Photometric Analysis of Open Star Clusters

by Andy Becker, School of Science

Advisor: John P. Finley

Abstract

After extensive repair and restructuring of Lafayette's Cumberland Observatory, photometric CCD observations of three open star clusters were carried out. Observations of clusters NGC 637 and 2169 were confounded by atmospheric phenomena, and information gleaned from the incorrect observational procedures used on these clusters was assimilated to produce a correct observing method used on NGC 2281. These data, along with a National Optical Astronomy Observatory standard field of the globular cluster 47 Tucanae, were analyzed using aperture photometry algorithms and the IRAF software package. Color-magnitude diagrams of these clusters were produced, showing the evolution of each cluster along the locus of points of Hydrogen burning stars, the "main sequence."

Observatory Preparations

(Carried out with David Bainbridge and Anthony Roach)

Removing spiders / dust from telescope interior and corrector plate
Refurbishing telescope drive system
Metalwork on dome perimeter and doors to prevent blowing dust and nesting birds. This included climbing on top of the dome to reshape the door tracks
Purchase, through the Physics Dept., of clean eyepieces, corrective optics, and standardized filters
Introduction to CCD technology and astronomical concepts
Equipping observatory to handle CCD observations -> data lines, computers, allowing remote focusing and slewing of telescope, etc...
Eventual observations of the SL9/Jupiter collision as a test run to determine our progress

Open Clusters & Stellar Evolution

Stars are characterized by their luminosities in certain color bands, Ultraviolet Blue Visual Red Infrared
The 'color' and therefore the temperature of a star are determined by the relative luminosities in these bands (Temperature is inversely proportional to the stellar color B-V, a logarithmic measure of the flux ratio in the 2 bands)
Photons are scattered by the interstellar medium. The scattering cross-section increases with decreasing wavelength, largely due to the physical size of the material (appx. 200 nm). Accordingly, photons in the B band (380 - 480 nm) are attenuated more than in the V band (500 - 580 nm)
If were are to make an accurate color- magnitude diagram, we must find groups of stars that are the same distance from Earth, so that interstellar attenuation and luminosity fall-off (proportional to 1/distance2) are the same. This can be done using either globular or open clusters, groups of stars that are the same distance from the earth with a common temporal origin
There are between 10,000 - 1,000,000 stars in globular clusters, easily beyond the resolving power of a 14 inch telescope; therefore open clusters were observed
V plotted against B-V (the Hertzsprung-Russell or color-magnitude diagram) for an open cluster will provide an indicator of the stellar evolution of the cluster and also its age

Hertzsprung-Russell Diagram

Come back later

The vertical axis is the V magnitude of the star we measure here on Earth. Lower numbers imply a brighter star in the V band, so stars with a negative magnitude are brighter than stars with positive magnitude.

The horizontal axis is a measure of the temperature T = 7090/[ (B-V) + 0.71 ] assuming radiation from a blackbody. The graph is historically presented with hotter stars on the left.

The locus of stable points for hydrogen burning stars is called the 'Zero Age Main Sequence' (ZAMS) which is where all young stars reside. Once a star consumes its hydrogen, it will evolve away from the ZAMS due to the changing stellar thermodynamics and nuclear processes. We say that the star 'turns off' of the main sequence. Based upon stellar composition and mass, the turn-off point, and therefore the age, of a cluster can be determined.

Determining the Magnitude of Stars

The method used to determine the magnitude of stars in these fields is called aperture photometry, calibrated with the observation of a standard star at the same airmass.

Aperture photometry involves summing the flux from a star inside a certain radius, generally 4.5 * FWHM of the star. This flux is proportional to the number of counts in a CCD pixel. The sky background is taken from an annulus concentric with the program star and extending 20 pixels in radius. The background is the mode of all pixels in this region, and is subtracted from the measured flux. This provides an instrumental magnitude which can be calibrated with offsets determined from the standard star observations.

A standard star is a star whose photometric characteristics are well known and constant. By observing a standard star at the same zenith angle (polar angle from ÔoverheadÕ) as the program field, you can compensate for atmospheric attenuation along the line of sight (airmass). The offsets determined this way are used to place the program stars on the magnitude scale.

In a crowded field, PSF fitting must performed. This involves determining a profile of the observed stars and subtracting off neighboring stars before the aperture photometry. In this way, only light from the program star contributes to the measured flux.

47 Tucanae

NOAO-supplied standard field of the outer edge of 47 Tucanae. This V frame is a 15 second exposure.

This HR diagram clearly shows a turn-off for the cluster. Since no standard stars were supplied, the actual position of this turn-off can not be determined, and only instrumental magnitudes were plotted.

NGC 2169

25 second V exposure of NGC 2169.

This zenith angle chart displays the first error encountered in these observations. This chart was made after the observations and shows that the standard star, Chi Orion, was observed at a different airmass than the standard. An optimum observation would have occurred at the same airmass, and also would have included both a red and a blue standard to better gauge the atmospheric attenuation.

This HR diagram cannot be considered to be an accurate description of the stellar composition of NGC 2169 for the reasons outlined above.

NGC 637

30 second V exposure of NGC 637.

This zenith angle chart displays the second error encountered in these observations. This chart was also made after the run and shows that the observations were made at such a low zenith angle that the atmosphere attenuation was considerable. In addition, the standard star, even though acquired at approximately the same zenith angle, is red in color and does not provide sufficient correction for the B band. An optimum observation would have occurred at a smaller zenith angle, and also would have included both a red and a blue standard to better gauge the atmospheric attenuation.

This HR diagram cannot be considered to be an accurate description of the stellar composition of NGC 637 for the reasons outlined above.

NGC 2281

60 second B exposure of NGC 2281.

This zenith angle chart displays the correct procedures for acquiring high-quality observational data. All observations occurred within the same range of zenith angles, and both a red (Iota UMa) and blue (Lambda UMa) standard were used to calibrate the magnitude scale.

This HR diagram can be considered an accurate description of the stellar composition of NGC 2281, and therefore can be inferred to lie upon the ZAMS appropriate for this cluster.

The Art of Point Spread Function Fitting

This is the original V CCD image for NGC 637

Here, all features in this frame with a Full Width at Half Maximum (FWHM) of 3 pixels (appx. 4 arcsec) and heights greater than 3.5 sigma above background are marked and their positions recorded

Bright, isolated stars are then manually chosen and their stellar profiles recorded up to a predetermined radius (11 pixels). These profiles are then integrated to fit a Point Spread Function (PSF) which is characteristic of the night's observations. Bright stars are most useful to define a PSF, as statistical fluctuations are much less significant. These stars and their registered neighbors are then subtracted to determine if the PSF is accurate. As you can see, the stars are cleanly subtracted, indicating a good PSF fit.

Now the PSF stars are left in the frame and only their neighbors are subtracted. Compared to the original frame, the bright stars remain but their dimmer neighbors are gone. This leaves totally isolated stars from which a second, more accurate PSF is determined.

This second PSF is then used in an iterative method in which each star has its neighbors subtracted and magnitude determined using aperture photometry. The cleanliness of this frame, which should be empty of all marked stars, indicates the accuracy of both the PSF and magnitude determination.

Conclusions

We have developed a standard set of procedures to acquire quality astronomical data at the Lafayette Cumberland Observatory
From our observations of NGC 2281 we have determined that
1. The distance to NGC 2281 based upon the distance modulus m - M = 5log(d) - 5 where m is the observed magnitude, M is the absolute visual magnitude, and d is the distance in parsecs (1 parsec = 3.26 light years) is appx. 575 parsecs assuming solar composition. This is in reasonable agreement with the accepted distance of 460 parsecs.
2. An upper limit on the age of this cluster, based upon the relation t = 10^10 (M/M¤)^-3 yr where M¤ is a solar mass and M is the mass of the star at the upper end of the main sequence, is appx. 2.97 x 10^8 yr. This is in excellent agreement with the accepted age of 3.02 x 10^8 yr.

Acknowledgments

David Bainbridge - For help in setting up observing procedures at Cumberland and in some of the more dangerous metalwork.

John P. Finley - For undertaking this venture as my advisor and for direction in research procedures.

Jim Gaidos - For assistance in and exposure to research opportunities.

Chang-Yung Lee - Help in observing

Tom Moffett - For assistance in using IRAF

Anthony Roach - For assistance in observing, buying me McDonald's, and organizing this display.

This page last updated on Friday, September 15, 2000.