Globular Cluster M3 (NGC 5272) was observed in V and I to a limiting magnitude of about 18.5 over 2 nights, one of which was photometric. Aperture photometry was performed on these stars and a color-magnitude diagram (V,V-I) was constructed from the calibrated photometry. The metallicity ([Fe/H]) and reddening E(V-I) of the cluster are derived using the Sarajedini method. From this plot and the calculated values of [Fe/H] and E(V-I), comparisons are made with published data.
The goal of this project is to obtain accurate photometry of the globular cluster NGC 5272 (M3) in V and I. From these data, the primary objective is to construct a color-magnitude diagram (V, V-I) to be compared to previous work, specifically that in Rosenberg et al. (2000) (Figure 10). Concluding that the data are visually reasonable, I proceeded to measure the cluster's metallicity and reddening directly from the CM diagram. I was only able to obtain data down to an apparent V magnitude of 18.5, so any hope of determining its age was lost, as one needs a measurement of the Main Sequence Turnoff, which is around 19.5 magnitudes in V. However, the photometry was good enough to produce a reasonable CM diagram, therefore warranting an attempt at a measurement of its metallicity and reddening, though these measurements require more accurate photometry than has been obtained.
In order to measure these quantities, I have used Sarajedini's method for the simultaneous determination of metallicity and reddening using (V, V-I) CM diagrams. (Sarajedini 1994) This method requires only 3 parameters determined from photometric data with an accuracy of at most 0.01 magnitude errors for results without unwieldy errors. These parameters are the shape of the RGB, the V magnitude of the HB, and the apparent V-I color of the RGB at the level of the HB. These data were easily obtainable due to M3's well-populated HB (Rosenberg 2000) and its fairly easily obtainable HB and RGB magnitudes in V and I (about 16th magnitude). The results of Sarajedini's method can then be compared to presently accepted values for these quantities, such as can be referred to from Harris (1996).
Night 1 I obtained both evening flats (6 in I and 2 in V) and
morning flats (5 in V and 5 in I), though the first 3
evening flats were most likely taken before the chip had fully reached equilibrium,
and the rest were count deficient. The morning flats turned out much better, though
I noticed dew on the corrector plate midway through, which was eliminated befor taking the
last 4 flat-field exposures, which were in I. I also gathered 5 x 600 s dark frames. Lastly,
8 x 600 s exposures in V and 7 x 600 s exposures in I were taken of M3, with one 540 s exposure in
I that ended early. The first 7 of these exposures, which include 5 in V
and 2 in I, were taken through clouds and were hindered by poor guiding.
The remaining 9 exposures were much improved. See Figure 1 for an example of one of the
unreduced images of M3 in V.
|
| Figure 1. An unreduced 600 s image in V from night 1, taken after the clouds had departed. |
Because Night 2 was photometric, standard stars we obtained. For 4 stars, 3 images in both I and V were taken for an exposure time between 10 to 30 s for each star except one, for which we only got 2 images in both filters. Two were taken in the beginning portion of the night, and the other 2 were taken in the latter part to ensure the consistency of the viewing conditions. Again, evening and morning flats in both filters were collected, of which the morning flats were taken on uneven clouds, and so were 12 darks at 3 exposure times of 600 s, 300 s, and 15 s. All zero calibration frames were taken several days later, when it was realized that there was a non-zero bias level of which I was previously unaware. I obtained 2 x 600 s in V and 2 x 120 s in I of M3, to obtain calibrated photometry for my night 1 data.
It is also important to note that the ccd was rotated about 180 degrees night 2 compared to night 1, for reasons unrelated to my project.
For the night 1 flats, I combined the zeros and explicitly subtracted that from the 5 dark frames, which I in turn combined and subtracted from all the flat field exposures. For the night 1 images of M3, I combined the darks without a zero subtraction and subtracted this in conjunction with the zeroed and combined flat frame from all the M3 images. I only used the morning flats for the combined flat frame, and I of course did the subtractions on each filter separately. Then I cleaned the 16 images of cosmic rays using the IRAF task XZAP in the package DIMSUM with a 5 sigma threshold above sky. It may have been prudent to use a threshold of 6 or 7 sigma, as it appeared after the fact that the routine may have been clipping high noise spikes as well as cosmic rays, but the number of noise spikes removed was not particularly large, so I assumed the damage would be negligible.
For the night 2 data I followed the same basic procedure, except I used both the evening
and morning flats, as they both seemed equally good. This time I had frames of varying
exposure time, though, so I used the procedure I described for the night 1 images of M3
for all the 600 s, 120 s, and 15 s exposures since I had darks at these exposure times.
For the flats and standard stars taken at 10 s and 30 s, I used the procedure described for
the night 1 flats. I then cleaned out the cosmic rays in the standard star fields and
the calibration frames of M3 using the same sigma threshold as before. At this point and
before, it became clear that there was strong evidence suggesting a charge transfer problem that becomes exaggerated
for bright objects in short exposure times due to IRAF's automatic scaling display,
as was the case for the standard stars. (Figure 2)
This problem could cause bad photometry if a significant amount of a star's light is spread
beyond the photometry aperture. However, since this effect does not show up on the
longer exposures, it is assumed to be a negligible error that does not grow with exposure time.
| Figure 2. An example of the charge transfer problem in a standard star exposure, in I in this case. The tail to the left of the star results when the CCD leaves electrons behind as it is being read out. |
At this point I determined which images of M3 to include in the final co-adds. For night
1 I only used the last 9, cloudless images. I also used the 2 V calibration
images from the second night, as they were 600 s like all the night 1 images, giving total
exposure times of 6 x 600 s in I (Figure 3) and 5 x 600 s in V (Figure 4).
I did not smear the good image point-spread functions (PSFs) to the worst PSF in each filter, as the
full width at half maximum (FWHM) for the worst image was less than twice that of the good image
FWHM. So, for the I
images I simply registered them, added them together, and trimmed the co-add so I only had the
overlap region. For the night 2 V images, however, I had to rotate them about 180.5 degrees
so they would line up with the night 1 images in order to compensate for the rotated CCD mentioned in the
observations section. I determined the best rotation by rotating
the images by amounts differing about .01 degrees, starting at a guess rotaton of 180.45 degrees, and finding the
minimum shift between several star's relative positions in the night 1 and night 2 images. This
shift averaged out to be about 0.2 pixels -- a small margin of error that will keep the natural shape of the stars
intact. Having determined the rotation, I registered the V frames as I
did the I and trimmed the resulting co-add as well. Similarly, I registered the calibration
images from night 2 and co-added and trimmed a final image for each filter. The pixel scale for these images, as
determined by Robert Salow, is 0.52 square arcseconds per pixel. The I
co-add had a FWHM of about 5 square arcseconds (10 pixels), while the V co-add had one of about 4 square arcseconds
(8 pixels).
| Figure 3. The completely reduced and combined I image from which the stellar photometry will be obtained. This image has a FWHM of about 10 pixels. |
| Figure 4. The completely reduced and combined V image from which the stellar photometry will be obtained. This image has a FWHM of about 8 pixels. |
Next, I found the coefficients of the photometric calibration equations by doing aperture photometry on the standard stars from Landolt (1983). I used an aperture of radius 30 pixels, an annulus of radius 40 pixels, and a dannulus beyond the annulus of 4 pixels. The dannulus is the width of a ring beyond the annulus that allows the program to compute a value for the sky. The instrumental magnitude is determined from the counts inside the radius of the aperture minus the sky value. These coefficients were found to be a=6.49362 and b=0.2580487 for the equation mV=V+a+b*airmass and a=6.860981, b=0.039039, and c=0.04749109 for the equation mI=V-(V-I)+a+b*airmass+c*(V-I).
Perhaps the most crucial stage in the reduction process is the aperture photometry of
the globular cluster itself. This was done by using the crowded field photometry
package DAOPHOT. It is run in stages, as follows. First, it finds potential stars based
on a certain threshold value above the sky level and obtains preliminary photometry of these
stars, using a predetermined aperture and annulus as before. Then I chose several "PSF stars",
which I used to construct a point-spread function based on a value for the fitting radius,
the PSF radius, which is the radius out to which the constructed PSF is subtracted around a
star, and the FWHM of a star. Once a good point-spread function has been created, it is used
to subtract all the stars found previously from the cluster image. Then, one by one, a star
is added back to the frame with all its neighbors subtracted off, and the instrumental
magnitude is obtained similarly to how it is obtained from the standard stars, using the
parameters described above. This subtracted frame can be used to determine whether the point-
spread function did a good job of removing stars. (Figure 5) As you can see, this run in
V, which was accepted to obtain the instrumental magnitudes, was still not perfect. This
discrepancy is most likely due to a variable PSF across the image.
| Figure 5. This is the resultant image in V when all the stars that were found and marked were subtracted from the image. Compare this with Figure 4 and especially notice how the brighter stars are the ones that are the most poorly subtracted. |
By varying which stars I used for my "PSF stars", I eventually settled on a point-spread function for the V and I frames, and collected the stars' instrumental magnitudes. The point-spread functions I determined for both filters in my cluster and calibration data do not do a wonderful job of fitting the actual PSF's of my images, as shown below. Though imperfect, especially for the brighter stars, the fainter stars appear to be well-subtracted.
For the final V magnitude and V-I color, it is necessary to calibrate the
cluster stars to the standard system. This was done by first finding the apparent magnitudes of
the calibration cluster stars from night 2 using the transformation equations determined
earlier, choosing a sample of those stars for the V magnitude correction and another
sample for the V-I correction. These samples were determined by plotting the quantity
against its error and visually setting a selection criteria. For the V magnitude
correction, I accepted stars with a V < 16.3 (Figure 6), and for the V-I correction I
accepted stars in the range 1.0 < V-I < 2.0 (Figure 7). I then matched these stars with the
same stars from the co-added cluster frames and found the mean shift. For V, I found
a shift of -6.81875 Mag with an error of 0.017523 Mag, and for V-I the shift was 0.393486 Mag
with an error of 0.0095518 Mag. These shifts and errors were then applied to the co-added
cluster stars, of which there are 657.
| Figure 6. This plot is taken from the night 2 V calibration frame. The only points that were used in determining the shift from instrumental to apparent magnitudes were those stars with a V < 16.3. |
| Figure 7. This plot is taken from the night 2 I calibration frame. The only points that were used in determining the shift from instrumental to apparent magnitudes were those stars colors between 1.0 < V-I < 2.0. |
| Figure 8. The calibrated color-magnitude diagram of M3, from which the metallicity and reddening were directly determined using the Sarajedini method. This plot has two main features, a vertical and a horizontal filament. These are the RGB and HB, respectively. |
| Figure 9. This plot shows how the photometric errors follow magnitude, and it shows that the limiting magnitude is right around 18.5 in V. |
Though the overall structure of the CM diagram is impressive, more quantitative results
would be desirable. Using the Sarajedini method, I would like to derive the metallicity and
reddening of the cluster. First, a fit of the RGB and the HB needs to be made. Due to the
large scatter in the data points, I have simply done this fit by eye. Now two more quantities are needed:
the V-I color of the RGB at the level of HB, i.e. the intersection point
of the two fits, which will be denoted by (V-I)g, and the difference in
V between the HB and the RGB at (V-I)0=1.2, where the subscript 0
denotes the V-I color of a dereddened cluster. This quantity will be referred to as
V1.2. Using Sarajedini's derived equations (Sarajedini 1994):
| Figure 10. CM diagram of M3 from Rosenberg et al. Notice the similarities in shape between this and Figure 8. Pay particular attention, however, to the small differences in magnitude and color. |
The general structure and proportion between the two CM diagrams seem to be in agreement,
but the actual V and V-I values are off. This shift could be due to an
inaccurate transformation between the calibrated cluster stars from the night 2 and the night 1
stars, but this does not make sense in light of Figure 11. Here, the night two stars are
plotted, showing that the same shift is at work as in the calibrated data. Therefore the
most likely source of this error probably comes from the transformation equations themselves.
In this calibration, we have assumed that the Landolt filter system is equivalent to our own
set of filters. However, this appears not to be the case. It is also evidenced by the
observation that the color is shifted away from the blue, which is expected for this kind of
situation since our CCD has poorer sensitivity the bluer you go. Thus you would get a
"blue deficient" CM diagram. This discrepancy can be corrected
by obtaining a much larger number of standard stars and inserting a color term for V
that corrects for the difference between the filters. This task is indeed a difficult one when
your equipment consists of an amateur telescope that requires lots of overhead time to find an
object in the sky. What is needed is a night or two devoted entirely to getting good standard stars
so these corrections to the filter system can be made and more accurate photometry obtained in the future.
| Figure 11. This is a CM diagram of only the night 2 cluster calibration stars. This plot shows that the errors in Figure 8 are not due to mistaken shifts from instrumental to apparent magnitude, as this diagram is also shifted to the red more than the diagram in Figure 10. |
Basically, these results are of limited scientific value, as globular clusters are well-studied objects, though they are useful for an evaluation of the telescope, CCD, and filter system. For instance, the guiding requires a fairly bright star, so one cannot place their object of interest optimally in the frame. Also, the telescope tends to produce football shaped stars or at the least oddly shaped stars, which creates a large FWHM. However, there is no reason, with more exposures and a properly calibrated standard system, why this project could not be repeated with results that agree more closely with published data and that reach down to the Main Sequence Turnoff, where an age estimate for the cluster can be made.