ANALYSIS OF THE HALO GLOBULAR CLUSTER M30 AND ITS VARIABLE STARS
Michael T. Smitka
A Thesis
Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
August 2007
Committee:
Andrew C. Layden, Advisor
John B. Laird
Dale W. Smith
ii
ABSTRACT
Andrew C. Layden, Advisor
Photometry of the metal-poor globular cluster M30 is presented in B, V, R and
I bandpasses. A color-magnitude diagram created from this photometry indicates that accurate magnitude measurements were obtained for stars from the red giant branch down to approximately 2.5 magnitudes fainter than the main sequence turn- off. Time-series photometry is presented for six RR Lyrae type variable stars, three of which are newly discovered. Four variable stars of other types, three of them newly discovered, are also discussed. A metallicity value of [Fe/H] = -2.02 was adopted for this study. Using the RR Lyrae stars’ mean colors at minimum light, a reddening of
E(B V ) = 0.053 0.010 was found for this cluster as well as an extinction value of − ±
AV = 0.165 0.031. A distance modulus of µ = 14.504 0.127 and the corresponding ± ± distance of 7.958 0.147 kpc was also computed using the RR Lyrae stars’ mean ± magnitudes. Isochrone fitting of the color-magnitude diagram yielded a cluster age of 15.8 1.8 Gyr. ± iii
ACKNOWLEDGMENTS
I would like to thank my advisor, Andrew C. Layden, for all of his help and patience with my undertaking of this project. His knowledge and guidance were crucial at every step and none could have been taken without him.
I would also like to thank my family. Particularly Mom & Dad for their love, support and for putting up with having a child in college for longer than four years.
I also wish to say thank you to Uncle Ray for his amazing generosity which helped me to get this far.
I thank Karen as well for her love and support.
Finally, I wish for years of happy marriage between Pig & Ben and Joe & Jen. iv
TABLE OF CONTENTS
Page
CHAPTER 1. Introduction ...... 1
CHAPTER 2. Observations ...... 6
CHAPTER 3. Photometry ...... 10
3.1 DAOPHOT Photometry ...... 10
3.2 ISIS Photometry ...... 12
CHAPTER 4. Calibration ...... 14
4.1 BGSU Calibration Set ...... 15
4.2 Calibration of All Stars ...... 21
4.3 Calibration of Variable Stars ...... 27
CHAPTER 5. The Color-Magnitude Diagram ...... 30
5.1 Variable Stars on the CMD ...... 35
CHAPTER 6. Variable Stars ...... 36
6.1 RR Lyrae Stars ...... 40
6.2 Other Variable Stars ...... 51
CHAPTER 7. Discussion ...... 60
7.1 Reddening and Extinction ...... 60
7.2 Distance ...... 63
7.3 Age ...... 65
7.4 Oosterhoff Type ...... 67 v
CHAPTER 8. Conclusion ...... 72
REFERENCES ...... 75 vi
LIST OF FIGURES
Figure Page
1.1 CMD: V vs. B-I Labeled ...... 2
1.2 The Zero-Age Horizontal Branch ...... 3
1.3 RRab & RRc Light Curves ...... 4
2.1 Sample M30 Image ...... 7
4.1 Stetson Calibration Stars ...... 16
4.2 Alcaino Calibration Stars ...... 17
4.3 BGSU Standard Star Magnitudes ...... 20
4.4 Post-Calibration Residuals in V ...... 24
4.5 Post-Calibration Residuals in B ...... 25
4.6 Post-Calibration Residuals in I ...... 26
5.1 Post-Calibration Residuals in V for CMD Data ...... 32
5.2 CMD of M30 ...... 34
6.1 Variability Index vs. V Magnitude ...... 37
6.2 Magnitude vs. HJD for Variable Star ...... 38
6.3 Magnitude vs HJD for a Non-Variable Star ...... 39
6.4 CMD of M30 with Variable Stars ...... 43
6.5 Horizontal Branch of CMD with Variable Stars ...... 44
6.6 Light Curves for s161 (RRab) ...... 45
6.7 Light Curves for s212 (RRab) ...... 46
6.8 Light Curves for s178 (RRab) ...... 47
6.9 Light Curves for s184 (RRc) ...... 48 vii
6.10 Light Curves for s181 (RRc) ...... 49
6.11 Light Curves for s193 (RRc) ...... 50
6.12 Blazhko Effect ...... 52
6.13 Magnitude vs. HJD for s5474 SS Cygni ...... 54
6.14 Magnitude vs. HJD for s65 ...... 56
6.15 Magnitude vs. HJD for s27 ...... 58
6.16 Magnitude vs. HJD for s1045 ...... 59
7.1 Dereddened CMD ...... 64
7.2 Isochrone Fits for Z=0.0001 ...... 68
7.3 Isochrone Fits for Z=0.0001 (MS) ...... 69
7.4 Isochrone Fits for Z=0.0001 (HB) ...... 69
7.5 Isochrone Fits for Z=0.0004 ...... 70
7.6 Isochrone Fits for Z=0.0004 ...... 71 viii
LIST OF TABLES
Table Page
2.1 Subsets of images of M30 analyzed independently ...... 8
4.1 Standard Magnitude Stars ...... 15
4.2 Calibration coefficients and relative uncertainties of the linear fitting
process for the data set gathered at BGSU...... 19
4.3 Magnitude Calibration Coefficients and Statistics ...... 22
4.4 Color Calibration Coefficients and Statistics ...... 23
6.1 Photometry of RR Lyrae Stars ...... 42
6.2 Data for RR Lyrae Stars ...... 45
7.1 Reddening Values from RRab Stars ...... 62
7.2 Metallicity Values ...... 62
7.3 Reddening Values ...... 62
7.4 Oosterhoff Type ...... 67 1
CHAPTER 1
Introduction
For many years the observation of globular clusters has contributed vast amounts of knowledge about our galaxy and the universe as a whole. Globular clusters are densely packed, gravitationally bound groupings of stars found distributed around a galaxy. Believed to have formed at the earliest epoch of star formation, globular clusters provide astronomers with a powerful window into a galaxy’s distant past as well as a useful tool for understanding stellar and galactic evolution models. One result of their old age is that the stars that comprise many globular clusters have very low metallicities. Typically, clusters are broken up into two categories based on their metallicity. Those with low metallicities ([Fe/H]< 0.8) lie in a spherical distribution − about the Galactic center, while higher metallicity clusters ([Fe/H]> 0.8) tend to − lie closer to the Galactic plane. It is thought that this distribution is the result of the metal-rich clusters forming after the metal-poor ones, after the Galaxy had been enriched with heavy elements and formed a disk shape. Another result of their old age is that globular clusters contain stars that are in greatly varying phases of evolutionary progress. This is most evident when viewed on a color-magnitude diagram (CMD) of a cluster (Fig. 1.1).
One phase of stellar evolution that is of particular interest is when an individual star has ventured onto the horizontal branch of the CMD. This occurs after the core helium flash at the tip of the red giant branch and the star has migrated down the
CMD toward dimmer and bluer values. Following this transition, the star then settles at a position somewhere along the zero-age horizontal branch (ZAHB) on the CMD.
The position an individual star takes on the ZAHB is dependent upon the total 2
Figure 1.1: A CMD of M30 with the phases of stellar evolution superimposed. mass, core mass and chemical makeup of the star. Stars with total masses of roughly
0.7 0.8M are positioned on the horizontal branch (HB) nearby to an instability − strip inside which they can develop instabilities and begin to radially pulsate. A pulsating star could have its ZAHB location within the instability strip or it can have evolved there from a ZAHB location outside the instability strip (Fig. 1.2). The pulsation results from the energy output of the star’s core cycling between ionizing atoms in the star’s partial ionization zone, and thus increasing its opacity, and being released. This pulsation is observable as a change in the luminosity and color of the star and defines the characteristics of an RR Lyrae (RRL) type variable star. RRL stars have been observed to occur in three distinct classes, types RRab, RRc and
RRd. The RRab type pulsate in the fundamental mode and display an asymmetric light curve with a steep rising branch, a pulsation period between 0.3-1.2 day and a 3
Figure 1.2: Evolutionary tracks moving away from the zero-age horizontal branch (ZAHB) are shown for stars of differing masses (in solar units). The dashed line rep- resents the ZAHB. The dotted vertical lines represent the boundaries of the instability strip. This plot was taken from RR Lyrae Stars by H. A. Smith (1995).
variability amplitude between 0.5-2.0 magnitude in the V bandpass (Fig. 1.3(a)). RRc type stars pulsate in the first overtone mode and display a nearly sinusoidal shaped light curve, a pulsation period between 0.2-0.5 day and a variability amplitude of less than 0.8 magnitude in V (Fig. 1.3(b)). RRd type stars pulsate simultaneously in the fundamental mode and the first overtone. Their periods always appear very near the threshold value between RRab and RRc type stars. It is thought that RRd stars may be RRL’s which are transitioning from an RRab type to an RRc type, or vice versa
(Smith 1995).
RRL variable stars are valuable to the astronomer because they function as a standard candle. A distance modulus can be calculated for an RRL with merely an observed mean apparent visual magnitude and an absolute visual magnitude, which 4
Figure 1.3: (a) A typical RRab light curve. (b) A typical RRc light curve.
can be calculated based on metallicity (Chaboyer 1998). Distance measurements of this type have enabled the mapping of our own Galaxy and the distances of others, such as the Large Magellanic Cloud (Walker 1992). RRL stars are also valuable because reddening caused by the interstellar medium can be calculated by analyzing the star’s color at minimum light (Blanco 1992). This reddening estimate provides non-trivial magnitude corrections for all stars within a cluster.
M30 (NGC 7099) is a Galactic halo globular cluster with three documented
RRL stars (Rosino 1949) and several other documented variable stars of differing or unknown types (Terzan 1968, Terzan et al. 1975, Harris 1996). It has been well established that M30 is a metal poor cluster, with observed [Fe/H] values ranging between -2.12 (Harris 1996) and -1.91 (Carretta and Gratton 1997). It lies within the constellation Capricorn at a right ascension (RA) of 21h 40m 22.0s and declination of
o 23 100 4500. Harris’ Catalog of Parameters for Milky Way Globular Clusters (1996) − compiles a large wealth of additional information from several sources pertaining to
M30. 5
This cluster was selected for analysis in this study for several reasons, the most striking of which is that the variable stars in the cluster have never been studied in detail with modern CCD technology. No light curves could be found in the literature for any of the 13 known variable stars. Another important factor in the selection of
M30 for study is that it was chosen to be one of 21 globular clusters inspected in a
Space Interferometry Mission (SIM) key project (Chaboyer et al. 2005). The 21 clus- ters were selected by SIM to span a wide range of parameters, including metallicity,
RR Lyrae abundance and Oosterhoff type. Based on these criteria, M30 was found to be a good candidate for the study.
Unfortunately, NASA has put the SIM satellite mission on indefinite hold since the undertaking of this study. The goal of this SIM key project was to refine the pop- ulation II distance scale, particularly MV RR (Section 7.2), by using direct parallax to measure the distance to cluster and field RRL. These measurements would have provided improved globular cluster ages and ultimately would have set a lower limit for the age of the universe.
A requisite for the SIM project was that accurate, dereddened time series pho- tometry of all RRL stars in M30 be obtained by ground based observing prior to the satellite’s launch. It was the intent of this study to provide the SIM project with the required photometry for M30. Despite the fact that SIM will most likely not be making use of the results found in this study, the scientific value of the findings presented here is still high. 6
CHAPTER 2
Observations
Images of M30 were gathered with the Swope telescope located at Cerro Las
Campanas, Chile during two observing sessions in 2003 and 2005.1 All images from both observing sessions were taken in queue mode on the telescope.2 The entire data set gathered for M30 by both observers was 385 images, which were broken down into subsets based on the filter used, exposure time and whether the images were gathered in the 2003 or 2005 observing run (Table 2.1). The filters used were standard B, V, R and I bandpasses. The exposure times were divided into two categories of short and long exposures. This division was designed to provide accurate photometry of both bright and faint stars and thus ensure good photometry of all variable stars regardless of their luminosity.
Both observers performed most of the image processing while at the observatory.
The image processing performed on site consisted of removing the bias and flat fielding each image. Bias correcting was done to remove the constant level of charge present on the CCD chip when unexposed to light, while flat fielding was performed to adjust for the varying sensitivity of each pixel comprising the chip matrix. Pixels that consistently displayed atypical behavior in all images were given a readout value of zero in a process known as masking. Evidence of the masking procedure can be seen most easily in a dark column that was masked because of its consistent poor detection on all images (Figure 2.1).
The CCD camera used on the Swope telescope for both observing runs was a 1Swope telescope website: www.ociw.edu/swope 2The telescope was operated in 2003 by Kaspar von Braun and by Brian Lee in 2005. 7
Figure 2.1: An image of M30 taken in the I bandwidth with an exposure time of 10s. 8
Table 2.1: Subsets of images of M30 analyzed independently Dates Filter Exposure Time (sec) Nights Images used 07/09/2005 - 07/30/2005 B 70 12 43 28 07/09/2005 - 07/30/2005 B 250 12 42 28 07/09/2005 - 07/30/2005 V 20 12 43 28 07/09/2005 - 07/30/2005 V 150 12 43 28 07/09/2005 - 07/30/2005 R 10 12 42 28 07/09/2005 - 07/30/2005 R 100 12 42 28 07/09/2005 - 07/30/2005 I 10 12 44 28 07/09/2005 - 07/30/2005 I 100 12 43 28 05/17/2003 - 06/20/2003 B 50 5 11 0 05/17/2003 - 06/20/2003 B 350 5 6 0 05/17/2003 - 06/20/2003 V 25 5 7 0 05/17/2003 - 06/20/2003 V 150 5 5 0 05/17/2003 - 06/20/2003 I 20 5 8 0 05/17/2003 - 06/20/2003 I 120 5 6 0
SITe3 model camera with a field of view of 14.50 X 23.00 (2048 X 3150 pixels). A small field rotation was detected between the 2003 and 2005 data sets indicating that the camera was removed and remounted at some time between the two observing periods.
It is also noteworthy that the particular SITe3 camera used on the Swope tele- scope has been documented by several sources to display a non-linear photon detection rate (Kaluzny et al. 2004, http://www.lowell.edu/users/massey/obins/swopeccd.html).
A CCD chip operates by converting photons from the incoming starlight into elec- trons, which are then stored within a pixel and later counted. The number of electrons counted in an individual pixel is representative of the brightness of the starlight that falls on that pixel. Ideally, a CCD chip exposed to a light source will display the same conversion rate of photons to electrons regardless of how many electrons are already stored withinin a pixel. A non-linear detection rate results when the conversion rate of photons to electrons for a CCD chip changes with the number of electrons con- tained in a pixel. The result of this effect is that with increasing brightness, the CCD 9 will register values that are increasingly too faint. This non-linearity effect on the
SITe3 CCD was corrected for in the calibration phase of this project. 10
CHAPTER 3
Photometry
Photometry of the 385 images comprising the main data set was performed us- ing two separate methods, both capable of detecting variable stars in crowded stellar
fields. Stellar crowding in compact objects, such as globular clusters, greatly compli- cates the determination of individual star parameters and requires the use of special computing techniques. In every step of the photometry process images of similar characteristics were processed together.1
3.1 DAOPHOT Photometry
The first method employed was examining the images using a set of software packages designed specifically for crowded field photometry titled DAOPHOT II,
ALLSTAR (Stetson 1987), ALLFRAME (Stetson 1994) and DAOMASTER. A unique method is used by DAOPHOT II and ALLSTAR that enables them to accurately measure individual star magnitudes in crowded fields. The special method is the use of a point spread function (PSF), which can be best described as a best suited single star profile that takes the shape of a bivariate gaussian. This technique of photometry made the use of these programs ideal for this project.
In the photometry process a cycling occured between DAOPHOT II and ALL-
STAR and each image had a unique PSF calculated based on the profiles of roughly
200 isolated and well exposed stars.2 This is advantageous because ill effects from 1E.g. all images taken in the V filter with a short exposure time from the 2005 observing run were processed in a single group. 2A star profile on a CCD image can be shown on a 3D plot with the brightness of a given pixel (X,Y) represented on the Z-axis. 11 factors that may change from image to image, such as the full width at half maximum
(FWHM) of star profiles, are minimized. Once the PSF was generated for an image, it was then matched to accurately emulate the profile of every detected star on the image. The PSF profile can be moved from pixel to pixel in X and Y directions and scaled to increase or decrease in height to most accurately match the location and brightness of a star. The shape of the PSF profile is not altered in the fitting process as it is assumed that any object that is a star will have a form similar to that of the PSF. An object, such as a galaxy, whose profile does not match well with the
PSF is flagged with a high error representative of the quality of the PSF fit to its profile. Once the PSF had been fitted to every star in the image, every fit’s location and height (magnitude) was documented as a star location and magnitude. These values were then subtracted from the original image leaving behind only the stars that went undetected initially due to their faintness or proximity to a brighter star.
The entire procedure outlined above was run through four consecutive iterations to ensure detection of all stars. Each iteration found increasingly fainter stars as well as stars that were hidden within the profiles of nearby bright stars.
Following the completion of the DAOPHOT II/ALLSTAR cycles, the results were entered into the program DAOMASTER. This program is designed to search through the lists of stars made in the previous steps and pick out measurements that correspond to common stars. It then uses the locations of stars found on all images to create transformation equation coefficients to describe the field shift between each image and a master image. These transformations are then used by the next program,
ALLFRAME, to determine exactly the location and brightness of each star from its profile in all images. These more precise results were then run through DAOMAS-
TER which compiled the measurements for each star and created two new forms of 12 output. One output format was a list containing a single, weighted mean magnitude, associated errors and a variability index for each star based on the measurements made in all the images combined. The other output format was a list comprised of the individual magnitude and error measurements taken from each image for each star. Both forms of output had specific purposes, the second format being crucial in identifying variable stars.
3.2 ISIS Photometry
Before proceeding with the next phase of the project another method of pho- tometry, a program called ISIS, was employed to analyze the images using a different method and provide data that we could use to form a second opinion in deciding which stars were variable. ISIS uses image subtraction and differential photometry as its method for determining a star’s variability (Alard 2000). Image subtraction is carried out by defining a master image with a low FWHM value, which is then blurred to match the seeing of another image from the data set and then simply sub- tracted pixel for pixel from that image. The process is repeated for each image in the data set (in this case an identical set as was processed by the DAOPHOT method).
Theoretically, the only residuals remaining on the images after subtraction would be light sources whose light outputs have varied away from the value in the master image with time. These variable stars could then easily be compiled and differential light curves generated.
One shortcoming of the ISIS method is that the only measurement made is how much a star’s brightness varies with time rather than its actual brightness. This single measurement was clearly insufficient for this study because our intent was to measure 13 the apparent magnitudes of individual stars, and in the process, their variability.
However, since ISIS was only used as a check for the DAOPHOT photometry, its shortcomings were tolerable. Another shortcoming of using the ISIS method is its lack of documentation and the time investment required to overcome the lack of clarity. Despite these problems, ISIS did provide valuable insight that was helpful in identifying variable stars in the DAOPHOT photometry (Chap. 6). 14
CHAPTER 4
Calibration
The instrumental photometry computed by DAOPHOT had to go through a cal- ibration process before it could accurately represent star magnitudes on the standard system (e.g. as defined by Landolt (1992)). This was required because DAOPHOT computes star magnitudes relative to an arbitrary zero point rather than standard magnitudes. Because of this, all magnitude measurements made by DAOPHOT are systematically offset when compared to the stars’ actual brightnesses. To correct for this systematic offset, standard stars in the M30 field had to be employed because no standard stars were imaged when the main data set images were taken. Standard stars are simply stars whose apparent magnitudes have been well established. Five sets of standards were investigated and three were used in the calibration of M30.
The calibration was carried out in two separate phases: the calibration of all stars present in the cluster based on their best suited magnitude measurement and the calibration of variable stars based on their magnitude in each frame.
The largest standard set used was that of Stetson (2000), who provided B, V and
I photometry of stars located in a ring about 30 wide with a minimum radius of about
10 from the cluster center (Fig. 4.1). The only standard R magnitudes found in the literature were provided in a journal article by Alcaino et al. (1987). Alcaino et al. also provided B, V and I photometry for these stars as well. In this article Alcaino provided fewer stars than did Stetson, but with brighter magnitudes and a wider radius from the cluster center (Fig. 4.2). Details of these standard sets, including the number of stars contained in each, can be found in Table 4.1. Standard sets by Bergbusch (1996) and Dickens (1972) were also investigated and deemed to be 15
Table 4.1: Standard Magnitude Stars Filter Set n Magnitude Range B Stetson 93 14.040 - 18.992 B Alcaino 12 10.86 - 15.44 V Stetson 94 12.980 - 18.550 V Alcaino 12 10.60 - 15.29 R Stetson 0 0 R Alcaino 12 10.45 - 15.25 I Stetson 65 11.840 - 17.898 I Alcaino 12 10.26 - 15.04
inaccurate or too old (photographic) and thus unreliable.
4.1 BGSU Calibration Set
The fifth calibration set was gathered at the 0.5 meter telescope at the Bowling
Green State University (BGSU) observatory in the Fall of 2006. The decision to create our own set of standard stars in the M30 field was made for two reasons; a non-linear detection rate of photons on the SITe3 CCD was discovered in an early attempt at calibration and the number of R band calibration stars in our possession was not sufficient to perform a reliable magnitude adjustment. It was unclear whether the non-linear detection trend was the result of our data being faulty or Stetson’s standards. It was initially thought that creating our own set of standards might solve this question.
Images of standard stars located near the celestial equator documented by Lan- dolt (1992) and of M30 were taken through B, V, R and I filters over the course of 6 nights to construct this standard set. The Landolt stars targeted were chosen to cover the widest possible color and magnitude ranges to ensure the most reliable calibra- tion results. Two nights were deemed photometric based on the images’ appearances 16
Figure 4.1: The locations of photometric standards documented by Stetson (2000). 17
Figure 4.2: The locations of photometric standards documented in Alcaino et al. (1987). 18 and seeing quality and were then analyzed using simple aperture photometry. The aperture photometry consisted of manually measuring star magnitudes on both the
Landolt and M30 images. It was decided that an aperture of 10 pixels would capture all the light from a star after inspecting several star radial profiles. The sky back- ground illumination was subtracted from each star by removing the mode pixel value detected in a ring that spanned from 20 pixels outward to 30 pixels from the star center. The magnitude measurements made of Landolt stars were then compared to their accepted magnitudes in each filter and systematic differences were analyzed for each night independently. The parameters found to cause changes in magnitude de- tection were color, airmass and time. These parameters were detected by plotting the deviations between our observed magnitude values and the Landolt magnitude values versus differing parameters and observing whether appreciable trends were evident.
To determine the degree of the magnitude corrections required for each param- eter, multivariate linear fitting was performed. Using the program MyStat, the dif- ference between the accepted visual magnitude and the observed instrumental mag- nitude (∆V) was plotted against color, airmass and HJD. Points that were deviant as a function of time tended to be single points that were clearly outliers and were removed from the fitting process. Using this method, a trend in detection rates on the CCD caused by any of the parameters was observed as a slope on its plot. These slopes and a zero point correction derived from the Landolt stars were documented and applied in calibration equations of the form V = v αv βv(AM) γv(B V ) to − − − − the 23 selected stars in the M30 field. The relative sizes of the corrections made for each parameter can be viewed in Table 4.2 along with uncertainties and the overall
RMS values of the fits.
Ultimately, the calibration from the BGSU data was only applied to the short 19
Table 4.2: Calibration coefficients and relative uncertainties of the linear fitting pro- cess for the data set gathered at BGSU. Night Filter n α σα β σβ γ σγ RMS 1 B 18 6.618 0.006 0.325 0.004 -0.094 0.001 0.018 2 B 14 6.493 0.012 0.486 0.009 -0.084 0.002 0.046 1 V 23 6.307 0.007 0.235 0.005 -0.004 0.001 0.023 2 V 13 6.282 0.002 0.241 0.001 0.023 0.001 0.012 1 R 23 6.163 0.006 0.214 0.004 0.035 0.001 0.020 2 R 8 5.988 0.005 0.371 0.003 0.028 0.001 0.013 1 I 24 6.818 0.008 0.119 0.006 -0.045 0.001 0.026 2 I 11 6.811 0.003 0.124 0.002 -0.046 0.001 0.016
exposure, R band images because there were so few standards provided by Alcaino and none by Stetson. The R magnitude calibration could not be performed for the long exposure images because the stars measured at BGSU appeared saturated in the main data set images. Also, any star that was not saturated in the main data set was too faint to obtain accurate photometry for on the BGSU images. In other
filters, despite the RMS values being small, the final uncertainties were too large to justify their use (Fig. 4.3). The uncertainties for individual star magnitudes were much larger in the BGSU data set than in Stetson’s. The question of whether our data or Stetson’s standard stars were to blame for the non-linear trend observed went unanswered because we could not accurately get photometry for faint enough stars.
While this exercise may appear to have been a wasted effort, it did demonstrate the ability of the BGSU observatory to perform fairly accurate all sky photometry un- der excellent sky conditions. The quality of the resulting BGSU photometry is evident in the low RMS values of the calibration linear fits (Table 4.2). This indicates that the effects of each parameter can be accounted for to a degree of certainty of roughly
0.02 magnitudes. It is also notable that the data showed that accurate measurements can be made within a 0.02 magnitude error margin up to approximately 13th magni- 20
Figure 4.3: The difference between the main data set (short exposure images) and the BGSU standard stars (∆R) is plotted vs R. Horizontal error bars represent the uncertainties in the BGSU standards. Vertical error bars represent the compounded uncertainties of the main data set and the BGSU standards. The horizontal line represents a weighted average of ∆R with the compounded uncertainties used as the weighting function. 21 tude in the R band. Especially striking is the fact that such good photometry was obtained for M30, a southern hemisphere object at a declination of 23o, despite it − never rising higher than 2.2 airmasses. This suggests that the BGSU observatory can obtain even better quality photometry for objects at higher declinations.
4.2 Calibration of All Stars
For all image sets in filters other than R, the standard stars used for calibrating were those of Stetson with Alcaino stars added when they did not appear saturated in our data. Using these stars as a guide, it was judged that in order to obtain accu- rate magnitudes it was necessary to make corrections based on a star’s instrumental magnitude and color. Both parameters were corrected for in individual calibration calculations. The magnitude-dependent calibration was calculated first in order to most accurately correct for the magnitude-dependent sensitivity of the CCD.
Linear fitting was again the technique used to calculate the calibration equa- tion coefficients, though this time the Image Reduction and Analysis Facility (IRAF) software package created by the National Optical Astronomy Observatory was used.
By plotting the difference between several stars’ instrumental magnitudes and stan- dard magnitudes (∆V) vs. their instrumental magnitudes and then selecting a best fit line with the uncertainties as a weighting function, the simple equation,
∆V = vus Vs = c1 + c2vus, is formed, which becomes useful for calibration pur- − 1 poses when rearranged to the form, Vs = vus c1 c2vus. A simple computer − − program was then written to calculate the magnitude-corrected (Vm) value for each 1Equations of this linear form were found to most accurately describe the documented non-linear behavior of the CCD. A well behaved CCD would not display the c2 slope term and would only nd rd require the c1 zero point correction. 2 and 3 order polynomial fits to the data were attempted but yielded larger RMS values and were rejected. 22
Table 4.3: Magnitude Calibration Coefficients and Statistics Filter Exp. Time n c1 c2 RMSmag B Short 103 -1.6698 0.0114 0.0219 B Long 92 -2.9202 0.0022 0.0197 V Short 104 -0.3290 0.0086 0.0348 V Long 94 -2.5034 0.0055 0.0294 R Short 10 0.0111 0.0138 0.0220 R Long 4 -2.5056 0.0218 0.0256 I Short 74 0.4319 0.0212 0.0237 I Long 64 -2.0629 0.0181 0.0230
star based on the instrumental magnitude (vus) for each star and the coefficients c1
2 and c2. Next, the color correction was performed. For this calculation the final equation took the form, Vs = Vm d1 d2(Color). Take note that the magnitude corrected − −
Vm value was used in this calculation in place of the instrumental magnitude. The filters used to define the color term were varied to include the filter being calibrated in the calculation. These filters, as well as the coefficients and RMS values of the fits can be found in Tables 4.3 and 4.4. A second Fortran program was then created to calculate the final calibrated magnitude (Vf ) for each star in the cluster in each filter based on the color calibration equations.
To ensure that our final calibration was successful, a ∆V value was again com- puted for each standard star, this time using Vf in place of the instrumental mag- nitude. These residual values were then plotted against magnitude, color, X pixel position and Y pixel position to view the agreement between our calibrated magni- tudes and the standard magnitudes (Fig. 4.4 - 4.6). The calibrations appear very acceptable (the largest ∆mag 0.08), though traces of the magnitude-dependent sen- ≈ 2The V filter was used in this example. Identical procedures were carried out in B, R and I filters. 23
Table 4.4: Color Calibration Coefficients and Statistics Filter Exp. Time n d1 d2 RMScolor Color
B Short 103 0.0461 -0.0530 0.0158 Bm Vm − B Long 92 0.0341 -0.0578 0.0112 Bm Vm − V Short 104 -0.0381 0.0672 0.0298 Bm Vm − V Long 94 -0.0117 0.0455 0.0264 Bm Vm − R Short 10 -0.0104 0.0057 0.0192 Vm Rm − R Long 4 -0.0068 0.0236 0.0251 Vm Rm − I Short 74 -0.0019 -0.0208 0.0228 Vm Im − I Long 64 0.0541 -0.0318 0.0205 Vm Im − sitivity can still be detected in faint stars. This result was expected because the linear
fits were weighted with the magnitude uncertainty as the weighting function. Since less light can be gathered for faint stars, their ratio of signal to noise on the CCD is smaller than that for brigher stars. This ratio is represented as a larger magnitude error for faint stars. So, the trend seen in the residuals where fainter stars are more deviant than brigher ones is to be expected. Also, subtle hints of a positional depen- dence trend appeared on the residual plots that was not detected before calibrating for magnitude and color. It is unclear whether this trend is real or the result of the tight and uneven distribution of standard stars about the cluster seen in Fig. 4.1 and 4.2. The location of the cluster center on our images was at an X location of
1030 pixels and a Y location of 1630 pixels.
The noticeable trends in the residuals present after calibration and the lack of sufficient R band standard stars have prompted us to submit a request for additional data from the National Optical Astronomy Observatories (NOAO). The data set we requested is nearly identical to the one gathered at the BGSU observatory and will serve an identical purpose. However, the requested data will be of much higher photometric quality due to the telescope’s superior location at Cerro Tololo, Chile 24
Figure 4.4: Post-calibration residuals in V. Blue stars are represented by filled circles, red stars with open circles, intermediate colored stars with X’s. Stars’ colors were assigned based on their locations on the ∆V vs. (B-V) plot. The three color groups were designed to contain approximately equal numbers of stars. The pixel location of the cluster center is X=1030 and Y=1630. 25
Figure 4.5: Post-calibration residuals in B. Blue stars are represented by filled circles and red stars with open circles, intermediate colored stars with X’s. Stars’ colors were assigned based on their locations on the ∆V vs. (B-V) plot. The three color groups were designed to contain approximately equal numbers of stars. The pixel location of the cluster center is X=1030 and Y=1630. 26
Figure 4.6: Post-calibration residuals in I. Blue stars are represented by filled circles and red stars with open circles, intermediate colored stars with X’s. Stars’ colors were assigned based on their locations on the ∆V vs. (B-V) plot. The three color groups were designed to contain approximately equal numbers of stars. The pixel location of the cluster center is X=1030 and Y=1630. 27 and its larger size (0.9 m). We believe that the resulting set of standard stars created from this data will enable us to definitively remove the residual trends and provide a more accurate calibration.
4.3 Calibration of Variable Stars
Documented variable stars (Rosino 1949, Terzan 1968, Terzan & Rutily 1975) and stars that were flagged as being likely variables in the photometry were calibrated using a more complicated method than described above. The previous method of calibrating a star based on a single representative magnitude and color is simply not sufficient to accurately calibrate a star whose magnitude and color vary as the star oscillates. This problem was solved by implementing a method of calibration that took into account the magnitude and color of each variable star in each individual image that made up the main data set.
It was necessary to perform the variable star calibrations after the non-variable star calibrations had been completed for two reasons. The first reason was that the equations defined in the non-variable calibration were manipulated for this process.
The sensitivity of the CCD to the varying parameters (cn and dn) had to be known in order for these equations to be completley defined. Second, in order for the ma- nipulated equations to be solvable, magnitudes for non-variable comparison stars had to be known. The magnitudes used were simply non-variable stars that had been calibrated by the method described in the previous step.
Since the calibration equations are valid for each star, variable or not, at a given instant of time it is implied that each star has its own unique calibration equation at every moment. For example, a variable star’s color calibration equation in the first 28
image of the short exposure, V band data set can be shown to be Vvar = vvar d1 − − d2(B V )var. For data taken from that same image, any non-variable star’s equation − is obviously Vcomp = vcomp d1 d2(B V )comp. Subtracting Vcomp from Vvar and − − − solving for Vvar yields, Vvar = Vcomp + (vvar vcomp) d2((B V )var (B V )comp), − − − − − which provides an instantaneous color calibration for the variable star based on the calibration applied to the non-variable comparison star. A similar calculation was carried out for the magnitude calibration as well.
The (B V )var term in the final equation above was derived through algebraic − manipulation of the calibration equations. vvar Vvar = dv1 + dv2(B V )var was − − subtracted from bvar Bvar = db1 + db2(B V )var, which yielded a final result of − − (b v)var (db1 dv1) (B V )var = − − − . (1+db2 dv2) − − The decision to calibrate variable stars by differential photometry was made be- cause it offers a more reliable calibration. This is because by using multiple compari- son stars, we obtain several magnitude estimates and thus decrease our uncertainty in the final value. This is more desirable than simply applying the calibration equations to each frame and obtaining only one estimate of the magnitude.
Six non-variable comparison stars were chosen to be used in the calibration of each variable star. An independent calculation was carried out for each comparison star and then the six resulting Vvar values were averaged together. Since this method was applied to each image individually, the averaged visual magnitude (Vavg) defined the variable star’s magnitude at the time the image was taken. Any individual Vvar with a deviation of > 2σ from the average of the six values was flagged and removed.
Very few values were removed because the selection process for comparison stars was designed to provide stars that would provide accurate calibrations. In order to be selected a star had to be of similar magnitude and color as the variable star. It 29 also had to be located nearby to the variable star and be sufficiently isolated so that its brightness was confidently determined without any concern of interference from other stars. Finally, the uncertainty for the star had to be less than 0.02 magnitude and display a low variability index. The requirements were kept strict and were only relaxed when fewer than six acceptable comparison stars were found within the ranges of 2 magnitudes, 0.2 difference in color and 300 pixels. In the cases where
finding six comparison stars within these ranges was impossible, the radius was the
first requirement to be eased. This was done because it was more valuable to compare a horizontal branch star to another horizontal branch star located further away on the CCD chip than it was to compare to a star of another evolutionary type. 30
CHAPTER 5
The Color-Magnitude Diagram
A color-magnitude diagram (CMD) of M30 was created. Our desire was to create a single CMD that would take into account data from all of the images in all of the
filters, excluding the less reliable R band. Using DAOMASTER, the short and long exposure image sets were combined into a single set for each of the B, V and I
filters. This was beneficial for two reasons. First, by combining the short and long exposure images into a single set for analysis the range of magnitudes that could be plotted was expanded. When combined, the full range of very bright to very dim stars was accounted for in one single data set for the first time. Up until this point the brightest stars only appeared in the short exposure images and the dimmest stars only in the long exposure images either because they were saturated or too dim. The benefit of doing this can be seen in Figure 1.1, where the range of stars stretches from the brightest stars at the tip of the red giant branch (RGB) down to very faint stars approximately 2.5 magnitudes fainter than the main sequence turn-off. Without having combined the image sets such total coverage would not have been possible in a single plot.
The second reason combining the data sets was beneficial has to do with the number of images available. Because we had such generously sized data sets for each exposure time in each filter, they became one enormous data set for each filter when they were combined. Rather than use all the images and have an enormous supply of data we opted to select the 20 best images from both short and long exposure time sets and combine them into a single set of 40. By selecting the the highest quality images we reduced the average error estimates for each star because magnitudes measured 31 with less certainty were weeded out. Also, since 40 total images were used, the uncertainty in the final calculated magnitude value (σ 1 ) was not compromised ∝ √n and was on the order of the original calculations. Low FWHM values as well as good appearance of the images were the standards used in selecting the 20 images from each subset to be kept.
The method of calibrating the entire cluster described in section 4.1 was applied to the resulting data for each star. While this did not calibrate the variable stars with the reliability the variable star calibration method (section 4.2) would have, it was sufficient for this purpose, as will be explained shortly. The residuals left after calibrating this set were very similar to those from the process where the calibrations were calculated, indicating that the equations were applied properly. A sample resid- ual plot in V is presented in Fig. 5.1 for comparison with Fig. 4.4. Visual comparison of these two plots shows that the residuals are nearly identical.
Precautions were taken to ensure that the final CMD most accurately reflected the cluster’s stellar makeup. Stars were removed from the plot if either their photom- etry or cluster membership was questionable. Any star whose magnitude error was larger than 0.03 magnitude was excluded from the plot as well as any star whose Chi value was larger than 2. Chi is a measure made by DAOPHOT of how well a star’s profile matched the PSF; it is a robust version of a typical χ2 calculation. All stars that resided within 1.450 (200 pixels) of the cluster center were also excluded from the CMD due to the extreme crowding of stars within that radius. This cutting radius is larger than the half-mass radius for M30 of 1.150 documented by Harris (1996), and thus removed more than half of the total number of stars in M30 from the CMD.
While DAOPHOT was designed to handle crowded fields, the cluster center was too crowded and prone to PSF fitting errors to justify the use of these stars for this pur- 32
Figure 5.1: Post-calibration residuals in V for the data set used in plotting the CMD are presented. Blue stars are represented by filled circles, red stars with open circles and intermediate colored stars with X’s. 33 pose. In this environment, DAOPHOT cannot resolve faint stars and thus magnitude measurements are more unreliable. Here we are more interested in studying reliable magnitudes rather than every magnitude we could squeeze out of the images. A sec- ond radial cut designed to remove all stars located at a radius larger than the tidal radius of M30 was investigated but not implemented. The second cut was not made because the tidal radius of 18.340 (Harris 1996) was larger than the span of the CCD in both the X and Y directions. Thus, since all stars were within the tidal radius, it was safe to assume that every star on the CCD could potentially be a cluster member and should not be removed. Finally, removing stars based on their Sharp value was also investigated and not implemented. Sharp is a measure made by DAOPHOT intended to flag objects that display light profiles not typical of stars. For example, a cosmic ray event would have a low Sharp value because its light profile is much narrower than the PSF (Sharp(PSF ) = 1). The opposite case would be true for a galaxy-like object.
The resulting CMD can be seen in Fig. 5.2. The CMD shows that we obtained photometry for bright stars near the tip of the red giant branch and our coverage spanned down to about 2.5 magnitudes below the main sequence turn-off. In all,
10,193 stars were plotted. The choice to use (B-I) for the color term on the plot was made for two reasons: we wished to use data from our three most reliable data sets and the (B-I) color term offered the widest wavelength range. Since our confidence in the
R band calibration is the weakest of all the bandpasses, using the I band photometry for this purpose was logical. Also, when CMD’s with color terms of (B-V) and (V-I) were created, the horizontal branches were not as well defined as in the (B-I) plot. 34
Figure 5.2: A CMD of M30 created from the calibrated and combined V, B and I data sets. Interstellar extinction and reddening have not been corrected for in this diagram. 35
5.1 Variable Stars on the CMD
As described above, using a mean value to describe the magnitude and color of a variable star is an ill concieved method of calibration. This is particularly true in this case where the CCD behaves non-linearly. This raises concerns that a variable star’s position on the CMD may be an inaccurate reflection of the star’s actual parameters and interfere with its proper identification. Luckily, it can be shown that this effect is only a small one.
Assuming a typical RRab amplitude of 1.5 magnitudes in V and the calibration coefficient values in Table 4.3, the maximum difference in two calibrated magnitudes would differ by ∆V = 0.1137 0.0063. This is the maximum difference for the worst ± case scenario where the difference is calculated from the maximum to the minimum of the oscillation. Realistically, the magnitude computed by DAOPHOT is nearer to the mean magnitude of the star, which is what would ideally be plotted. From this, it is easily seen on the CMD in Fig. 5.2 that the vertical shift due to this effect on the CMD is minimal and would not move a star enough to prohibit its proper identification. 36
CHAPTER 6
Variable Stars
Ten stars were found to be variable in our data set. Variable star candidates were detected by the ISIS photometry method (section 3.2) and by examining the variability index calculated by DAOMASTER for each star. The variability index is the ratio of the internal program error to the external error and is proportional to the standard deviation of the magnitude values for each star. Thus, a large variability index value should be expected for a variable star and a small value for a non-variable star. Since the vast majority of stars are non-variable, most showed a low variability index (< 3) and were ignored. An investigation of the variability index was carried out for each individual data set and stars found to be variable in three of the four bandpasses from each set of short and long exposure times were judged to be variable candidates. This method left a very small fraction of the cluster stars remaining as variable candidates (Fig. 6.1). The threshold value of three was chosen by inspecting these plots for each bandpass and looking for a value where stars began to consistently appear deviant. Nearly fifty stars were investigated based on their variability index values and ten based on the ISIS results. The ten ISIS stars were all common with the DAOMASTER stars.
All variable candidates were then calibrated by the variable star calibration method discussed in Chapter 4. At this point, a plot of magnitude vs. heliocen- tric julian date (HJD) was prepared for each candidate. Throughout this study, the
HJD values for each observation were trimmed down to remove the leading digits that were identical for all images. For example, the HJD of 2453581.83910373 has been reduced to 81.83910373 because all images used in this study had the leading digits 37
Figure 6.1: The DAOMASTER variability index is plotted against V magnitude for the short exposure, V data set. The horizontal line represents the threshold value of 3 which a star had to be above to be considered variable. Plots of this type were prepared for every individual data set. Stars that displayed a variability index greater than 3 in at least three filters were considered variable star candidates. 38
Figure 6.2: A plot of the calibrated magnitudes of each measurement vs. HJD for a variable star (s178). X’s mark B filter observations, empty circles mark V, filled squares mark R and filled triangles mark I. The HJD’s plotted are the trimmed values. in common. A visual inspection of these plots was the final determining vote as to whether each star was variable or not. Figure 6.2 shows a sample plot for a variable star, while Figure 6.3 shows a non-variable star. A variable star’s plot shows very erratic magnitude values due to the star being imaged at differing phases of its light cycle. A non-variable star’s plot is easily identified because it simply shows little or no variation in magnitude beyond the typical scatter left following calibration. The variable star candidates that were shown to not be variable stars typically showed more scatter than stars with lower variability indices. It is suspected that this scatter is what placed the stars’ variability indices above the threshold value. This suggests that a slightly larger threshold value may be better suited for selecting candidates.
Only 10 stars were judged to truly be variable stars.
Next, a computer program was implemented to attempt to determine the period of each variable star. The program, designed by Layden et al. (1999), fits the observed 39
Figure 6.3: A plot of the calibrated magnitudes of each measurement vs. HJD for a non-variable star (s66). X’s mark B filter observations, empty circles mark V, filled squares mark R and filled triangles mark I. The HJD’s plotted are the trimmed values. data to ten variable star template curves over a specified range of periods. The resulting χ2 fit value is then plotted versus period for each template and the location of the minimum is chosen as the period. Each filter was examined individually with this program and a period was determined for each one with a precision of 0.00001 days. The period values for each filter were consistently in good agreement when the program made a reliable fit, which was only when analyzing an RRL star. A straight average was calculated to form a single period for each star.
A second program by Layden (1998) was used next to attempt to form light curves for each variable star. This program also works by fitting the data to ten light curve templates, though this time the period found by the previous program is used as input. The program computes an RMS value for each template fit and presents the four best fits to the user to select the template that best fit the data points.
The selection is done based on the visual appearance of each fit to the data and the 40
RMS value computed for each fit. In all cases where a reliable fit was made, the fit that appeared the best visually had the lowest RMS value. Next, the program takes the selected fit and computes several characteristic values for the light curve. These values include the intensity mean magnitude, amplitude, and the color at minimum light. A final light curve is then generated for each star in each filter.
All light curves created in this study were drawn from the long exposure data sets for each filter. The decision to use the long exposures rather than the short ones was made because the HB had a higher signal to noise ratio in the long exposures and did not appear saturated. The creation of light curves from the short exposure data sets had to be set aside due to time constraints. Also, the addition of data points derived from the short exposure images to those from the long images would probably have contributed more scatter due to electronic noise effects than useful signal.
6.1 RR Lyrae Stars
Six stars were found to be RR Lyrae type variables. Stars V1-V3 had previously been documented by Rosino (1949) and the remaining three were undocumented. All three known RRL stars were of the RRab class, while the three newly discovered ones are all RRc type. This was not an unexpected result since RRc stars have smaller amplitudes and shorter periods than RRab types. These characteristics make them more difficult to identify, particularly with the photographic methods that were available to Rosino.
The light curves of star s161 show that it is an RRab class variable star. The amount of scatter around the light curve fit is minimal. It displays normal behavior in the V, R and I bands, but the shape of the curve deviates in the B band. This 41 is the result of the light curve fitting program finding a different best fit template in the B band than the other three bands. Because of this odd behavior in the B band, no reddening value (E(B-V)) was calculated from this star that included the B band data.
The light curves of star s212 show that it too is an RRab class variable star. It displays normal behavior in the B, V and R bands and is deviant in the I band. The best fit template found by the light curve fitting program for the I data is that of an
RRc class star. It was concluded that this fit is erroneous and the star is an RRab type variable despite the I band finding. Due to the deviant I band, no reddening value (E(V-I)) was calculated from this star using I data.
Star s178 showed an RRab light curve in all four bandwidths. The curve fits are all very well behaved and show little scatter. Reddening values were calculated from these light curves using data from the B, V and I bandwidths.
The light curves of star s184 show that it is an RRc class variable. The same RRc template was found to best match the V, R and I data and a differing one was found to match the B. The fact that the B light curve shows a different point of minimum light than the other three curves suggests that the fit for the B band data was faulty.
The root of this error can lie within our data set, the calibration or the light curve
fitting.
Star s181 shows a small amount of scatter around the light curve fits for the V,
R and I band data for this RRc type variable. Again, for this star the B light curve was created using a different template than the other three bands. It is unclear why the same error occured twice.
The light curves of star s193 make it clear that it is an RRc type variable star.
A moderate amount of scatter is seen around the template fits, though not enough 42
Table 6.1: Photometry of RR Lyrae Stars ID Name Type
to hinder its classification. The same template was found to most accurately match all four bandpasses for this star.
All six RRL stars were determined to be cluster members, as opposed to field stars, based on their location on the CMD. When plotted, all six RRL stars fall on the horizontal branch in a roughly linear, grouped pattern (Fig. 6.4 and 6.5). The grouping indicates the location of the instability strip for this cluster. It is easily seen that the RRab stars lie toward the redder (cooler) side of the horizontal branch, while
RRc stars lie toward the blue (hotter) side. No field RRL stars were detected in this study.
The amplitude and period values documented by Rosino for the known RRL’s were found to match closely the values found here. Since the period of variable stars can change with time, slight differences in these values were not unexpected. Details for the individual stars can be found in Tables 6.1 and 6.2 and the individual light curves can be viewed in Figures 6.6 - 6.11.
It is notable that the light curves of s161 and s178 exhibit some scatter at their points of maximum light, which may be evidence of the Blazhko effect. The Blazhko effect is a well-documented phenomenon in RRL stars that displays itself as a periodic modulation of the light curve shape and amplitude on a time scale several times longer 43
Figure 6.4: A CMD of M30 with detected variable stars shown. Filled triangles mark RRab stars, filled squares mark RRc stars, the solid pentagon marks a foreground SS Cygni star (V4), the hollow square (s65) and asterisk (s27) mark suspected Ceh- peids and the hollow pentagon marks a suspected δ Scuti. Interstellar extinction and reddening have not been corrected for in this diagram. 44
Figure 6.5: A closeup view of the horizontal branch of the CMD. Filled triangles represent RRab stars, filled squares represent RRc stars, the hollow square represents a suspected Cehpied. Interstellar extinction and reddening have not been corrected for in this diagram. 45
Figure 6.6: Light curves for the RRab star s161 (V1) are shown in each filter. The B light curve displays atypical behavior near the point of minimum light, which may be due to the increased scatter of points in that part of the plot. This star was not used in the E(B-V) calculation for this reason.
Table 6.2: Data for RR Lyrae Stars ID Name (B V )min (V I)min B Amp V Amp R Amp I Amp − − s161 V1 0.402 0.757 1.119 0.889 0.678 0.594 s212 V2 0.445 0.643 1.284 1.019 0.758 0.656 s178 V3 0.467 0.708 1.409 0.962 0.758 0.590 s184 0.225 0.555 0.699 0.509 0.368 0.288 s181 0.335 0.585 0.716 0.417 0.335 0.263 s193 0.195 0.491 0.723 0.315 0.269 0.246 46
Figure 6.7: Light curves for the RRab star s212 (V2) are shown in each filter. The light curve fitting program found an RRc type curve to be best suited to match the I band data and RRab curves for the other filters. Despite this, it was concluded that this star is of the RRab type. 47
Figure 6.8: Light curves for the RRab star s178 (V3) are shown in each filter. This star may be undergoing Blazhko cycling. 48
Figure 6.9: Light curves for the RRc star s184 are shown in each filter. The point of minimum light in the B band data was found to not coincide with the other filters. This may be because a slightly different light curve shape was found to best fit the B data than the other three filters. The root of this behavior lies either in our data set, the calibration or the light curve fitting. 49
Figure 6.10: Light curves for the RRc star s181 are shown in each filter. Once again the B observations were matched to a differing light curve shape with a differing point of minimum light. 50
Figure 6.11: Light curves for the RRc star s193 are shown in each filter. 51 than the period of normal variability (Fig. 6.12). There is no correlation between the normal variability period and the Blazhko period.1 The cause of the modulation remains unexplained, though it is thought that the effect may be the result of a mixing of pulsational modes and/or that it may be related to magnetic cycles interacting with the star’s rotation. Additional observations over a sufficiently long time scale would be necessary to properly determine whether or not these stars are undergoing Blazhko cycling (Smith 1995).
6.2 Other Variable Stars
Of the remaining four variable stars found in this study, only one has previously been documented as a variable star. Star s5474 was originally discovered as being variable in the same study by Rosino as the three RRab stars. It was later identified as a cataclysmic variable (CV) by Naylor et al. (1989) and then as a foreground star one year later in a paper by Machin et al. (1990). Clement (2001) lists it as
V4, a SS Cygni type variable - an interacting binary system composed of a white dwarf primary and a main sequence secondary star that is transferring mass into an accretion disk producing semi-regular dwarf novae. Our analysis shows this star to be variable and nearly on the main sequence of the cluster. From this we cannot make any conclusions about the cluster membership of this binary system, but since a typical main sequence star cannot be variable, the conclusion that the variability observed is due to a very faint companion star producing dwarf novae outbursts is reasonable.
A high quality light curve could not be created for s5474 because our sample 1The range of observed Blazhko periods spans from 10.9-533 days. 52
Figure 6.12: A visual example of the Blazhko effect observed in RR Lyrae stars. The hollow circles and filled circles represent measurements made during differing phases of the Blazhko cycle. It is easily seen that amplitude and light curve shape change with time. This plot was taken from RR Lyrae Stars by H. A. Smith (1995). 53 did not provide enough data points to capture the variability of a non-periodically varying star. Also, the light curve fitting program did not contain a template for this type of variable star, so a light curve could not be formed by “folding” the data over as was done for the RRL stars. Typically for a star of this type the variability is best seen on a plot of magnitude vs. HJD. Our data set simply does not have enough points to form a plot of this type with enough coverage to identify the star properly.
Also, the reliability of the photometry for this star is questionable due to its location very near to a very bright star that appeared saturated in all images. The magnitude vs. HJD plot for this star can be found in Figure 6.13.
Star s65 appears to be a Type II Cepheid. Type II Cepheid variables are periodic and radially pulsating giant stars with typical periods ranging anywhere between 0.75 and 40 days. Their mass is thought to be on the order of 0.6 solar masses and they are commonly found in globular clusters. The conclusion that this star may be a Type
II Cepheid was reached based on several factors. First, on the CMD the star falls within the instability strip defined by the RRL stars and appears more luminous than the RRL’s by approximately 1 magnitude (Fig. 6.4 and 6.5). Type I Cepheids are typically 2.5 to 6.5 magnitudes brighter than RRL stars, but since Type II Cepheids have a lower mass than their type I counterparts, their magnitudes should be expected to be fainter and closer to those of RRL stars. The observed period of roughly 15 days falls within the expected range for a Type II Cepheid. Also, a plot of magnitude vs. HJD appears to show a sinusoidal shape (Fig. 6.14). This is the expected shape for the light curve of a Cepheid with a period in the longer range of the available spectrum, though it is not impossible for a shorter period Cepheid to have this shape as well (Sterken & Jaschek, 1996). The light curve fitting programs could not find a period or create a light curve for this star because the data did not match any of the 54
Figure 6.13: Magnitude vs. HJD for the star s5474 (V4) is plotted. This star is documented as being a foreground SS Cygni type cataclysmic binary system. No conclusion about the classification of this star was made in this study. X’s mark B filter observations, empty circles mark V, filled squares mark R and filled triangles mark I. The HJD plotted is the HJD of each observation with the leading digits trimmed. 55 light curve templates used by these programs.
There are factors that should be noted that draw caution to the classification of s65 as a Type II Cepheid. Most obvious is the fact that little more than one cycle was imaged. The data contained in the 2003 data set may be very helpful in developing an estimate of whether the long-term variability of this star is indeed simply periodic or whether we merely observed one oscillation in a complex pattern. Unfortunately, time constraints prohibited the inclusion of the 2003 data in the analysis for this thesis. The relatively small number of images contained in the 2003 data set might also have proven to be of minimal usefulness for this purpose as well. The amplitude also appears small compared to the normal amplitude of 0.9 magnitudes in V. Finally, the photometry of this star is of questionable quality because its brightness brought it near the saturation level on the CCD chip. If a more definitive classification of this star is desired, additional observations will be necessary over several cycles.
Star s27 may also be a Type II Cepheid. It appears brighter than the RRL stars by approximately two magnitudes in V, but displays a small amplitude as seen in star s65. The brightness of s27 compared to the RRL put it at a location on the CMD where it can conceivably be a Type I Cepheid. If s27 is a cluster member, it is unlikely to be a Type I Cepheid because Type I Cepheids are of much higher mass than those of Type II. It would be unlikely to find high mass Cepheids in the same cluster as low mass RRL. This is because the time spent on the HB is short compared to the lifetime of a globular cluster. As a result, it is assumed that most stars on the HB at any time were of roughly the same main sequence mass with their differing masses being attributed to mass loss in the RGB phase (Smith 1995). By this rationale, a massive Type I Cepheid should not exist in M30 at this phase of its evolution. This, combined with s27’s suspected period of approximately 10 days and location on the 56
Figure 6.14: Magnitude vs. HJD for the star s65 is plotted. This star is suspected to be a type II Cepheid with a period of approximately 15 days. X’s mark B filter observations, empty circles mark V, filled squares mark R and filled triangles mark I. The HJD plotted is the HJD of each observation with the leading digits trimmed. 57
CMD in the instability strip above the HB make it likely that this star is a Type II
Cepheid.
Star s1045 is a suspected δ Scuti type variable. This conclusion was drawn based on the star’s location on the CMD in the instability strip at a magnitude approximately 2.5 magnitudes fainter than the RRL stars. This places the star just inside the range of absolute visual magnitudes for δ Scutis, which spans 0 to +3.0. A plot of magnitude vs. HJD for s1045 does not show any discernable light curve shape
(Fig. 6.16). This comes as no surprise since δ Scutis must have periods of 0.3 days or less and change their light curve shape on the timescale of mere hours. Our data acquisition and light curve fitting programs were not designed to properly work with stars of this nature, thus a complete light curve could not be formed. However, the plot does show that the amplitude is within the normal limits for δ Scuti stars of a few thousandths of a magnitude to 0.8 in the V band.
The variable stars V5-13 documented by Terzan (1968) and Terzan & Rutily
(1975) were not found to be variable in this study. All of these variable stars were unclassified by the authors and no light curves could be found. This study concluded that stars V5-13 are not variable stars. 58
Figure 6.15: Magnitude vs. HJD for the star s27 is plotted. This star is suspected to be a Type II Cepheid with a period of approximately 10 days. X’s mark B filter observations, empty circles mark V, filled squares mark R and filled triangles mark I. The HJD plotted is the HJD of each observation with the leading digits trimmed. 59
Figure 6.16: A plot of magnitude vs. HJD is shown for star s1045, a suspected δ Scuti. X’s mark B filter observations, empty circles mark V, filled squares mark R and filled triangles mark I. The HJD plotted is the HJD of each observation with the leading digits trimmed. 60
CHAPTER 7
Discussion
7.1 Reddening and Extinction
In its long journey from the halo of the galaxy to our observation point, the light of M30 passed through light years of dust-filled space. The dust in the interstellar medium affects the starlight in two ways: it dims and reddens it. Both effects are the result of two separate ways in which the interstellar medium interacts with the light passing through it. First, the dust scatters and absorbs some photons away from their normal path. This is observed as a dimming of the star since fewer photons can be gathered along the line of sight than were originally present upon leaving the cluster. Second, the typical size of a dust grain is such that short wavelength light is readily absorbed or scattered while longer wavelengths pass by nearly unaffected.
This energy absorbed by the dust is then reemitted as infrared radiation, some of which is directed along our line of sight and detected. The net result of this effect is that blue light is essentially converted into infrared light. It is observed that the extinction and reddening are related by the equation, Av = 3.1 E(B V ), where Av ∗ − represents extinction in V and E(B V ) represents the excess in the (B V ) color. − − For RRab stars, Sturch (1966) and Blanco (1992) demonstrated that the redden- ing could be calculated based on the stars’ (B V ) color at minimum light. Blanco − 2 presented the equation, E(B V ) =< B V >min +0.0122 ∆S 0.00045 (∆S) − − ∗ − ∗ − 0.185 P 0.356, for calculating interstellar reddening assuming that the period (P), ∗ − intrinsic color at minimum light (< B V >min) and the metallicity index ∆S are − all known. This calculation was performed for each RRab star in our study (Ta- 61 ble 7.1). Due to the odd behavior of its B light curve, the reddening value for s161 was not included in the reddening calculation for the cluster. The results for the other two RRab stars were averaged to provide a single reddening estimate based on this method.
In order for the above calculations to be performed properly, an accurate metallic- ity value for M30 had to be used. Our data set could not yet provide any metallicity measurements, so the literature for M30 was consulted and six reliable metallicity measurements were gathered (Table 7.2). The documented metallicities have a range of 0.21 with a standard deviation of σ = 0.091. A straight average of the values yielded a value of [Fe/H]= 2.02. The relationship [Fe/H]= 0.02( 0.34) 0.18( 0.05)∆S, − − ± − ± was conveniently supplied by Blanco in his article for conversion. A value of ∆S =
11.11 0.39 was found using this method. ± To test the sensitivity of our reddening results to our adopted metallicity value,
∆S values were also calculated for the most metal poor and metal rich cases. The metallicity of [Fe/H]=-2.12 yielded ∆S = 11.67 and E(B-V)= 0.056, an increase of
0.01 from the results with our averaged metallicity. For the more metal rich case, the metallicity of [Fe/H]= 1.91 converted to ∆S = 10.50 and gave E(B-V)=0.054, − a decrease of only 0.01. The small changes observed in these sample cases display that even though our choice of metallicity value impacts our reddening and extinction estimates, the effects of us being mistaken by a factor of 1 dex are minimal. ≈ A similar reddening calculation was also performed based on the RRab’s (V-
I) color at minimum light (Table 7.1). This method was derived by Guldenschuh,
Layden, Wan et al. (2005) and is independent of metallicity. In this calculation the results from s212 were not included due to its erroneous light curve (Chapter 6.1).
The results of this method were converted to E(B V ) values, which is the common − 62
Table 7.1: Reddening Values from RRab Stars ID Name E(B-V)Blanco E(V-I)Guldenschuh E(B-V)Guldenschuh s161 V1 -0.011 0.177 0.110 s212 V2 0.048 0.063 0.039 s178 V3 0.062 0.128 0.080
Table 7.2: Metallicity Values [Fe/H] Source -2.12 Harris, 1996 -2.11 Minniti et al., 1993 -2.05 Zinn & West, 1984 -2.03 Salaris & Weiss, 1997 -1.92 Carretta & Gratton, 1997a -1.91 Carretta & Gratton, 1997b
system.1 Two additional reddening values were acquired from other studies of M30
(Harris 1996, Schlegel, Finkbeiner, Davis 1998). The results of each method can be found in Table 7.3. The range for these values is 0.047 and their standard deviation is 0.019. The final reddening value settled upon was the average of the four values,
E(B V ) = 0.053 0.010, which is equivalent to E(B I) = 0.142 0.027.2 The − ± − ±
final extinction value was calculated to be Av = 0.165 0.031. ± Both the reddening and extinction values were applied to all star magnitudes
1 Binney & Merrifield (1998) gave the relations AV = 3.1 E(B V ) and E(V I) = AV AI , 1.000 AV 0.482 AV ∗ − E(V I) − − where AV = ∗ and AI = ∗ , which yielded E(B V ) = − AV AI 1.606 2This conversion was done in the same manner as the one− for E(V I). −
Table 7.3: Reddening Values E(B V ) Source − 0.077 equations of Guldenschuh, Layden, Wan et al., 2005 0.055 equations of Blanco, 1992 0.051 Schlegel, Finkbeiner, Davis, 1998 0.030 Harris, 1996 63 to produce a final CMD. The reddening value was applied to the color of each star and produced a shift of the entire plot toward the blue. Reddening was assumed to be equal over the entire face of the cluster. This was assumed because the cluster’s location in the halo at galactic coordinates b = 27.18, l = 46.83 puts it well away − from both disks and the dust they contain. Also, since the reddening could only be determined for three points it would have been impossible to apply a differential reddening method as was done by Sarajedini & Layden (2003). The extinction was applied to the V magnitude and produced an upward vertical shift on the plot toward brighter values. The final dereddened CMD can be seen in Figure 7.1.
7.2 Distance
In addition to being a tool for deriving reddening values, RRL stars are also valuable in making distance measurements. This is possible because RRL stars have a known absolute visual magnitude (Mv(RR)), which enables them to be used as standard candles. In a 1998 article Chaboyer compared six methods of observing
Mv(RR) and concluded that the equation, Mv(RR) = (0.23 0.04) ([Fe/H]+1.6) + ± ∗ (0.56 0.12), was the most appropriate. The value of [Fe/H]= 2.02 was adopted for ± − this calculation, which yielded Mv(RR) = 0.46 0.121. ±
It was also necessary to compute a value for the visual magnitude (mv(RR)) in order to be able to measure the distance to the cluster. For this the six mean visual magnitudes of the RRab and RRc stars were averaged together. The resulting extinction corrected value was mv(RR) = 14.964 0.037. ± These two values were then used in the standard distance modulus formula,
µ = (m M) = 5 log(d) 5, to calculate the distance modulus (µ) and the distance − ∗ − 64
Figure 7.1: The CMD that has been corrected for reddening and extinction is plotted. A shift is visible when compared to the uncorrected CMD. Variable stars have been dereddened based on their mean magnitude values. Filled triangles mark RRab stars, filled squares mark RRc stars, the solid pentagon marks a foreground SS Cygni star, the hollow square and asterisk mark suspected Cepheids and the hollow pentagon is a suspected δ Scuti. 65 to M30. A value of µ = 14.504 0.127 was found with the corresponding distance ± of d = 7.958 0.147 kpc. These values are in excellent agreement with the values ± quoted by Harris (1996) of µH = 14.62 and dH = 8.0 kpc. We wished to test the sensitivity of our distance measurements to our adopted metallicity value. To do this we computed Mv(RR) for the most metal poor and metal rich cases, similarly to what was done to test our reddening results. For the most metal poor case, with [Fe/H]= 2.12, µ was seen to increase by 0.019 and the − distance to increase by 0.072 kpc. In the most metal rich case, with [Fe/H]= 1.91, − µ decreased by 0.029 and the distance decreased as well by 0.105 kpc. These results exemplify that our choice of metallicity affects the distance measurements we compute by a factor smaller than the uncertainty in our computations.
7.3 Age
An age estimate was made by comparing the appearance of the reddening and extinction corrected CMD with theoretical isochrones of globular clusters. For this we adopted the isochrones presented by Girardi et al. (2002). These isochrones were computed for set metallicity values, so we chose the two lowest available values of
Z=0.0001 and Z=0.0004, which correspond to [Fe/H]= 2.28 and [Fe/H]= 1.68 re- − − spectively, because they bracket our adopted [Fe/H] value. The isochrones were cal- culated by Girardi et al. to represent absolute visual magnitudes. Because of this it was necessary to adjust for the cluster’s distance by shifting the isochrones to fainter magnitudes by the value of the distance modulus. A small adjustment of 0.11 mag- nitude was then made to adjust the isochrones to most accurately match the main sequence on the CMD. This adjustment was within the bounds of the acceptable error 66 value of the distance modulus. No adjustment was made for the color term on the x-axis.
The CMD plots with overlaid isochrones can be found in Figures 7.2- 7.6. These plots were inspected visually and the isochrone that matched the CMD’s overall star distribution most accurately was selected as the best candidate. The quality of each isochrone fit was measured based on how well it matched up with the star distribution at the main sequence turn off (MSTO), the horizontal branch (HB), the sub-giant branch (SGB), and the red giant branch (RGB). More weight was applied to the
fitting of the MSTO and HB than was to the SGB and RGB. This analysis of the isochrone fits showed that the most appropriate metallicity value was Z=0.0001 with an age of 15.8 1.8 Gyr. Neither fit properly matched the RGB, suggesting that an ± intermediate metallicity value, ideally [Fe/H]= 2.02, would be most appropriate. − The associated error for the age was determined by shifting the CMD by a factor equal to the reddening and extinction errors as well as shifting the isochrones by the distance modulus error. The lines representing 14.1 Gyr and 17.8 Gyr were found to match most appropriately in the most extremely shifted situations.
The age found here for M30 is in disagreement with the results from other studies’ conclusions. For example, the Wilkinson Microwave Anisotropy Probe (WMAP) found the age of the universe to be 13.7 Gyr (http://map.gsfc.nasa.gov). Since it is currently the consensus within the field that the WMAP measurements are accurate, it seems unlikely that the age of M30 determined by this study is accurate. The source of the discrepancy is the result of our having used isochrones which predate current cosmological models. Also, the latest cosmological models have not yet been used to create a revised relationship between MV (RR) and [Fe/H]. Since our age determination is strongly affected by our MV (RR) value, it is expected that this will 67
Table 7.4: Oosterhoff Type Cluster < Pab > < Pc > [Fe/H] n(c)/n(ab + c) Oo I 0.55 0.32 1.0>[Fe/H]> 1.8 0.17 Oo II 0.64 0.37 − 2.0>[Fe/H]− 0.44 M30 0.6969 0.4169 − 2.02 0.50 − alter age estimates as well.
7.4 Oosterhoff Type
It is common practice for globular clusters to be classified by their Oosterhoff type. All Galactic globular clusters have been seen to fall into either the Oosterhoff
I or II categories. The categories are defined based on mutually exclusive trends observed for three parameters; period, metallicity and the ratio of RRc stars over the total number of RRL stars present (Smith 1996). Table 7.4 shows the general classification values for both cluster types and the values observed for M30 in this study. It was concluded that M30 is of Oosterhoff II type by this study.
It is worth noting that prior to this study the ratio of RRc variables to the total number of RRL within M30 was zero. This value was not in agreement with the typical ratio seen in Oosterhoff II clusters of n(c) 0.44 . Now, with the discovery n(ab+c) ≈ of three new RRc variables by this study, the ratio has increased to 0.50. Because of this new finding, M30 now classifies as an Oosterhoff II type cluster with respect to all of the Oosterhoff parameters. 68
Figure 7.2: Isochrones for Z=0.0001 are overlaid on the dereddened CMD. From left to right (near the MSTO) the lines represent 10.0 Gyr, 11.2 Gyr, 12.6 Gyr, 14.1 Gyr, 15.8 Gyr and 17.8 Gyr. 69
Figure 7.3: Isochrones for Z=0.0001 are overlaid on the main sequence. The leftmost line corresponds to an age of 14.1 Gyr, the center line to 15.8 Gyr and the rightmost to 17.8 Gyr.
Figure 7.4: Isochrones for Z=0.0001 are overlaid on the horizontal branch. The lowest line corresponds to an age of 14.1 Gyr, the center to 15.8 Gyr and the uppermost to 17.8 Gyr. 70
Figure 7.5: Isochrones for Z=0.0004 are overlaid on the dereddened CMD. From left to right (near the MSTO) the lines represent 10.0 Gyr, 11.2 Gyr, 12.6 Gyr, 14.1 Gyr, 15.8 Gyr and 17.8 Gyr. 71
Figure 7.6: Isochrones for Z=0.0004 are overlaid on the main sequence. From left to right (near the MSTO) the lines represent 10.0 Gyr, 11.2 Gyr, 12.6 Gyr, 14.1 Gyr, 15.8 Gyr and 17.8 Gyr. 72
CHAPTER 8
Conclusion
We present photometry of the metal-poor globular cluster M30. The main pho- tometry was gathered using DAOPHOT and the accompanying software packages.
ISIS was used to help ourselves form a second opinion for which stars were variable stars. Following a careful calibration, a color-magnitude diagram and light curves for variable stars were created. Three previously documented RR Lyrae stars were found in our photometry as well as three newly discovered ones. Four additional variable stars, three of them newly discovered, were found and classifications were attempted based on the data available to us.
We assumed a metallicity of [Fe/H]= 2.02 for the cluster and used this value − in performing calculations. The three RRab variables showed a foreground red- dening of E(B-V)= 0.053 0.010, which corresponded to an extinction value of ±
AV = 0.165 0.031. Using all six RR Lyraes, a distance modulus of µ = 14.504 0.127 ± ± was derived and from this value a cluster distance of 7.958 0.147 kpc was determined. ± This distance determination was in excellent agreement with previously derived val- ues and serves to increase our confidence in the mapping of the Galaxy using this method. Isochrones overlaid on a color-magnitude diagram corrected for reddening and extinction yielded a cluster age of 15.8 1.8 Gyr. M30 was also shown here to ± n(c) clearly be an Oosterhoff II type cluster. In this classification, the ratio n(ab+c) = 0.50 was shown for the first time to be in agreement with the typical ratio observed in
Oosterhoff II clusters.
Most of the conclusions drawn in this study are dependent in some way on the metallicity value we chose to adopt. An inspection of the equations presented show 73 that all calculated cluster parameters presented here are a function of our chosen metallicity value in some way. It was shown that if we assumed the most metal poor case of [Fe/H]= 2.12, E(B-V) increased by 0.01 and the distance modulus increased − as well by 0.019. For the more metal rich case of [Fe/H]= 1.91, E(B-V) was shown − to decrease by 0.01 and the distance modulus to decrease by 0.029. These effects were within the limits of the uncertainties associated with each measurement and when applied to the isochrone fits did not change the age detmination.
The CMD created by this study is of exceptional quality. The range of magni- tudes covered on the CMD is larger than any available in the literature. Also, the small amount of scatter and the well defined evolutionary states, particularly the main sequence turn-off and the horizontal branch, make it an ideal CMD for age es- timation. When new isochrones are generated and a new relation between MV (RR) and [Fe/H] is derived that are in agreement with the latest cosmological models, this
CMD would be an ideal tool for determining an updated age for M30.
Had the SIM key project continued as planned, several of the measured values cited in this study would have been adopted, namely the mean RRL magnitudes in all bandpasses. These mean magnitudes would have served as apparent magnitudes in each filter, which in conjunction with the parallax distances derived from the SIM observations, could have been used to calibrate the absolute magnitude functions for RRL stars. The knowledge of these functions would have greatly increased the confidence level in distance measurements made to RRL stars by photometric means, which span further than the reach of SIM.
Since the writing of this thesis was completed, the additional observations of M30 and Landolt standard stars we requested thorough the NOAO have been approved.
The additional observations will be available for analysis in late 2007. Our plan is 74 to use this data set to create a set of standard stars in the field of M30 for B, V, R and I bandpasses. These standard stars will be used to perform a reliable calibration of our main data set and conclusively resolve the questions surrounding the non- linear behavior of the SITe3 CCD for all four bandpasses. In addition, the possible dependence of the CCD sensitivity on X and Y position will be resolved with this new standard set. Also, these new observations will provide a large set of standard stars in the R band, which will enable an accurate calibration to be computed for the
first time for the images taken in that filter.
Further work can also be done to properly identify the three newly discovered variable stars whose classifications remain ambiguous. The improved calibration we expect to obtain from the NOAO data may enable us to use all of the images we have available to identify these stars more precisely (Table 2.1). The inclusion of all images would provide approximately 50% more data that could be used in variable star characterization. 75
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