the distance, we take the absolute magnitude from a calibrated published result, de Bruijne et al. (2001), in this case.  The CMD compared against is that of the Hyades cluster, an open cluster of similar age (2 Gyr) and metallicity to NGC 6819. The CMD of the Hyades cluster is calibrated with the Hipparcos catalog so that it may be displayed in and absolute magnitude scale.

  This project was originally planned for observation using the Great Ohio Telescope (GOT) of the Department of Physics and Astronomy at Ohio University.  A lack of clear nights during the spring quarter forced us to look elsewhere for data.

  Open cluster NGC 6819 was chosen for observation for several reasons.  1) Its published V magnitude turn off is approximately 15 and is well within the sensitivity of the GOT.  Because the cluster’s bright turn off point from the Main Sequence, the GOT would be able to image the fainter stars still on the Main Sequence, down to approximately 18th magnitude.  2) Its location relative to the sun at this time of year allows us at least three hours of observing time on target per night (early May) and increasing to five hours on target (late May) as the sun increases in RA.  This gives enough time to set up the telescope, calibrate the guiding, and image standard stars before NGC 6819 rises above two airmasses.  3) At a declination of +40.18, the cluster transits near the zenith in Athens, OH, giving a favorable airmass most of the night.  4) NGC 6819 is a tightly bound open cluster with the majority of its members within 6.9 parsecs, well within its estimated tidal radius of 17 parsecs (the radius within which member stars are bound).  Most open clusters are less gravitationally bound and members become harder to detect as they are pulled from the cluster by tidal forces.  This tightly bound cluster provides a wonderful opportunity to capture a great number of member stars in a dense region.  5) Its angular diameter of 5' fits comfortably within our CCD dimensions of 12' x 18'.  Fortunately, there is a guide star to the north and to the south so we can auto guide on our longer exposures.

  Previous work on this cluster was done by Kalirai et al. (2001) down to a limiting magnitude of V ~ 24.  They measure the age to be 2.5 Gyr using isochrone models. 

  In 2002, Jared Withers observed NGC 6819 using the GOT. The results of that lab project detected the brightest stars (down to V ~ 15) with 1 x 120s exposures in V and R.  The Main Sequence stars require more exposure time in order to calculate the turn off point. The IRAF task ccdtime was used to calculate the signal-to-noise ratio (S/N) of the faintest stars the GOT would be able to image, around V ~ 18.

    The S/N acquired by N exposures is calculated in the following equation.

S/Naquired = S/Nexposure ( N )1/2

  Exposures of 600s are possible while guiding the GOT, but we quickly realized that shorter exposures would be more appropriate with NGC 6819.  Much consideration went into deciding how long the exposures should be.  NGC 6819 has many bright stars and quickly saturates the CCD.  We settled on 120s exposures to balance between the brighter stars as well as keeping the overall number of images to a minimum while capturing the faintest stars possible.  With 10 x 120s exposures in each filter we expected to achieve S/N of 12.6 in B and 18.6 in V, each at 18th magnitude (B has the lower transmission percentage of these filters).  Photometric calibration is required in order to plot the CMD. Ten standard stars were selected in the B-V range of magnitudes from 0 to 2 that would allow us to calibrate the CMD.  This range of B-V was chosen from the results of Kalirai et al. (2001) (see Figure 8, below).

2. Observations

  Due to consistently cloudy skies during the majority of the month of May, we were unable to use the GOT and image NGC 6819 ourselves; the 3.6m ground-based Canada-France-Hawaii-Telescope (CFHT) archival data from the Canadian Astronomy Data Centre (CADC) was used instead. These data files were created using the CFH12k Mosaic camera, which is arranged in a 2 x 6 CCD array that covers 42’ x 28’ on the sky.  The CCDs are labeled 00-05 and 06-11 in the lower and upper rows, respectively.  Each fits file held all twelve CCD images.  For each filter there were 1 x 10s, 1 x 50s, and 9 x 300s available.  These files are dated 1999 Oct 16 UT.  Archival flats include thirteen frames in V taken just prior to the observations of NGC 6819 as well as twelve frames in B taken the previous morning. The bias and dark frames were taken on 15 Oct 1999 UT.  Landolt standard stars were observed on 1999 Oct 14 UT in two fields: SA 92 and SA 98. These files were downloaded in order to do photometric calibration on the reduced object frames.  Another 1 x 1s frame from 2000 Apr 24 was also examined for the very brightest cluster members.

3. Reductions

  Of the twelve CCDs on the CFH12k Mosaic camera, the outer four chips in the 2 x 6 array only include field stars (Kalirai et al. (2001)), the intermediate four CCDs contain some cluster members and some unknown fraction of field stars, and the innermost four CCDs contain the densest region of the cluster with lowest ratio of field stars.  We decided to use images from one of the four inner CCDs.  After we reduced one series of frames, using chip02, it provided enough data points to produce a CMD and we did not proceed onto another chip.  In order to capture a variety of brightnesses, multiple exposure times were used, where short 10s and 50s exposures would be able to capture magnitudes of bright stars without saturation, and long 300s exposures would be able to provide magnitudes of the very faint, Main Sequence stars.

 

  The ten dark and nine bias frames associated with chip02 were combined to create master dark and bias files. The 10 x 300s flat frames in V were combined, as were the 10 x 300s frames in the B band, making sure to keep the two file groups separate from each other. The dark and bias masters were combined with the master flats to create a uniform image to be subtracted against each of the object files. Once the flat subtraction had taken place, the new object frames were analyzed.  It was determined that the resulting images were in worse condition than the original frame. Upon further inspection, we were able to conclude that the downloaded RAW files had in fact already been flat fielded; by completing the initial reduction steps, we had multiplied the flats back onto the source images.  We reverted back to the original frames for the rest of the reduction.

 

  In order to find stars and their magnitudes throughout the field, the IRAF subroutines daofind and phot were used.  The full-width half-maximum value is found using imexamine and used in the parameter fwhmpsf.  This parameter is essential to find the correct stars in each field and thus it was essential to find the radius of brightest (unsaturated) stars in each exposure.  daofind is run in order to locate stars in the fits file and tvmark is applied to the file in order to visually verify the accuracy of these star coordinates by placing a dot at the center of each star that daofind found.  The portion of the field closest to the cluster center contains the largest overexposed region and is essentially useless in the 300s frame (see Figure 1).

 

Figure 1.  Shown here is the brightest region of chip02.  Notice how the IRAF task tvmark finds too many “stars” within the brightest (saturated) stars.  Any star with even a faint diffraction spike has two or more dots.  It correctly identifies the unsaturated stars with one dot each.  During the psf stage we stayed away from any star with diffraction spikes.  The scale of this image is approximately 2.4’ x 3.3’.

 

  A magnitude file was created next, and it was used to run the psf routine, which accommodates for the point spread function (PSF).  The PSF is calculated in order to correctly count the brightness of each star across the image.  Approximately 130 candidates are chosen by hand from all regions of the image, near every possible edge and corner, and read into a group file, which lists stars and their closest faint neighbors.  nstar (neighboring stars) and substar (subtract neighboring stars) are run next, which subtract the faint neighbors from the original image using the psf shape of the hand-selected stars.  Visual inspection is necessary to make sure the neighbor stars were subtracted correctly.  No bright spots or dark spots were left behind after the stars were subtracted (success in psf calculations).  allstar is run next, which subtracts all but the overexposed stars, and lists the magnitudes of the unsaturated stars.

 

  In order to create the final B-V color, the B and V frames are displayed once again and imexamine is employed to determine any coordinate shift that may be present between B and V frames. The pixel shift is then entered into the mkobsfile routine, which creates a file of apparent magnitudes of all of the detected stars in the field.  The stars were then plotted, V vs. B-V and a noticeably dark stripe of stars reveals the Main Sequence.  Each star contributes a single point in the following plot. 

 

Figure 2.  Color-magnitude diagram in V vs. B-V of open cluster NGC 6819.  The data points are solely from the 300s frame and thus include only the faintest stars.  Notice the brightest stars on the Main Sequence reach V ~ 16.5.  The age of the cluster is unclear from this figure and brighter cluster members must still be included.  The graph largely resembles the faint stars plotted by Kalirai et al. (2001).

 

  The reduction process was repeated for a shorter exposure.  It was expected that the 50s exposure would provide enough stars to show the turn off point.  The faintest stars were no longer visible and some of the bright stars were now below saturation.  These stars that transitioned from saturated to unsaturated are the most important at this stage and are plotted in Figure 3. 

 

Figure 3.  Similar to Figure 2, but includes data points from the 50s exposure.  Notice the brightest stars on the Main Sequence reach closer to V ~ 15.  In creating this graph, there was more focus on adding the bright points than worrying about the overlap of the fainter stars and some data points may thus be duplicated.  The Main Sequence is much more prominent than in the previous figure, but is at least partly due to the overlap of some stars between the 300s and 50s frames.  Brighter stars are needed to clearly show the turn off point.

 

  Next, we attempted to reduce a 1s exposure to jump right to the brightest stars and catch them unsaturated.  Unfortunately, the faint neighbors that the psf step requires were not bright enough; the 1s exposure was not included in our data.  Reduction of the 10s frame finally gave us the turn off point of the cluster and its contributing points are seen in Figure 4.

 

Figure 4.  Similar to Figure 2 and 3, but now the 10s exposure has revealed the turn off point from the Main Sequence.  Notice the turn off point just brighter than V ~ 15. 

 

  As we combined the 50s exposure data to that of the 300s exposure data, there was no noticeable difference (visually) in the Main Sequence formed from the stars in each data set.  Numerically, they were actually different by an average 0.005 magnitudes.  The 10s exposure data formed a Main Sequence dramatically separated from the first two data sets and those bright stars are what we need to calculate the turn off point.  B and V magnitudes were an average of 0.281 and 0.075 higher in the 10s exposures.  We shifted the B-V value of these 10s stars by –0.206 to line up the Main Sequence of the 10s exposure horizontally with the 50s and 300s data sets.  Vertically, the 10s data points were adjusted by –0.075.

 

  To account for the extinction of NGC 6819 we adopted the reddening, E(B-V) = 0.1, and the extinction, AV = 3.1 E(B-V) = 0.31, from Kalirai et al. (2001).  The data points were thus shifted leftward by 0.1 and upward 0.31 to correct for the extinction.  This reduces the age of a cluster by brightening the turn off point.

 

  The next step in calibrating the data was comparing these reduced frames with standard stars (also labeled RAW).  Upon inspection of the downloaded standard star files, we were unable to match stars in the SA 92 or SA 98 fields.  Because the object frames were listed as RAW, but had been dark-, bias-, and flat-corrected, it is possible that they were also photometrically calibrated.  We chose to proceed on this basis.

4. Results

  The results from Figure 4 give us an apparent magnitude at which the open cluster NGC 6819 turns from the Main Sequence to the Asymptotic Giant Branch (AGB).  This apparent magnitude is approximately 14.5 or 15 in V and is the starting point for our calculation of the age and distance of this open cluster.

 

  Figure 5 is a close up on the turn off point.  We need to look carefully here, as this value calculates the age of NGC 6819.

 

Figure 5.  This is a portion of the data plotted in Figure 4.  We zoom in on this section to get a good visual estimate of the turn off brightness.

 

  To calculate the age of the cluster, we use the distance modulus equation and the distance 7200 ly (2200 pc) provided by SEDS, to calculate its absolute magnitude.

 

M ~ m – 5 log10 ( 2200 pc / 10 pc ) = m – 11.7

 

  We need to decide which apparent magnitude m to use from Figure 5 to solve for the absolute magnitude M.  Sandage (1957) shows that the absolute magnitude M of a cluster directly relates to its age (see Figure 6).  The brighter the absolute magnitude of the turn off point of a cluster, the younger the cluster is.  Small differences in m, and thus M, change the age estimate by a large factor since the age is exponential.

 

Figure 6.  This figure resembles the Main Sequence on the HR diagram in that the vertical axis shows brightness and the horizontal axis shows the color of stars.  The vertical axis (right side of plot) also shows age calculations based on the turn off point.  The brightness of a cluster directly determines its age.  (Figure taken from Sandage 1957)

 

  Figure 7 plots this age vs. absolute magnitude relation from the values on the left and right vertical axes of Figure 6 and gives a best-fit equation so we can calculate the age of NGC 6819.  The best-fit line is

 

age ~ 2 x 108 e0.8385 M

 

Figure 7.  The age of a cluster is determined by its absolute magnitude M as shown in Figure 5.  This graph’s values come directly from Figure 6 and the equation of the solid line is y = 2 x 108 e0.8385 M. 

 

  Now we are ready to calculate the age of NGC 6819.  A few sample age calculations, based on visual estimates from the turn off magnitude in Figure 5, are shown in Table 1.  At V ~ 15.0 it appears that the stars might be leaving the Main Sequence; by V ~ 14.75 they are leaving or have left the Main Sequence; and by V ~ 14.5 the stars have definitely left the Main Sequence.

 

m (mag)

M (mag)

Age (Gyr)

14.5

2.78

2.06

14.75

3.03

2.54

15.0

3.28

3.13

Table 1.  A few apparent magnitudes, m, as estimated from Figure 5 result in an absolute magnitude M through the distance modulus equation.  The age of open cluster NGC 6819 is approximately 2.5 Gyr; which agrees with Kalirai et al. (2001), who also calculate the age of the cluster to be 2.5 Gyr.  Three significant figures are shown in this step only to show error estimates.  The distance to the cluster from SEDS and our visual estimates of the turn off magnitude are no better than two significant figures.

 

  Therefore, we conclude that the age of NGC 6819 is ~ 2.5 ± 0.5 Gyr.  This is in good agreement with Kalirai et al. (2001) who calculated the age of the same cluster using isochrone models that follow the Main Sequence stars as well as giant branch features (see Figure 8).

 

Figure 8.  This CMD is taken from Kalirai et al. (2001).  The red curve is the best-fit isochrone that calculates NGC 6819 to be of age 2.5 Gyr.  The same data files from CADC taken on 1999 Oct 16 UT produced this figure as well as the data plotted in Figure 4.

 

  Main sequence fitting is a technique used to calculate the distance of a cluster by aligning the horizontal B-V axis, and measuring the shift in the vertical axis.  This shift in magnitudes is the distance modulus, m – M, where the m is given by our results in Figure 4, and M is given in the CMD presented by de Bruijne et al. (2001) (see Figure 9).

 

Figure 9.  This color-absolute magnitude diagram was published by de Bruijne et al. (2001).  It displays points along the main sequence for the Hyades cluster. The original apparent V magnitudes have been calibrated to the Hipparcos catalog in order to convert them to absolute magnitudes.

 

  Points are selected on the produced CMD from the CFHT and compared against the Main Sequence in Figure 9.  The data is then entered into the distance modulus equation given in the introduction, and the distance to NGC 6819 is obtained. The error bars are found by measuring the width of the main sequence on both diagrams, which appear to be 0.3 mag, and adding it onto the selected data points to recalculate the distance. The error of 0.3 is added to m and subtracted from M to calculate the maximum distance:

 

Dmax = 100.2 * [ ( m + 0.3 ) – ( M – 0.3 ) + 5 ]

 

  The error is subtracted from the apparent magnitude and added to the absolute magnitude to calculate the minimum distance:

 

Dmin = 100.2 * [ ( m – 0.3 ) – ( M + 0.3) + 5 ]

 

  Many data points are selected along the Main Sequence and are entered into all three equations for distance calculation and errors. The results are averaged together and the distance is determined to be 2.16 ± 0.57 kpc. This agrees fairly well with the value of 2500 pc obtained by Kalirai et al. (2001), and reasonably well to other published works of 2350 pc by Rosvick and VandenBerg, 2170 pc by Auner, and 2200 pc by Lindoff.  The reasoning for the low value could be due to a photometric calibration error not provided with the CFHT data.

5. Discussion

  BV photometry was used from images taken with the CFH12k Mosaic camera on the CFHT and analyzed to show the age and distance to the open cluster NGC 6819.  We reduced the data from one of the twelve available CCDs from the fits files and a CMD was produced that shows a clear turn off of the Main Sequence.  The apparent magnitude m of the stars at this turn off point is converted to an absolute magnitude M through the distance modulus equation.  M determines the age of the cluster through

 

age ~ 2 x 108 e0.8385 M.

 

  We have shown the age of NGC 6819 to be 2.5 ± 0.5 Gyr and the distance to be 2.16 ± 0.57 kpc.  Both of these values agree with previously published values.

 

  The reduction of CFHT data showed that object frames were pre-processed with dark, biases, and flats.  We presume that the frames were also pre-processed with photometric calibrations from standard stars or that such calibrations would not significantly change the brightness of our CMD figures.

6. Acknowledgements

  We would like to sincerely thank the special members of our TAC: Dr. Statler, Dr. Clowe, Dr. Böttcher, Dr. Shields, and Dr. Sharma for their insight in reducing data and their review of our project proposal.  We would also like to thank Manasvita Joshi, Desireé Cotto-Figueroa and David Riethmiller for their help in data reduction.

 

  This research used the facilities of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency.

 

References

Auner, G. 1974, A&AS, 13, 143

Carroll, B. & Ostlie, D. 1996, An Introduction to Modern Astrophysics

de Bruijne, J. H. J. et al. 2001, A&A, 367, 111

Kalirai et al. 2001, AJ, 122, 266

Lindoff, U. 1972, A&AS, 7, 497

Rosvick, J. M., & VandenBerg, D. 1998, AJ, 115, 1516

Sandage, A. 1957, AJ, 125, 435

http://seds.lpl.arizona.edu/messier/Xtra/ngc/n6819.html