PROPERTIES OF BRIGHT VARIABLE STARS IN UNUSUAL METAL RICH
CLUSTER NGC 6388
Gustavo A. Cardona V.
AThesis
Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
August 2011
Committee:
Andrew C. Layden, Advisor
John B. Laird
Dale W. Smith ii
ABSTRACT
Andrew C. Layden, Advisor
We have searched for Long Period Variable (LPV) stars in the metal-rich cluster NGC
6388 using time series photometry in the V and I bandpasses. A CMD was created, which displays the tilted red HB at V = 17.5 mag. and the unusual prominent blue HB at V = 17 to 18 mag. Time-series photometry and periods have been presented for 63 variable stars, of which 30 are newly discovered variables. Of the known variables nine are LPVs. We are the
first to present light curves for these stars and to classify their variability types. We find 3
LPVs as Mira, 6 as Semi-regulars (SR) and 1 as Irregular (Irr.), 18 are RR Lyrae, of which we present complementary time series and period for 14 of these stars, and 7 are Population
II Cepheids, of which we present complementary time series and period for 4 of them. The newly discovered variables are all suspected LPV stars and we classified them, using time series photometry and periods, as Mira for 1 star, SR for 15 stars, Irr for 7 stars, Suspected
Variables for 7 stars, out of which there are 3 very bright stars that could have overexposed the CCD, with no definite borderline between the SR and Irr stars. Once classified we used probable distance for the cluster center and location on the CMD to establish possible membership, which left us with 63 possible cluster members, but the crowdedness of the cluster and the fact that the cluster is located near the bulge of the Milky Way prevents us from establishing a better certainty for its membership. iii
Dedicado a mis padres Humberto Cardona y Magaly Velasquez, por haberme introducido el “Cosmos” y por ensa˜narme que nunca hay l`ımite para lo que
queremos lograr mientras uno no deje de so˜nar iv
ACKNOWLEDGMENTS
First and foremost, my utmost gratitude to my advisor, Dr. Andrew Layden, for his patience, enthusiasm, encouragement and countless amount of hours he spent imparting knowledge while guiding me through this project. I would also like to thank the faculty and staffat the Physics and Astronomy department in BGSU for their support for the past two years.
Special gratitude to my classmates,and expcially to Moe Abbas, my partner in crime, whose help while we raked through innumerable journals, books and across many obstacles to understand the material so we could apply it to our thesis, will never be forgotten.
Words fail to express my appreciation to my parents, Humberto and Magaly, and my two best friends, my wife, Soo Choi, and my brother, Juan David Cardona, for their unwavering support and faith in what I was doing, and because each day they reminded me of the fact that following your dreams is never the wrong path to undertake.
Finally to my friends and family, because they were all uniquely important in the suc- cessful realization of my thesis. v
TABLE OF CONTENTS
Page
CHAPTER 1. INTRODUCTION ...... 1
CHAPTER 2. PROCESSING ...... 8
2.1 Observations ...... 8
2.2 Calibrations ...... 9
2.3 Combining...... 14
CHAPTER 3. PHOTOMETRY ...... 17
3.1 ISIS ...... 18
3.1.1 Setting up for ISIS ...... 18
3.1.2 Running ISIS ...... 19
3.2 DAOPHOT ...... 25
3.2.1 SettingupforDAOPHOT ...... 25
3.2.2 RunningDAOPHOT ...... 26
CHAPTER 4. CALIBRATION ...... 37
4.1 Standard Stars ...... 37
4.2 Variable Stars ...... 47
CHAPTER 5. COLOR MAGNITUDE DIAGRAM ...... 51
5.1 Isochrones ...... 56
CHAPTER 6. VARIABLE STARS ...... 59
6.1 Variability Detection ...... 59
6.1.1 Variability detection with ISIS ...... 59
6.1.2 VariabilitydetectionwithDAOPHOT ...... 59
6.2 Magnitude vs. time Detection ...... 63
6.3 Variable Properties ...... 69
6.4 Known Variables ...... 70 vi
6.4.1 Comparison with LEM ...... 72
6.4.2 Comparison with PSCS ...... 83
6.4.3 Comparison With Corwin et al...... 106
6.5 NewFoundVariables ...... 113
CHAPTER 7. CLUSTER MEMBERSHIP ...... 142
7.1 Projected distance from the center ...... 142
7.2 Location on the CMD diagram ...... 143
CHAPTER 8. CONCLUSIONS ...... 150
8.1 Summary ...... 150
8.2 Future Research ...... 154
REFERENCES ...... 158 vii
LIST OF FIGURES
Figure Page
2.1 Dark current across the CCD ...... 11
2.2 Comparison of frame after calibration ...... 15
2.3 Comparison between good and bad frame stacking ...... 16
3.1 Comparison between original and trimmed image ...... 19
3.2 Convolution of two square pulses ...... 22
3.3 Comparison of two star profiles ...... 24
3.4 PHOT task values ...... 28
3.5 Subtracted image ...... 32
3.6 Montage Image ...... 35
4.1 Carreta et al. CMD with studied stars ...... 40
4.2 Comparison between Carreta et al. and Stetson standard stars ...... 41
4.3 Dependence of calibrated data ...... 48
4.4 V4locatedintheCMD ...... 49
5.1 Color Magnitude Diagram for the whole field ...... 52
5.2 Tidal radius in the master frame ...... 54
5.3 SelectiveCMDforNGC6388...... 55
5.4 Isochrones plotted over CMD ...... 58
6.1 ISIS var.fits image ...... 60
6.2 Variability index for Season 3 ...... 62
6.3 Zoomed-in variability index ...... 62
6.4 θ vs. Period graph ...... 64
6.5 Folded curve using θ close to 1 ...... 65
6.6 Folded curve using θ close to 1 ...... 65
6.7 Sample light curve ...... 67 viii
6.8 chi2 vs trial periods for template fitting method ...... 67
6.9 Foldedcurveusingtemplatefittingmethod ...... 68
6.10 CandidatevariablestarsfoundusingISIS ...... 71
6.11 CandidatevariablestarsfoundusingDAOPHOT ...... 71
6.12 VariableV2lightcurve ...... 74
6.13 VariableV3lightcurve ...... 75
6.14 VariableV4lightcurve ...... 76
6.15 VariableV5lightcurve ...... 77
6.16 VariableV6lightcurve ...... 78
6.17 VariableV7lightcurve ...... 79
6.18 VariableV8lightcurve ...... 80
6.19 VariableV9lightcurve ...... 81
6.20 VariableV12lightcurve...... 82
6.21 VariablestarscomparedwithPSCS ...... 84
6.22 Light curve vs. Folded curve for RRLyrae ...... 85
6.23 Difference in periods for sample RRL ...... 85
6.24 Variable17lightcurve...... 86
6.25 Variable18lightcurve...... 87
6.26 Variable21lightcurve...... 88
6.27 Variable22lightcurve...... 89
6.28 Variable23lightcurve...... 90
6.29 Variable26lightcurve...... 91
6.30 Variable26lightcurvewithPSCSperiod ...... 91
6.31 Variable27lightcurve...... 92
6.32 Variable28lightcurve...... 93
6.33 Variable29lightcurve...... 94 ix
6.34 Variable30lightcurve...... 95
6.35 Variable31lightcurve...... 96
6.36 Variable35lightcurve...... 97
6.37 Variable36lightcurve...... 98
6.38 Variable36foldedlightcurve ...... 99
6.39 Variable36lightcurve...... 100
6.40 Variable49lightcurve...... 101
6.41 Variable50lightcurve...... 102
6.42 Variable51lightcurve...... 103
6.43 Variable53lightcurve...... 104
6.44 Variable53foldedlightcurve ...... 104
6.45 Variable55lightcurve...... 105
6.46 SuspectedVariableSV2lightcurve...... 107
6.47 SuspectedVariableSV5lightcurve...... 108
6.48 VariableV59lightcurve...... 109
6.49 VariableV67lightcurve...... 110
6.50 VariableV68lightcurve...... 111
6.51 VariableV69lightcurve...... 112
6.52 VariableNV30lightcurve...... 113
6.53 VariableNV7lightcurve ...... 114
6.54 VariableNV14lightcurve...... 115
6.55 VariableNV1lightcurve ...... 116
6.56 VariableNV15lightcurve...... 117
6.57 VariableNV10lightcurve...... 118
6.58 VariableNV9lightcurve ...... 119
6.59 VariableNV12lightcurve...... 120 x
6.60 VariableNV22lightcurve...... 121
6.61 VariableNV5lightcurve ...... 122
6.62 VariableNV21lightcurve...... 123
6.63 VariableNV18lightcurve...... 124
6.64 VariableNV26lightcurve...... 125
6.65 VariableNV28lightcurve...... 126
6.66 VariableNV27lightcurve...... 127
6.67 VariableNV4lightcurve ...... 128
6.68 VariableNV16lightcurve...... 129
6.69 VariableNV3lightcurve ...... 130
6.70 VariableNV23lightcurve...... 131
6.71 VariableNV25lightcurve...... 132
6.72 VariableNV24lightcurve...... 133
6.73 VariableNV2lightcurve ...... 134
6.74 VariableNV17lightcurve...... 135
6.75 VariableNV17lightcurve...... 136
6.76 VariableNV20lightcurve...... 137
6.77 VariableNV8lightcurve ...... 138
6.78 VariableNV6lightcurve ...... 139
6.79 VariableNV19lightcurve...... 140
6.80 VariableNV11lightcurve...... 141
7.1 Location of Rcore,Rhalf mass and Rtidal in our field ov view ...... 144 − 7.2 Isochrones over plotted CMD ...... 146
7.3 Isochrone over plotted CMD with LPV candidates ...... 148
8.1 Variable stars ...... 152
8.2 LPV stars compared using Isochrone ...... 153 xi
8.3 Classified variables in the CMD ...... 155 xii
LIST OF TABLES
Table Page
3.1 ALSfileoutput...... 30
4.1 Standars stars in comparison datasets ...... 38
4.2 Cluster comparison ...... 44
4.3 Coefficient Values ...... 45
4.4 Output of the transform.e program ...... 46
6.1 LEM available data ...... 72
6.2 PSCS available data ...... 83
6.3 Corwin et al. availabledata...... 106
8.1 PhotometricPropertiesofVariablesinNGC6388...... 157 1
CHAPTER 1
INTRODUCTION
Galactic Globular Clusters (GGC) are stellar populations characterized by a gravita-
tionally tightly bound group of stars, located mostly around the halo, some located in the
thick disk and some appear to be members of the bulge of the Milky Way. In the past
half-century GGCs have been significantly studied, and give scientists a unique chance to
analyze unique samples on a wide range of variable stars and also help us understand the
evolutionary state of the variable star because stars in a given GGC come from the nearly
the same chemical composition and are located at the same distance from us[5].
Variable stars are stars that change spectral type, radius or brightness over a period of
time. The change in brightness is due to either internal or external properties in the star, and
the change for most of these stars happens in a periodic behavior with some happening over
minutes, some hours, days and even years, and the remaining stars display a dramatic change
that is a one time happenstance. They are categorized into two categories depending on their
observable properties: Extrinsic Variables and Intrinsic Variables. Extrinsic Variables are
stars that vary brightness by means external to the stars such as binary variables. Intrinsic
variables are stars that vary brightness due to internal processes in the star and are divided
into two groups: cataclysmic variables (stars that change brightness in a dramatic, one
time and rapid moment [i.e. Supernovae, Novae, etc.]) and Pulsating Variables (stars that
change brightness due to a periodic contraction and expansion of their outer layers), and are
located in the instability strip of the CMD (with the exception of LPV and Gamma Doradus
variables). Pulsating variables would be the base of our research.
Pulsating variables stars are physically characterized by stars in a post-main sequence
stage of stellar evolution (for the exception of δ Scuti which are Main Sequence pulsators), and they are classified according to the length and regularity of their period, light curve shape, amplitude and range of their light curve. 2
The main goal of this research is the search and study of Long Period Variable (LPV) stars, which are a type of pulsating variables that display a period of 30 to 1000 days. Phys- ically they are characterized an inert helium core and all the energy is generated by fusion in the outer hydrogen shell. In the CMD they are located in the Asymptotic Giant Branch
(AGB)[32]. LPV stars are categorized into Mira, Semi Regular or Irregularvariables, − all according to their observable properties: light curve, amplitude and periodicity.Mira
LPV stars are variable giants with characteristic late-type emission spectra (Me, Ce, Se).
They are characterized with amplitudes in the V-bandpass of 2.5 to 11 magnitudes and infrared amplitudes generally less 2.5 magnitudes. Their light curves have noticeable peri- odicity, display an almost sinusoidal curve, with periods usually ranging from 80 to 1000 days. Semi Regular (SR)LPVstarsaregiantsorsupergiantsofintermediateandlate − spectral type. Their amplitudes usually range from 1 to 2 magnitudes in the V-bandpass and their light curves display evident periodicity, accompanied by numerous irregularities, with periods ranging from 20 up to 2000 days. Irregular (Irr)LPVstarsarestarsthatshow very poorly defined or no evidence of periodicity, with amplitudes of up to 1 magnitude in the V-bandpass. Many of these stars are classified as Irr but have been insufficiently stud- ied and they could be SR or other type of variable[14]. LPV stars’ light curves sometimes display a phenomenon of multiperiodicity, refer either as Long Secondary Period (LSP) or
Short Secondary Periods (SSP). LSP occur on a time-scale of 10-15 times the period of the variable star, most common in carbon Miras, and in some cases maybe due to episodic dust emissions, as for SSP occur on a scale of a few pulsation periods and may be due to interference between adjacent radial pulsation modes[20]. Mira variables can also be used as standard candles because of their well-studied period-luminosity relation by Feast (1996), who was able to define a period-luminosity relation in the infrared which follows:
M = 3.47logP +0.91 (1.1) k − 3
where Mk is the absolute infrared magnitude and P is the period of the Mira star in days, and understanding the relation does not require understanding the physical reasons for the
light variation, since the variation of the star is caused by the radial pulsation on the star,
pulsations that are rhythmical as it alternatively becomes dimmer or brighter.
Population II Cepheids (P 2C)areanothertypeofbrightvariablestarwithaverywell defined relation between their period and luminosity, which makes them anchors to be used as standard candles. Their periods usually span from 1 to 30 days and amplitudes from
0.3 to 1.2 magnitudes in the V-bandpass[14]. Another group of variable stars are RR Lyrae stars, which are frequently located in Globular Clusters. They are classified following the
S.I. Bailey classification, which is defined according to their period, amplitude and light curve shape, as either RRab Lyrae characterized by longer periods, with a light curve that has a steep rise in their magnitude and amplitudes between 0.5 to 2 magnitudes in the V- bandpass or RRc Lyrae characterized by shorter periods, with a more sinusoidal shape in their light curve and amplitudes not greater than 0.8 magnitudes in the V-bandpass[14]. We are expecting to be able to locate, plot and study these three type of variables in NGC 6388.
NGC 6388 is a galactic globular cluster (GGC) located at l =345.5o,b= 6.7o according − to Silbermann et al. (1994), in the direction of the Galactic center in the galactic bulge of the
Milky Way. Compared to the similar cluster 47 T ucanae, NGC 6388 has a slightly higher
metallicity ([Fe/H]=-0.44;Carretaet al. 2007). It has a prominent blue Horizontal-
Branch (HB), an atypical characteristic of high-metallicity clusters, where a thick red HB
and a lack of a blue HB is the rule, a characteristic not found until the late 1990s when
researchers plotted the first CMD for NGC 6388[23]. Age and/or mass loss are the two
main parameters that are generally used to explain the behavior of a GCC according to
its metallicity, but for NGC 6388 these two parameters do not explain the existence of the
prominent blue HB. This line of reasoning drove researchers to include NGC 6388 as one of
the slightly high metallicity clusters to display the second parameter like effect. This effect is 4 not completely understood but models point out to non-canonical characteristics that could explain the unusual behavior: (1) a high abundance of helium, (2) a high rotation during the
RGB phase, and (3) a helium-mixing scenario (Sweigart et al., 1998). Also another study proposed that the unusually long periods for RR Lyrae stars in NGC 6388 (Pritzl et al.,
2001) could be attributed to the HB in NGC 6388 being unusually bright.
There has been extensive research done on the NGC 6388 variable star population, most of which has been very productive in locating short period variables, mainly RR Lyrae stars.
The first main survey was done by Lloyd Evans & Menzies (1973) that specifically targeted the search of LPV stars using photographic plates from previous research by Eggen (1972), where they found 12 variable stars. Of these 12 variables, 3 were classified as Mira LPV stars, but periods were not provided. The second main survey for variables was conducted by Hazen & Hesser (1986) using the 1-meter telescope at Cerro Tololo, where they added
14 new variables to the known list for NGC 6388; of the 14 variables 9 were defined as RR
Lyrae (RRL) stars. One of the issues up to this point was the fact that research was done using photographic plates and research near the center of the cluster was unreliable and accurate light curves were not obtained. The next survey that located new variables was by
Silbermann (1994), where CCD observations of NGC 6388 were done for the first time. The research produced 3 new variables, all three classified as RRL variables; Silbermann also plotted light curves for the known variables V17 and V20, found by Hazen & Hesser (1986).
The next main survey by Pritzl et al. (2001) is one of the most comprehensive surveys done on NGC 6388. This research located and plotted light curves for 28 new variables: 14 RRL variables, 8 Binary systems, 3 LPV stars, 2 Population II Cepheids (P2C) and 1 ? Scuti star.
It also complemented previous research: it reclassified three variables, previously believed to be RRL, two as P2C and one as a Binary system. The latest main survey by Corwin et al.
(2006) located and plotted light curves for eighteen variable stars, classifying 9 as RRL stars,
3asP2Candtheothersixassuspectedvariables(4P2Cand2RRL)usingthesamedata 5
obtained by Pritzl (2001) but working with the ISIS photometric package. Also worth noting
that in addition to Pritzl (2001) data they also obtained data using HST1(high resolution data) to study stars near the center of the cluster. Accounting for all these surveys brings the known variable stars in NGC 6388 to a total of 75, making it one of the most variable populated GCCs on record. Of these 75, 43 have been found or suspected to be RR Lyrae, the same for 9 binary systems, 12 Population II Cepheids (P2C) stars and 10 LPV stars, and one δ Scuti star.
It is known that GGCs with high metallicity have a redder HB and Asymptotic Giant
Branch (AGB). Since LPVs are red stars and are located in the giant branch, this makes
NGC 6388 a prime candidate to search for and study LPV stars, especially since most of the data on LPVs does not provide any time vs. magnitude data.
Three of the main articles that we will compare our data to are: Lloyd-Evans & Menzies
(1973) (hereafter LEM), Pritzl et al. (2000, hereafter PSCS) and Corwin et al. (2006, here- after Corwin et al.). We picked these articles because they are based on research of variable stars in NGC 6388 and the combination of the three papers combines the best studies and catalogs all of the known variable stars in our cluster.
LEM’s research goal was the search of red variable stars in metal rich GCC, and to know whether the colors of the red variable stars in globular clusters depend on the metal content of the cluster. A second paper[17] in the series used near IR photometry on the same metal-rich clusters, but with the goal of finding the differences in the red GB for these late spectral type clusters. The research was able to compare models to observations and confirm the view that the red GB becomes fainter and its tip redder the higher metallicity of the cluster. These papers complemented observations and cataloguing of stars in NGC
6388 done by Hogg (1955). This article shows 12 possible variable stars (V1 through V12) in NGC 6388, where three of them (V1, V2 and V4) are cataloged as Mira variables.
PSCS’s research goal was the search of variable stars in NGC 6388 specifically RR Lyrae
1Hubble Space Telescope 6 stars. From the data collected their observing was better suited to research short period variables, they collected data over a period of 8 days (a fitting amount of time to obtain suitable data for variables with periods of less than 1 day but not for variables with periods greater than 20 days) with exposures of 600 seconds in both B and V filters, which makes it non-suitable for Long Period Variable research. PSCS showed that RR Lyrae periods in NGC
6388 are unusually long, compared to RR Lyrae field stars. The existence of these unusual periods was attributed to the fact that NGC 6388 has an unusually bright HB, compared to other metal rich clusters. The research added to number of variables found in LEM. It found twenty-three RR Lyrae; it also estimated periods for four candidate Population II
Cepheids, nine Binary systems, one δ Scuti, and three LPV stars, bringing the number of possible variables to 57 (V1 through V57). Also this paper suggested that V12 is an LPV, which brings the total number of proposed LPV to seven (V1, V2, V4, V12 from LEM and
V45, 46 and 47 from PSCS).
Corwin et al. used images taken by Pritzl et al. (2001, 2002). The original research used DAOPHOT for its photometry, and only ground-based telescope images. The new research incorporated space-based observations done with HST, and used both ground-based and space-based images and used ISIS, a photometry software more suitable to study the crowded center of the cluster. After the photometry the mean periods for the RR Lyrae stars are as large as, or larger than, those in OosterhoffII systems, with periods larger than
0.8 days. At the end the research confirmed twelve variables (V58 through V69) previously found by Pritzl et al. (2001, 2002), and found six more suspected variables (SV1 through
SV5).
We have seen that LPV stars have not been carefully studied in NGC 6388, where the known LPV stars where found and classified by extrapolating data that was meant for short period variables, or lacks visual comparison such as magnitude vs. time plots. We aim to locate, study the properties and classify Long Period Variables stars in NGC 6388 in order 7 to aid the restriction of the stellar models for the cluster and provide new tools that can assist the understanding of the unusual behavior of NGC 6388. 8
CHAPTER 2
PROCESSING
2.1 Observations
Images for the study were obtained remotely using the 0.4 meter Prompt 5 telescope
located on the Cerro Tololo, Chile1. The CCD camera installed on PROMPT 5 provides a
10 arc minute field of view and a pixel scale of 0.59 arc seconds per pixel.
The observation run to collect images was done over two years. The first year was
February 2009 through November 20092,andthesecondyearfromFebruary2010through
November of the same year. At the end we collected 87 nights of workable data, where images were taken in the V and I band-pass filters. For the V filter we obtained 60-second exposure images, and for the I filter obtained 50-second (IL from now on) and 12-second exposures
(IS from now on). The images were taken in sets of V , IL,andIS in an interleaved sequence: V I I ,V I I ,V I I ,V I I ,V I I ,astepnecessary ⇒ L ⇒ S ⇒ L ⇒ S ⇒ L ⇒ S ⇒ L ⇒ S ⇒ L ⇒ S to create a dithering effect for the set of images because this will create a small shift from image to image. This dithering effect is a method used to shift the telescope slightly from image to image which will cause the bad pixels to be misaligned and when the final stacked images are averaged the bad pixels can be removed. Dithering on the research is necessary since the Prompt 5 telescope lacks active guiding and tracking, which will let bad pixels and cosmic rays drift through the image as if they were stars. The drift will move the stars slightly across the CCD image, but once processing begins this drift will help correct for bad pixels present in the images.
1The telescopes are operated by the UNC system. Our access was obtained through collaboration with Dr. Michael Corwin at UNC Charlotte. 2Data collected by undergraduate research assistants 9
2.2 Calibrations
Using SKYNET3we obtained the calibration images: Bias, Darks and Flats (these im- ages are taken automatically by the telescope on an almost-nightly basis), which were ac- quired the same day or a day or two after NGC 6388 images were taken. Bias images are needed because CCD chips even when not exposed has activity or unwanted signals on them.
To remove these, a set of zero-second exposures are taken right after collecting data. To set abaselevelitissomewhatimportantthatthebiasesarefromthesamenightasthedatais collected since the bias levels of can change from day to day. This level will tell us where the
CCD’s own bias signal ends and where our collected light signal begins. From PROMPT5 we obtained 20 bias images per night, being certain that the images were taken the same night as our observations.
Dark images are required to remove the dark current (a signal from the moving electrons in the CCD chip) created by the CCD. The dark current, which is temperature dependent, is created due to the thermal motion of electrons contained by the CCD chip, and the fact that even in the dearth of light the CCD still collects a signal. To remove the dark current effects, we need to take exposures when the telescope is not collecting any light. To achieve this the dome needs to be closed or the telescopes needs to be covered. These exposures are supposed to be taken at the same temperature as the light exposures since the dark-count rate changes logarithmically with temperature[18]. It is known that every pixel in the CCD will have some dark-current, and thus we expect some level of current to be present in our images. For normal current the pixels are called warm pixels and are pixels where the charge current can be corrected, but there are also some pixels with greater than normal or variable current known as hot pixels and pixels with zero or very low response known as cold or dead pixels. The latter appear around the edges and they are mainly a problem in older CCD chips. All three type of pixels can be grouped as bad pixels.Onelasttype
3http://skynet.unc.edu/index.php 10 problematic pixels due to cosmic rays,donotcomefromthetelescopebutfromenergitic subatomic particles that strike the CCD, and can be corrected. W arm pixels are corrected
once the scaled dark is subtracted from the image and cosmic rays are corrected due to the
dither effect in our images. Cold pixels are not a problem for the CCD used in PROMPT 5.
Therefore we used the darks to remove hot pixels from our images, as they occurred when
individual pixels in the CCD display higher than average amounts of charge current. In
figure 2.1 the charge current across the CCD can be seen where for PROMPT 5’s CCD it
is expected that most of the dark counts don’t go higher than 30 counts, and on/or below ∼ this value pixels can be defined as warm pixels, but as it can be seen there are pixels that go
above the expected value, an one very noticeable around column 75, these are the previously
described hot pixels. From PROMPT5 we obtained twenty 80-second dark exposures for
each night, once again assuring that they were taken no more than a day before or after our
cluster images were taken. These dark images will help remove hot pixels from our images
because they can hinder our ability to do photometry on the frames.
Flat images are required because the effects of illumination in the CCD differ from pixel
to pixel. The flat image is obtained by exposing the telescope for a small amount of time to a
uniform light source. Some telescopes use a white screen inside the dome, others use a patch
in the sky devoid of any stars (done before evening or after morning, astronomical twilight).
These flat images are required because: (1) The optical system can cause vignetting; (2)
Dust on filters and optical windows also reduce intensity; (3) Some mechanical shutters may
cause uneven exposure across a detector; (4) pixels differ in their relative sensitivity due to
variations in quantum efficiency[19]. We can use the flat field to map out the sensitivity of
each pixel in the CCD. From PROMPT5 we obtained 10 images per filter per night and no
more than a night or two after our images were taken. It is important to get the flat for
each filter since as explained by (4) each filter wheel comes with its own unique disruptions.
Once the data have been collected IRAF4 was used to reduce the astronomical images in
4Image Reduction and Analysis Facility 11
Figure 2.1: Dark current across the CCD 12 the form of an array of pixels and then calibrate them by removing the Bias, Dark and Flat
field from each image, which will remove the effects of the telescope, CCD and how data are collected. First I use the calibration images taken from SKYNET and create a master Bias,
Dark, and Flat. The more images collected the greater the Signal to Noise (S/N) ratio I can get for our calibration masters. Since these calibration images only record the effects they have on the pixels and not where the telescope is pointing, I can stack the images collected for each field without the need to account for any rotation in the system.
Before getting into processing its important to describe how each of the group of frames
(Dark, Bias, Flats, Cluster Images) are combined. Each set of frames has a combination task
(zerocombine, darkcombine, flatcombine, imcombine) that works using pixel rejection. Our pixel rejection uses a process called sigma clipping,whichisthedispersionofthedistribution of pixels for one pixel in every image; here σ is taken as the standard deviation of the pixel stack and every pixel in the stack that is an X value σ (X value is set by the combining task
depending on which type of image we were combining) away from the standard deviation
then the pixel will be rejectd. If the problematic pixel resides on the bad pixels there could
be two reasons: First, for the problematic night only we only had two or three images to
combine, which will not help us remove most of the bad pixels once we stack the images.
The second reason can be caused by one of the parameters (in this case the reject parameter)
in the imcombine task. With the help of Dr. Layden, we found that two settings for this
parameter could be changed depending on how many negative pixels. The first setting,
crreject,willrejectonlypositivepixelsusingCCDnoiseparameters.Thisisthestandard
setting for the parameter. If this setting does not remove bad pixels we changed the setting
to avsigclip,achangenecessarytolessthan 25% of our images, which will reject pixels ∼ using an average sigma-clipping algorithm. It is necessary to correct for bad pixels as well
as possible because these types of errors can cause false detections once the data is used for
the star selection stage. 13
The first task used in IRAF is zerocombine,ataskusedtoaverageallthetwentybias images and create master image called Zero.fits.Themasterbiasisthenusedinthenext
task, ccdproc,whereItakeeachdarkframeandremovetheeffectsofthebiasfromeachof them by subtracting the master bias from the frames. Next, I use the task darkcombine,
which will take all of the bias-subtracted dark images and create a master dark image named
Dark.fits.
The master dark will then be used on all of our flat images for both filters. It is
imperative that the bias and then dark are corrected before correcting for flat fielding,
because the bias and dark are subtracted from pixel to pixel, but the flat field is removed
by dividing the flat field across the image. To remove the effects of bias and dark from our
flat images once again the ccdproc task is used, where the task will scale the Dark.fits to
the exposure time of each image and then subtract the dark-current effect from the flats.
After the bias and dark frames have been subtracted from the flat field images I use the
flatcombine task to average the flat images and create a master flat image for each filter
named flatv.fits and flati.fits. Note that is not required to make a separate calibrated flat
IL,andIS image; we can use the same flati.fits for both of them. Since the bias and dark effects in our images have were subtracted I will remove any effects created by bad pixels
(though hot pixels will be incompletely fixed at this stage) in the CCD.
Once this is all done we observe each of the master images and ascertain that they were all processed and created correctly, a step mostly necessary to look for huge discrepancies in the image combining process, such as blurred images or gaps in them, or unusual behavior,
IwillcheckforhighphotonscountsontheDark.fits image, making certain that most of the pixels (no lower than 99 % of them) are less than 250 counts per pixel.
After this is done I take the Zero.fits, Dark.fits and F lati.fits and F latV.fits for
each filter, and one more time use ccdproc on each of our cluster images, a necessary step
to finally subtract the effects of bias, the scaled dark and divide the flat fielding from the 14 images. Once this is done I run the ccdlist task, which shows which images have been corrected, an image that has been calibrated will display a Z for zero, a D for dark, and a
F for flat field correction done. Finally I will check our images and ascertain for myself that most, if not all of the effects created by the CCD and the telescope (instrumental effects) are subtracted from our images.
2.3 Combining
One could expect that after the instrumental effects have been removed the images are ready for photometry but there are other effects that need to be corrected for. We still use
IRAF to combine images but some user inspection is required before combining. For a small percentage ( 5%) sets of images we did not have the same number of images to average, ∼ these night had only 2 or 3 images to average, all because of the dither effect, the rotation of telescope, additional effects or the fact that all the image sets were not taken the same night and the lack of tracking prevents images from being taken at the same spot from night to night. One of the first things needed is to account for the dithering effect, a necessary step because when the images are combined they are actually averaged and the images need to be stacked correctly. The next effect comes from the way the telescope tracks around the night, because PROMPT 5’s mount can not track stars across the meridian, therefore it rotates 180o at the zenith, so it is necessary to check the images to account for this rotation.
Another necessary check point is to make certain that all the images are of the same quality, and by this I mean making sure that atmospheric (such as clouds or moonlight hitting the atmosphere) or human (planes, light reflected on the dome) effects are not present on any of the images.
After calibration has been completed, (see figure 2.2) our cluster images will be ready to be combined and create our primary images for each night. Before stacking the images there may be a need to correct for sky background. This step is done because even though 15
Figure 2.2: The frame on the right is the raw frame, before calibration. The frame on the right is the calibrated frame where the bias and dark have been subtracted and the flat has been divided from frame. In the corners of the calibrated frame we can see effects of vignetting removed, also it can be seen that stars are clearer??
all the images are processed from the same night, there could be significant changes in the
sky background, due to moonlight or variable clouds. We use the imstatistics task in IRAF
to the mean (MEAN)andmedianpixelvalue(MIDPT)(accountsfortheskybackground)
of a region in an image, and then we take the average of the MIDPT values, if an image’s
MIDPT deviates more than 10% of the average MIDPT,weneedtocorrectthisvalueby using the imarith task, which will add or subtract the percentage that the image is away from the average. This step is necessary because an non-average sky background can lead to a poor bad-pixel rejection, leaving artificially high noise (a grainy appearance to the sky background).
Once the sky background has been corrected, we will select a star and get the coordinates for the same star in all the images. The selected star needs to be close to the center of the cluster to reduce the potential x and y coordinate shift of stars in near the center. Once we catalogued the coordinates for the star, the shift from one image to the next image are calculated, an essential step since throughout the night because the sky moves and pictures are not centered at the same spot in the picture, caused mostly by the dithering effect. 16
Figure 2.3: Comparsion between a bad and a good frame stacking process
After correcting for sky brightness and obtaining the images shifts, we used the imcombine
IRAF task, which uses pixel rejection, and staked the images to create the three primary images for each filter. After running the task the images are displayed and ascertained, that the combining process was correct and that the images are not populated by bad pixels, this done by displaying the image with IRAF and comparing our combined image with one of the original uncombined images. If there was a problem with the stacking (figure 2.3) it will be required to go back and recheck the coordinates for the selected star and run the task once again.
The final result is a processed frame where the instrumental effects have been removed, and where the combination process has rejected bad pixels and increased the S/N ratio.
From each night we will have three images of the cluster on each filter, IL, IS,andV .We used each of the collected final frames on each filter and combined with photometry done with ISIS and DAOPHOT study the LPV stars in NGC 6388. 17
CHAPTER 3
PHOTOMETRY
Photometry is the method of measuring the apparent magnitude of stars in a picture frame. For this research two groups of software programs were used to obtain the pertinent data. The first software is a stand-alone program called ISIS [1], and the second group is a series of software called DAOPHOT [26] and [28] containing programs DAOPHOT II,
ALLFRAME, DAOMASTER and DAOMONTAGE.
The first software used was ISIS, an image subtraction and differential photometry program that uses seven routines to obtain the stars’ variability. The image subtraction is aconvolutedkernel,amethodwheretheprogramusesausercreatedreferenceimageand subtracts every star in a reference image from its counterpart in all the available frames, and providing a flux difference measurement between the zeroed level (reference frame) star and the star in the comparison frame.
The second software used is DAOPHOT, a stellar photometry program for obtaining precise photometric indices and astrometric1measurements for stellar objects. DAOPHOT will be used to confirm most of the results found, and will also work on the regions of the image that were cropped using ISIS.
One of the main differences between the results from ISIS and DAOPHOT is that
DAOPHOT calculates and porduces the stellar magnitudes and not their fluxes, also using the apparent magnitude a color magnitude diagram (CMD) can be constructed, which is a tool to identify cluster membership for all variable stars. Also ISIS will allow us to identify variable stars near the center of the cluster, but neglect the edge, while DAOPHOT II is better suited to used for the whole image having some issues in the center of the cluster, and also better used in crowded regions where two or more stars in the image seem to blend in to one star. 1http://www.astro.wisc.edu/sirtf/daophot2.pdf 18
3.1 ISIS
3.1.1 Setting up for ISIS
Before starting work with ISIS a master frame needs to be selected. The master is necessary to create a zeroed position for the coordinates of the stars. The center of the cluster in the master image will be (0,0) in the x- and y-coordinates and then every other frame can be referenced for this location. The master image was selected to have the best seeing, which will provide a better resolution of the stars in the image, low sky background, so the light hitting the atmosphere of the earth does not obscure most of the star’s incoming
flux, and better fit full-width at half maximum (FWHM), which approximates the radial profile of a star inside the frame.[13] All these values were measured for selected stars in all the frames. These stars were bright stars that would not overcrowd the measured field, were available in all the images, and had a low FWHM value.
Once the master frame was selected we proceeded with the selection of a reference star.
The selection of the reference star was not based in the same categories of picking a master frame but mainly on a star that is near the center of the cluster, and that can be seen in all the images, and with this using the center of the star and the reference star we have our two points to aid us account for the small rotation from image to image.
Using these data I was able to adjust the images to work ISIS. Adjusting the images consists of trimming each image, so that the cluster center is in the same place for each image. The trimming process is necessary because while the program accepts small shifts between the images it expects the stars in every single image to be located at the same location. The process will trim images from 1031 by 1043 pixels (10 by 10 arcminutes in all frames) for the master frame to 661 by 778 pixels (6.50 by 7.65 arcminutes) for all the frames. The difference between the original frame and the trimmed frame are displayed in
figure 3.1 The process does cut away some stars from the image, but one of the main reasons to use ISIS is that it is better to study the crowded part of the cluster, which is near the 19
Figure 3.1: The image on the left is the original calibrated image. The image on the right is the trimmed image used for ISIS. While a lot of stars in the edges are trimmed away the stars near the center, the image mostly includes cluster stars, and excludes field stars.
center, and also ISIS has some problems determining variability in stars near the edges of
the image. Once we trim our images, so every image is the same size and the cluster center
is at the same position for each star, we began using ISIS.
3.1.2 Running ISIS
The ISIS software uses seven routines to obtain the data to create the light curves for
our possible variable stars. The following paragraphs will descr be in some detail how each
of the routines work on all the images.
The first ISIS routine (interp.csh)isanimageandinterpolationroutine,whichisneeded to remove any small rotation and shifts remaining between the images after the trimming process. This routine is necessary since ISIS will use a convoluted kernel to measure the
flux differences and any significant shift could create discrepancies in the variable detecting process because if the measured star in a frame is off-center from its counterpart in the master frame then the measured flux difference would not be accurate. The routine uses the master 20
image and a dimension polynomial degree (we use a two-dimensional for our processing) to
correct for any shifts in the images. The dimension polynomial degree is calculated using
the following equations:
x = a +(c x) (e y)(3.1) × ± ×
y = b +(d y) (e x)(3.2) × ± ×
where x and y are the coordinates for the star in the comparison frame, x and y are the coordinates of the star in the master image and a, b, c, d, e & f are fit coefficients that can
have any value and they are calculated using the xm y, x and y values. After completion the routine produces a log file containing four values: σx, σy, nrest and ndata. σxandσy
are the residuals along the x- and y-axis respectively. These values needed to be less than 1
pix and consistent from frame to frame. Values for the images were 0.0569 to 0.3369 pixels
for σxand0.0571to0.3361forσy, which were expected since the frames were set up to be
centered at the same location, but due to human error there are small discrepancies. The
ndata value is the initial number of stars used to compute the astrometric solution. There
was no required value for ndata, but it was observed that the better resolved a frame was
(low sky background, better seeing) the more stars were used to compute. Finally, nrest is
the effective number of stars used to compute the astrometric transform. This value should
be from 3 to 500 to have a decent amount of stars for the calculation, which was the standard
for all our images. Even though ndata and nrest consists of the amount of stars used to
calculate the astrometric solution we are only concerned with the final amount of stars,
nrest,andnotwithintialamount,ndata.
The second ISIS routine (ref.csh)createsareferenceframe.Thereferenceframeis
created using 10% of the total amount of frames (the master frame being part of this per-
centage), and they are selected by the best seeing, sky background and FWHM for selected
stars. The selected frames are stacked, which helps remove some errors in the frames such as
cosmic rays or bad pixels. Once the routine is run, it produces a new frame called ref.fits. 21
We compare this frame with our selected stack and looked for errors in the stacking proce- dures, such as double stars or unexplained lines that should not be present in the ref.fits image.
The third ISIS routine (subtract.csh)isasubtractionroutine,anecessaryroutineso that all the non-variable stars can be weed out in the observed field. The subtraction uses the reference frame created in the second routine, which will be convolved with a kernel in order to match as closely as possible each of the frames2,wherethematchshouldproduceanice profile between the reference star and the star in the frame (see figure 3.2). This convolved frame is then subtracted from the current frame to create a new frame. The subtraction is done pixel by pixel in all the frames so all the non-variable stars subtract away to zero and only the variable stars should leave any considerable residual and remain in the frame.
The fourth ISIS routine (detect.csh)usestheframesfromthesubtractroutineand detects the possible variable stars in all the frames. Even though this routine seems repetitive, it is certainly required because even up to this step there could still be bad pixels in the image, defects that could be confused with faint stars. After the subtract routine is completed and all the created frames have been normalized, where sky background has been zeroed throughout the frame, the detect routine stacks all the images, and uses a rejection method to detect bad pixels still remaining in the frame. The end result of this routine is two images, var.fits and abs.fits.Theabs.fits image displays the mean absolute deviation for all the pixels in the stacked image while the var.fits image is the mean absolute normalized deviations, and will display all the possible variable stars in the frame.
The fifth ISIS routine (find.csh) is used to find all the possible variable stars in the var.fits frame. This routine uses a threshold parameter set by the user. The var.fits frame
is used to select this threshold, where IRAF’s imexamine command is used to look at the
FWHM for the possible variables. All possible star profiles are measured with the goal of
trying to approach the lowest peak value possible before the star will mainly produces a low
2http://www2.iap.fr/users/alard/page3.html 22
Figure 3.2: The red square represents the convoluted kernel whole the blue square represnets the star in the frame. [2] 23 scatter. Figure 3.3 shows a good star profile and a scattered profile. The lowest good star profile is selected as the threshold, and the find routine uses this threshold to produce a list with the x- and y- coordinates of all variable star candidates, their peaks and an ID number.
Also the routine produces a frame for each night containing the remaining possible variable stars.
The sixth ISIS routine (phot.csh)usesthelistcontainingthevariablestarsfoundandthe
frames created in the fifth routine to create light curves. The routine needs four parameters:
the first two values are used to estimate the background around the star, so as to set up a
threshold where none of the flux for the star or any other star should be seen. The second
set of values are the photometric radius (inner and outer) and are used by the routine to
specify where the flux of the star will mainly fall (photometric radius), and where this flux
will normalize (a point the star fluxes ends). Using these parameters the routine assigns
all the possible variables an lc number, and produce an lc(number).data file containing the
Julian date, the coordinates, the flux, and flux error for a specific variable star.
The final ISIS routine (Czerny)isaCimplementationofSchwarzenberg-Czernymethod3to calculate the possible period for the variables. The method is not well explained but mainly uses many different sine curve fits, which represent different possible periods, to the lc(number).data file produced in the previous step and finds the sine curve with less scatter for these data. Another possible tool comparable to the Czerny routine is the PDM task available in IRAF. The task calculates the θ(theta) statistic:
∆t ∆t θ = integral( )(3.3) period − period
It will then produce a possible period that can be used to fold the data, a process that will be explained in chapter 6 Once this is done we can use the SuperMongo software to plot our light curves and approve or discard the possible variable stars.
3http://www2.iap.fr/users/alard/page5.html 24
Figure 3.3: The profile on the top represents a non-crowded, star with a good FWHM. The profile in the bottom is a crowded star which produces a scatter profile 25
3.2 DAOPHOT
3.2.1 Setting up for DAOPHOT
To set up for DAOPHOT the frames were converted from a fits format to an imh format, which is the type of file that DAOPHOT software handles. This is done with the rfits task
in IRAF. Once this is done the table we used in ISIS containing the coordinates for the
reference star and the FWHM, among other characteristics, for each night on each of the
three filters, will be used with DAOPHOT and this will complete setting up the images to
run the software.
A couple of documents are required to set up for the software run, to make the DAOPHOT
with run less user interaction. The first document is called daophot.opt;thisfileissuggested
by the software as a way to set up the initial parameters for the run. The file contains the
entry for the (a) High Good Datum, which tells the program how high of a pixel readout
should be considered defective, (b) Read Noise,whichindicatesthereadoutnoiseofasingle
exposure made with the CCD, (c) Gain,whichindicatesthegainfactoroftheCCD,the
number of electrons per pixel divided by the number of counts per pixel, and (d) V ariable
PSF, which indicates the degree of complexity with which the point spread function (PSF)
is to be modeled (usually a Gaussian first approximation, or in other cases a function that
varies linearly or quadratically). Each of these values changes from detector to detector,
therefore this file is created so the user does not have to do an entry for each of these values
every time the software is run. Instead the entries will be read from the file automatically.
For the combination of this research on Prompt5 and NGC 6388 the recommended values
are (a)52, 000, (b) 6.6, (c) 1.5 and (d) 2 (indicating a quadratic varying PSF).
The next step is to create a file, inlist.fwhm,whichindicatesthecenterofthecluster,
the best fwhm found in a star and how many images were combined to create each of the
images. The file is created using the ISIS table, the approximate center of the cluster for
our master image, and a Fortran code, daophotprep.e, provided by Dr. Layden. Also when 26 running the Fortran code an inner and outer radius will be provided for the inlist.fwhm file,
a necessary precaution when running DAOPHOT because the crowded center of the cluster
needs to be excluded while running some of the tasks in the software.
Finally a file was created that contained the aperture photometry. The aperture pho-
tometry file indicates the inner radius for our star in a sequence from A1 to A12; also it
contains the inner annulus and outer annulus radius for the star. The reason why this file is
needed will be explained in the following section.
3.2.2 Running DAOPHOT
The software is divided into three programs: DAOPHOT II, MONTAGE and ALL-
FRAME. DAOPHOT II is run on each single night per filter, while MONTAGE and ALL-
FRAME are run using the whole set of nights.
The following accounts for a single image while it is run with the DAOPHOT II program.
Before the first task is run, the user enters six new parameters that will be used by the
tasks. First, threshold is the desired level where the local noise will be set, which means
that any candidate stars below the threshold will be considered noise; second, watch is a
simple command indicating whether the user wants to run the software automatically (-1)
or interactively (-2); third, F itting Radius lets the program know the circular area where pixels need to be read in order to calculate an appropriate PSF; fourth, FWHM is the
typical value for the FWHM of stars; fifth PSF Radius, lets the program know the radius at which radius the PSF should be subtracted; and sixth Analytical Model P SF indicates which function (each function with a different number of free parameters) will be used to calculate the first approximation of the PSF.
The first task, FIND, uses the set detection threshold and finds the stars that are above the local noise. The program uses the amount of images used to combine the primary image per night and adjust for the gain and readout noise. The program reads pixel by pixel and 27 identify which stars are above the High Good Datum and uses the Analytical P SF Model
and FWHM to create a Gaussian profile to compare it to each pixel in the image, and uses the profile to account for any pixels that are below the threshold and eliminates them. Once the task completes its comparison with each pixel in the image, it produces a file (.coo file) containing all the found stars.
Once the file is completed the next task, PHOT,usestheaperturephotometryfile and makes the first approximation at calculating the stars magnitude. The task uses the
first value for aperture photometry (A1) and integrates the counts within this aperture. It then moves to the next aperture (A2) and proceeds with the same calculation. Because the stars in our images are not expected to have an inner radius greater than 3 (three) pixels the value for A1 is 3.0 and the value for A2 is zero. This way the program can move on to the next step and not integrate counts for any other star aperture. Once this is done it integrates the counts per pixel in the circle with a radius between the inner annulus radius and outer annulus radius, which accounts for the background brightness (see figure 3.4). The background brightness is then subtracted from the inner aperture counts, obtaining a rough estimate of the star brightness (apparent magnitude). This is done for every star in the .coo
file and once is done it produces a new file (.ap file) containing a star ID for each star, its
coordinates and the magnitude estimate.
The following task, PICKPSF,selectsthePSFcandidatestarsamongthestarsinthe
.ap file, a simple procedure that simply organizes all the found stars by apparent magnitude
and then uses the fitting radius and eliminates any candidates that are one fitting radius
away from the edge, since these stars may not produce a good PSF profile and when the
light hits the CCD on the edges stars tend to spread a little compare to stars towards the
center. The program also rejects stars that are too close together. The standard use here is
within one P SF radius plus one fitting radius,whichisnecessarybecausethesestarscould
be saturated or close to bright stars making their FWHM profile hard to calculate. Once 28
Figure 3.4: The images displays how the PHOT task uses the inner radius and outer radius with the aperture photometry to locate each star in the frame 29 completed the program produces a file (.lst file) with the best 150 candidates coordinates, and magnitudes.
Following this task a python script, excludeio.pl,is run to organize the .lst file by the x-coordinates and then it eliminates stars that are too close to the cluster’s crowded center
(a radius of 130 pixels) since these stars would not produce unique FHWM profiles and
should not be used as PSF candidates. Since DAOPHOT has rejected stars that are too
close together running this code should not eliminate too many candidates (roughly from
the original 150 candidates the night ends up with roughly 130 good candidates).
The next task, PSF,usesthecandidatesinthelstfileandscalesthemtoauniform height, and then averages their PSF profiles and produces an archetypal PSF profile. In order to create the model the program uses the Analytical Model P SF ,inthiscaseaMoffat function, to create the profile for each star and then create the model. Later this PSF model is scaled down and compared to each individual star in the frame. The program may reject some of the PSF stars if it finds them to have bad pixels that are higher than the High
Good Datum but generally all the stars present in the lst file would be used to create the
PSF profile. Once completed the program produces a new file (.psf file), and a list of the
PSF stars and their neighbor stars (.nei file).
The next program, ALLSTAR,isusedtoasatooltogetmoreaccurateapparent magnitudes and positions for all the stars in the frame. The program will take all the stars in the .ap file and scales down the PSF profile and then subtracts it from the image.
Brightness residuals are used to create an estimate of the star’s apparent magnitude and accurate position. The procedure is run again once the scaled down PSF is subtracted and the stars in the frame have a corrected brightness and position. At the end there will be 200 iterations (the amount iterations is a default value set by the programmer) of the same procedure. The high amount of iterations is required to be able to get accurate measurements of dim stars that may be obscured in crowded fields by brighter counterparts, 30
[1] [2] [3] [4] [5] [6] [7] [8] [9] 2101.783-0.45915.6680.392789.18743.159-0.152 14 640.832 0.140 17.431 0.3328 94.957 4 1.853 -0.370 10 374.135 0.583 17.657 0.1670 88.066 4 1.687 -0.003 ......
Table 3.1: ALS file output [1]Star ID number, [2]X-coordinate, [3]Y-coordinate, [4]Star’s magnitude relevant to the PSF star’s magnitude, [5] Estimated standard error of the star’s magnitude, [6]Estimated modal sky value for star, [7]Number of iterations required for the non-linear least-square converge, [8]chi,[9]Sharp
since they tend to have overlapping PSF profiles. If only one iteration is run it will account for the full brightness of both stars, but a series of iterations will eventually remove the influence of the brighter star and let the program get a more accurate measurement for the dimmer star. At the end the program produces a file (.als file) containing the star id, x and ycoordinates,star’sapparentmagnitudeandestimatedstandarderrorofthemagnitude, among other values(see table 3.1)
One of the values from this table, chi,willbeofimportanceinselectingstarsforthe
CMD. chi is a robust estimate of the ratio of the observed pixel-to-pixel scatter from the model image profile divided by the expected pixel-to-pixel scatter from the image profile4.
The value represents how far away from the fit a star is and it is expected that the brighter and less crowded stars will have really small values of chi,whilethefainterandmorecrowded stars (especially towards the center of the cluster) will have greater chi values.
This concludes the first iteration with DAOPHOT II/ALLSTAR, but it is better to get a more accurate PSF profile that can help the program get more accurate readings for the star’s apparent magnitude. The best way to do this is to remove the PSF candidates neighboring stars, and once these stars are removed, a sharper PSF profile can be obtained for each of the PSF stars, which will produce a better PSF model. The command SUB in
4http://www.astro.wisc.edu/sirtf/daophot2.pdf 31
DAOPHOT will remove the neighbor stars creating a new PSF neighbor-less image. Once the command completes the subtracted image is attached and PSF task is run once again on the subtracted image, which produces a sharper and improved PSF model. The task is run until all neighboring stars are subtracted and the best PSF model is achieved. Once this is completed ALLSTAR is run once again with the improved PSF model and once again the found stars are removed from the image, producing an image without the brightest and least crowded stars in it.
Once this is completed a second iteration of DAOPHOT II/ALLSTAR was run, a step necessary because the first iteration was run using the stars found after the FIND command, and most of the obscured, fainter stars were not found. Also the threshold set at a high number needs to be lowered in order to account for the fainter stars. Once the threshold has been lowered, the subtracted image (the one created after removing the brightest and least crowded stars) is attached and FIND is run on this image. This will produce a new
file containing the remaining stars in the field. Next, PHOT is run and it produces a file containing the new apertures for the remaining stars. The PICKPSF and PSF tasks are not required to be run since the program will be using the same improved PSF model created at the end of the last iteration. ALLSTAR is run once again for this new iteration and it produces a table with the star ID (a number is added to the star ID so it does not get confused with the one in the first iteration) and the run gives us a new .als file for this iteration. Finally both als files are combined and a final run with ALLSTAR is done on the whole field. This run is just so the star ID’s for the stars are in consecutive order and also to have one single file with all the stars in the image. At the end the final als file contains a range of 5000 to 14,000 stars, with a median of 8,880 stars. Before moving onto next program the images for the final subtracted ALLSTAR images are checked to make sure that DAOPHOT II/ALLSTAR has done a good job locating all the stars in the image.
Figure 3.5 shows all the subtracted stars from one of the nights. Recognizing that there is 32
Figure 3.5: Image on the right is the original frame. The image on the left displays the subtracted stars. The center of the cluster is really crowded therefore DAOPHOT can not subtract all the stars, also overexposed stars still show presence
still a lot of light in the crowded center and there are a couple overexposed stars, DAOPHOT
has located and subtracted most of the stars in the image.
The following step was a conjunction of the DAOMASTER and MONTAGE pro- grams. DAOMASTER is used to calibrate the star’s position according to the master image. This is done because it is necessary to know the exact location of every single star from frame to frame, which varies due mostly to the dithering effect but also due to the telescope maintenance that may have caused the CCD not to be precisely located where it was originally located. DAOMASTER has problems with big shifts, due mainly to telescope maintenance because when the CCD is removed it is not replaced exactly in the same posi- tion, and for these reasons the data are split in seasons that are delimited by when the last maintenance occurred. The data obtained with PROMPT 5 was split into three seasons:
Season 1 from Feb 2009 to June 23rd 2009, Season 2 from July 9th 2009 until the end of
2009, and Season 3 from the beginning of 2010 until October 26th 2010. There were some data collected after Season 3 but there were not enough frames to make it a good dataset for DAOMASTER, but once more data are collected, the late 2010 data can be used with the new data as Season 4.
The DAOMASTER run is done in each of the single seasons and it begins with the 33 original table containing the reference star location in each of the frames, and then using
Dr. Layden’s daomasterprep Fortran script, an .mchfile is created containing the frame’s name, the location in the x- and y-coordinates of the reference star relative to the master frame (so for the master frame these two numbers will be 0.0 and 0.0), and will be the initial transformation coefficients. (For more information on the transformation coefficients see [27]).
DAOMASTER begins to run once the .mchfile is ready, but to start the run six pa- rameters are set. The first parameter, minnum, tells the program the minimum amount of frames where the star needs to appear, usually at least one-fifth of the frames. If the candi- date star does not appear in at least this number of frames then it will not be considered to be read by DAOMASTER. The second parameter ,minfrac,istheminimumfractionofthe star that should appear from frame to frame, usually 0.25%. The third parameter enufrm is a boundary that tells the program that if a star appears in a set number of frames, usually
1 /2 of the frames, it should be kept no matter what is read in the remaining frames. The fourth parameter, maxsig,tellstheprogramwhatisthelargestphotometricerrorallowed to keep the star, usually 0.6 sigma, so a star with too great of an uncertain magnitude will be rejected. The fifth parameter, transf, tells the program how complicated of a transfor- mation you want (refer back to [27]). Usually 6 will be an adequate number of constants.
The final parameter ,matchup, tells the program the original match-up radius. Usually 5 is agoodplacetostart.Itisgoodtopointoutthatthevaluesusedfortheseparametersare appropriate for this research and the telescope being used, so for this run if there were 40 frames the parameters were: 8, 0.25, 20, 0.6, 6 & 5.
Once the parameters are entered DAOMASTER begins to look for the 30 brightest stars in the master frame, and then proceeds to locate them in each of the remaining frames in the season. Once it has located them it calculates the shifts from the location of the star in a frame to the location of the star in the master frame. After this is done it takes the 34 original matchup and calculates the magnitude within this radius for each of the stars in the frame. After this is done a smaller matchup radius is entered and the program repeats the same procedure but this time uses the previous transformation equation and tries to make a more accurate approximation of the shifts. The program displays the values for each of the variables in the transformation equation but also gives an approximation of the root-mean square (rms)residualsforthexandy.Iftheframepresentsnoproblemtherms should be be below one, but with frames that are not lined up well or that were nights with bad seeing, the rms tends to be bigger. This procedure is repeated with a smaller radius, that gives a more accurate transformation equation and lower rms,untilitgetstoamatchup radius of
1.0. Lower than this is unnecessary because well resolved stars in the frames should not be smaller than a radius of 1.0. Once this is completed DAOMASTER provides a list of stars with given ID’s, the magnitude for each of the stars, location according to the master frame, a variability index (which is an index calculated using the mean magnitude error and the standard deviation of the magnitude, the larger the value for the index the greater variability of the star), the chi and the sharp5for each star.
One of the advantages of working with DAOMASTER is that frames from different
filters can be combined together as long as most of the stars are resolved in both frames. For example frames in the IS and IL cannot be combined together well since most of the faint stars present in the IL will not be present in IS, making the star search tool inaccurate. Also DAOMASTER produces the position for all the stars available throughout a season according to the master frame, and with this position we can create a main image that displays the entire field being studied. Here is where MONTAGE comes in handy. MONTAGE takes the position and magnitude and creates a composite image. Before running MONTAGE the best nights in all the filters and all the seasons are selected. The selection needs to be done carefully to select frames that spans the whole season, and that have good seeing and low sky background. DAOMASTER is run again on the selected nights, producing a
5Describes how much broader the value of the star’s profile appears than the profile of the PSF [26] 35
Figure 3.6: The image on the left is the original master frame, while the image on the right is the composed frame using MONTAGE new .mchfile for the set of images. Once it completes processing MONATGE can be run.
MONTAGE takes the coordinates and magnitude from the new .mchfile and creates the montage picture. Once it completes the program will provide the option of the size of the image and finally the coordinate shift from the montage image to the master frame. Later on these coordinates can be used to locate stars in the CMD (5). Figure 3.6 displays the master frame and the montage frame for season 3 in the IL+V filter combination. The composite MONTAGE image provides a visual aid to locate the stars’ available to be studied in our research.
Once DAOMASTER and MONTAGE are run, the next program, ALLFRAME, can be run on all the images on order to get a more accurate magnitude value for the stars in the image. Since the coordinates from MONTAGE were obtained using the three seasons and not the whole set of images ALLFRAME needs to be run per season as well. The program uses a robust non-linear least-square fit model of the PSF[13] to calculate the most accurate location and magnitude for each of the stars found in the montage frame. Since ALLFRAME 36 is being fed the information from the DAOMASTER run, some of the stars that were not found during the ALLSTAR portion of the run, due to a frame with bad seeing, will be accounted in the ALLFRAME run. Also ALLFRAME obtains more accurate position and magnitude readings for the stars in the frame, becuase it’s using the DAOMASTER instead of the FIND data. ALLFRAME will run a psf-profile fitting iteration, subtracting the stars found after each iteration, just as the ALLSTAR was run. After 200 iterations the program will produce a new .alf file for each frame, similar to the .als file produced after ALLSTAR , containing the ID, location, instrumental magnitude and measurement errors, chi and sharp for each individual star in the frame. 37
CHAPTER 4
CALIBRATION
4.1 Standard Stars
The magnitudes calculated by DAOPHOT are instrumental, meaning that they are relative to an arbitrary zero point dependent on the instrument used (PROMPT5’s camera and CCD). Therefore the data needs to go through a calibration process in order to properly represent the standard magnitudes for the stars in the field.
Standard magnitudes are basically the apparent magnitude of stars that are carefully measured and calibrated to a well-defined standard photometric system. The usual way to establish the calibration in a star cluster is to use the standard stars for the cluster found in other studies and compared with the instrumental data using the following transformation equations:
v = V a + b(V I)(4.1) − −
i = V a + b(V I)(4.2) − − where v and i are the instrumental magnitudes,V and I are the calibrated magnitudes, a and b are the transformation coefficients for the V bandpass and a and b the ones for the I bandpass.
Two sets of data were used to calibrate the field, the first one, and largest, was from
Stetson (2011)[30], which provided B and V photometry for standard stars intended for photometric standards, which are generally selected to be not crowded, covering a wide range of colors and magnitudes and observed repeatedly over many nights which reduces the errors in the values and rejects variable stars.
The second one was from Carreta et al. (2007)[4], who provided BVI magnitudes cali- brated to the standard system (secondary standard stars). The smaller number of standard 38
Set Filter Number of Stars Stetson B 602 V602 I0 Carreta et al. B13 V13 I13
Table 4.1: Standard stars available in the comparison datasets stars in this dataset was because they were used to study the chemical composition of the peculiar bulge in NGC 6388, and therefore they looked for stars in their field of view that were dependent on the criteria required to complete their research, and 13 stars was good enough number to complete their research. Details for each set are provided in table 4.1.
Our standard stars were chosen by two criteria. The first one is the location on the frame, since we want them to represent all possible locations of our field of view and this will allow us to correct any dependence of the calibration on the x- or y- coordinates so we can trust our data in any position of the frame. The second criterion is the location on the
Color Magnitude Diagram (CMD), which would allow us to the account for dependence of the calibration on the magnitude (the V component of the CMD) which will confirm that the PROMPT CCD behaves linearly, and will help us represent a good range of surface temperature of the stars (red and blue stars) in the field of view.
Since both Stetson and Carreta et al. data were taken with different telescopes their coordinates needed to be converted to match the data taken with PROMPT5 due to the fact that each telescope has a different field of view. To perform the match bright and uncrowded stars were located in each of the datasets and a table was created with the x- and y-coordinates. After this the same stars were located in the master image, and then we recorded the x- and y-coordinates for the stars in our system. The reason these types of stars (bright and uncrowded) were selected was that they would be easy to locate in either dataset and in the master image. 39
Acomparisonbetweenbothdatasetswasrequiredsincebothdatasetsneededtobeused due to their individual predicaments; Stetson had no data in the I-Filter and Carreta et al.
only had 13 stars, all of which are bright red stars thus excluding photometry for blue stars
(Figure4.1).
With this information we used the fitrot2.e Fortran program (created by Dr. Andrew
Layden) that takes the input list and solves for the polynomials in the transformation equa-
tion (equation 3.1 and equation 3.2) between the datasets’ coordinates and the master image
coordinates. To make certain that the rotation, scale and offset are even throughout the im-
age the selected stars were located all around the field of view. The good thing about the
fitrot2.e program is that it reads first the coordinates that are provided in the table and then
uses a dimensional polynomial degree (section 3.1.2) to account for the shifts between frames.
Once it finds the transformation coefficients, they were used to transform the coordinates
of stars in the given dataset to our XY system. Once these new coordinates were obtained
they were plotted in the master image using tvmark, an IRAF task which draws a point at
the selected x- and y-coordinates, a necessary step to make sure that every star found in the
two datasets has a match in the master images.
The comparison between Carreta et al. and Steson was done by plotting the (V V ) s − c and (B B )versusthe(V I) and (B V ) ,representing the true color of the stars s − c − c − c in common between both studies; V representing the V filter data, and x position and c − y position representing the spread of the data around the image (c represents the data − by Carreta et al. and s represents the Stetson data). Figure 4.2 displays the difference for
these two datasets, and clearly shows that all the data is right about the zero point, a point
where we expect their magnitude scales to be in close agreement with ours. There is a slight
magnitude difference in the V, 0.0170 rms error, and B, 0.0170 rms error, a small difference,
which led us to believe that using the data from Carreta et al. for the I-filter will land around
or about the same magnitude difference. 40
Figure 4.1: Dereddened V,B V color magnitude for NGC 6388 in a 5.0 selection box around the cluster’s center. WFI− photometry is from Momany et al. (2003); only stars with absolute SHARP values are plotted. Stars observed with UVES and members of NGC 6388 according to their RVs≤ are indicated by (red) filled circles; open circles indicates non member observed with UVES.[4] 41
Figure 4.2: Plot comparing Carreta et al.(blue triangles) and Stetson (black squares) data. [1] Represents the dependence on the color, [2] Represents the dependence on surface tem- perature, and [3] & [4] represent the dependence on the location in the frame 42
Once we confirmed good agreement between Stetson and Carreta et al. data, we pro- ceeded to obtain the calibration coefficients to transform our instrumental magnitudes to the standard system. Here the research was divided in two, first working with the Stetson dataset to calculate the coefficients for the V filter (the I-filter too but more on that below), and then using the Carreta et al. dataset to calculate the coefficients for the I-filter. To obtain the initial values for the coefficients a program provided by Dr. Layden, matchphot.e,
was first used to locate the standard stars in the Stetson dataset in the instrumental data
produced by DAOPHOT and produces a file containing the (v i)(instrumentalcolorin- − dex), the (v V )[thedifferencebetweentheinstrumentalmagnitudeandStetson’sstandard − s magnitude) and the uncertainty in (v V ) calculation. Using this information the IRAF − s routine, curfit plots (v i)vs.(v V )andusingequation4.3calculatesthecoefficients − us − s for the transformation.
v V = a (v i)+b (4.3) − s v − v where v and i are the instrumental magnitudes, Vs is Stetson’s V-magnitude, av is the slope of the line and bv is the y-intercept. A better approach would be to use the values already
calibrated Stetson stars (instead of (v i)use(V I) )butasstatedabovethereisno − − s I-filter photometry for Stetson’s standards.
Next the same program, matchphot.e,arrangedtheCarretaet al. data, and then the
data were used by the curfit task to obtain the coefficients. But since the dataset has such
a limited range of magnitudes for the I-filter was only used only to calculate the y-intercept.
(For the Carreta et al. dataset we have to extrapolate the value of the fit for blue stars).
In order to calculate the value the program used an equivalent to equation 4.1 as shown in
equation 4.4
v V = a (V I) + b (4.4) − c v − c v where V is the standard magnitude in the V-filter for Carreta et al. and (V I)c is the c − color index for Carreta et al.’s data. We only used the coefficient for the y-coefficient because 43 when we add these values to a plot we are secure that the y-intercept does not need abnormal extrapolation whereas the slope coeffcient may require to accommodate the blue stars, this due to the fact that plenty of curves can be drawn to explain the slope seen for the red stars.
Using Stetson’s data only on the V-bandpass meant having no data to compare for the
I-filter. To solve this issue Dr. Layden proposed an approach to find the coefficients for our
Il and Is instrumental magnitudes. Two globular clusters NGC 6352 and NGC 5927 having similar metallicity, location and reddening as NGC 6388 (see table 4.2) but having I as well as B and V photometry in Stetson’s data, were selected to be observed for one night using
PROMPT5. Using these data provided an average for the values of the coefficients needed to calibrate the DAOPHOT data. Once the data were obtained for both clusters, they were processed with DAOPHOT the same way as the data for NGC 6388 (see 3.2.2), and .raw
files containing the instrumental photometry for the clusters stars were produced. Using the instrumental photometry the transformation coefficients for the cluster were found using the following the equations:
i I = a (V I) + b (4.5) l − s il − l il
i I = a (V I) + b (4.6) s − s is − s is where i and i are the instrumental magnitudes for the i long and i short filter respectively, l s − − I is Stetson’s photometry for the I-filter, a and a are the slope coefficients for the i long s il is − and i short filter, respectively, (V I) is the true color from Stetson’s data and b and − − s il b are the y-intercept coefficients for the i long and i short filter, respectively. is − −
Using the slope coefficients [av, ail, ais] found in v (using Stetson’s data in NGC 6388 via Equation 4.1) and il and is (using 6352 and 5927) we proceeded to find the coefficients for the y-intercept for all three filters. The matchphot Fortran program arranges the information that the curfit task then uses to find the actual value of the y-intercept coefficient through aleast-squaresfit.Thetasktakesthe13availablestarsinCarretaet al. and finds their counterparts in the research data. Once the matches are found the program then takes the 44
Cluster Right Ascension Declination [Fe/H] E (B-V) NGC5927 152800.69 -504022.9 -0.49 0.45 NGC6352 172529.11 -482519.8 -0.64 0.22 NGC6388 173617.23 -444407.8 -0.55 0.37
Table 4.2: Comparison of the different characteristics between the clusters chosen for cali- bration and NGC 6388.
coefficients for the slope in each filter and using the following equations for each filter to
calculate a value of the y-intercept coefficient for each of the matched standard stars
a = i I b (V I) (4.7) il l − c − il − c
a = i I b (V I) (4.8) is s − c − is − c
a = v V b (v i ) (4.9) vl − s − v − l us
a = v V b (v i ) (4.10) vs − s − v − S us
The routine takes the (V I)(or(v i)) values used, the values of the slope for each of the − − stars, and the uncertainty for the slope in the filter and produces a value for the y-intercept for the cluster and the overall RMS (scatter of the data about the linear fit) values to the
fit. These values can be seen in table 4.3. This same procedure was repeated for the Stetson data but curfit was used to find the values for both coefficients; the results are also in table
4.3.
Once the coefficients were found another Fortran program, transform.e,providedby
Dr. Layden, uses them to calculate the standard V and I magnitudes as well as the true color
(V I)fortheallthe12,683starsfoundinsection3.2.2.Theprogramusesthefollowing − transformation equations to calculate the standard values
(v i) (1 b ) (a a ) (V I ) = − ∗ − v − v − il (4.11) − l us 1 b − il 1Number of stars used for the fit. For Carreta only 9 stars where in our field of view 45
Stetson Filter a(y-intercept) b(slope) RMS #ofStars1 Comments V-0.50620*0.04161*0.02619327
Carreta et al. V(long)[2] -0.4958 0.04161 0.01531 9 Using the IL filter instru- mental photometry to find the coefficient V(short)[3] -0.49291 0.04161 0.01567 9 Using the IS filter instru- mental photometry to find the coefficient I-Long[4] 0.14672 -0.05058 0.00475 9 Usingtheslopecoefficient found using the NGC 6352 data I-short 1.7619 -0.0566 0.00786 9 Usingtheslopecoefficient found using the NGC 6352 data I-Long[5] 0.2758 -0.11235 0.00758 9 Usingtheslopecoefficient found using the NGC 5927 data I-short 1.88067 -0.11342 0.01013 9 Usingtheslopecoefficient found using the NGC 5927 data I-Long[6] 0.21125* -0.08145* 0.0048 9 Using the average of the slope coefficient from the NGC 6352 and NGC 5927 data I-short 1.82128* -0.08501* 0.00826 9 Using the average of the slope coefficient from the NGC 6352 and NGC 5927 data
Table 4.3: Coeffcients values obtained with each approach. The * marks the coeffcients we used for calibration 46
Star ID X Y V (mag) Error V I (mag) Error I Il or IS2 Chi Sharp 1312.994221.2499.2040.00577.9690.005523.173-0.037 2441.095465.28611.1280.00519.3660.005312.121-0.022 34.067525.08310.1870.00859.9540.008411.9180.086 4348.153517.49212.2350.00518.9870.00532 2.07-0.095 5623.999682.74410.2890.00519.990.00511 1.93-0.006
Table 4.4: The table displays the calibrated values for each of the 12,683 stars found using DAOPHOT
(v i) (1 b ) (a a ) (V I ) = − ∗ − v − v − is (4.12) − s us 1 b − is V = v a b (V I) (4.13) us − v − v − us
I = i a b (V I ) (4.14) l(us) l − v − il − l us
I s(us)=i a b (V I ) (4.15) − s − v − il − s us where (V-Il)us represents the color index for the standard magnitude, (v-i) represents the color index for the instrumental magnitude. The programs allows the option to either use the Il or Is ,this was chosen according to the error in the magnitude if the Il filter magnitude error was smaller than the Is then it will be used if its great thenthe Is magnitude was used. Then the program simply writes the V and I for each star. Table 4.4 displays the output reported by the program
After running the transformations and finding the standard magnitudes for the stars in the data, an equivalent to matchphot was used to compare the values for the standard magnitudes in the Stetson dataset to those in our DAOPHOT data. The program once again tries to locate all the standard stars in Stetson but this time compares them against our calibrated magnitudes. A comparison was done between both datasets in order to choose the more accurate set of coefficients to provide the accepted values for the standard magnitudes.
At the end the selected coefficients (marked with an * in table 4.3) were the average of the
2 One (1) refers to when the Il magnitude was used and two (2) is for when the program used the Is magnitude. 47 coefficients found using the reference clusters for the I-filter and the coefficient for the V-filter found using Stetson. The coefficients were chosen after a trial and error approach that gave us the values closest to zero and with our slope in the comparison plot. Figure 4.3 displays the comparison between Stetson’s data and our data. If the data are centered around zero
(0) with no slope then we correctly transformed our instrumental photometry to Stetson’s V system. We found that our calibrated magnitudes show no dependence in the color, surface temparature and position on the frame.
4.2 Variable Stars
We used differential photometry in order to calibrate individual variable stars. The procedure uses a group of non-variable comparison stars with reliable VI calibration to obtain the standard magnitude for the variable stars in each of the nights. This approach for variable stars is needed because its color and magnitude change as the star goes through its phases, and also it will remove any discrepancies caused by location (X and Y) dependence, and uncertainties of the airmass and atmospheric absorption. The selected comparison stars for the differential photometry were selected via two criteria: 1) Neighboring stars, which are physically located near the variable stars. Figure 4.4 shows variable star V4 and neighboring comparison stars. 2) Similar location on the CMD, meaning similar color and similar magnitude as the variable star. Figure 4.4 shows V4 in the CMD and comparison stars. Once comparison stars are selected, differential photometry is accomplished using the instrumental magnitude for the variable and comparison stars and the standard magnitudes for the comparison stars (these magnitudes obtained from the previous processes). The calibration is obtained by subtracting the color calibration equation for the comparison star
(equation 4.16) from the color calibration equation for the variable star (equation 4.17)
(v V ) = a b (V I) (4.16) − comp v − v − comp 48
Figure 4.3: Each square displays the dependence of our calibrated data about the color, surface temperature, and location around the image. Since all the seems to be centered about the zero (0) point without slope we can be confident that our calibration process was done right. 49
Figure 4.4: The figure show V4 marked by a circle in the CMD sourrounded by different comparison stars(marked by their (V-I) value) 50
(v V ) = a b (V I) (4.17) − var v − v − var
Once subtracted we solve for Vvar which is the color calibration for the variable star using equation 4.18
V =(V v)comp + v b [(V I) (V I) ](4.18) var − var − v − var − − comp
(V-I)var is found from equation subtracting equations:
(v V ) = a + b (v i) (4.19) − var v v − var
(i I) = a + b (V I) (4.20) − var i i − var which results in (1 b )(v i) (a a ) (V I) = − v − var − v − i (4.21) − var (1 b ) − i
This gives us an estimate of the Vvar from each comparison star. Then we take the median of the N comparison stars to obtain a best estimate of the true magnitude of the variable, and
compute the standard error (rms/√N), which describes the uncertainty of the magnitude.
This process is repeated for each night in our dataset to be able to derive the magnitude vs.
time behavior of the variable star. Once this is done the magnitudes for the stars are ready
to plot light curves. 51
CHAPTER 5
COLOR MAGNITUDE DIAGRAM
We created a suitable CMD that will include all the data present in our research to represent a full range for the color and surface temperature in our cluster. We wanted to make sure that all the brightest stars (which don’t appear overexposed in the Is)andall the really faint stars (mostly available in the Il)wereaccountedfor.Sincethedatawere divided into three seasons it was decided that season three with the most data would be the best representation of the CMD for NGC 6388; we came to this decison after comparing the intial CMD plotted using the instrumental magnitudes. We used the iiv.raw obtained by
DAOMASTER to create the CMD, reason be is that all the stars taken in the research will
be accounted for (this will include the dim and bright stars). Also only the best nights (8
nights, 20% of season 3 data) were used to create the montage data, which will provide more
accurate magnitudes for the stars in the field, due to lower values in the FWHM, fewer star
blending and darker skies. With these data we created a CMD containing all the stars in
our field (Figure 5.1).
After calibrating the data in our frames we needed to remove field stars, which con-
taminate the our field of view, in order to display an acceptable CMD. We requested frames
that were offset by an entire field of view (10 arcmin north of the cluster center) the offset
was chosen because it will only include stars outside a radius of 6.25arcmin (which is the
NGC 6388 Rtidal) which will assure us that the frame is probably populated only by cluster members. These frames were processed using the methods described in chapter 2 and 3 and
calibrated using methods described in chapter 4. Once the field stars were processed a CMD
containing the field stars frame was created as well (Figure 5.3b).
The following is an approach on how to minimize the presence of field stars in our CMD.
First we proceeded to define our what would constitute different criteria for subtraction: 1)
by definition cluster members must exist within the Rtidal and outside a radius that does not 52
Standard CMD Season 3
01234 V-I mag
Figure 5.1: Color Magnitude Diagram for the whole field. The error lines on the right represent the margin of error on V and V-I. 53 include the crowded center, which was chosen to be 130 pixels (which is the radius of the crowded center), 2) the cluster is really crowded so errors in magnitude need to be accounted for (to estimate this value we used DAOPHOT’s chi value, where a value greater than 2.5 will be discarded as too high to be considered for the CMD). We then proceeded to remove data defined by the criteria for both our cluster (Figure5.2) and field star data, to make our approach constant in both fields. The data is also removed from the field to keep both datasets statistically the same. The data is removed by a Fortran program, qcmd.f, which produces a file containing the remaining stars V and I magnitudes, the (V-I) magnitude, the error for this magnitudes, the chi and sharp (Figure 5.3c). In the image we can observe the red clump better, a good amount of field stars over the AGB have been removed as well, but the HB is still not clearly recognized and the field star branch that stars around (V I)=1 − and V =17andslopesuptotheleftisstillpresent;thissamebranchcanbeseeninfigure
5.3b, which indicates us there are still field stars that can be subtracted from our calibrated
CMD. If we observe at figures 5.3b and 5.3c, we can see that the field star branch stars
sloping at the same location display the same slope on both plots, which is a good indication
of the absence of differential reddening between our cluster’s images and field star images;
the absence is also demonstrated by the reddening vector in Fig. 5.3a, which demonstrates
that because the reddening factor between our cluster and the field had a difference we will
see our cluster shift in magnitude and color by the amount seen in reddening vector.
Once the field frames are processed we proceeded to subtract the field from the remaining
cluster stars in our cut data. To do this we used a Fortran program, subcmdxrad.f,which uses a statistical approach to remove the field stars. First the program will read the file
produced by qcmd.f,andtaketheV magnitude and (V I) magnitude for the field stars − file, and then will try to locate a star in the cluster file that has the same V and (V − I)magnitudes.Ifitfindsitbetweenasmallrange(0.001by0.001magnitudes)thenit
will remove the star from the cluster list. Once this run was completed, if there are still 54
Figure 5.2: The image shows the tidal radius (outer circle) and half-mass radius (inner circle) for NGC 6388. Observing how the half-mass radius still lies inside the crowded center it is more logical to use the tidal radius as a measurement of cluster membership. 55
Standard CMD Season 3
0123401234 V-I mag
Figure 5.3: (a)The top left box show the entire data obtained by DAOPHOT and the reddening vector for NGC 6388. (b)The top right box displays the CMD for the offset field. (c) The bottom left box shows the initial cut using Rin =130pixels,Rout =RTidal and rejecting all stars with a chi 2.5. (d) Shows the subtraction of the field stars from the remaining stars in (c) which shows our most precise CMD. 56 unmatched field stars the range will be increased (1:3 ratio on (V I):V )onarateof0.001 − magnitudes until either all the field stars have been matched or the program reaches a range of 0.5 by 0.5 magnitudes (We did not have a problem with the big val;ue since we expect most of the field stars in the crowded parts of the CMD will be subtracted away and the 0.5 by 0.5 magnitudes will be necessary in the parts of the CMD that are populated by a low amount of stars). Once the run is completed the program will produce a file containing all the remaining cluster members. We created a plot displaying each of the different processed data used for subtraction with the final result (figure 5.3d).
A couple of details can be seen on the subtracted CMD. First dim stars with magnitudes less than 18 mag will not be considered as variable star candidates, due to very low signal to noise ratio, which is expected since our study was not driven to study such faint stars; second the HB is clearly visible, at V =17andV I lower than 1 which let us confirm that − the subtraction method was a great approach to remove field stars; third most of the stars above the RGB and the field star branch have been removed with gives us confidence that when we establish cluster membership using the subtracted CMD will provide a great tool.
5.1 Isochrones
We can use our CMD and isochrones to assess if or data agrees with the values of red- dening and metallicity found by Harris (1996)[9]. Girardi (2002)[8] provided the isochrones, which brackets the known metallicity of NGC 6388 ([Fe/H]=-0.44):z =0.004and0.008,
[Fe/H] = -0.7 and -0.4, respectively. Figure 5.4 shows the two isochrones (both with Age
=11.22Gyr)plottedoveroursubtractedCMD;theywereshiftedbythereddeningfactor,
E(V-I), and apparent distance modulus , Av, using the equations of Cardelli etal. (1989)[3]
E(V I) − =1.24 (5.1) E(B V ) − 57
A v =1.2(5.2) E(V I) − since we have E(B-V) = 0.37 as defined by Harris (1996), then we obtained an E(V-I) =
0.458 and Av = 1.10. The reddening vector on Figure 5.3a employs this relation.
We can see that both isochrones bracket at the red clump and the upper and AGB stars; further inquiry shows that the z = 0.008 isochrone follows the AGB closer, which agrees with the latest values for the metallicity found for NGC 6388.
We can sum up that our data is in agreement with the isochrones provided by Girardi
(2002)[8], and the values of reddening and distance modulus agrees with Harris (1996)[9], while the [Fe/H] agrees with Carreta (2007)[4]. 58
Standard CMD Season 3
[Fe/H]=-0.7
[Fe/H]=-0.4
01234 V-I mag
Figure 5.4: The subtracted CMD is plotted against two isochrones provided by Girardi(2002) [8], with both isochrones corrected for reddening and distance. It can be seen that the isochrone for [Fe/H]bettermatchesourCMD,whichconfirmsthevalueof[Fe/H]published by Carreta etal.(2007)[4] 59
CHAPTER 6
VARIABLE STARS
Once photometry was completed in our dataset we use the data obtained from both photometric software, DAOPHOT and ISIS, to identify candidate variable stars. Variability in ISIS is obtained using the star’s flux while DAOPHOT uses the star’s apparent magnitude.
6.1 Variability Detection
The following sections will discuss how each software uses different methods to identify our variable stars.
6.1.1 Variability detection with ISIS
ISIS uses a subtraction method to find variable stars. As discussed previously ISIS detect.csh creates a frame, var.fits (Figure 6.1), which displays all the possible variable stars within a given radial profile threshold. Each of the possible variables is label by ISIS with an lc (number).data id, so each of the possible variables in the var.fits has a file
containing its flux data and time of observation. We examined the radial profile for all
the possible variable stars in order to narrow down the pool of candidates (we found 47
candidates for Il(out of 123), Is(out of 8xxx) and V(out of xxxx)). As explained in chapter 3, the profile will tell us if a star is just a really bright star, which will produce a saturated
profile, a bad pixel, which produces a scatter profile, or a good candidate for variable star,
which will produce a profile between the desired range. (Figure 3.3 in chapter 3 shows a
scatter and good profile).
6.1.2 Variability detection with DAOPHOT
The main tool to select our candidates for variable stars in DAOPHOT is the variability
index (A), which is the ratio of the standard deviation of the magnitude and the weighted 60
Figure 6.1: The var.fits lets us know all the stars that display some variability in ISIS. 61 average of the errors assigned by DAOPHOT to the particular star on each image (equation
6.1) σ = (6.1) ∧ error where the higher the index the more likely a star will be variable. This is due to the fact that as the star varies over time the deviation from the mean (a point where the magnitude is the same) changes over time; therefore we have done a correct job with DAOPHOT and calculated the correct magnitude for the star.
To select variables using the variability index we plotted it against the weighted mean found using DAOPHOT, as displayed in Figure 6.2. It can be seen that the index changes from filter to filter and therefore the threshold selection is different as well. Before explaining the threshold it’s important to explain what we are seeing in the graph. If we take a look at the index for the IL filter we can see that at fainter magnitudes (I 18) the variability ≥ index is flat and not greater than 4, so we can take this is as a starting selection point. We can take a closer look at the graph where 4andI 18, (zoom-in section in figure 6.3). ∧≥ ≤ On the zoomed-in part we can see there are three sections where the curves up, the first ∧ one when V = 16 magnitudes, the second when V = 14 magnitudes and the final one after I
= 12 magnitudes. Remembering the different types of variables we suspect the first slope to be the RR-Lyrae stars present in the cluster, due to the fact that they are the least bright variable stars and therefore the first ones to show greater variability. The second slope we suspect to be from Population II Cepheid stars, a group redder and brighter that RR-Lyrae stars. Last the third slope, we suspect them to be our LPVs since they are the redder and brighter stars in our plot. Also since they have larger range of magnitudes they would also display greater variability index.
Now that we know where we expect to locate the stars in our plot we can set up a threshold for our variable stars. The selected threshold is different from filter to filter therefore we selected a threshold of 15 or IL, 10 for IS and 23 for V (visually ∧≥ ∧≥ ∧≥ 62
Magnitude vs Variability Index for Season 3
V Filter - Green I Short - Blue I Long - Red
8 10 12 14 16 18 20 22 Instrumental Magnitude
Figure 6.2: Variability index ( )isplottedagainstthemagnitude,whichgivesapossible criterion to judge the variability∧ of our stars
Figure 6.3: Variability index ( ) is zoomed in to display the three slopes (at I = 16, I = 14.5 and I = 12) which could describe∧ three different types of variable stars (RRLyrae, P2C and LPV respectively. 63 selected and which gives us about 64 candidates out 12432 total stars).
6.2 Magnitude vs. time Detection
Our next step was to narrow our candidates by plotting magnitude (or flux) vs. time of the stars, which is necessary because some of the possible variable found in the previous step could be blended stars which display greater magnitude, or stars located at the edges of the master frame which will not have an accurate reading on their magnitude and be suspected as variable stars and other anomalies that would cause a star to have a high . ∧ The period detection with ISIS for our dataset was done by using two tools. First we used
IRAF’s PDM1task, which applies a phase dispersion minimization algorithm to light curve data to determine periodicities in the data[25], the method is also known as period folding, which is done by creating a phased light curve (magnitude vs. phase), where the phase is obtained using equation 6.2
HJD HJD HJD HJD P hase = − o int[ − o ](6.2) P − P
where HJDo is a selected epoch (for our research we used 4800), HJD is the remnant of the Julian date for the observation and P is the period for the variable star. This approach is
very fitted to our observations due to the fact that we have a gap in our data for the period
when the cluster did not rise, this value of the phase allows us to represent the whole two
years in one cycle.
PDM will read the lc (number).data file containing the HJD, the flux and error in the
flux for each of the dates. The PDM will use trial periods to evaluate the scatter of our light
curve about these periods by dividing the light curve into phase bins, and use a statistical
quantity, θ,theratiooftheweightedscatterinthebinstothatforthewholelightcurve,
to evaluate the periods[15]. Since we don’t know the period for the star PDM folds the
1Phase Dispersion Minimization 64
Figure 6.4: θ vs. Period graph produced by PDM. Here the lower value of θ near the period of 250 represents the values that best fitted the trial period time/mag data with a wide range of periods (see x-axis on Figure 6.4) and at each period it calculates the theta statistic over our light curve and produces a graph of θ vs. period
(Figure 6.4)
When θ has a value near zero,itmeansthatthevariationofthelightcurvearound the mean has the smallest scatter, and therefore a good candidate for a variable star, but when theta has a value near 1 then the variation of the light around the mean is mainly scatter and therefore an incorrect period Figure (6.5). After this we used the period with the lowest value of theta to obtain the folded light curve for our star (Figure (6.6). In the case of Figure 6.4 we are able to see that clearly the period of 257 6daysprovidesthemost ± regular variation. Even if the folded curve was really accurate (it shows good periodicity, the amount of scatter around the mean fit is very small) we checked other values where theta displayed a small value (closest to zero) and plot the theta vs. magnitude plotted using that period.
As a complementary for PDM tool we used ISIS’s Czerny Method. The method was used to find periods for stars where the PDM task could not produce one (in less than 1% of the cases PDM will crash due to software issues), or when we needed to confirm the period 65
Figure 6.5: Folded curve using θ close to 1 which shows mainly scatter
Figure 6.6: Folded curve using θ close to 1 which shows mainly scatter 66 for a curve for which we were not completely certain of its accuracy, most likely due to the scatter the folded curve produced using the trial periods. The point of using PDM task first and then the Czerny method too is that PDM allows us to select different possible periods
(sort of a trial and error approach), whereas the Czerny tool takes the data itself and prints out what it believes to be the most accurate value for the period.
A second light curve detection method tool was used only for DAOPHOT data. The method, STDLC, is a template fitting method4. The method was applied in a series of three Fortran programs created by Dr. Layden. The first program, stdlc per iiv.e,will
take the calibrated data file (varstd.(starid)) and folded the light curve over a series of 10 template curves (Template 1-6 were for RRab type variables, template 7 was for a RRc
type variable, template 8 was a simple sine-curve, template 9 was for W UMa type variable
[Eclipsing Binary star] and the last template curve was for an Algol type [detached Eclipsing
Binary]) and they were fitted according to a given range and amount of periods (i.e. for our
sample star we used a period between 200 to 300 days every 0.25 days), where the range
was obtained by looking at the unfolded light curve (Figure 6.7). Once the program finishes
it creates a SuperMongo plot that displays a chi2 vs. magnitude plot for the six template
curves that better fit to the given data (Figure 6.8) where chi2 is the measure of the standard
deviation over the error of the magnitude, a value that describes how small is the scatter
of the observed mag/phase points around the fitted LC template. Using the plot we can
observe the different templates that fitted our data, and with the chi2 we can select a more
acute periodicity range that will work better for our data.
The second Fortran program, stdlc peranal iiv.e,willtakethefilecreatedinthepre-
vious program and using a given periodicity range (i.e. for the sample star we used a range
150 to 300, where the value of chi2 displays a minima) finds the lowest chi2 for each template
and reports the period at which it occurs for each of the ten templates for the given range.
For the third and final program, stdlc iiv.e,weusedtheperiodforthetemplatecurve 67
Figure 6.7: In this curve we visually obtain an extimate of the period for the variable star
Figure 6.8: chi2 vs trial periods for template fitting method. The lower value of chi2 repre- sents lower scatter of the trial period using the selected template 68
Figure 6.9: Folded Curve using the template fitting method
that has the lowest chi2 and then the program uses the periods to fold the data for all the
template light curves according to this period. The folded data will use a φ value found and
then the program creates two files. The first file is an SM file displaying the best fit folded
curve for the period (Figure 6.9); the second file is an output containing the mean magnitude
for the variable, the range, amplitude, period-index among other values for the light curve.
(Range and amplitude will be explained in the Section 6.3 below.) The period-index is
similar to the variability index in the first part of the chapter. This value is a calculated
using equation 6.3 ∆V P.I = (6.3) σ where ∆V, calculated when the least squares fitting in stdlc adjusts each template (at a given period) by scaling it shifting it vertically (amplitude) and horizontally (mean magnitude), is the amplitude from the best-fit template LC and σ is the rms of the points around the
fitted template. Once this is completed in the I-Filter we move and do the same procedure
for the V-Filter data. 69
We had cases where the first program in the tri-set of Fortran programs will not be able to give us a clear chi2 value and therefore we went back and used IRAF’s PDM task in order to obtain a period for the stars. This issue, which was a software issue that we are trying to resolve for future research, was only present for variables with short periods (such as RR
Lyrae and Pop II Cepheids).
6.3 Variable Properties
Using the variabilitydetection and magnitudevs.time criteria we selected our candi-
dates; subsequently we looked at each light curve and their different properties and catego-
rized them according to three properties: Period, Amplitude and Regularity.
The data for the periods were obtained from the phase plots obtained with either PDM
or STDLC approach, which aids the light curve since some of our light curves are missing
data, and all of our curves dont have complete cycles (due to the part of the year our cluster
does not rise over the horizon). Using the period we can give an initial prediction at what
type of variable is our candidate: periods between 0.05 and 1.2 days are classified as RR
Lyrae type periods, 2.0 to 50 days are classified as Population II Cepheids and periods of 50
to 1000 days are classified as Long Period Variables.
Amplitude is obtained from the light curve plot, and simply put is the average range
of magnitudes (the observed peak to trough behavior of the light curve). Two values would
be reported later on, range (the difference between the highest peak and the lowest trough)
and amplitude,wherethecloseragreementbetweenbothvalues,thebettertheperiodicity
of the star. The amplitude on the V filter is typically 0.5 to 1.0 magnitudes for Population II
Cepheid stars, RR Lyrae stars range up to 1.5 magnitudes and 2.5 magnitudes or higher for
LPV stars. One of the problems that we may encounter with our amplitudes is dilution of the
actual amplitude caused by blending. Dilution happens when a bright variable stars located
in a crowded are blends with a non-variable star and the photometric software recognizes 70 both stars as one star; therefore because of the blending the calculated variation of the star will diminish (i.e. a star that originally percentage variation 50%, when diluted it could have a percentage variation of 25%), this is better seen when the amplitude in the V-bandpass is less than that of the I-bandpass, since a blackbody has a bigger range in the visual than the red bandpass. In the next chapter we will show light curves displaying possible stellar dilution.
Regularity of our variables can be observed by looking at the light curve, where we looked at the constant of the behavior of the light curve. For LPV stars the more sinusoidal curves, where the magnitude for the peak and trough in each cycle is almost the same, are classified as Mira. Light curves that vary slightly more in their periodicity (showing some sinusoidal regularity with numerous irregular) and which amplitudes tend be lower than 2.5 mag are classified as semi-regular. And finally, stars that display some variability but no discernable period and lower amplitude than semi-regular variables are classified as irregular[14]. The reason why Miras tend to have greater amplitudes than semi-regular and irregular stars would be due to the mode which the variable is vibrating. Mira stars are believed to vibrate in the fundamental mode and therefore their expansion tends to be slower, while semiregular vibrate in the first and second overtone, respectively, making them faster vibrators. It is important to point out that the distinction between semi-regular and irregular variables will depend on the actual observation of the light curve, where some irregular stars may just require additional observations to find a detectable period.
6.4 Known Variables
Once all of the possible candidates were studied and all the thresholds applied we ended with 47 candidates using ISIS (Figure 6.10) and ended up with 47 candidates for variable stars using DAOPHOT (Figure 6.11) (there were 32 candidates shared by both softwares).
Now that we have all our candidates we can start compiling our results and identify the 71
Figure 6.10: Candidate variable stars found using ISIS
Figure 6.11: Candidate variable stars found using DAOPHOT 72
Known Name Type X Y ID Comments V1 Mira - - - Out of FOV V2 Mira 392.53 392.87 29 - V3 - 330.92 469.83 99 - V4 Mira 45.84 451.93 82 - V5 - 481.33 389.88 164 - V6 - 376.65 248.81 119 - V7 - 211.48 318.11 152 - V8 - 385.92 484.35 132 - V9 - 326.91 503.68 156 - V10 - - - - Out of FOV V11 - - - - Out of FOV V12 - 267.83 409.7 68 - Table 6.1: Data from LEM. The x and y coordinates and the ID are according to our research. The ID is from season 3 of the calibrated DAOPHOT data properties in each of our candidates.
Initially we are reporting on the known variable stars. We decided to take this approach to prove that our research was properly conducted and it can expand on previous knowledge for these stars. The report will be divided in three sections, one section for each three papers that contain periods and/or light curves that can be used to compare with values we found. But before we could compare datasets we first needed to match the coordinates in our catalogue to each of the articles coordinates, a step necessary since our images are taken with the Prompt5 telescope.
6.4.1 Comparison with LEM
LEM data was taken with the 1.88-meter reflector at Radcliffe Observatory, Pretoria.
Table 6.1 shows the variable stars found in LEM. The LEM study was one of the first ones to publish variable data about NGC 6388, but the data used was not taken specifically for the study of variables; the small number of images taken were intended to identify LPVs but not to provide well-sampled light curves or determine periods. In comparison ours was dedicated to locate variable stars and the first one to obtain period and classification for most of these LPV’s (other studies have published data on V4 and V12)
To locate the stars in LEM we used their finding chart and compared it visually with our master frame. We could not use fitrot2.e since there were no analogous coordinates to 73 compare the data. For the comparison the stars we rotated LEM finding chart 90 degrees clockwise, and then we were able to find four stars (V6, V7, V4 and V10), and then used these four stars to locate the remaining stars. We did not have any light curves or period to compare with, but through visual identification we are confident about that the stars in our research are the actual ones found in LEM. 74
V2 (ISIS) I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days] V2
I-Long
I-Short
V0 Filter
-1 0 1 2
Figure 6.12: Variable V2 light curve Top Left - ISIS, Top Right - DAOPHOT, Bottom - Folded ISIS curve)
Variable V2 (Figure 6.12) is located 0.268 arcmin away from the cluster center, and because of its crowded location we were not able to obtain a full set of data, a problem visible using DAOPHOT. The period obtained using the PDM method was of 227.4 ± 5days.TheIfilterinbothsoftwaredisplaysamorecontinuouscurve,wheretheVfilter displays flatness when the star’s magnitude gets dimmer, an expected behavior for the redder star where at low magnitudes the magnitude in V mays display a non-variable behavior. The visual amplitude in I is 1.25 and 0.84 in V and a range of 1.38 for the I Filter and 0.910 for the V filter. The photometry for this star shows a clear sample of stellar dilution, which is expected from the location of the star. Using the light curve, period, amplitude and range
V2 can be classified as a Mira variable. 75
V3 (ISIS) I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days] V3
I-Long
I-Short
V0 Filter
-1 0 1 2
Figure 6.13: Variable V3 light curve Top Left - ISIS Top Right - DAOPHOT Bottom - Folded ISIS curve)
Variable V3 (Figure 6.13) is located 0.701 arcmin away from the cluster center. Using the PDM method we found a period of 156.8 4days.Itdoesnotdisplayaperfect ± sinusoidal periodicity but the imperfections in the curve appear to be regular. It displays a visual amplitude of 0.92 in the V and 0.67 magnitudes in the I, while having a range of 1.43 in the V and 0.90 magnitudes in the I-filter. Therefore V3 can be classified as a semi-regular variable. 76
V4 (ISIS) I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.14: Variable V4 light curve Top Left - ISIS Top Right - DAOPHOT)
Variable V4 (Figure 6.14) is located 3.233 arcmin away from the cluster center. Using the PDM method we found a period of 253.3 4days.Thisisaperfectsampleofwhat ± we expect of a Mira variable. It has a close sinusoidal curve with close to two full periods in the light curve, and amplitude of 5.47 in the V and 2.730 in the V filter, with a range of
6.09 mag in the V and 2.73 mag in the I filter. Using its light curve, period, amplitude and range V4 can be classified as a Mira Variable. 77
V5 (ISIS) I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days] V5
I-Long
I-Short
V Filter
-1 0 1 2
Figure 6.15: Variable V5 light curve Top Left - ISIS Top Right - DAOPHOT Bottom - Folded ISIS curve)
Variable V5 (Figure 6.15) is located 1.583 arcmin away from the cluster center. The period was obtained using the PDM method ending up with a period of 98.6 3 days. The ± light curve has a clear regularity for the period, with an amplitude of 1.660 for the V and
0.81 magnitudes in the I-filter and a range of 2.88 magnitudes in the V and 1.220 magnitudes in the I-Filter. Because of these characteristics V5 can be classified as a Mira Variable. 78
V6 (ISIS) I-Long lc52 I-Long
I-Short lc136 I-Short
V0 Filter lc111 V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days] -1 0 1 2
Figure 6.16: Variable V6 light curve Top Left - ISIS Top Right - DAOPHOT Bottom - Folded ISIS curve)
Variable V6 (Figure 6.16) is located 1.605 arcmin away from the cluster center. The period was obtained using the PDM method ending up with a period of 69.9 7 days. The ± light curve displays some regularity but in the IL displays a drop in magnitude for season 2, which is most like caused by the montage (reference to chapter) processing. This is because when DAOPHOT is trying to match stars between different seasons the star in season 1 and season 3 could be blended with another stars, while the blending was not present for season
2, so the matching program may not find the proper star from season to season and report the magnitude for the wrong star. Using the average flux curve we can see the star maintains its regular periodicity. The light curve has an amplitude of 0.38 magnitudes in the V and
0.12 magnitudes in the I-filter, with a range of 0.87 in the V and 0.51 magnitudes on the
I-filter (we used the Ishort photometry to obtain these values). Using these properties V6 can be classified as a semi-regular variable. 79
V7 (ISIS) I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.17: Variable V7 light curve Top Left - ISIS Top Right - DAOPHOT)
Variable V7 (Figure 6.17) is located 0.511 arcmin away from the cluster center. The period was obtained using the PDM method ending up with a period of 105.1 12 days. The ± light curve for the DAOPHOT photometry was not expected to agree with the ISIS curve since this variable star is located inside the crowded center. It displays an amplitude of 0.15 mag and 0.28 mag in the V and I filter, respectively, and a range of 0.49 mag in the V filter and 0.66 mag on the I filter. V7 displays another possible sample of stellar blending since we got I amplitude greater than V amplitude. Using the average flux light curve, period, and amplitude V7 can be classified as a Semi-Regular Variable. 80
V8 (ISIS) I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.18: Variable V8 light curve Top Left - ISIS Top Right - DAOPHOT)
Variable V8 (Figure 6.18) is located 0.728 arcmin away from the cluster center. The period was obtained using the PDM method ending up with a period of 73.9 5days. ± Because of its location so close to the cluster center its magnitude data points tend to have greater error bars. The flux curves display a more continuous semi-regular periodicity and the indication of a probable LSP (Long Secondary Period) where the mean of the curve tends to be first decreasing and then increasing. It shows an amplitude of 0.44 mag in the V filter and 0.33 in the I-Filter, with a range of 1.21 mag in the V filter and 0.70 in the I. V8 can be classified as a Semi-Regular Variable, noticing a somewhat continuous sinusoidal period with a probable LSP in its light curve. 81
V9 (ISIS) I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.19: Variable V9 light curve Top Left - ISIS Top Right - DAOPHOT)
Variable V9 (Figure 6.19) is located 0.511 arcmin away from the cluster center. The period was obtained using the template-fitting method ending up with a period of 59.50 ± 3days.Itislocatednearthecenterofthecluster,whichisthereasonwhytheerror-barsin
DAOPHOT are more pronounced. It has an amplitude of 0.15 mag in the V filter and 0.04 mag in the I filter, with a range of 0.60 mag in the V-filter and 0.43 mag in the I-filter. This variable star could require more study since it could have a probable LSP that can be seen by the rising behavior of the light curve through all three season. Using all its properties
V9 has been classified as an Irregular LPV star, but more data are required to confirm the classification. 82
V12 (ISIS) I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.20: Variable V12 light curve Top Left - ISIS Top Right - DAOPHOT)
Variable V12 (Figure 6.20) is located 1.026 arcmin away from the cluster center. The period was obtained using the PDM method ending up with a period of 81.6 8days. ± The light curves for both the flux and magnitude agree in their shape, with an alternating high-low peak behavior. It has an amplitude of 0.37 mag in the V filter and 0.23 mag in the
I-filter with a range of 0.970 mag in the V filter and 0.49 in the I-filter. V12 can be classified as a Semi-Regular LPV. 83
PSCS Name Type (PSCS) Period (PSCS) X Y ID Comments V14 Binary - 1532.5 1858 - Too close to cluster center V16 RRL 0.251 - - - Too close to cluster center V17 RRL 0.611 308.27 370.03 68 - V18 P2C - 322.26 489.99 481 - V20 RRL 0.467 - - - Too close to cluster center V21 RRL 0.814 478.31 642.67 778 - V22 RRL 0.587 488.24 408.04 3038 - V23 RRL 0.338 67.97 441.02 1130 - V26 RRL 0.239 561.62 308.26 3059 - V27 RRL 0.365 473.53 387.63 1444 - V28 RRL 0.84 413.17 328.42 226 - V29 P2C - 338.62 421.8 498 - V30 RRL 0.951 454.72 398.56 2333 - V31 RRL 0.341 574.7 577.44 3429 - V32 RRL 0.522 - - - Too close to cluster center V33 RRL 0.558 - - - Too close to cluster center V34 RRL 0.236 - - - Too close to cluster center V35 RRL 0.3 485.49 766.72 202 - V35 P2C - - - - Too close to cluster center V36 P2C - 418.44 440.82 279 - V37 Binary - 373.86 372.43 1630 - V39 Binary - - - - Too close to cluster center V40 Binary - - - - Too close to cluster center V41 Binary - - - - Too close to cluster center V42 Binary - - - - Too close to cluster center V43 Binary - - - - Too close to cluster center V44 Scuti or SX Phe 0.08 - - - Too close to cluster center V45 LPV - - - - Too close to cluster center V46 LPV - - - - Too close to cluster center V47 LPV - - - - Too close to cluster center V48 RRL? 0.355 - - - Too close to cluster center V49 RRL? 0.384 390.13 345.66 472 - V50 RRL? 0.364 334.47 452.28 102 - V51 RRL? 0.397 417.93 368.46 452 - V52 RRL? 0.387 - - - Too close to cluster center V53 RRL? 0.986 235.19 472.66 432 - V54 Binary - - - - Too close to cluster center V55 RRL? 0.489 398.5 304.77 371 - V56 RRL? 0.552 - - - Too close to cluster center V57 Binary - - - - Too close to cluster center Table 6.2: Data from PSCS. The x and y coordinates and the ID are according to our research. The ID is from season 3 of the calibrated DAOPHOT data
6.4.2 Comparison with PSCS
Data for PSCS was taken using the 0.9 meter telescope at CTIO. For PSCS we used their available coordinates to match them with our studies (see fitrot), but once we found the stars the paper contained periods and light curves to compare, in contrast with LEM, which means that our light curves and periods can be corroborated with data obtained from
PSCS. Figure 6.21 shows the stars found in our research that were also in PSCS. Table 6.2 contains the data of all the variables present in PSCS. 84
Figure 6.21: Variable Stars compared with PSCS
Since our data collection is based on the study of Long Period Variables it presents achallengeofcomparingourdatawithPSCS,whichwasdedicatedintofindingshortpe- riod variables (mainly RR Lyrae variables). Because of this the best way to compare both datasets is to use the PDM method (period folding) approach for our light curves, because the magnitude vs. time light curves will just display scatter (Figure 6.22) due to our data not being set for these short period variables. Also because we observe the short period stars
(P 1d) over a relatively long time interval ( 600 days), we observe many pulsation cycles ∼ ≤ and therefore can determine the period to a higher precision than with the LPVs. These high precision periods are useful for comparison with PSCS periods, and in many cases greatly improve their periods. (Figure 6.23) Finally, since most of PSCS’s stars were located near the center of the cluster therefore most of the data obtained with DAOPHOT is inaccurate or we were not able to obtain photometry for the star, and with this we cannot get a mean magnitude, amplitude, or range for the star. Therefore we will use the folded ISIS curves and the periods to classify the variable stars. 85
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
4800 4900 5000 5100 5200 5300 5400 5500 5600
Figure 6.22: Light curve vs. Folded curve for RRLyrae using our research data. Top plot is the scatter light curve, and bottom one is the folded curve for the same variable star
-1.5 -1 -0.5 0 0.5 1 1.5 2-1.5 2.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.23: Variable Stars compared with PSCSThe plot displays how critical is to get an accurate period for an RRLyrae variable, where a simple change of 0.001 days could affect the folded period plot 86
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.24: Variable 17 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V17 (Figure 6.24) is located 0.810 arcmin away from the cluster center and was found using PSCS finding charts. The PDM method was used to find the period, resulting in a period of 0.6114 days. Because of its light curve, showing a sharp rise in magnitude followed by a slow descent, and a period between 0.2 and 1.2 days we can classify V17 to be an RRab type star. Comparing it with PSCS our data agrees and complements the period of V17. 87
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.25: Variable 18 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V18 (Figure 6.25) is located 0.906 arcmin away from the cluster center and was found using the finder charts provided in PSCS. The PDM method was used to find the period for the light curves, resulting in a period of 2.87 0.3 days. Because of its period and ± light curve we can confirm PSCS’s designation that V18 is a Population II Cepheid, which can be seen in that fact that our light curves lack any phase gaps and this convinces us that we got the correct period. 88
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.26: Variable 21 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V21 (Figure 6.26) is located 2.487 arcmin away from the cluster center. The
PDM method for ISIS was used to calculate the period, resulting in a period or 0.8135 days.
It is necessary to indicate that even though the star was only found on the I-Long filter, it was also physically present in the V and I-Short filter. We did not have a light curve for the last two filters because this would mean lowering the ISIS profile threshold to a really low value (lower than 0.5), which will it make it very inaccurate to calculate the period for this star. After obtaining the period and plotting the light curve we can confirm PSCS’s period and classification of V21 as a RRab type variable. 89
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.27: Variable 22 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V22 (Figure 6.27) is located 1.114 arcmin away from the cluster center. Light curve data for V22 was created in the V and I-Short filter, as we were unable to locate a suitable candidate in the I-Long filter probably to the blue color for V22. The PDM method for ISIS was used to calculate the period, resulting in a period of 0.5869 days, and using this period and a light curve with a sharp increase in magnitude followed by a slow descent, we can confirm PSCS’s period and classification of V22 as an RRab type star. 90
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
V23 (DAOPHOT) Period = 0.337
IL
IS
V0
-1 0 1 2
Figure 6.28: Variable 23 light curve Left - PSCS Light Curve Center - ISIS Light Curve Right - DAOPHOT light curve)
Variable V23 (Figure 6.28) is located 3.015 arcmin away from the cluster center and was found using the converted coordinates from PSCS. The star was only found in the V
filter for ISIS, which is somehow expected since is simpler to locate RR Lyrae stars using the
V Filter rather than either I-filter, because RR Lyrae are bluer stars in color and therefore more easily detectable in the visible filter than in the infrared. On the other hand we were able to obtain good photometry for this star in DAOPHOT, which allows us to confirm its period. Using the PDM method in DAOPHOT the period was calculated as 0.3776 days.
Because of its period and light curve we can confirm PSCS’s period and classification of V23 of an RRc type variable. 91
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.29: Variable 26 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.30: Variable 26 folded light curve with PSCS period of 0.239 displays more scatter than with the period we found using PDM of 0.3136)
Variable V26 (Figure 6.29) is located 2.117 arcmin away from the cluster center and was found using the converted coordinates from PSCS. Using the PDM we obtained a period of
0.3136 days. Because of its periodicity and light curve V26 can be classified as an RRc type variable. The period found for our data has a great scatter to it and it disagrees with the one shown by PSCS. We tried folding our data with their period but it just showed scatter
(Figure 6.30). Because of the amount of scatter we trust the period obtained with PSCS more than the one we obtained. 92
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.31: Variable 26 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V27 (Figure 6.31) is located 0.832 arcmin away from the cluster center and was found using the converted coordinates from PSCS. The PDM method for ISIS was used to calculate the period, resulting in a period of 0.3648 days. Because of its periodicity and a more sinusoidal light curve V27 can be classified as an RRc type variable. It was unusual to find a good candidate for this variable in the I filter, since V27 has such a short period and it’s a very blue star, but one was found with a lower radial profile threshold and as can be seen in the light curve for IS bandpass has a greater error margin of error. 93
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.32: Variable 28 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V28 (Figure 6.32) is located 0.939 arcmin away from the cluster center and was found using the converted coordinates from PSCS. The PDM method for ISIS was used to calculate the period, resulting in a period of 0.8408 days. Because of the period and light curve it can be classified as an RRab type variable. A candidate for this star was not found in the I-Short filter most likely because of its location and/or because the star may be too faint to be found via a 12 second exposure on the I-Filter. 94
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.33: Variable 29 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V29 (Figure 6.33) is located 0.337 arcmin away from the cluster center and because of its location near the center of the cluster we could only find a suitable candidate by using PSCS converted coordinates. The PDM method for ISIS was used to calculate the period, resulting in a period of 1.865 0.4 days. Using our data the period and the light ± curve showing a clear periodicity V29 can be classified as a Population II Cepheid variable. 95
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.34: Variable 30 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V30 (Figure 6.34) is located 0.767 arcmin away from the cluster center. For this variable we were only able to find a suitable candidate for the I-Long filter, whereas for the V- and I-Short filter suitable candidates were not found even using the lowered ISIS profile threshold. Using coordinate matching we were to locate the star for DAOPHOT photometry, but its closeness to the center prevented us from getting any good data. The
PDM method for ISIS was used to calculate the period, resulting in a period of 0.9509 days.
Using these properties it can be V30 can be classified as an RRab type variable. 96
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.35: Variable 31 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V31 (Figure 6.35) is located 2.578 arcmin away from the cluster center. Because of its luminosity it was not very likely to find a suitable star in the I-Short filter. The PDM method for ISIS was used to calculate the period, resulting in a period of 0.3409 days. Using period and light curve V31 and it can be classified as an RRc type variable. 97
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.36: Variable 35 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V35 (Figure 6.36) is located 3.662 arcmin away from the cluster center. Because of its luminosity and short period we were unable to find a suitable candidate for V35 in the V and Is filter. The PDM method for ISIS was used to calculate the period, resulting in a period of 0.3581 days. After plotting the light curve and comparing with the light curve for PSCS we could observe that the error margin in the flux could be an indication that of the discrepancy between our period and the one found by PSCS. Also our light curve does not clearly resemble the steeper rise of an RR Lyrae variable, but PSCS light curve displays the Blazkho Effect2. Using the period and light curve V35 could be classified as an RRc type variable, but the data presented by PSCS displays less scatter so theirs could be more accurately trusted.
2A light curve that has variations in amplitude from one cycle to the next 98
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
IL
IS
V0
-1 0 1 2
Figure 6.37: Variable 36 light curve Left - PSCS Light Curve Right - ISIS Light Curve Bottom - DAOPHOT Light Curve)
Variable V36 (Figure 6.37) is located 0.508 arcmin away from the cluster. Because of its proximity to the center of the cluster it lessened the probabilities of finding suitable candidate stars for V36. In ISIS, the location of the candidate can overexpose the IL filter, and for the IS filter the overcrowding can make it harder to find the right star, as for the
V-filter we were able produce a good light curve. In DAOPHOT the folded curve resembled some periodicity, and especially in the V-filter we could see some affinity towards a sharper light curve developing. To be more through we decided to plot the curve using IRAF’s PDM task, and use the option to remove the trend by removing a best-fit line. This procedure will center the magnitude about a new zero point, and after this we can try to find the period 99
Figure 6.38: Variable 36 DAOPHOT Light Curve folded using period of 3.146 days)
and then display the folded light curve (Figure 6.38) which now resembles the ISIS curve.
The PDM method for ISIS was used to calculate the period, resulting in a period of 3.146 ± 0.25 days. V36, even though some data points are away from a good plot, can be classified as a Population II Cepheid. 100
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
IL
IS
V0
-1 012
Figure 6.39: Variable 37 light curve Left - PSCS Light Curve Right - ISIS Light Curve Bottom - DAOPHOT Light Curve)
Variable V37 (Figure 6.39) is located 0.399 arcmin away from the cluster center. The light curves created using the ISIS and DAOPHOT data for V37 can be compared to V36, due to the trend of the curve and closeness to the cluster center, giving enough reasons why we could only find a suitable candidate in the V-filter in ISIS and displaying higher than usual error-bars for DAOPHOT. Also as V36, V37’s light curve is not as tight as other light curves, but it stills displays a good enough periodicity to assure classification. Using the
PDM method for ISIS we calculated a period of 10.75 0.6 days, and with the light curve ± V37 can be classified as a Population II Cepheid. 101
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.40: Variable 49 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V49 (Figure 6.40) is located 0.649 arcmin away from the cluster. Its brightness and variable type make it harder to find in either I-filter and therefore only the data produced are the V-filter data. Using the PDM method for ISIS we calculated a period of 0.3846 days.
Using the period and light curve V49 can be classified as an RRc type variable. 102
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.41: Variable 50 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V50 (Figure 6.41) is located 0.515 arcmin away from the cluster. For the
ISIS data due to its location and variable type there were difficulties finding appropriate candidates in either I-filter. Using the PDM method for ISIS we calculated a period of
0.3643943 days. Using the period and light curve V50 can be classified. Even with the greater margin error found in the light curve, which could be explained by the closeness of
V50 to the cluster center, and also the fact that our data was not primed to find short period variables we can classify V50 as an RRc type variable. 103
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.42: Variable 51 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V51 (Figure 6.42) is located 0.598 arcmin away from the cluster. For the same reasons as V50, location and type of variable we were not able to find suitable candidates for
V51 in either I filter. Using the PDM method for ISIS we calculated a period of 0.3967269 days. Because of its period and sinusoidal light curve it can be classified as an RRc type variable. 104
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.43: Variable 53 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Figure 6.44: Variable 53 DAOPHOT Light Curve folded using period of 0.98595 days pro- ducing a similar curve as PSCS)
Variable V53 (Figure 6.43) is located 1.417 arcmin away from the cluster. Even with the lowered profile ISIS threshold we could not find a suitable candidate for the IS filter for the
ISIS data. As for DAOPHOT we used the removal of the fit using IRAF’s PDM task, and the folding produced a similar curve as PSCS (Figure 6.44. This was an unusual variable to compare with PSCS data since their data has a very large phase gap and this always makes the resulting period somewhat suspect. On the other hand our data shows a full cycle of phases despite the larger error-bars. Using the PDM method for ISIS we calculated a period of 0.9859539 days, and using this period and the light curve, V53 can confirm PSCS classification as an RRab type variable. 105
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Figure 6.45: Variable 55 light curve Left - PSCS Light Curve Right - ISIS Light Curve)
Variable V55 (Figure 6.45) is located 1.108 arcmin away from the cluster. Once again due to its variable type and brightness, it is less likely to find suitable candidates for this star in either I-filter. Our ISIS light curves display similar characteristics in the periodicity of the curve, as well as the magnitude of the error; using the PDM method for ISIS we calculated a period of 0.4902565 days and using this period and the light curve V55 can be classified as an RRc type variable. 106
Corwin et al. Name Type Period (Corwin et al.)X Y IDComments V58 RRab 0.683 - - No star found V59 RRab 0.589 381.63 435.16 - V60 RRc 0.372 - - - No star found V61 RRab 0.657 - - - No star found V62 RRab 0.708 - - - No star found V63 Ceph 2.045 - - - No star found V64 RRab 0.595 - - - No star found V65 RRc 0.395 - - - No star found V66 RRc 0.35 - - - No star found V67 Ceph 2.27 612.794 384.525 13 - V68 RRab? 0.946 625.015 596.467 119 - V69 Ceph? 3.6 611.535 539.715 332 - SV1 Ceph? 8 - - - SV2 RRab? 0.847 380.95 419.53 12 No star found SV3 RRc? 0.333 - - - No star found SV4 Ceph? 12 - - - No star found SV5 Ceph? 4.5 606.769 536.842 113 No star found SV6 Ceph? 7 - No star found Table 6.3: Data from Corwin et al. The x and y coordinates and the ID are according to our research. The ID is from season 3 of the calibrated DAOPHOT data
6.4.3 Comparison With Corwin et al.
Corwin et al. data was taken partly by PSCS using the 0.9 m telescope at CTIO (for these data Corwin et al. applied ISIS instead of DAOPHOT) and partly obtained using the
WFPC2 (Wide-Field Planetary Camera 2) aboard the HST. For Corwin et al. there was
no finding chart to visually compare our data to their data. The available data was the
coordinates from their known variables, which were in the same coordinate system (Right
Ascension and Declination) as PSCS; therefore we used the coordinates in PSCS to convert
the coordinates from Corwin et al. to our coordinate system using the fit2rot.e script. Table
6.3 shows all the variable stars present in the research.
We want to point out that the stars in this research are close to the center and therefore
finding suitable candidates or obtaining appropriate light curves for the DAOPHOT data
was not always possible, and for ISIS, Corwin et al.isworkingintheverycrowdedcenter
of the cluster using data that has higher resolution (eg, PROMPT5 is 0.56 arcsec/pix, while
HST is 0.1 arcsec/pix!), so they obtained much better photometry, even with ISIS. 107
I-Long
I-Short
V-Filter
-1 0 1 2
Figure 6.46: Suspected Variable SV2 light curve Left - Corwin etal. Light Curve Right - ISIS Light Curve)
Variable SV2 (Figure 6.46) is located 0.114 arcmin away from the cluster center. We use the PDM method to find the period and obtained a period of 0.8134650 days. Using the light curve and found period SV2 is classified as an RRab Lyrae star. 108
lc48 I-Long
lc134 I-Short
lc108 V-Filter
-1 0 1 2
Figure 6.47: Suspected Variable SV5 light curve Left - Corwin etal. Light Curve Right - ISIS Light Curve)
Variable SV5 (Figure 6.47) is located 0.108 arcmin away from the cluster. Using the
PDM method the period for the candidate star was found to be 26.153 6days.Becauseof ± its light curve and period we can assess SV5 to be a Population II Cepheid variable star. Our period does not agree with the one found by Corwin etal.,thereforeweappliedbothperiods, the one from Corwin et al. and the one found using PDM to the ISIS and DAOPHOT data and given their gaps and misaligned light curve for Corwin etal. vs. the clearly gapless and aligned ISIS light curve, we are much more inclined to believe that we obtained a correct period of 26.15 days. 109
-1 0 1 2
Figure 6.48: Variable V59 light curve Left - Corwin etal. Light Curve Right - ISIS Light Curve)
Variable V59 (Figure 6.48) is located 0.248 arcmin away from the cluster center. We were able to detect this star in ISIS and confirmed that it is variable, but the signal to noise ratio is too low for us to derive any useful light curve information. 110
I-Long
4900 5000 5100 5200 5300 5400
Figure 6.49: Variable V67 light curve Left - Corwin etal. Light Curve Right - ISIS Light Curve)
Variable V67 (Figure 6.49) is located 0.245 arcmin away from the cluster center. As with V59 were able to detect this star in ISIS and confirmed that it is variable, but the signal to noise ratio is too low for us to derive any useful light curve information. 111
I-Long
I-Short
V-Filter
-1 0 1 2
Figure 6.50: Variable V68 light curve Left - Corwin etal. Light Curve Right - ISIS Light Curve)
Variable V68 (Figure 6.50) is located 0.507 arcmin away from the cluster center. The light curve for the both I-filters has a large amount of error, most likely due to the star’s faint luminosity, while the V-filter displays a clearer light curve. Using the PDM method to find the period we found a period of 0.937 days. We would trust our period over that in
Corwin et al. since their data has a huge phase gap, which would account for the significant difference. Using the obtained period and light curves we can confirm classify V68 as an
RRab type variable. 112
I-Long
V-Filter
-1 0 1 2
Figure 6.51: Variable V69 light curve Left - Corwin etal. Light Curve Right - ISIS Light Curve)
Variable V69 (Figure 6.51) is located 0.084 arcmin away from the cluster center, making it the closest known variable to the center of the cluster. Using the PDM method to find the period we obtained a value of 18.028 6 days. Using the obtained period and light curves ± we can classify V69 as a Population II Cepheid, but further study is required to calculate which a more accurate period, but comparing our light curve with the disjointed nature of
Corwin etal.’s light curve lead us to trust our results. 113
Figure 6.52: Variable NV30 DAOPHOT Light Curve)
6.5 New Found Variables
Twenty-nine additional previously unknown variables were found in our variable star research. We used all their available properties —light curves , calculated periods, amplitude and range— and classify them. We are introducing them according to their variability index
(from highest to the lowest index).
Variable NV30 (Figure 6.52) is located 5.502 arcmin away from the cluster center. It is located in an uncrowded field of the cluster, and using the template fitting method we obtained a period of 138.1 7days.ThestarwastrimmedoutoftheframefortheISIS ± photometry therefore no data is available. For DAOPHOT (figure) we observed a periodic curve, especially for season 3, with an observed range of 2.39 magnitudes in the V-filter and 3.58 mag in the I-filter and amplitude of 1.9 magnitude in the V-filter and 1.22 in the
I-filter. The period and low scatter support the high period index, 88.6, and with the other properties NV30 can be classified as a semi-regular variable star. 114
I-Long
I-Short
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.53: Variable NV7 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV7 (Figure 6.53) is located 0.106 arcmin away from the cluster center. It is located near the center of cluster, which makes any photometry using DAOPHOT compro- mised by blending. For ISIS we used the PDM task and obtained a period 149 6days.The ± light curve observed using ISIS photometry displays a small regularity, and looking at the folded curve we see a scatter to the data around the fitted curve, which would agree with the semi-regularity observed in its periodicity, but we could not obtain a candidate star in for the
V Filter. It has an amplitude of 0.14 magnitudes in the I-filter and 0.68 magnitudes in the
V-filter, with a range of 0.47 magnitudes in the I-filter and 3.05 in the V-filter. Observing the scatter in the folded light curve with certain regularity, the period between 20 to 1000 days we can classify NV7 as a semi-regular LPV star. 115
I-Long
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.54: Variable NV14 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV14 (Figure 6.54) is located 2.027 arcmin away from the cluster center, and its located in a region where crowding was not an issue with the closest star being about 8 pixels away. For DAOPHOT the light curves agree in shape in all three filters, but for season
1intheVfilter,thiscouldbeanissueofoverexposureofthestarduringtheperiod.ForISIS we were only able to find a suitable star for the I-filter, where we clearly see a periodicity occurring especially in the data right of the gap. Using the PDM task we obtained a period
369.2 12 days, with a range of 0.355 mag in the I filter and 0.73 mag in the V-filter and ± an amplitude of 0.01 mag in the I-filter and 0.05 mag in the V-filter. It can be seen that this star may have a greater period or there is a LSP that could be observed by obtaining more data. Using the available properties of a long period but lacking regular periodicity and an amplitude less than 1.0 mag in V we can classify this star as an irregular LPV star. 116
NV 1 (ISIS) Period = 73.436404747 I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.55: Variable NV1 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV1 (Figure 6.55) is located 2.058 arcmin away from the cluster center and its located in an uncrowded region of the frame. Using the template fitting method we obtained aperiodof73.43 5 days. Both light curve in ISIS and DAOPHOT agree in shape and ± periodicity and display the possibility of a LSP observing how the light curve displays a rising behavior before the gap and a descent after the winter gap. Its range is 0.29 for the
I-filter and 0.17 mag for the V-filter, with an amplitude of 0.1 mag in the I-filter and 0.05 mag in the V-filter. Because of its light curve, low amplitude and long period we can classify it as an irregular LPV star but the folded curve (even though has a higher scatter) displays aperiodicalbehavior,sowecouldclassifythisasasemi-regularLPVstar. 117
NV15 (ISIS) Period = 144.630071640 I-Long
I-Short
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.56: Variable NV15 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV15 (Figure 6.56) is located 0.512 arcmin away from the cluster center, which locates it near the cluster center. The light curves for DAOPHOT display some periodicity but also great range in their magnitudes, which could be expected for a star near the center when using DAOPHOT photometry, most likely this could be attributed to blending between our variable and another star, a behavior that can be seen in season 1 where the star is fainter in Il than IS. For ISIS we observe the same behavior for both average flux light curves. Using the PDM task in the ISIS photometry we obtained a period 144.6 5days.Itshowsavisual ± range of 0.62 mag in the I-Filter and 0.49 in the V-Filter, with an amplitude of 0.09 mag in the I-filter and 0.15 mag in the V-filter. Using the amplitude lower than 1 magnitude in the
V and a somewhat periodic but light curves we classify NV15 as a semi-regular LPV star, bordering into Irregular. 118
I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.57: Variable NV10 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV10 (Figure 6.57) is located 1.481 arcmin away from the cluster center, in a region where crowding could occur with 4 neighboring stars about 4 pixels away from NV10.
The light curves for both photometry agreed in their periodicity for the exception of season
2 for the V filter in DAOPHOT, which could be explained by blending with neighboring stars. It has an observed range of 0.3 mag for the I-filter and 0.7 mag for the V-filter and amplitude of 0.1 mag for the I-filter and 0.2 mag for the V-filter. Using the PDM task with the ISIS data we obtained a period 278 5daysandusingthetemplatefittingmethodwe ± obtained a period of 292.2 9 days for the DAOPHOT data. Once obtaining the period we ± could suggest that this is the period for the LSP for the variable by observing the way the light curve as a whole has one cycle for seasons 1 and 2 and another cycle for just season 3.
Using the available data with a long period, low amplitude and non-periodical behavior in the light curve we can classify NV10 as an irregular LPV star. 119
I-Long lc64 I-Long
I-Short lc158 I-Short
V0 Filter lc138 V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days] -1 0 1 2
Figure 6.58: Variable NV9 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve Bottom - ISIS folded light curve
Variable NV9 (Figure 6.58) is located 0.83 arcmin from the cluster, very close to the center, which makes it a very unlike candidate to find good photometry for DAOPHOT.
The light curves for ISIS display a periodical behavior that could be greatly complemented if we were able to obtained data during the gap. The light curves for DAOPHOT display blending behavior for the first two seasons and shows a periodicity that resembles that of
ISIS for season 3. Using the PDM task on the ISIS data we obtained a period of 335.8 ± 13 days, while using the template fitting method we obtained a period of 321.0 5days ± for DAOPHOT (we want to point out that we only used the data for season 3 to calculate this period), where both periods agree within their uncertainty. It displays a range of 0.32 mag in the I-filter and 0.60 for the V-filter and amplitude of 0.13 mag for the I-filter and
0.32 mag for the V-filter. Using its period and amplitude and observing the periodicity with some scatter in the folded light curve we can classify NV9 as a semi-regular LPV star. 120
I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.59: Variable NV12 light curve ISIS
Variable NV12 (Figure 6.59) is located 0.161 arcmin for the cluster center, located inside the crowded cluster center. We could not obtain appropriate photometry for DAOPHOT, which just displays scatter in its light curve. For ISIS, the light curves for all three filters agree in shape and periodicity with a couple of bad nights at the end of the run. Using the
PDM task in ISIS we obtained a period of 137.9 8days.Sincenoappropriatecandidate ± was found for DAOPHOT we could not obtained a value for the amplitude and range for the variable; therefore using the light curve, with an observed yet slightly scattered periodicity in the folded light curve, and period found in ISIS we can classify NV12 as a semi-regular
LPV. 121
Figure 6.60: Variable NV22 light curve DAOPHOT
Variable NV22 (Figure 6.60) is located 6.01 arcmin away from the cluster center, very close to CCD edge and outside ISIS field of view. The photometry obtained in DAOPHOT is very infrequent due to its location, but the light curve shows signs of periodicity. Using the available data we obtained a period of 324.46 15 days, with an observed range of 0.62 ± mag in the I-filter and 0.86 mag in the V-filter and amplitude of 0.46 mag in the I-filter and
0.18 mag in the V-filter. Using the found period, amplitude and light curve, and also the red color we could infer that NV22 may be an LPV star of some type, but more data is needed to confirm this statement. 122
I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.61: Variable NV5 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV5 (Figure 6.61) is located 0.594 arcmin away from the cluster center.. The light curves for DAOPHOT and ISIS agreed in shape and periodicity of curve, and their folded curves shows a likely periodicity with a slow rise and fast descent in the average flux.
Using the PDM task we obtained a period 358 7days,withanamplitudeof0.16magin ± the I-Filter and 0.25 mag in the V-Filter, with an observed range of 0.3 mag in the I-filter and 0.59 mag in the V-filter. Using the period and amplitude and observed light curves we can classify NV5 as a semi-regular LPV star. NV9 and NV5 are good samples of semi-regular
LPV with blended magnitudes, causing their amplitudes to be lower than 1 magnitude, all because of their location near the center of the cluster. 123
Figure 6.62: Variable NV21 light curve DAOPHOT
Variable NV21 (Figure 6.62) is located 5.975 arcmin away from the cluster, which locates it near the edge of the CCD and offISIS field of view. NV21’s location makes it harder to obtain data for every single night making the data points very infrequent and therefore we cannot certify our results as complete. Using the available points we used the PDM task and obtained a period of 85.8 15 days, with an amplitude of 0.1 mag in the I-Filter and ± 0.12 mag in the V-Filter and an observed range of 0.2 mag in the I-filter and 0.38 mag in the V-Filter, but given the amount of available data we cannot be confident of these values.
Due to scarce amount of data, the observed light curve, amplitude and color we would not clearly sub-classify NV21 as an LPV star; more data is required to make an assessment. 124
Figure 6.63: Variable NV18 light curve DAOPHOT
Variable NV18 (Figure 6.63) is located 3.33 arcmin away from the cluster center. Ob- serving the light curve we can see that this is a very bright candidate and therefore it could be overexposed in some of our images and by this present high margin errors throughout our data run; this also could be by the fact that we have two other possible variable stars between 10 pixels of NV18 (add figure). All three light curves agree in shape and periodicity.
Using the available data we obtained a period of 11.52 1.2 days, with an amplitude of ± 0.01 mag for the I filter and 0.03 mag for the V-filter, and observable range of 0.26 mag for the I-Filter and 0.14 mag for the V-filter. Observing the light curve with not only a lack of peridocity but flatness to it, a very small amplitude for both filters, and location of NV18 we should classify it as a suspected variable, but more study will probably show that it is just a bright star that is saturating the CCD. 125
Figure 6.64: Variable NV26 light curve DAOPHOT
Variable NV26 (Figure 6.64) is located 1.092 arcmin away from the center of the cluster, and its located in uncrowded region of the cluster, aiding us into obtaining better data for our study. All three light curves in DAOPHOT agreed in shape and regularity, with a little more margin of error present on both I-Filters. The shape of the curve is almost sinusoidal and begins to lose coherency through season 3, which could be explained by a multi-periodicity, that more years of data could give us data to explain this behavior. Using the template
fitting method we obtained a period of 100.3 8 days, with an amplitude of 0.29 mag in the ± I-Filter and 0.56 mag in the V-Filter and a visual range of 0.43 mag in the I-Filter and 0.95 mag in the V-filter. Using the obtained properties and observing the light curve we classify
NV26 as a semi-regular LPV star. 126
Figure 6.65: Variable NV28 light curve DAOPHOT
Variable NV28 (Figure 6.65) is located 1.225 arcmin away from the center of the cluster.
Its location is precarious since it has two bright stars, 4 and 12 pixels away and another pos- sible variable 9 pixels from it, and these stars could cause some blending on the photometry readings for NV28; therefore we could not fully trust the data obtained with DAOPHOT.
The light curves agreed in their shape and regularity for the I-Filter, while the V-filter does not agree with either curve, which hints of critical blending, where the stars sometimes merge and sometimes split. Using the template fitting method we obtained a period of 3.29
0.25 days with an amplitude of 0.06 mag in the I-filter and 0.61 mag in the V-filter and ± an observed range of 0.27 mag in the I-filter and 0.94 mag in the V-Filter. NV28 was within
ISIS field of view but was not detected as a variable gives us a hint that NV28 maybe not be a variable but a critically resolved star. 127
Figure 6.66: Variable NV27 light curve DAOPHOT
Variable NV27 (Figure 6.66) is located 2.412 arcmin away from the cluster center, in a very uncrowded portion of the field, but was not detected by ISIS. The three light curves in DAOPHOT agree in their shape and regularity with a usual margin of error expected for the location of the star. Using the template fitting method we obtained a period of 47.5 ± 5 days, with an amplitude of 0.06 mag in the I-Filter and 0.18 mag in the V-Filter, and an observed range of 0.3 mag in the I-Filter and 0.65 mag in the V-Filter. Also observing the light curve we could see the possibility of a LSP since we see the data for season 1 and 2 in a downward pattern while the data for season 3 seems to be going in an upward pattern.
Because of its amplitude, period and light curve with a coherence seen in seasons 1 and 2 that disappears in season 3, we can classify NV27 as an irregular LPV star. 128
I-Long
I-Short
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.67: Variable NV4 light curve ISIS
Variable NV4 (Figure 6.67) is located 0.433 arcmin away from the cluster center, which puts it near the crowded center, which made it difficult to find good photometry with
DAOPHOT. For ISIS we were only able find suitable stars in I-Filter most likely due to the luminosity of the star, which could possibly overexposed the V-filter. The observed light curves agree in shape and periodicity and also display an indication of a LSP since we see a downwards trend for the data left of the gap and upwards trend right of the gap. Using the PDM task we were able to calculate a period of 68.4 4 days. The lack of DAOPHOT ± photometry does not allow us to obtain an amplitude or range for the variable, therefore using the found period and light curve we can assess that NV4 is a semi-regular LPV star. 129
NV 16 (ISIS) PERIOD = 41.568 I-Short
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.68: Variable NV16 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV16 (Figure 6.68) is located 1.285 arcmin away from the cluster center. The light curves for DAOPHOT agree on their shape and periodicity. As for ISIS we found a suitable candidate but we could have a blemish in our var.fits image that could prevents us from obtaining suitable data. Using the template fitting method we obtained a period of
41.08 4 days, with an amplitude of 0.13 mag in the I-Filter and 0.36 mag in the V-filter, ± and an observed range of 0.40 mag in the I-Filter and 0.82 mag in the V-Filter. Using the properties and the observed light curve we can classify NV16 as a semi-regular LPV star. 130
I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.69: Variable NV3 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV3 (Figure 6.69) is located 0.348 arcmin away for the cluster center. The light curves for both photometry and all three filters agreed in shape and periodicity. Using the PDM task in ISIS and the template matching method we obtained a period of 177 ± 3 days, with an amplitude of 0.83 mag in the I-Filter and 0.99 mag in the V-Filter and an observed range of 1.09 mag in the I-Filter and 1.81 mag in the V-Filter. Observing the light curve and period NV3 could be classified as a Mira Variable star, also understanding that if we take into account that the magnitude could be blended, so the amplitude readings could be lower than the actual value. 131
Figure 6.70: Variable NV23 light curve DAOPHOT
Variable NV23 (Figure 6.70) is located 3.436 arcmin away from the cluster center. The three plotted light curves agree in shape and periodicity, but a sinusoidal trend can be observed throughout all three seasons. This periodic trend could be explained by a LSP or by a neighbor merely 3 pixels away, which could cause a blending issue. Using the template
fitting method we found a period of 76 5 days, with an amplitude of 0.23 mag in the ± I-Filter and 0.64 mag in the V-Filter, and an observed range of 0.4 mag in the I-Filter and
1.07 mag in the V-Filter. With a period between 50 to 1000 days, an amplitude between 1 and 2 magnitudes and the observed light curve with some regular periodicity we can classify
NV23 as a semi-regular period variable with a possible LSP. 132
Figure 6.71: Variable NV25 light curve DAOPHOT
Variable NV25 (Figure 6.71) is located 6.679 arcmin away from the cluster center, which puts it at the edge of the CCD (out of ISIS field of view), which does not allow us to obtain data for every available night. The plotted light curves agreed in shape but a trend is not easily observed without too much extrapolation. Using the PDM task we obtained a period
2.5 1.1 days, which could probably be noise due to small amount of data. It has an ± amplitude of 0.04 mag for the I-Filter and 0.02 mag V-filter and a range of 0.09 mag for the
I-filter and 0.16 mag for the V-Filter. Using its amplitude, range and period and the fact that we have an incomplete light cure we can classify NV25 as an a suspected variable but more data on the star could clarify this assessment. 133
Figure 6.72: Variable NV24 light curve DAOPHOT
Variable NV24 (Figure 6.72) is located 4.579 arcmin away from the cluster center and is located in a very uncrowded region of the frame. The plotted light curves agree in shape and periodicity with not many offset margin of errors. Using the template matching method we obtained a period of 77 3days,withanamplitudeof0.16magintheI-filterand0.35 ± mag in the V-filter, and an observed range of 0.46 mag in the I-Filter and 1.02 mag in the
V-Filter. Using these properties and the observed light curves we can assess that NV24 is a semi-regular LPV star. It is important to point out that the irregularities in the light curve could be displaying a SSP (Secondary Short Period). 134
I-Long
I-Short
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.73: Variable NV2 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV2 (Figure 6.73) is located 0.510 arcmin away from the cluster center, which puts it near the center of the cluster with a neighbor star less than 3 pixels away. We were not able to find a suitable star in the V-Filter for the light curves in the ISIS photometry, but the remaining two filters agree in shape and periodicity, with usual margin of error. The light curves for the DAOPHOT data exhibit periodicity, but the shape varies from filter to
filter, where for example we see the data for the IL go to lower magnitudes from season 2 to season 3, whereas the data for the IS seems to go to higher magnitudes and the V seems to remain in the same range; this could be attributed to blending due to its location in the crowded center. Using the PDM task in ISIS we obtained a period 62.2 4daysandusing ± the template fitting in DAOPHOT we obtained a period of 64 5days,withamplitudeof ± 0.14 mag in the I-Filter and 0.17 mag in the V-Filter, and an observed range of 0.34 mag in the I-Filter and 0.49 mag in the V-Filter. Using these properties and its light curve we can classify NV2 as a semi-regular LPV star. 135
Figure 6.74: Variable NV17 light curve DAOPHOT
Variable NV17 (Figure 6.74) is located 2.577 arcmin away from the cluster center. The plotted light curves agreed in shape with the exception that the V-Filter at the end of season
2doesnotdisplaythesamedescentastheothertwofilters;alsothegreaterrangeofthe margin-errors can be explained by the brightness of the star, which could saturate the star throughout our research, the plot tends to display more scatter than periodicity. Using the
PDM task we were able to obtain a period of 30.4 4 days, with an amplitude of 0.05 ± mag in the I-Filter and 0.1 mag in the V-Filter, with a range of 0.17 mag in the I-Filter and 0.29 mag in the V-Filter. The low amplitude and the fact that this star’s magnitude could saturate the readings in the CCD, and since the star was not located by ISIS makes us believe that this is probable a non-variable star. 136
Figure 6.75: Variable NV29 light curve DAOPHOT
Variable NV29 (Figure 6.75) is located 5.782 arcmin away from the cluster center, mak- ing it located near the edge of the CCD and therefore we could not always obtain data for every single night; therefore we cannot ascertain that our results as complete. The observed light curve does not display much agreement between the filters. We could not obtain a reliable period with either the PDM task and the template matching method and therefore we could not calculate an amplitude. The observed range is 0.057 mag for the I-filter and
0.140 mag for the V-Filter. Using the properties and the light curves, we could classify NV29 as a candidate variable star, but further study on this star is needed. 137
Figure 6.76: Variable NV20 light curve DAOPHOT
Variable NV20 (Figure 6.76) is located 4.802 arcmin away from the cluster center, mak- ing it located near the edge of the CCD but even with this we were able obtain data for almost every night. The plotted light curves display the same pattern of variation, but the shape in the V-Filter seems to disagree with its counterparts, especially at the beginning of season 3 where its range does not agree at all with the behavior observed in both I-Filters.
Using the PDM task we used the best fit method, which removes a linear trend from the curve, and obtained a period of 102 13 days, with an amplitude of 0.14 mag in the I-filter ± and 0.68 mag in the V-Filter with an observed range of 0.47 mag in the I-Filter and 0.73 mag in the V-Filter. Using these properties and light curves we can classify NV20 as an irregular variable. 138
I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.77: Variable NV8 light curve ISIS
Variable NV8 (Figure 6.77) is located merely 0.02 arcmin away from the cluster center,
which makes it the closest variable star near the center of the cluster. Also due to this
proximity we were not able to find any photometry with DAOPHOT. The plotted ISIS light
curves agree in shape and periodicity, and the folded light curve shows clear variability with
more scatter than seen in less crowded environments. Since no magnitude photometry was
obtained we cannot obtain an amplitude or range, but using the PDM task on the ISIS data
we obtained a period of 155 5 days, and using this period and the light curve we can ± tentatively classify NV8 as a semi-regular variable but a magnitude assessment is needed to confirm the classification. 139
I-Long
I-Short
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.78: Variable NV6 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV6 (Figure 6.78) is located 0.662 arcmin away from the cluster center. The observed light curves for both photometry agree in shape and periodicity, with a somewhat regular margin of errors, which could be explained by the closeness to the cluster center.
Using the PDM task in ISIS we obtained a period of 313.6 . 12 days, and in DAOPHOT ± obtained a period of 324.3 15 days, with an amplitude of 0.1 mag in the I-Filter and 0.14 ± mag in the V-Filter, and an observed range of 0.25 mag in the I-Filter and 0.6 mag in the
V-Filter. At close inspection it seems that there seems to be a shorter period superimposed on the longer period, so the reported period could be the period for our LSP and if we used software to remove this period trend from the light curve we might be able to obtain the primary period. Using the obtained properties and observed light curve we could classify
NV6 as an irregular LPV star. 140
Figure 6.79: Variable NV19 light curve DAOPHOT
Variable NV19 (Figure 6.79) is located 3.265 arcmin from the cluster center and outside
ISIS field of view. The plotted light curves agree in shape and periodicity and show NV19 is a bright star, which can explain why the V-Filter has greater errors of margin in comparison to the IL and IS filters; also there is a small trend where the data seems to be sloping downwards in the early seasons and then upwards in the late season, which could signify the existence of a LSP. Using the PDM task we obtained a period of 48.1 6dayswith ± an amplitude of 0.05 mag in the I-Filter and 0.10 mag in the V-Filter, and an observed range of 0.23 mag in the I-Filter and 0.49 mag in the V-Filter. Using these properties and the observed light curves we can classify NV19 as an irregular LPV star; though season 3 displays good regularity, another year of data could help us clarify the classification. 141
I-Long
I-Short
V0 Filter
4800 4900 5000 5100 5200 5300 5400 5500 HJD [days]
Figure 6.80: Variable NV11 light curve Left - ISIS Light Curve Right - DAOPHOT Light Curve)
Variable NV11 (Figure 6.80) is located 0.215 arcmin away from the cluster center. The
ISIS plotted light curve agrees in shape and periodicity in all three filters with a couple discrepancies in what could be saturated images for the star. Due to this location and the fact that it has two neighboring stars located 3 pixels away the obtained DAOPHOT photometry does not show any sign of variability as the ISIS data, and also there is the possibility of blending therefore the magnitude readings could be questioned. Using the
PDM method we obtain a period of 71.3 4days.Ithasanamplitudeof0.14maginthe ± I-Filter and 0.19 mag in the V-Filter with an observed range of 0.35 mag in the I-filter and
0.29 mag in the V-Filter. Using these properties and the observed ISIS light curve we can classify NV11 as an irregular LPV star, but because of blending if we were to use only the light curve then NV11 could possibly be a semi-regular LPV star. 142
CHAPTER 7
CLUSTER MEMBERSHIP
It is clear that we care to study variable stars that are cluster members, but the fact that NGC 6388 is located near the bulge of the Milky Way gives us a high density of field stars along the line of sight to the cluster, which makes it more complicated to establish membership for the stars in the cluster. Different tools, such as radial velocities, proper motion, location on the CMD and distance from the center would help would help to establish membership in the cluster.
Since radial velocities and proper motions require very different observational strategies, we use only the CMD location and projected radius of each variable star to characterize the likelihood of its being a cluster member.
7.1 Projected distance from the center
1 For this method we take into account the core (Rcore = 0.12 arcmin = 12.2 pixels ), half-mass (Rhalf mass =0.67arcmin=68.1pixels)andthetidalradius(Rtidal =6.21arcmin − = 631 pixels) field of view [Harris(1996)], as a selection gauge for our variable stars in our cluster, since we know that at greater distance from the cluster center, the less dense the population of the cluster. Stars inside the core are more likely to be cluster members (CCM), inside the half-mass radius are less-likely but still probable cluster members (HCM), inside the tidal radius are even less likely but still possible cluster members (TCM), and stars outside the tidal radius should all be field stars (FS)providedthatthevalueforthecore, half-mass and tidal radius were calculated correctly. The candidates found using ISIS are more likely to be cluster members since we trimmed our images and all of the stars lie inside the tidal radius. At the end we located 5 stars within CCM,17starswithinHCM,39 stars within TCM and 1 star outside TCM. Figure 7.1 displays the combination of all our
1This value was calculated but know that PROMPT5 CCD’s pixels per arcsec ratio is 0.59. 143
frames together in one frame, where the inner circle represents the Rcore,themiddlecircle represents the Rhalf mass and the outer circle represents the Rtidal of the cluster. From the − figure we can infer that most of our stars should be selected as member candidates, but field stars lie along the exact line of sight as the cluster and therefore we needed a second method in order to establish a better likelihood between probable cluster members and field stars found in our images.
7.2 Location on the CMD diagram
Because using the distance as our only gauge seems limited, we can use the CMD as a secondary tool to clarify cluster membership, to distinguish field stars within the Rtidal. It’s important to point out that only the stars detected using DAOPHOT will be used for
CMD comparison due to the fact that the CMD is created using the apparent magnitude of the stars and not their flux difference (which is used for the ISIS photometry). Their location on the CMD can be used to establish membership. Figure 7.2 displays our CMD with Girardi’s [Fe/H] = -0.4 isochrone plotted over it. In our Color Magnitude Diagram,
Chapter 5, we establish that this isochrone was a good fit for the AGB observed in our CMD, also we indicated that we shifted the isochrone using the apparent distance modulus (muV = 16.13) as established by Harris (1996). Using the distance modulus equation we can see in the image how a small change in magnitude (0.1 magnitudes) can affect the location where our stars would be located in the CMD and therefore the reason the CMD is a good tool to indicate probable cluster membership.
We have observed that our candidates have very low uncertainty in their magnitudes ( ≤
0.1 magnitudes), so a star inside the Rtidal =6.21arcmin(or18pc)thatfallsontheAGBin the CMD gives us better reassurance of cluster membership. We can attest to this by taking 144
Figure 7.1: Location of R ,Rhalf mass and R in our field ov view, where the inner core − tidal circle represents the Rcore,themiddlecirclerepresentstheRhalf mass and the outer circle − represents the Rtidal 145
the distance modulus of 16.13 [9] and using the distance modulus equation (equation 7.1)
(16.13 Av+5) − d =10 5 (7.1) where we obtain a distance of 10.1 kpc to the cluster. If we use the same equation with values of 16.03 and 16.23 (0.1 magnitudes lower or higher) we obtain a distance of 9.68 and
10.61 kpc, respectively. The differences of 0.68 kpc for dimmer and 0.61 kpc for brighter stars are three times the amount of our tidal radius, so when we observe the plotted LPV stars, that are located inside the tidal radius, on the CMD their distance from the AGB can give us some certainty of them being likely field stars or possible cluster member, but this can only be done with more surety with the stars where crowdedness was not an issue.
Each type of variable is treated differently, for example LPV stars closer to the AGB are more likely to be cluster members (a field star at a different metallicity and/or distance could still fall in our CMD) but this could not be an exact criterion since some of our stars are located near the center and therefore blending could be causing the magnitudes to be brighter and bluer than their actual value. P2C stars located in the instability strip just above the HB, and RRL stars located in the HB are more likely to be cluster members but since we only located these two type of variables near the center of the cluster, and our study was designed (the exposure time and filters selected) to obtain magnitudes of redder stars will not give us the most accurate representation of their magnitudes, so we cannot be entirely confident of their membership using the CMD. Also these faint stars (P2C and
RR-Lyrae) were studied in the Pritzl and Corwin research, and our 5-10 days observing modulation is not well suited to study them; therefore we only analyzed a subset of faint stars that are well exposed and in un-crowded regions.
Figure 7.3 shows our CMD with classified LPVs according to their V and (V-I) mag., and stars are classified according to their probable distance from the center (Two LPVs that are core members are not plotted because we could not obtain magnitudes for them). 146
Standard CMD Season 3
Original Isochrone - Magenta Isochrone + 0.1 mag - Green Isochrone - 0.1 mag - Red
01234 V-I mag
Figure 7.2: The original isochrone by Girardi(2002) is in the center, the brighter isochrone is red and on top and the dimmer isochrone is green and on the bottom. 147
We used the isochrone to establish the zero point where we would expect the different types of variables to fall, but blending of stars, which happens when an unresolved star merged with the profile of the variable so we detect their combined magnitude making the magnitude of the variable star brighter than when the star is by itself, and crowdedness near the center, which happens when neighbor stars overlapping the variable adding uncertainty to its magnitude, in the cluster creates an incertitude of the precise location of the stars.
The next paragraphs shows examples of stars that are affected by the crowded center near the center and/or blending with a non-variable stars, which affects their location on the CMD.
We can observe how there are the two Miras located nearer the cluster center (inside
Rhalf mass)notlocatedovertheAGBofthecluster,butafterobservingtheirlightcurves − (Figures 6.12 and 6.69) we can observe a diluting behavior that would be explained by blending and therefore their location on the CMD cannot be certainly taken into account unless we remove the presence of the diluting non-variable star.
Another star NV11 (Fig. 6.80), which its the brightest of the variable stars, which ac- cording to its position in the CMD would likely be a field star, but its location so close the center of the cluster does not give us confidence in the magnitudes obtained with DAOPHOT photometry and therefore its location in the CMD is unreliable to indicate possible mem- bership.
Other stars such as NV29 appears bluer with the same brightness but the lack of data in its light curve (Fig. 6.75) does not give us confidence in its classification according to location, but due to its location near the edge it is more likely to be a field star. The same is the case for NV21, which appears to be a field member for its position in the CMD, and since the star is too close to the edge it will also appear to be a likely field star though the few obtained magnitudes (Fig. 6.62) cannot aid us into drawing clearer conclusions.
One interesting case is V4 (Fig. 6.67), a star that is located in an uncrowded part of the 148
Standard CMD Season 3
Triangle - Mira Square - SR Circle - Irr Filled - Tidal Empty - Half-Mass
01234 V-I mag
Figure 7.3: The LPV stars are define as Mira with triangles, Semi-regular with squares and Irregular stars with circles. TCM are defined with filled objects while HCM are defined by empty objects. 149
field of view, and produces a great light curve, which leaves us confident that using probable distance and location in the CMD would help us establish it as a likely cluster member, but in an interesting twist V4 falls above the cluster AGB, which lead us to believe that the star could actually a field star closer to us than the cluster, but we need to get radial velocities to further clarify membership.
All of the 63 variables presented in this chapter lie within our Rtidal and therefore we can draw conclusions on their probable cluster membership based on their light curves, variable properties, probable location in the frame and location according to the CMD. In the following chapter a summary of all the variables and their properties will be offered and afinaldiscussionaboutourresultwillbemade. 150
CHAPTER 8
CONCLUSIONS
8.1 Summary
We obtained VI photometry for 63 variable stars, observed over a period of 2 years.
Our search was conducted over our entire field of view for the metal-rich cluster NGC 6388, where all 63 variables stars end up being located inside the cluster’s Rtidal radius of 6.25 arcmin. Most stars were individually calibrated using DAOPHOT photometry software, while some stars were only studied using ISIS photometric package and no calibration data is available for them, the reason being that ISIS works better in the crowded center of the cluster. We were able to classify them using their found properties (periodicity, regularity and amplitude) and plotted light curves. The following chapter will assess our results and provide ideas for further research.
Of these 63 stars, 34 have been previously studied and we compared them with three different papers. We can conclude that our photometry is in agreement with all of the 9 variables from LEM (1973) located within our field of view among these stars. We observed three Mira variables with periods of 255.5, 227.4 and 98.6 days; with one of these Mira variables displaying a diluted effect in its light curve, which can be observed by a range in
I greater than range in V. Also we classified the remaining 6 stars in LEM as LPV either
Semi-Regular or Irregular, mostly according to the shape of their light curves.
The remaining 25 known variables were plotted and classified and our data also agrees with and complements the data in PSCS (2000), where we obtained data for 19 out of 40 stars in their research. Also while two stars (SV2 and V68) agreed with the data in Corwin et al. (2006)(where we obtained data for 6 out of 13 stars in their research) the remaining four stars display certain dissimilarities, which can be explained by these stars being located so close to the crowded cluster center and also by the fact that the resolution for Corwin et al. using HST is greater compared to one we had using PROMPT5. We presented refined 151 periods for 18 of their RR Lyrae variables, since our observations covered more data, and also provide ¡I¿ mean magnitudes to complement their ¡B¿ and ¡V¿ mean magnitudes, which was not the original goal of our research, but shows that using the appropriate tools our data can be extended to research shorter period variables.
The remaining 30 variable stars were revealed to be previously unknown. Out of these
30 stars we classified 1 as Mira LPV variable, 15 of them as semi-regular LPV variables, with periods as long as 358 days, 7 stars classified as Irregular LPV variables, and the remaining
7 stars classified as Supected Variables. We do want to point out that 3 of the irregular stars could have a LSP that could be better defined by obtaining more data points. The data for all the variables is provided in Table 8.1, which gives their location according to our field of view, mean VI magnitude, range, amplitude, period, period-index and sub-classification.
Figure 8.1 displays all the variable stars, with circles for known variable stars and squares for the newly discovered variables.
Our CMD is clear in showing the location of the red clump and once we subtracted the
field stars we were also able to distinguish the blue HB, which is the unusual characteristic of NGC 6388. We observed how our LPV stars are located in the CMD according to their classification. In order to do this we take the mean VI magnitude values for each of our variables and plot them over our calibrated CMD (Figure 8.2)
On the image the triangles are the Mira LPV stars, the circles are the semi-regular LPV and the asterisks are irregular stars. It is shown that most of the stars are located in the
AGB (dashed lines) as is expected for LPV stars, but there are a couple of stars that do not follow this rule. The first one V2 is the only Mira that displays a bluer behavior and does not lie on the AGB, a behavior explained by the dilution of V2’s magnitude by another non-variable star. If we were to remove the presence of the non-variable blending with V2, then we believe V2 will like in the same location as the other two Mira stars. A second star
NV30 falls below the AGB; since this star is not located near a crowded part of the cluster 152
Figure 8.1: Variable stars. Orange circles are known variables. Red squares are newly discovered variables. 153
Location of LPV in the CMD
01234 V-I mag
Figure 8.2: Differentially dereddened. Variable stars are represented: Triangles represent Miras, circles represent Semi-Regulars and asterisks represent Irregulars. Girardi etal. (2002) isochrone for [Fe/H] = -0.4 is shown, shifted by (V I)=0.4588andV by 16.13. The isochrone AGB are shown as dashed lines, and the RGB− as the solid line 154 we believe this a variable that is actually part of the field because if an SR variable star is located behind the cluster it would appear underneath the AGB; another case could be an eclipsing binary but our plotted light curve does not point us towards this case. A third star
NV17 is located over the AGB further above than any other star; this could be explained by the fact that NV17 is a really bright star and it could be overexposed in the V and give us false readings of its flux and therefore lead us to calculate a wrong magnitude. A fourth star
NV21 is the bluest of all the LPV, which can be explained by the fact the star is located near the edge of the CCD and we did not get photometry for our whole run, and the values for the V and V-I magnitude are calculated with the limited amount of data.
Also using the CMD and the added isochrone we were able to confirm the values of extinction (E(V-I) = 0.4588) and apparent distance modulus (Av =1.10)publishedby Harris (1996) and the value for the metallicity ([Fe/H] = -0.44) published by Carreta et al.
(2004). Also we could see how our LPVs follow the AGB trend given by the isochrone, which gives us yet another substantiation that those variables are likely to be cluster members.
All of the variables (including RRL and P2C) are plotted against the CMD in Figure 3, where the LPVs are marked by triangles, circles mark P2C variables, red stars mark RRab and blue stars mark RRc variables. We can see that even though we were able to obtain good data to plot some RR Lyrae and P2C variable stars, when we plotted against the CMD not all of them lie in the areas we would expect to see them. This could be because most of these two type of variables are located near the center of the cluster and therefore blending would cause false reading on their magnitudes, or in other cases like NV17, which is a very bright star, overexposure will give a false magnitude.
8.2 Future Research
Additional science can be done with our data; we are planning to obtain infrared (K- band) photometry from the 2MASS 1archive, in order to present a period-luminosity (P-L) 155
Location of Variable Stars in the CMD
01234 V-I mag
Figure 8.3: CMD shown with the positions of found variables. Triangles represent LPVs, circles represent Population II Cepheids and asteriks represent RRLs. 156 relation for the stars in our cluster. We need to obtain the K-band data because LPVs are brightest in K-band, so K-band is a good observational surrogate for the stars’ luminosities.
Once obtained we can use our periods and compare our data with the P-L relation published by Ita, Y. et al. (2004), so we can identify if the behavior of the LPV stars in our research follows the properties presented by their research.
There are also a couple of stars near the edge, which could be better classified with more data, specially since the stars in our research that are near the edge have been classified as cluster members, and some of them have the probability of being LPV stars and this will complement the data used for a P-L relation.
The use of other period determination methods could help us improve our data, for example the Fourier fitting method could help remove some of the trends in LPV stars with probable LSP in their light curves and provide us with better light curves to enhance our
LPV classification. Another method, self-correlation analysis, is a method that uses a simple time-series analysis that measures the cycle-to-cycle behavior of the star, averaged over all the data3, and the method is especially useful in stars whose periodicity is not entirely regular.
Finally another year or two of data (currently we are downloading and requesting data for a third year) will prove to be beneficial to confirm our classifications, and to possibly correct the classification of some stars, for example irregular stars that have a possibility of a LSP will completely benefit by using more data, since we will be able to observe the full periodicity of the LSP and using the other period determination methods we could remove the LSP trend and try to observe the primary period for the variable star, which would help us confirm or provide a more accurate sub-classification to our LPV stars.
1The Two Micron All Sky survey(http://www.ipac.caltech.edu/2mass/) 157 11.481 Mira HCM / Diluted 62.794P2CCCM 64.320P2CCCM 85.032SRTCM 77.083SRFallsbelowCMD/LikelyFS 8-SRHCM 5SRHCM/BorderingonIrr 41.785SRTCM 48.753SRTCM 420.895MiraTCM 51.682SRTCM 5-SRCCM 31.547SRTCM/SSP 1552.227SRTCM/LSP 3.67651.215IrrTCM SV TCM 61.086IrrTCM 1231.937-SaturatedStar 0.473 Irr TCM 37.681MiraTCM 72.415SRTCM 1253.362SRLSP 31.888IrrTCM 82.446SRTCM 0.187 SR HCM 4-SRHCM 1213 2.40242.180IrrHCM/PossibleSR 2.026 Irr HCM / SR LSP TCM 1.2 1.971 - Saturated Star 38.363MiraHCM 73.229SRHCM 6SRCCM 50.876IrrTCM 0.3 -0.4 P2C TCM -0.6 3.216 P2C HCM P2C HCM 15 4.193 SV TCM 13 1.337 Irr TCM 42.081SRHCM 0.25 1.438 P2C HCM ± ± ± 1.10.25 2.542 2.697 SV Edge of - the CCD Crit. Resolved ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± #Cycles #Obs. RangeV RangeI Amp.V Amp.I Period Per.Index Type Comments geq I geq leq V leq V2V3V4 628.30V5 567.08V6 529.04 282.12V7 605.73 447.50V8 587.84 612.79V9 454.06 587.84 0.268 384.53 622.01 0.701 499.92 447.55 3.233 620.44 1.831 13.52 454.06 1.605 14.64 0.511 14.83 0.728 11.13 15.20 1.830 11.96 15.37 11.69 14.55 12.34 14.08 2.5 12.26 15.32 4.1 12.12 2.3 12.14 6.0 12.38 8.0 40 6.5 81 7.3 81 7.5 81 0.91 81 1.43 64 6.09 79 2.88 79 1.38 0.87 0.90 0.49 2.73 1.21 1.22 0.60 0.84 0.51 0.92 0.66 5.47 0.69 1.66 1.25 0.29 0.37 0.67 0.15 2.39 0.44 0.81 227.4 0.15 0.12 156.8 0.28 253.3 0.33 98.6 0.04 69.9 105.1 73.9 59.5 V12V17V18 504.09 539.16 545.70 557.34 504.29 624.39 1.026 0.804 0.906 14.37 - 11.68 - 8.5 - - 81 - - 0.97 82 82 0.49 - 0.37 - 0.23 - - 81.6 - - - - 2.875 0.6114 - RRab TCM V21V22V23 712.73V26 721.66V27 778.10 303.18V28 544.94 797.58V29 576.72V30 444.85 648.88 2.487 -V31 575.10 1.114V35 461.15 685.53 3.015V36 555.74 811.77 2.117V37 17.09 536.07 720.06V49 - 713.13 651.42 0.939V50 16.87 - 902.89 607.73 0.337V51 15.97 576.39 627.17 0.767V53 - 507.05 577.17 2.578V55 16.03 479.59 648.93 3.662V59 - 589.63 476.84 0.508 -V67 - - 15.52 - 503.56 634.47 0.399V68 606.37 617.60 0.694V69 - - 17.14 - 437.99 843.81 0.515 14.07 14.70 571.11 625.02 0.589 - 14.24 778.89 611.54 1.417 64 16.23 - - 15.07 - 596.47 1.108 12.75 13.98 539.72 0.248 63 12.79 - - - 14.98 3.245 13.48 15.63 0.507 1.00 12.09 - - 15.04 0.084 82 13.46 - - - 0.59 13.35 - 14.46 - 79 82 13.18 - - 0.79 - 12.30 - 74 82 12.13 - 0.69 - 79 82 - - 13.68 40 0.74 10.59 - - - 81 82 5.0 0.78 79 0.40 - - 14.21 0.71 56 0.54 - - 0.21 79 82 - 0.31 79 - 0.18 0.38 - - 0.25 0.02 80 0.40 0.22 - 0.8135 0.17 - 1.55 0.34 - - - 0.27 37 0.02 0.3776 0.14 0.48 0.76 0.07 82 0.38 - - 0.13 0.38 6.320 0.02 82 0.09 0.12 - 0.34 0.04 0.9509 0.10 0.21 3.324 - - 0.03 - 0.11 RRab - 1.14 0.03 - 3.146 - 0.03 0.3582 TCM 0.12 0.21 - RRc 0.19 10.75 0.08 1.156 - 0.38 0.5869 - TCM - 0.3846 0.02 - 0.18 0.3644 0.06 0.3137 2.004 - Rrab 0.3967 - 1.865 0.9860 0.8409 TCM 0.4903 0.13 0.507 - - RRc 2.2690 1.774 - 0.3409 0.861 - TCM 18.028 7.813 - RRc 1.033 RRab - RRc 0.3649 2.194 RRc TCM TCM - Rrab HCM RRc - RRc HCM TCM - RRab P2C TCM TCM TCM TCM 0.3542 RRc 0.9370 TCM RRc - - RRab HCM RRab HCM SV2SV5 616.93 606.77 555.53 536.84 0.114 0.108 12.24 - 10.37 - - - 40 82 0.46 0.61 - 0.24 - 0.33 26.153 - - 0.8135 - RRab CCM NV23NV24 585.06 200.13 896.30NV28 323.77NV29NV30 632.24 3.436 399.34 4.579 669.96 884.06 1097.22 15.56 1034.52 15.95 1.225 5.782 12.24 5.502 12.34 15.34 15.22 8.4 16.95 7.2 12.87 13.30 13.73 76 81 - - 4.5 1.07 1.02 79 12 42 0.40 0.46 2.08 0.14 2.39 0.64 0.35 0.27 0.06 3.58 0.23 0.16 0.61 1.90 76.0 - 77 .0 0.06 1.22 3.29 - 138.1 - - SV TCM NV20NV21NV22 664.76 380.33 1032.73 921.29 1110.87NV25 1072.46NV26 4.802NV27 152.56 5.975 717.32 6.008 1051.18 365.76 525.95 13.31 583.55 13.25 6.679 16.39 11.15 1.092 11.57 2.412 12.33 14.62 6.0 14.75 15.48 12.61 - - 12.37 12.69 32 - 12 6.1 28 14.0 3.05 0.38 39 79 4.44 81 0.47 0.20 0.16 0.95 7.15 0.64 0.68 0.12 0.09 1.82 0.43 0.14 0.30 0.10 0.02 5.58 0.56 102 0.18 85.8 324.4 0.04 0.29 0.06 2.5 100.3 47.5 NV14NV15NV16 711.25NV17 587.84NV18 487.43 526.58NV19 499.92 348.16 649.47 440.93 517.47 898.71 1.172 842.34 0.512 386.42 1.285 2.577 14.97 3.333 14.55 3.265 15.01 12.56 12.16 12.11 11.76 12.62 14.24 9.10 3.0 9.56 6.0 10.90 14.0 - 79 14.5 - 56 79 0.73 81 81 0.49 0.82 78 0.35 0.49 0.29 0.62 0.40 0.14 0.01 0.23 0.15 0.17 0.36 0.26 0.05 0.09 0.10 0.10 0.13 0.03 369.2 144.6 0.05 0.05 41.01 0.01 48.1 30.4 11.52 NV03NV04NV05 575.29NV06 577.17NV07 535.20 596.14NV08 516.61 595.97NV09 488.48 605.42NV10 613.83 610.28 0.348NV11 557.99 680.26 0.433NV12 548.54 751.78 0.594 592.07 586.78 0.662 13.79 501.50 603.46 0.106 544.72 0.020 14.98 - 563.30 0.830 11.28 14.64 1.481 0.215 12.44 - 0.161 12.19 14.68 - 3.5 - 15.03 13.14 2.0 12.55 6.0 12.20 - - 65 11.15 - - 2.0 79 8.0 81 1.81 - - - - 0.59 79 82 0.60 79 1.09 40 82 - 0.30 0.60 82 0.25 - 0.73 0.99 0.29 0.25 0.32 - 0.14 82 0.83 0.26 - - 0.16 0.35 0.32 0.10 177 0.17 - - - 358 0.19 313.6 0.13 - 0.11 335.8 0.14 - - - 278 - 71.3 - - - 68.4 149 155.0 - 137.9 NV01NV02 462.49 573.80 397.58 508.99 2.058 0.510 15.26 12.19 12.10 14.69 9.0 6.0 81 56 0.66 0.49 0.27 0.50 0.13 0.17 0.11 0.10 73.43 64 Star ID x y R(arcmin) Table 8.1:Lyrae type The ab, RRc types forby RR CCM Lyrae are for type most Clikely difined and likely Field P2C to star. for be by Population AlsoSecondary cluster II in Period SR Cepheid. member, the in HCM In for the comments the probable light LSP comments semi-regular, curve cluster is the for member, membership possible are TCM established long for secondary Irr possible period cluster for in member the and Irregular ligth FS curve for and SSP variable, is possible Short SV for suspected variable, RRab for RR 158
REFERENCES
[1] Alard, C. 2000, A&A Supplement, 144, 363
[2] Amberg, Brian, Convolution of box signal with itself, Website, 2010. http : //upload.wikimedia.org/wikipedia/commons/6/6a/Convolution of box signal with itself2.gif
[3] Cardelli, J. A., Clayton, G.C., & Mathis, J. S., 1989, ApJ, 345-245
[4] Carreta, E., Bragalia, A., Gratton, R.G., et al. 2007, A&A, 464, 967
[5] Catelan, M., Smith, H. A., Pritzl, B. J., et al. 2006, Mem. Soc. Astron. Italiana, 77, 202
[6] Corwin, T. M., Sumerel, A. N., Pritzl, B. J., et. al. 2006, AJ, 132, 1014
[7] Eggen, O. J.: 1972, A.J. 172, 639
[8] Girardi et al., 2002, A&A, 391, 195
[9] Harris W.E. 1996, AJ, 112, 1487
[10] Hazen, M. L., & Hesser, B. H., 1986, AJ, 92, 1094
[11] Hogg, H. S, Catalog of Variable Stars and Globular Clusters 1973 as updated by Clement 2001
[12] Ita, Y., Tanab´e, T., Matsunaga, N., etal., 2004b, MNRAS, 347, 720
[13] Kager, Elisabeth, Pulsation Properties of Long Variable Stars in Globular Cluster NGC 6533,BGSUThesis,2010
[14] Kholopov, P.N., 1985, General Catalogue of Variable Stars, 4th edition, Vols I-III (Nauka, Moscow)
[15] Lee, Kevin, Period Determination - Variable Star Photometry - NAAP, Website, 2011. http : //astro.unl.edu/naap/vsp/pdm.html
[16] Llyod Evans, T., & Menzies., J. W. 1973, in Variable Stars in Globular Clusters and in Related Systems, ed. J.D. Fernie (Boston: Reidel), 151
[17] Llyod Evans, T., & Menzies., J. W. 1977, MNRAS, 178, 163
[18] Newberry, M. V., Dark Frames CCD Astronomy (1995) 159
[19] Newberry, M. V., Pursuing The Ideal Flat Field CCD Astronomy (1996)
[20] Percy, J. R., & Bagby, D. H. 1999, PASP, 111, 203
[21] Pritzl, B., Smith, H. A., Catelan, M., & Sweigart, A. V. 2001, AJ, 122, 2600 (erratum 125, 2750[2003])
[22] Pritzl, B., Smith, H. A., Catelan, M., & Sweigart, A. V. 2002, AJ, 124, 949 (erratum 125, 2752 [2003])
[23] Rich, M. R., Sosin, C., Djorgovski, S. G., et al. 1997, ApJ, 484, L25
[24] Silbermann, N. A., Smith, H. A., Bolte, M., & Hazen, M. L., 1994, AJ, 107, 1764
[25] Stellingwerf, R. F. 1978, ApJ, 224, 953
[26] Stetson, P. B. 1987, PASP, 99, 191
[27] Stetson, P. B. The Technique of Least Squares and Stellar Photometry with CCD’s, Chapter 5,1990
[28] Stetson, P. B. 1994, PASP, 106, 250
[29] Stetson, P. B. 2000, PASP, 112, 925
[30] Stetson, P. B., Photometric Standard Fields, Website, 2011. http : //cadcwww.dao.nrc.ca/community/ST ET SON/standards/
[31] Sweigart, A. V., & Catelan, M. 1998, ApJ, 501, L63
[32] Uttenthaler, S, Van Siphout, K., Voet, K. et al., 2011, A&A, 1105, 2198