THE SEARCH FOR TRANSITING EXTRASOLAR PLANETS
IN THE OPEN CLUSTER M52
A Thesis
Presented to the
Faculty of
San Diego State University
In Partial Fulfillment
of the Requirements for the Degree
Master of Sciences
in Astronomy
by
Tiffany M. Borders
Summer 2008 SAN DIEGO STATE UNIVERSITY
The Undersigned Faculty Committee Approves the
Thesis of Tiffany M. Borders:
The Search for Transiting Extrasolar Planets in the Open Cluster M52
Eric L. Sandquist, Chair Department of Astronomy
William Welsh Department of Astronomy
Calvin Johnson Department of Physics
Approval Date iii
Copyright 2008 by Tiffany M. Borders iv
DEDICATION
To all who seek new worlds. v
Success is to be measured not so much by the position that one has reached in life as by the obstacles which he has overcome.
–Booker T. Washington
All the world’s a stage, And all the men and women merely players. They have their exits and their entrances; And one man in his time plays many parts...
–William Shakespeare, “As You Like It”, Act 2 Scene 7 vi
ABSTRACT OF THE THESIS
The Search for Transiting Extrasolar Planets in the Open Cluster M52 by Tiffany M. Borders Master of Sciences in Astronomy San Diego State University, 2008
In this survey we attempt to discover short-period Jupiter-size planets in the young open cluster M52. Ten nights of R-band photometry were used to search for planetary transits. We obtained light curves of 4,128 stars and inspected them for variability. No planetary transits were apparent; however, some interesting variable stars were discovered. In total, 22 variable stars were discovered of which, 19 were not previously known as variable. Ten of our variable stars were identified as eclipsing-type W Ursa Majoris contact binaries, 5 were identified as detached binaries of the Algol type, 1 was identified as a slowly pulsating B star, and 6 were irregular and require further investigation before they can be classified. A color-magnitude diagram constructed from V and R photometry with fitted isochrones is also presented to help determine cluster membership of our variable stars. We find that 3 of our W Uma stars lie within a region of high cluster membership probability. Radial velocity follow up observations are needed to confirm cluster membership. If confirmed, this would be highly interesting as W Uma stars are not excepted to be found in such a young cluster. vii
TABLE OF CONTENTS PAGE ABSTRACT ...... vi LIST OF TABLES...... ix LIST OF FIGURES ...... x ACKNOWLEDGEMENTS...... xv CHAPTER 1 INTRODUCTION ...... 1 1.1 Planetary Transits ...... 1 1.2 Fraction of Stars withPlanets ...... 5 1.3 Planet-Metallicity Correlation ...... 6 1.4 OpenClusters ...... 8 1.5 M52...... 9 2 OBSERVATIONS OF M52...... 11 3 DATAREDUCTION ...... 14 3.1 Overscan Correction and Trimming...... 14 3.2 BiasRemoval...... 14 3.3 FlatFielding...... 15 3.4 Correcting Bad Pixels...... 15 3.5 Header Corrections...... 15 3.6 ImageRejection...... 16 4 ISIS ...... 17 4.1 ISISSetup ...... 17 4.2 The interp.csh Routine...... 17 4.3 The ref.csh Routine ...... 18 4.4 The subtract.csh Routine ...... 20 4.5 The detect.csh Routine...... 23 4.6 The find.csh Routine ...... 24 4.7 The phot.csh Routine ...... 24 5 PLANETARY TRANSIT SEARCH ...... 28 viii 5.1 Box Least Square Algorithm ...... 28 5.2 BLS Implementation...... 30 5.3 SYSREM ...... 33 5.4 Transit Selection Criteria ...... 34 5.5 Planetary Transit Results ...... 35 6 VARIABILITY...... 56 6.1 Period Determination ...... 57 6.2 Variability Results...... 64 6.2.1 W UMaVariables...... 64 6.2.2 Slowly PulsatingB Stars ...... 75 6.2.3 Detached Eclipsing Binaries ...... 75 6.2.4 Irregular Variables or Unclassified...... 85 7 CONCLUSION ...... 95 REFERENCES ...... 96 ix
LIST OF TABLES PAGE Table1.1 ...... 2 Table 2.1 R Filter Observations of M52...... 11 Table 2.2 V Filter Observations of M52...... 12 Table 4.1 ISIS Process Configuration File ...... 18 Table 4.2 ISIS Default Configuration File...... 20 Table 4.3 ISIS Phot Configuration File...... 21 Table 5.1 Input Parameters Used in BLS ...... 33 Table 5.2 BLS Results...... 36 Table 5.3 BLS Final Results ...... 36 Table 6.1 Variable Star Information ...... 57 x
LIST OF FIGURES PAGE Figure 1.1 Light curve of HD209458b from Brown et al. (2001) showing the characteristic light curve of a planetary transit...... 4 Figure 1.2 Figure from Fischer & Valenti 2005 shows the occurrence of exo- planets vs iron abundance [Fe/H] of the host star measured spectroscop- ically. The occurrence of observed giant planets increases strongly with stellar metallicity. The solid line is a power law fit for the probability that a star has a detected planet...... 7 Figure 2.1 CMD with overlaid theoretical isochrones obtained from Cassisi et al. (2006)...... 13 Figure 4.1 Composite reference image from ISIS...... 19 Figure 4.2 var.fits produced from ISIS . Most of the really bright spots are satu- rated stars...... 25 Figure 5.1 BLS example results from Kovacs et al. (2002) from a test set of data. This shows the time series in the upper panel, the normalized BLS frequency spectrum and the folded time series in the lower panel. The signal parameters are displayed at the top where n is the number of bins, P0 is the period, q is the fractional transit length, δ is the transit depth, and δ/σ istheSNR...... 31 Figure 5.2 The top panel shows the RMS of the 4128 stars which appear on the var.fits and have 323 out of 423 observations. The middle panel shows the RMS of the 3935 stars remaining after filters have been applied. The bottom panel shows the 1238 stars remaining which are suitable for BLS study after filters were applied including an RMS < 0.015 magnitude cutoff...... 32 Figure 5.3 Binned phased plot for candidate ID 1956...... 38 Figure 5.4 Phase vs. unbinned delta magnitude of the points in transit for can- didate ID 1956. Error bars have been added to convey the uncertainty in the residual flux within the transit phase...... 39 Figure 5.5 Residuals of candidate ID 1956. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th...... 40 Figure 5.6 Normalized signal residue versus trial frequency for candidate ID 1956. The SR peak corresponds to a period of 1.5096 days...... 41 Figure 5.7 Binned phased plot for candidate ID 2563...... 42 xi Figure 5.8 Phase vs. unbinned delta magnitude of the points in transit for can- didate ID 2563. Error bars have been added to convey the uncertainty in the residual flux within the transit phase...... 43 Figure 5.9 Residuals for candidate ID 2563. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th...... 44 Figure 5.10 Normalized signal residue versus trial frequency for candidate ID 2563. The SR peak corresponds to a period of 1.5096 days...... 45 Figure 5.11 Binned phased plot for candidate ID 1347...... 46 Figure 5.12 Phase vs. unbinned delta magnitude of the points in transit for candidate ID 1347. Error bars have been added to convey the uncertainty in the residual flux within the transit phase...... 47 Figure 5.13 Residuals for candidate ID 1347. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th...... 48 Figure 5.14 Normalized signal residue versus trials frequency for candidate ID 1347. The SR peak corresponds to a period of 1.4552 days...... 49 Figure 5.15 Binned phased plot for candidate ID 1267...... 50 Figure 5.16 Phase vs. unbinned delta magnitude of the points in transit for candidate ID 1267. Note that 1 “low” data point has been removed. Error bars have been added to convey the uncertainty in the residual flux within the transit phase...... 51 Figure 5.17 Phase vs. unbinned delta magnitude of the points in transit for candidate ID 1267 including “low” data point. Error bars have been added to convey the uncertainty in the residual flux within thetransitphase...... 53 Figure 5.18 Residuals for candidate ID 1267. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th...... 54 Figure 5.19 Normalized signal residue versus trial frequency for candidate ID 1267. The SR peak corresponds to a period of 1.3598 days...... 55 Figure 6.1 var.fits frame with location of variable stars...... 58 Figure 6.2 Composite reference image with location of variablestars...... 59 Figure 6.3 CMD highlighting the location of variable stars detected...... 60 Figure 6.4 ID 0533 Lomb-Scargle period analysis. The peak of maximum power corresponds to a P = 0.607 days...... 62 xii Figure 6.5 ID 0533 Lafer-Kinman period analysis. Two of the lowest r values corresponds to a period P = 0.607 days and P = 1.214 days. Lower r values with larger periods can be ruled out based solely on the unphased lightcurve...... 63 Figure 6.6 Phased light curves of suspected W UMa stars...... 65 Figure 6.7 Light curve of ID 0533. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 66 Figure 6.8 Light curve of ID 0981. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 67 Figure 6.9 Light curve of ID 1107. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 69 Figure 6.10 Light curve of ID 1133. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 70 Figure 6.11 Light curve of ID 1558. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 71 Figure 6.12 Light curve of ID 1834. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 72 Figure 6.13 Light curve of ID 2513. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 73 Figure 6.14 Light curve of ID 2673. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 74 Figure 6.15 Light curve of ID 2830. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 76 xiii Figure 6.16 Light curve of ID 3727. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 77 Figure 6.17 Light curve of ID 1855. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 78 Figure 6.18 Phased light curves of suspected EA variables...... 80 Figure 6.19 Light curve of ID 0681. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 81 Figure 6.20 Light curve of ID 0980. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 82 Figure 6.21 Light curve of ID 1261. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 83 Figure 6.22 Light curve of ID 1284. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 84 Figure 6.23 Light curve of ID 4109. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 86 Figure 6.24 Light curve of ID 2409. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 88 Figure 6.25 Light curve of ID 2773. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 89 Figure 6.26 Light curve of ID 3096. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 90 xiv Figure 6.27 Phased light curve of ID 3096...... 91 Figure 6.28 Light curve of ID 3928. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 92 Figure 6.29 Light curve of ID 4540. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 93 Figure 6.30 Light curve of ID 4762. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first obser- vation (HJD(1)) taken on August 24th...... 94 xv
ACKNOWLEDGEMENTS First and foremost, my gracious thanks must be extended to my advisor Dr. Eric Sandquist. I am exceedingly grateful for the 2 years of financial support you have provided for me which has made this thesis possible. Thank you for your insight, patience, sense of humor, endless advice, and for having a “test” for just about any situation. I have become a better astronomer because of your guidance. I would like to thank my family for their wholehearted support. A special thanks goes to my loving and proud parents who always encourage me to fulfill my dreams. Thank you to Matt Davis for being my motivation. I am thankful for all the tremendous amounts of help and patience you’ve provided for me along the way. I would like to thank Georgia Grossman and Azalee Bostroem for their friendship. The support you’ve both provided for me is beyond words. Thank you to De Marie Garcia for her insight, help, and for expanding my mind to new possibilities of exploring the universe. I would like to thank Leila Perello and Patty Baker for teaching me the beauty and hard work required to dance ballet. Thank you to the members of my thesis committee, Dr. William Welsh and Dr. Calvin Johnson for their feedback on my thesis. Thank you to Dr. Etzel for allowing me to complete my thesis with the use of his computer “MEGADEATH.” Finally, I would like to thank our department administrator, Margie Hoagland for all her support and help. 1
CHAPTER 1 INTRODUCTION
The field of planet searches has grown tremendously since the first confirmed extrasolar planet detections were made in the 1990s. One of the techniques for planet detection that has had recent successes is the search for planets transiting their host stars. To date, more than 2901 extrasolar planet candidates have been detected using various techniques. There are 51 known transiting planets. Transits of bright stars have great scientific potential, giving clues to information such as the internal structure of planets (Guillot 2005) and their atmospheric composition (Charbonneau et al. 2002).
1.1 PLANETARY TRANSITS The planetary transit method is based on the observation of the temporary dimming of the apparent brightness of a parent star that occurs when a planet moves across the stellar disk. One condition for the use of this method is, of course, that the planet should (from the observer’s viewpoint) pass in front of its star. The probability of this occurring also depends on the size of the star, and is greater when dealing with a large star. Another factor to consider is the distance of the planet from the star since the nearer it is, the greater the chance that a transit will occur. So, what is the probability of being able to observe a planetary transit across a star at a distance a? If the stars were indeed a point source, the transit would occur only if the star, the planet, and the observer were in exact alignment. However, the star has a finite radius. In the case of planetary-stellar transits one can estimate the probability to observe transits as a function of three parameters, the star radius R∗, the transiting planet radius Rp, and the distance between both objects at the time of transit a. The probability to observe a transit assuming random orientation of the orbit is (Sackett 1999):
R∗ + R P robability = p (1.1) a
In the case of planetary transits, this probability becomes close to R∗/a showing that it is more likely to observe a transiting planet at small orbital distances. In general, the nearer a planet is to its star, the greater the possibility of a transit; and the larger the star, the greater the chance that the planet will be seen to pass across it. However, the range of inclinations can
1see J. Schneider’s Extrasolar Planets Encycolpedia at http://exoplanet.eu/ for an updated list. 2 change as the planet gets closer or further away from the parent star and this must also be taken into account.
If R∗ = R⊙, then for a planet at 1 AU (P = 365 days assuming a 1M⊙ star), the probability of being able to observe a transit is 0.5%, rising to a not insignificant 10% if the planet orbits at 0.05 AU (P = 4 days). As seen in Table 1.1, in the case of the solar system observed by a person at a random orientation, the probability to observe a transit of Mercury is of order 1% while it drops down to 0.1 % for Jupiter. For the configuration of “hot” Jupiters, large planets close to their parent stars, such as 51 Pegasi b and HD209458 b they favor the visibility of transits. The probability that the planet, as seen from Earth, will cross the face of the star (assuming a solar-type star) attains 10%.
Table 1.1. Probability of Transit % Duration of Transit (Hours) Variation in Flux % Mercury 1.2 8 1.2 10−3 Venus 0.64 11 7.6×10−3 × − Earth 0.47 13 8.4 10 3 Jupiter 0.09 30 1 × Saturn 0.05 41 0.75 51Pegasib 9.1 3 1 HD209458b 10.8 3 1.6
The diminution in brightness due to the transit of the planet is easy to determine. It is simply the ratio of the apparent surfaces of the planet and the star:
R 2 ∆F = p (1.2) R∗ Consequently, if the radius of the star can be estimated then the radius of the planet can be deduced. The duration of the transit depends firstly upon the period of revolution of the planet around the star. The further away the planet is from the star, the longer it will take to pass across the face. Secondly, the duration of the transit depends upon the inclination of the orbit. It is possible from geometrical calculations to infer the duration of the transit event. The maximum transit duration Tmax (when the planet crosses over the center of the stellar disk), in front of a star of radius R∗ and mass M∗, for a planet orbiting with a period P at a distance a is (Lecavelier Des Etangs & Vidal-Madjar 2006):
−1/2 P R∗ a 1/2 M∗ R∗ Tmax = × 13.0 hours (1.3) π a ≈ 1AU M⊙ R⊙ × 3
assuming a planet radius much smaller than R∗. So, for a star with known mass and size, the maximum transit duration is constrained by the orbital period and the size of the parent star. For planets at different distances, the transit may last periods ranging from hours to several days. The actual transit duration, however, depends on the inclination of the planetary orbit with respect to the observer (Sackett 1999). For instance, if the planet’s orbit is at an inclined angle then it might only graze a small region of the star therefore reducing the measured transit duration. It is also worth mentioning that the transit duration becomes increasingly more difficult to observe if the transit is long. A typical observation run is on average 10 ∼ hours and if the transit is longer than this, like in the case of Jupiter with a transit duration of 30 hours, an observer could easily miss the transit. Planets that have transit durations of less than a day require rapid and continuous sampling to ensure high detection probabilities. Another factor worth noting is that it is impossible to observe an object 24 hours a day from a single site because of the alternation of night and day which produces yet another challenge to finding transiting planets. It is also possible to infer the shape of the photometric light curve. To calculate the theoretical transit light curve, one must take into account the non-uniformity of the stellar flux over the different parts of the stellar disk. It is in general affected by the limb darkening which induces a curved bottom shape for the transit profile. This can be seen in Figure 1.1 showing the high quality transit profile HD 209458b obtained by Brown et al. (2001) with the Hubble Space Telescope. This observed profile can be very well fitted by a theoretical light curve taking into account the limb darkening of the solar-type star HD209458. To produce a detectable transit, most planets will require an orbital inclination of less than a few degrees from edge-on (Sackett 1999). So, the planet’s orbit needs to be nearly perpendicular to sky (inclination close to 90◦). While it is quite challenging to find this, pre-selecting favorable inclination targets through measurement of the rotational spin of the parent could be a way to favor transit discoveries. However, due to the precision of such evaluations and to the probable spread of the planets’ orbital plane inclinations relative to the star a gain of no more than a factor of three to five in detection probability is expected (Sackett 1999). Other proposed ways to favor transit detection are to select already transiting binary star systems in which the orbital plane of the the binary is known to be close to edge-on and by assuming that planets could be present in the orbital plane of the stellar system (Sackett 1999). However, the evolution and dynamics of double star systems are quite different from single star systems which could affect the formation and frequency of planetary companions. Also, the gain in probability remains of the order of a factor of three to five (Sackett 1999). It should be noted that in order to detect an exoplanet by the transit method, the luminous flux from the star has to be measured very accurately over an extended period, in the 4
Figure 1.1. Light curve of HD209458b from Brown et al. (2001) showing the characteristic light curve of a planetary transit. 5 hope of being able to observe regular fluctuations as the star dims slightly for a certain repeated amount of time. Accuracy to at least 1% in the measurement of the flux (0.01 mag) is necessary for the detection of giant planets (Casoli & Encrenaz 2007). In the final analysis from transit observations one can deduce the radius of the planet, its period, and the inclination of its orbit but not its mass. Velometric observations are also needed to allow for the minimum mass (Msini) of the planet to be determined. Since there is no clear way to improve the probability of detecting planetary transits, searches have to cope with probabilities in the range of 0.1 to 1%, except in the case of the “very hot” Jupiter which can be detected with a much higher probability, up to 20% for the ∼ shortest orbital period (Bouchy et al. 2004). The consequent strategies are to look for a large number of targets such as fields containing thousands of stars to survey photometric variations. Open clusters which contain up to a few thousand stars, for example, provide an ideal environment for searching for transiting extrasolar planets. This strategy, however, entails the analysis of lots of data. While hundreds of candidates stars may be found a vast majority of these candidates will be revealed as variable stars or eclipsing binaries but even if one planet is detected it will be a scientific treasure worth the hunt.
1.2 FRACTION OF STARS WITH PLANETS In order to answer the question “what fraction of stars have planets?” we must rely on the analysis of statistical distributions of extrasolar planets (also known as exoplanets) detected so far. To estimate the fraction of stars with planets it can be calculated from the raw numbers of stars that host exoplanets divided by the number of stars monitored. For example, Marcy & Butler (2000) report a fraction of 5% of main-sequence stars harbor companions of
0.5 to 8 Mjup within 3 AU. Lineweaver & Grether (2003) report an analysis from radial velocitites of 1800 nearby Sun-like stars monitored by eight high-sensitivity Doppler ∼ exoplanet surveys that approximately 90 of these stars host exoplanets massive enough to be detectable. Thus, at least 5% of targets stars posses planets. Further analysis by Lineweaver ∼ et al. (2003) estimate that at least 9% of Sun-like stars have planets in the mass and orbital ∼ period ranges Msini> 0.3M and P <13 years and at least 22% have planets in the jup ∼ larger range Msini> 0.1Mjup and P < 60 years. Marcy et al. (2005) also report statistical properties from the 152 exoplanets that have been discovered orbiting 13 normal stars using the Doppler technique. They found that >7% of stars have giant planets within 5 AU (most beyond 1 AU) and 1.2% of spectral type F,G, and K stars have hot Jupiters (a< 0.1 AU). Lineweaver & Grether (2003) also attempt to answer the question of “what fraction of Sun-like stars have Jupiter-like planets?” This fraction is important to consider because Jupiter is a dominant orbiting body in our solar system and probably had a significant influence on the formation of our planetary system. So, it is interesting to consider how 6 typical is Jupiter. Lineweaver & Grether (2003) estimate that the fraction of Sun-like stars hosting planets to be 5% in a “Jupiter region” which is defined by orbital periods between ∼ the period of the asteroid belt and Saturn with masses in the range MSat < Msini< 3MJup. Using the transit method, the probability of detecting a transit in best in the case of a hot Jupiter (as discussed in the previous section). Hot Jupiters typically have masses and radii similar to that of Jupiter with short orbital periods between 1 - 10 days. So, what is the probability of finding a transit of a hot Jupiter? The factors that need to be considered in order to answer this question include the frequency of hot Jupiters around surveyed stars, the likelihood of the geometrical alignment between the star and planet that is necessary to detect transits, and the binary fraction (von Braun et al. 2005). von Braun et al. (2005) calculates the probability by making several assumptions including a planet frequency around isolated stars of 0.7% for planets with a semimajor axis of a 0.05. It is also assumed that approximately ∼ 10% - 20% of those hot Jupiter systems would have a favorable orientation (nearly edge-on) that a transit would be visible from Earth. Since von Braun et al. (2005) assumes that planets can only be detected around single stars a binary fraction of 50% is assumed. Under all these assumptions, it is estimated that 1 star in 3000 (a 0.05 AU) has a transiting hot Jupiter ∼ around a main-sequence star.
1.3 PLANET-METALLICITY CORRELATION Soon after the discovery of the first exoplanets, stellar spectroscopists noticed that the stars hosting giant planets were systematically metal-rich (Udry & Santos 2007). Planet occurrence appears to correlate strongly with the abundance of heavy elements in the host star where the frequency of planets rises steeply as a function of the metallicity of the star (Figure 1.2). The frequency of planetary systems depends on the metallicity of the host star, with stars of low metallicity having a lower probability of planetary formation. Current numbers suggest that at least 25% of the stars with twice the metal content of the Sun( [Fe/H] +0.3) are ∼ ≥ orbited by a giant planet, and this number decreases to below 5% for solar metallicity objects (Udry & Santos 2007). The correlation between planet occurrence and metallicity can be expressed as a power law (Fischer & Valenti 2005):
(N /N ) 2 P (planet)=0.03 Fe H (1.4) × (N /N )⊙ Fe H This correlation applies to FGK-type main sequence stars and is valid over the metallicity range -0.5 < [Fe/H] < 0.5. This relationship (shown in Figure 1.2) quantifies the probability P(planet) for forming a gas giant planet with orbital period shorter than 4 yrs as a function of metallicity. Thus, from this power law, the probability of forming a gas giant planet is nearly 7
Figure 1.2. Figure from Fischer & Valenti 2005 shows the occurrence of exoplanets vs iron abundance [Fe/H] of the host star measured spectroscopically. The occurrence of observed giant planets increases strongly with stellar metallicity. The solid line is a power law fit for the probability that a star has a detected planet. 8 proportional to the square number of the number of iron atoms. So, it appears that metallicity seems to play a crucial role in the formation and/or evolution of planets. One explanation for the physical mechanism for the observed planet-metallicity correlation is that the high metallicity enhances planet formation because of the increased availability of small particle condensates which are the building blocks of planetesimals. This high metallicity found in planet-bearing stars is argued to be inherited from the primordial cloud, rather than an acquired asset. Furthermore, planet-bearing stars with super-Solar metallicity are more than twice as likely to have multiple planet systems than planets-bearing stars with sub-Solar metallicity. The observed metallicity correlation does not imply that giant planets cannot be formed around more metal-poor objects but rather that the probability of formation among such systems is lower. To test the dependence of metallicity on planets formation globular clusters can be used as a direct study. These clusters are among the oldest of astronomical objects, and therefore, their stars typically have very low metallicity. Gilliland et al. (2000) used WFPC2 on the Hubble Space Telescope (HST ) to search for transits on 34,000 main-sequence stars ∼ in the globular cluster 47 Tucanae. While 47 Tuc is metal-rich as far as globular clusters are concerned it is metal-poor ([Fe/H] = -0.76; Harris (1996)) compared with objects in the solar neighborhood and has considerably lower metallicity of any star known to harbor an extrasolar planet. Based on statistics from a sampling of planets in our local stellar neighborhood, Gilliland expected that 1 out of 1,000 stars in the globular cluster should have planets transit once every few days and predicted that HST should discover 17 hot Jupiter-class planets. However, no planets were found. The lack of planets can be attributed to not only the low metallicity but also the extreme environment of a globular cluster which might not be the best place for planets to survive. Davies & Sigurdsson (2001) showed that a planet in the densest core region of 47 Tuc, sampled by Gilliland et al. (2000), would survive disruption by stellar encounters for 1 108 years with an orbital separation d 5 AU. Short period planets, ∼ × ∼ those to which transit surveys are sensitive, would survive for significantly longer.
1.4 OPEN CLUSTERS As discussed in the previous sections, one way of overcoming the difficulties of finding transits is to search for transits in dense stellar fields. While globular cluster do contain thousands to millions of stars and seem like good laboratories for searching for extrasolar planets the globular cluster’s low metallicity and harsh conditions may not support planets (as discovered in the case of 47 Tuc). Other searches have undertaken a wide-field search for transits in the Galactic plane since the Galactic plane provides a high density of stars in a long narrow survey volume. Teams such as OGLE III (Optical Gravitational Lensing Experiment) have monitored 52,000 galactic disk stars for 32 nights, and report 59 transit ∼ 9 candidates with periods ranging from 1 to 9 days (Udalski et al. 2002b,a). Open clusters (OC) also provide a potentially ideal environment for the search of transiting extrasolar planets since they feature relatively large number of stars ( 10,000 member stars) of the same ∼ known age, metallicity, and distance. Open clusters are essentially at the same distance from the Sun because the distance between member stars in the cluster is much smaller than the distance to the cluster. The stars have nearly the same age since they formed together. Since they all formed from the same nebula, cluster members should have virtually the same chemical composition. However, cluster members do differ in mass. Open clusters are less crowded and offer a range of metallicites which can further be used to resolve the effects of metallicity and high-density environment on planet frequency. With this motivation a number of open clusters have been monitored by different groups. Examples of such teams include PISCES (Planets in Stellar Clusters Extensive Search; (Mochejska et al. 2002, 2006)) and EXPLORE/OC von Braun et al. (2005), STEPPS (Survey for Transiting Extrasolar Planets in Stellar Systems; Burke et al. (2004)) and UStAPS (University of St. Andrews Planet Search; Street et al. (2003) which target selected open clusters to find exoplanets. However, no cluster survey has yet confirmed the detection of a planet. Despite no planets yet being confirmed, these surveys have provided promising candidates awaiting follow-up, as well as cluster parameters and variable stars. Careful cluster target selection is important in OC planet transit surveys. Some challenges to consider suggested by von Braun et al. (2005) include the somewhat low number of stars in an open cluster, determining OC cluster membership in the presence of significant contamination, and differential reddening along the cluster field and long the line of sight. To reduce some of these challenges careful selection can help maximize the number of stars, maximize the probability of detecting transits, and reduce line-of-sight and differential reddening. One of the biggest challenges in the selection of target clusters is the lack of data on many OCs. The physical parameters of the cluster such as distance, foreground reddening, age, and metallicity, are frequently either not determined or have large uncertainties in the published values.
1.5 M52 The open cluster M52 was carefully selected for this photometric planetary transit survey. M52 is relatively close at a distance of 1.4 0.2 kpc (Bonatto & Bica 2006) and is ± easily observable from our location and facilities available. M52 is located in the direction of ′ ′′ Cassiopea at (J2000) α = 23h24m42s and δ = 61◦35 42 . It is a rich cluster that is strongly concentrated and contains a moderate range of star brightnesses. As discussed previously, metallicity is an important consideration in planetary searches. We attempted to determine the metallicity of M52 for this project. However, there 10 are yet no spectroscopic measurements. We also attempted to determine [Fe/H] using Stromgren photometry however, there is no Stromgren photometry in the F and G star range where the metallicity calibrations are most trustworthy. Thus, we assume M52 is close to solar metalicity based on the following reasons. M52 is relatively young with an estimated age of 60 10 Myr (Bonatto & Bica 2006). ± It is presumed that because the cluster is young it has stars that are generally metal rich having formed from remnants of previous supernovae explosions. During supernova detonations iron is ejected, enriching the stellar medium and therefore, younger stars can be created with a greater abundance of iron in their atmospheres. Thus, based on the youth of M52 we assume that it is close to solar metallicity. Younger clusters are typically concentrated in the center of the Galaxy and are close to the Galactic plane. Within the Galactic plane the metallicity content is found to be higher. Within the thin disk of the Galaxy, where open clusters reside, typical values of [Fe/H] range from -0.5 to +0.3, while stars in the thick disk (further from the Galactic plane) range from -0.6 to -0.4 (Carroll & Ostlie 2006). Also, in the Galaxy as a whole there is a general trend for the metallicity to increase towards the central regions. Metal-rich stars are found to be more common within the solar circle. Bonatto & Bica (2006) determined the location of M52 to be 7.9 0.2 kpc from the Galactic center which is 0.7 kpc outside the solar circle. Thus, also ± ≈ based on the position of M52 within the Galaxy is likely that it is close to solar metallicity. One caveat to this cluster is that it has a low Galactic latitude (ℓ = +112.81◦, b = 44◦) and is affected by Galactic star contamination. On average, the closer the OC is to the Galactic disk, the higher the contamination due to Galactic field stars. However, transit detections around main-sequence field stars are still possible and would also be scientifically valuable. 11
CHAPTER 2 OBSERVATIONS OF M52
Observations of M52 were obtained in 2001 between August and November and 2007 in December from Mount Laguna Observatory with the 40 inch telescope. Table 2.1 lists the observations dates, the number of observed hours on the target source taken the in R band, and the average seeing including the 1 σ uncertainty. Table 2.2 lists the observation dates, the number of observed hours on the target source taken in the V band, and the average seeing including the 1 σ uncertainty. Observations were taken in the V band for the construction of a color-magnitude diagram (CMD). A range of exposure times were taken for individual images from 60 seconds to 600 seconds. A total exposure time of 70.49 hours was taken in the R filter and a total exposure time of 2.82 hours was taken in the V filter.
Table 2.1. R Filter Observations of M52 Date Heliocentric Julian Day Duration (hr) Seeing (′′) 2001Aug24 2452146.0 4.94 3.08 0.58 2001Aug25 2452147.0 5.07 2.73 ± 0.26 2001Aug26 2452148.0 4.88 2.92 ± 0.27 2001Sept17 2452170.0 6.53 2.73 ± 0.26 2001Sept18 2452171.0 6.02 2.71 ± 0.15 2001Sept19 2452172.0 6.52 2.70 ± 0.16 2001Sept20 2452173.0 6.52 2.76 ± 0.18 2001Oct13 2452196.0 5.52 2.72 ± 0.22 2001Oct14 2452197.0 5.73 2.82 ± 0.19 2001Oct15 2452198.0 5.16 2.89 ± 0.28 2001Oct16 2452199.0 5.91 2.84 ± 0.20 2001Nov14 2452227.0 3.15 3.18 ± 0.43 2001Nov15 2452228.0 0.29 2.67 ± 0.19 2001Nov16 2452229.0 3.12 2.91 ± 0.33 2007Dec06 2454444.0 1.13 2.51 ± 0.29 ±
The color-magnitude diagram (CMD) was constructed from a DAOMATCH and DAOMASTER combination of the R data and V data. Four images were used for the CMD including two V band observations from September 17th and September 19th 2001 and two R band observations from September 18th and September 19th 2001. Because the observed data are uncalibrated, the magnitudes and colors were shifted to match calibrated data of M52 12 Table 2.2. V Filter Observations of M52 Date Heliocentric Julian Day Duration (hr) Seeing (′′) 2001Aug25 2452147.0 0.24 2.73 0.26 2001Aug26 2452148.0 0.20 2.92 ± 0.27 2001Sept17 2452170.0 0.18 2.43 ± 0.02 2001Sept19 2452172.0 0.42 2.70 ± 0.16 2001Sept20 2452173.0 0.83 2.76 ± 0.18 2001Oct13 2452196.0 0.39 2.72 ± 0.22 2001Oct14 2452197.0 0.42 2.82 ± 0.19 2001Oct15 2452198.0 0.14 2.89 ± 0.28 ± from Stetson (2000) obtained from the WEBDA1 online database. A star from our data was matched to the same star from Stetson (2000) and an offset in both (V-R) and V was used to shift the data. An offset of +2.0162 magnitudes was applied to the instrumental magnitudes and an offset of +1.3213 was applied to the (V-R) color index. Figure 2.1 shows the CMD. Overlaid on the observed CMD are theoretical isochrones obtained from the BASTI 2 interactive database of updated stellar evolution models from Cassisi et al. (2006). We selected a metallicity of Z = 0.0198 since the cluster is assumed to be near solar and an age of 60 Myrs determined from Bonatto & Bica (2006). The CMD can be used as a tool for estimating cluster membership for any detected variable stars in the cluster CMD. This will be discussed in 6. §
1http://www.univie.ac.at/webda/ 2http://193.204.1.62/index.html 13
CMD of M52
8
10
12 V 14
16
18
0.2 0.4 0.6 0.8 1 1.2 1.4 (V - R) Figure 2.1. CMD with overlaid theoretical isochrones obtained from Cassisi et al. (2006) . 14
CHAPTER 3 DATA REDUCTION
We must apply a series of corrections to each raw CCD image in order to seperate instrumental signals and imperfections from the astronomical signals before photometric analysis is implemented. Observations of the target object were reduced in the standard fashion, using IRAF 1 routines to correct the raw data. Calibration images used for the image reduction include dark frames and twilight flat fields which were taken on each night of an observation. The basic processing steps are: overscan correction and trimming, bias removal, flat-fielding and bad pixel corrections. Each is described below.
3.1 OVERSCAN CORRECTION AND TRIMMING The overscan strip is the narrow region of the CCD image usually running down either side of the image and contains virtual pixels generated by the CCD electronics when the CCD is read out. The overscan strip must be subtracted and trimmed from all target and calibration images. The mean level of the pixels in the overscan region provides a measure of the average signal introduced by reading the CCD. The values of the signal in the overscan strip may be fitted as a function of row and subtracted from the value in each pixel in that row. Once this is completed, the image is overscan corrected and the overscan region can thus be trimmed and discarded. The overscan region and trim section for this project is determined using the implot IRAF routine. This plot provides a drop in the CCD pixel values in the region of the overscan strip. We used the IRAF task COLBIAS to perform the overscan correction and trimming using the chebyshev fitting function of order 25. A bias section of [2095:2195, 2:2045] and trim section [21:2065, 2:2045] is used for all data sets.
3.2 BIAS REMOVAL The bias is the pixel-to-pixel structure in the read noise on an image. Since the bias varies across the CCD, a bias frame must be used to remove the bias structure from other images. The bias frames are zero second exposure where the the CCD is not exposed to any light, so the measured signal is merely the bias. Multiple bias frames (typically 10 - 20) are taken and then averaged to create a master bias frame to de-bias all the other images.
1IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Associ- ation of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. 15 The IRAF routine IMCOMBINE is used to create the master bias frame with a median combine for this project. We use the IMARITH task to subtract the master bias from the target images and flat fields.
3.3 FLAT FIELDING Since the sensitivity of individual pixels on the CCD is not constant the images need to be corrected with flat-fielding. Flats (typically 5 - 10) using the twilight sky as the illumination souce are used for this project. A seperate master flat is constructed for each filter. The flat field correction is made with the master flat field, by dividing the image to be corrected by the flat field. The individual flat field images are overscan corrected, trimmed, and de-biased. We use the IRAF task IMCOMBINE to median combine flats in each filter to create a master flat. The master flat is then normalized. The normalized flat is then divided into the target object frames of the corresponding filter.
3.4 CORRECTING BAD PIXELS Bad pixels can be replaced with an interpolated value based on the values in adjacent non-bad pixels. Two flat field images of different exposure levels are used to create a pixel mask in the IRAF routine CCDMASK. By using a ratio of two flat fields having different exposures all features which would normally flat field properly are removed and only pixles which are not corrected by flat fielding are found to make the pixel mask. This mask is then used for the IRAF routine FIXPIX which replaces the bad pixels with a linear interpolation along lines or columns using the nearest good pixels.
3.5 HEADER CORRECTIONS In a number of observations the header information was recorded incorrectly and needed to be corrected or input into the header. For all observations the date needed to be input in the header since this value is not the date in which the observation was taken but instead the date in which the data was uploaded on the computer. The actual date the observation was taken could not be recovered electronically. For the dates of 2001 August 24th, September 20th, and October 15th and 16th the time of observation was not recorded properly in the header. Based on times recorded in a log during the observation the times were recreated based on the exposure times of the observations and the beginning and end times recorded in the log. A program was written to recreate these times and these new times were input in the header. 16 For the dates of 2001 August 24th, September 20th, October 15th, and October 16th the RA and DEC were not recorded correctly. The correct RA of 23:24:48.00 and DEC of +61:35:00.0 for M52 were input in the header for these observations.
3.6 IMAGE REJECTION Using the IMEXAM routine in IRAF, and average FWHM was determined for at least 5 stars on various locations of the image to determine the average seeing. Images with bad seeing (seeing > 3.5′′) were not included in this survey. Images with bright satellite or meteor tracks were also not included. Other images which were rejected were due to poor telescope tracking or poor focus. In total 746 images were taken for this survey but after implementing our image rejection we only used 423 images from August 2001, October 2002, and November 2001. While it appeared that our September observations were useable it was later determined that these images were causing problems with our analysis. It was reported that the telescope anti-reflection coating was damaged from bad UV flooding at the time. Our September images were run in ISIS (to be discussed in 4) however, they were treated § separately from the rest of the observations. 165 images from September were processed separately. Also, all of our December images were rejected in the end because they were too noisy to be trustworthy. 17
CHAPTER 4 ISIS
We have implemented the Image Subtraction Method of Alard & Lupton (1998), available in ISIS 2.1 1, on our reduced images to identify variable candidates. We have selected to use ISIS because it is one of the methods of choice to search for variability in crowded fields. The entire process requires running six scripts: interp.csh, ref.csh, subtract.csh, detect.csh, find.csh, and phot.csh. The basic steps involved in these scripts include transforming all frames to a common grid, construction of a reference frame, subtraction of each frame from the reference frame, construction of a median image of all subtracted images, selection of stars to be photometered, and extraction of profile photometry from the subtracted images. The following subsections will provide a detailed description of each of the ISIS scripts. Before they are described, the general setup of the ISIS directories will first be presented.
4.1 ISISSETUP In order to run ISIS modifications need to be made to the configuration files in the register folder. The configuration files include the process config, default config, and phot config whose parameters are displayed in Tables 4.1, 4.2, and 4.3. In process config, some basic parameters about the directory structures must be inputted. The keyword IM DIR denotes the directory where the user’s images are located. MRJ DIR represents the location of the installation directory. INFILE points to the location of the file where all the images and their dates in Heliocentric Julian Day are housed. This file can be in the register directory and is called dates. CONFIG DIR is the directory that houses the configuration files the register − directory in other words. All other user specific inputs, especially those contained in default config and phot config, will be discussed in later subsections. It should be noted that there is no set formula to produce the best results, as the parameters need to be fine tuned over and over again until satisfactory results are produced. We did find, however, that some parameters did not effect our overall results and these parameters are mentioned in the proceeding sections.
1ISIS is available for download at: www2.iap.fr/users/alard/package.html 18 Table 4.1. ISIS Process Configuration File Parameter Value Definition IM DIR ../images Directory where the images are stored MRJ DIR .. 1 Installation directory REFERENCE a2m52r13rbtzf.fits Reference image for astrometry REF SUB ref.fits Reference image for subtraction INFILE ../register/dates Dates of the frames VARIABLES phot.data Coordinates of objects to make light curves DEGREE 2 Degree of the polynomial astrometric transform between frames CONFIG DIR ../register2 Where to find the configuration files SIG THRESH 3.0 Threshold for variable detection in var.fits COSMIC THRESH 3 Parameter for cosmic ray rejection REF STACK interp a2m52r13rbtzf.fits 5 Image for subtraction (only for sub image N REJECT 2 If Nth brightest value in series too large, reject it MESH SMOOTH 3 Size of smoothing mesh for var.fits
4.2 THE interp.csh ROUTINE The interp.csh routine is used for image registration and interpolation. It removes translations and rotations in all the images by applying a reference image and astrometric transform to each image. In other words, it essentially maps each frame onto a reference image, so that all the stars are in the same place in each image. For the astrometric transform, stars in the reference image are cataloged and then matched to a catalog of each image. Any offset is identified, and finally the astrometric transform (a first order two-dimensional polynomial) is fitted to the data. The astrometric transform then defines new grid points, and interpolates the values in the original grid using bicubic splines. The new image frame that is constructed is aligned with the reference frame as well as conserving the total flux. The most important input in the process config for this process is the REFERENCE keyword, which denotes the reference image to be used throughout the process. The reference image (also referred to as the template image) should be an image of good seeing and good cluster core position. We have selected to use image a2m52r13rbtzf.fits (taken on August 25th 2001) because the position of the cluster is among the best of our best seeing images (seeing 2.1′′). Also, the DEGREE keyword is the degree of the polynomial used in the astrometric transform between the frames.
4.3 THE ref.csh ROUTINE The ref.csh builds a composite reference frame to transform all images to the same seeing and background level. REF SUB is an important parameter for this routine. This keyword indicates the name of the file that includes a list of reference frame images to be stacked. These images are typically the best seeing images and should have a field similar to 19
Figure 4.1. Composite reference image from ISIS. those of most of the images in the series, which will later be transformed to the same seeing and background level as the best image (REF STACK). The images chosen to be stacked should have no visible defects, or the images will throw off succeeding steps, as the stacked reference image is further applied to all images. We used 12 of our best seeing images to create the stacked reference frame called ref.fits which is the placed in the images directory. We initially used a much larger set of images to build the ref.fits however, a number of the images were contributing to problems found in the ref.fits. Some of the images we initially selected did not get subtracted properly when transformed in order to match the seeing and background level of REF STACK. By looking at the convr interp images produced from this routine we selected only the best seeing images which did not have subtraction problems to build our ref.fits. This step was an important part for optimizing our results in ISIS. From the plethora of test runs we performed to determine the best parameters in ISIS we have discovered that choosing the images for your ref.fits is among the most important step for this process. Figure 4.1 shows our final ref.fits. It should be noted that for our September images, which were processed separately due to telescope complications, all parameters were kept the same as our big run except the ref.fits was composed of only September images. 20 Table 4.2. ISIS Default Configuration File Parameter Value Definition nstamps x 15 NumberofstampsalongXaxis nstamps y 15 NumberofstampsalongYaxis sub x 1 Numberofsub division of the image along X axis sub y 1 Numberofsub division of the image along the Y axis half mesh size 12 Half kernel size half stamp size 15 Halfstampsize deg bg 3 Degree to fit differential background variations saturation 45000 Saturationvalueforeliminatingpixels pix min 7 Minimumvalueforthepixelstofit min stamp center 100 Minimumvaluefor objectsto enter kernel fit ngauss 3 NumberofGaussians deg gauss1 8 Degreeassociatedwith1stGaussian deg gauss2 6 Degreeassociatedwith2ndGaussian deg guass3 4 Degreeassociatedwith3rdGaussian sigma gauss1 0.8 Sigmaof1stGaussian sigma gauss2 1.67 Sigmaof2ndGaussian sigma gauss3 4 Sigmaof3rdGaussian deg spatial 3 DegreeofthefitofthespatialvariationsoftheKernel
4.4 THE subtract.csh ROUTINE Once we have built a composite reference frame, we can apply image subtraction to all images. To do this, the ref.fits image will be convolved with a spatially varying kernel in order to match the background and seeing of the reference frame to each image. This is done by essentially fitting gaussians to each object. Then the convolved image is subtracted from each image and stored in the images directory. According to Alard & Lupton (1998), the kernel satisfies the following equation with x and y as coordinates:
Reference(x, y) Kernel(u, v)= I(x, y) (4.1) ⊗ The kernel(u, v) represents a transform over a region of pixels(u, v) that when convolved with the Ref(x, y) pixels will match the seeing in those pixels on the image frame. Because this non-linear equation is computationally expensive to solve it is thus not practical for crowded fields where we are interested in measuring the flux in many pixels. By decomposing the kernel using a set of basis functions a standard linear least squares method can be applied and the solution for the kernel is computationally easier to solve:
Kernel(u, v)= aiBi(u, v). (4.2) i X 21 Table 4.3. ISIS Phot Configuration File Parameter Value Definition sub x 1 Numberofsub division of the image along X axis sub y 1 Numberofsub division of the image along the Y axis rad1 bg size 15 Innerradiusofannulusforbackground rad2 bg size 20 Outerradius nstars 5 mesh 2 saturation 45000 Saturation value for eliminating pixels min 7 Minimumvalueforthepixelstofit psf width 100 Minimumvalueforobjectstoenterkernelfit ngauss 23 radphot 5 Radiusofcirclewithinthepixelswillbefittedtoestimate flux nstars max 8 nb adu el 0.5 GaininunitsofADU/electrons rmax 0.5 first 1 keep 5
The ai term is the contribution of the different basis functions describing the kernel(u, v). Bi are the basis functions (a Gaussian) used to model the seeing differences with the form:
(u2+v2) − d x d y B(u, v) e 2σn2 u n v n (4.3) ≡
Solving the least squares problem yields the following matrix equation for the ai coefficients:
Ma = V, (4.4)
with: C (x, y) M = C (x, y) j dxdy ij i σ(x, y)2 Z C (x, y) V = Ref(x, y) i dxdy i σ(x, y)2 Z C (x, y) = I(x, y) B (x, y), i ⊗ i where the variance is defined as:
σ(x, y)= k I(x, y) (4.5) where k is a constant set according to the gain ofp the detector. The key is that this process allows for PSF variations by subdividing the image − processing it in subsections so that different objects can have different profiles and by − 22 adding a polynomial weighting factor in the kernel decomposition. First we must understand that in dense field, a transformation kernel can be determined in a small area small enough − that we can ignore the PSF’s variations. Thus, it is easier to model variations of the PSF in a crowded field (such as an OC). To modify the previous kernel, we must make the coefficients spatially dependent, so that:
Kernel(u, v)= a (x, y) B (u, v). (4.6) n · n n X This process is robust and explained in further detail in Alard (2000). It should be noted that this takes the longest of all the ISIS processes (can take a day or two depending on the number of images). This method allows for self-consistent fitting of the kernel variations while imposing constant flux scaling that is, in solving our least squares we must add the condition that the − sum of the kernel must be constant at all points of the image. Rather than doing a messy Lagrangian, Alard uses a slightly different form of the kernel expressed in equation (4.7). The new set of basis functions is described in such a way that all basis vectors, except the first one, have zero sums:
′ Kernel(u, v)= a B (u, v)+ a (x, y) B (u, v), (4.7) 0 · 0 n · n X1,N where ′ B = B B (4.8) n n − 0 ′ ′ Provided that Bn vectors are normalized, the Bn will all have zero sums except B0 which will equal B0. The most important parameters for the image subtraction are in the process config file in the register directory. The kernel size is represented by half mesh size, while the half stamp size is the area taken by the program around each object. It should be slightly larger than the kernel size. We used values of 12 and 15 respectively and found that this produced the best results. We also discovered that by increasing the kernel size up to 12 improved some background issues in the reference image. This background problem might be attributed to a smaller kernel size not having enough background in it to do accurate fits. The number of stamps can be chosen by using the nstamps x and nstamps y keywords, to control the number in the x and y directions. The program looks for a number of bright objects (not necessarily stars) and defines a small window around each of them. The part of the image in these small windows are called stamps and are used to model the kernel. By increasing the nstamps x and nstamps y values, we also increase the total number of stamps: T otal stamps = nstamps x nstamps y (4.9) · 23 In doing so, we have more data to be processed, and thus the process becomes more CPU intensive. However, better results are also produced, so more stamps are recommended. We used 10 for both nstamps x and nstamps y. We did not see any significant improvement with nstamps 15. ISIS also allows for the images to be processed in parts, by breaking up the ≥ image into several sub-images. We used sub x and sub y set to 1. Typically increasing this parameter reduces PSF variation across the modeled part of the subimage and generally helps ISIS fit better. However, we found through many experiments with our data that sub x and sub y set to 1 produces realistic photometric results not achieved with 3 3or2 2. Among × × other benefits of using the 1 1 with our data set include a reduction in background problems × and a significant decrease in the RMS. We also have found that the frames that are poorly fit in one run are not necessarily poorly fit in another run with just slightly different parameters, which points to bad fitting routines in ISIS. We can also control the degree of spatial variations through the deg spatial keyword, which specifies the degree of fit of the spatial variations of the kernel within a subimage. We used a second order variation. It is important to make sure that the total number of stamps is high enough for the degree of spatial variations the spatial variations involves: − [(deg spatial + 1) (deg spatial + 2)]/2 (4.10) · coefficients, and needs a number of stamps that is at least 3 or 4 times larger than this number. The degree of differential background variations within a subimage can also be changed, which is represented by deg bg parameter. For our data, we use a value of 3. From looking at our subtracted images (conv images) it appears that the kernel determination (least squares fit) seems to have problems. There are a large number images whose background or kernel seems to go wrong leaving a messy looking background on the subtracted image. This background problem seems to vary significantly with different parameter choices. Using deg bg = 3 seems to give a good fit for a larger number of images overall. Some of the less important parameters are the saturation limit, the minimum value for the pixels to be fitted, and the minimum value for the central pixel of a stamp. The keywords are: saturation with a value of 45000 counts, pix min with a pixel value of 7, and min stamp center with a pixel value of 100. Finally, sigma gauss1, sigma gauss2 and sigma gauss3 represent the Gaussian sigmas of the kernel expansion; we have used values of 0.8, 1.67, and 4 pixels. Experimentation showed that the largest sigma gauss is not particularly important.
4.5 THE detect.csh ROUTINE Once we have successfully applied this method to all the images, only variable stars should have any significant correlated residual. The var.fits image shows positions of variable 24 stars and relative strength of their variability. A faint signature indicates that the star has small amplitude brightness variations, while large amplitude brightness variations would result in a bright signature on the var.fits. Cosmic rays, however, will produce false positives, so a rejection of some sort needs to be performed. Thus to remove defects from the images, such as cosmics and atmospheric disturbances the ISIS software builds a time series of the values of corresponding pixels on each frame and removes data points more than a user defined standard deviation values from the median residual flux. This means that the two measurements with the largest deviations are removed since most cosmics are removed in earlier steps. The pertinent keyword here is N REJECT in the process config file. We have used a value of 2. The images are then smoothed using the user specified parameter MESH SMOOTH, which specifies the size of the smoothing mesh; we used a value of 3 for MESH SMOOTH. Running the detect.csh script produces two images: var.fits and abs.fits and are stored in the images directory. The smoothed, composite image of all these pixels is var.fits, shown in Figure 4.2. The var.fits represents the mean of absolute normalized deviation from each of the convolution images while the image abs.fits is the mean absolute deviation. Our original var.fits constructed using the detect routine had noticeable features which could be attributed to our December observations which we initially tried using in our ISIS run. The December frames made a pretty big contribution to the var.fits. For the purpose of variable detection, December images were removed from the var.fits to search for variability. It should also be noted that a number of residuals on the var.fits had broken or split like features. The cause of this phenomenon was not determined but these residuals were of suspect and disregarded for the rest of our survey. Figure 4.2 shows our final var.fits. Note that most of the really bright features on the image are from saturated stars.
4.6 THE find.csh ROUTINE After inspecting the var.fits, one can select a threshold in order to identify the variables. The parameter is represented by SIG THRESH. We have set this detection limit to 0.075. This value is the pixel value cutoff and should be chosen by looking at the size of the background spikes and deciding what stars to be a significant detection. The higher the value the less variables will be identified. Such a low value, however, produced many false variables, mostly attributed to the noisy edges of var.fits but can be easily eliminated by other means. This script determines the location of the stars to be used for the photometry by recording the coordinates of each of the mean of the absolute normalized deviations on the var.fits that are above a certain threshold. This routine outputs a file called phot.data, which contains the position of the variables, and is stored in the register directory. 25
Figure 4.2. var.fits produced from ISIS . Most of the really bright spots are saturated stars. 26
4.7 THE phot.csh ROUTINE Light curves are produced using the ISIS routine phot.csh. The necessary configuration file for this process is phot config. Most importantly, one must specify a value for the radius of the annulus in order to estimate the background. This is set by rad1 bg, which represents the inner radius, and rad2 bg which represents the outer radius, and should be chosen according to the mean size of the PSF in the images. We used values of 15 and 20 pixels for rad1 bg and rad2 bg respectively. Two other important parameters are rad phot and rad aper, which we used values of 5 and 7 respectively. The keyword rad phot is the photometric radius the radius of the circle within which the pixels of the object will be fitted − in order to estimate the flux. The rad aper parameter represents the radius for flux normalization. For all other values, we did not alter the original phot config configuration files that comes with the ISIS package. It should be noted that for this project we wanted to build light curves for all the stars in the field and not just the variable stars that ISIS finds since the ISIS routines for variable detection may not be sensitive to planets. In order to do this, we built a phot.data file from all the stars found using the IRAF routine DAOFIND. After running phot.csh, 4128 light curves for all the stars which appeared on the var.fits were produced. As a final step, not included in the ISIS package, the light curves need to be converted from flux residuals to magnitude with the template image flux as the zero-point. In order to do this the template frame was reduced with the IRAF routine APPHOT to determine the relative magnitude for each star’s zero-point. A program was used to extract the star number, coordinates, magnitude, fluxes, and their uncertainties from the APPHOT output file. This file is then read into the program which converts between the residual flux measured in ISIS into their corresponding residual magnitudes using the reference zero-point magnitudes and fluxes from APPHOT. Using the method described in Mochejska et al. (2002), the light curve is
converted point-by-point to magnitudes (mi) by computing the total flux (ci) as the sum of the counts on the template (∆ctpl), and the counts on the subtracted template (ctpl), decreased by the counts corresponding to the subtracted image (∆ci):
c = c + ∆c ∆c (4.11) i tpl tpl − i The magnitude is then calculated using the following equation:
m =2.5 log 10mo−mtpl/2.5 + ∆c ∆c + m (4.12) i ∗ tpl − i o 27
To convert the photometric error in flux to magnitudes we used the following relation:
c σm =2.5 log i (4.13) i ∗ c + σc i i The light curves have been plotted using a SM 2 script.
2http://www.astro.princeton.edu:80/ rhl/sm/sm.html 28
CHAPTER 5 PLANETARY TRANSIT SEARCH
In this survey we have searched our data for transiting extrasolar planet candidates. The following sections will describe this process in further detail including the method and implementation which we have used to search for transiting planets. Also described in the following sections is the attempted use of SYSREM for removing systematic errors, our transit selection criteria and finally our results.
5.1 BOX LEAST SQUARE ALGORITHM We implemented the Box Least Square (BLS) algorithm by Kov´acs et al. (2002) 1 to search for planetary transits. This method effectively fits a box to photometric observations using two levels; one high level to simulate the starlight outside the box (out-of-transit light level), and a lower level of a small width to simulate the data points in the box. The advantage of the BLS method is that transits have a nearly box-shaped form, which means that this method gives a reasonably good fit. The BLS algorithm was chosen because it has been used extensively in similar searches (Mochejska et al. 2002, 2005, 2006) and quantitative comparisons indicate it is as good as others in literature (Tingley 2003). BLS searches for the non-sinusoidal periodic signal by minimizing the following equation: i1−1 n i2 D = w (x H)2 + w (x H)2 + w (x L)2 (5.1) i i − i i − i i − i=1 i=i +1 i=i X X2 X1 The boundaries of the transit are i1 and i2 within the phased binned data. The observations i are sorted by phase using a trial period. The algorithm searches to minimize D over all trial periods with all possible transit phases (i1, i2). The points in the box are represented by (i1, i2) and xi are the light curve magnitude measurements. H is the magnitude level out of transit on either side of the transit box ([1,i1) and (i2,n]). L is the in-transit level
([i1, i2]). Since the magnitude scale is an inverse scale, L actually has a higher value than H. L and H are defined as:
s L = (5.2) r s H = (5.3) −1 r − 1The BLS code is available for download at: http://www.konkoly.hu/staff/kovacs.html 29 where r is the fraction of one period spent at level L (in transit) which is given by the sum of the weights of these data points: i2
r = wi (5.4) i=i X1 s is given as the sum of the product of the weights and the data points:
i2
s = xi (5.5) i=i X1 With these formulae, Kovacs shows that the minimization equation reduces to:
n s2 D = w x2 (5.6) i i − r(1 r) i=1 X − Kovacs’ defines the BLS frequency spectrum by the amount of Signal Residue (SR) defined as:
1 s2(i , i ) 2 SR = MAX 1 2 (5.7) r(i , i )[1 r(i , i )] 1 2 − 1 2 The SR is calculated over all trial periods with trial transits in the interval i1, i2. The maximum value of SR minimizes D and therefore corresponds to a potential transit observation. Over the entire spectrum of frequencies tested, the SR global maximum corresponds to the period yielding the highest probability of an observed transit. However, the SR alone is not enough to determine whether a candidate planetary transit has been observed. Two additional quantities– the Signal Detection Efficiency (SDE) and the signal-to-noise ratio (SNR(α)) help characterize the strength of the SR. The SDE is defined as:
SR
δ α = √nq, (5.9) σ 30 where n is the number of data points, q is the fractional transit length, δ is the transit depth, and σ is the RMS of the magnitude measurement. α and the SDE serve as a useful way to gauge signal detection against the noise in the data. Adopting cutoff values of SDE and α can be used to filter out false detections. This can be especially useful in the case where the SDE might be high enough to suggest a likely transit but the noise is too high for the detection to be trustworthy. To demonstrate the power of the BLS method Figure 5.1 is provided. This example shows a time series, the normalized BLS frequency spectrum and the folded time series in an artificial dataset.
5.2 BLSIMPLEMENTATION For our dataset the BLS program was only run on stars with an RMS scatter in measurements < 0.015 mag. A star with an RMS greater than 0.015 mag would not have the photometric precision required to detect a transit. The RMS for each star was calculated as:
1 RMS = (x
Figure 5.1. BLS example results from Kovacs et al. (2002) from a test set of data. This shows the time series in the upper panel, the normalized BLS frequency spectrum and the folded time series in the lower panel. The signal parameters are displayed at the top where n is the number of bins, P0 is the period, q is the fractional transit length, δ is the transit depth, and δ/σ is the SNR. 32
RMS vs. Magnitude
1 0.1 0.01 0.001 0.0001 10 12 14 16 18 20 22 1 0.1 0.01 RMS 0.001 0.0001 10 12 14 16 18 20 22 0.1
0.01
0.001
0.0001 10 12 14 16 18 20 Magnitude Figure 5.2. The top panel shows the RMS of the 4128 stars which appear on the var.fits and have 323 out of 423 observations. The middle panel shows the RMS of the 3935 stars remaining after filters have been applied. The bottom panel shows the 1238 stars remaining which are suitable for BLS study after filters were applied including an RMS < 0.015 magnitude cutoff. 33 Table 5.1. Input Parameters Used in BLS Parameter Definition Value nf Numberoffrequencypoints 200000 df Frequency step (day−1) .00001 fmin Min frequency to be tested (day−1) .1 nb Numberbinsinfoldedtimeseries 100 qmi Minfractionaltransitlength .01 qma Maxfractionaltransitlength .2
included in the original code) was the inclusion of weights based on uncertainties in the measured residual fluxes from ISIS. BLS returns the Signal Residue (SR) for each frequency tested and for each transit length, and records the maximum. The transit candidate frequency corresponds to the SR global maximum found in the BLS spectrum. The BLS routine also returns the period, depth, fractional transit length, and the bin index of the star at the beginning and end of the transit. Included in our implementation of the code are a frequency spectrum, a normalized frequency spectrum, average binned phase plots, the SDE, and the SNR(α).
5.3 SYSREM Searching for transits involves finding a signal in noisy data. The signal is expected to be weak for a planetary transit. It is therefore worthwhile to find a way to reduce the noise in the data by removing systematic effects. The SYSREM (Tamuz et al. 2005) detrending method works without prior knowledge of the effects as long as the effects appear linearly in many stars of the sample. Basically, this algorithm identifies and subtracts out linear trends that appear in a large portion of lightcurves in a given data set. The algorithm is especially useful in cases where the uncertainties of the measurements are unequal. For equal uncertainties, the algorithm reduces to the Principal Component Analysis (PCA) algorithm.
Consider a set of M observations with N stars. The residual of each observation, rij, is defined to be the stellar magnitude after subtracting the average magnitude of the individual star. The goal is to try to find an effective extinction coefficient for each star and an effective airmass for every measurement, so we find sets c ; i =1, ..., N and a ; j =1, ...M that { i } { j } minimize the global expression
(r c a )2 S2 = ij − i j . (5.11) σ2 ij ij X First an estimate of the extinction coefficient is found by
2 (rijaj/σ ) c = j ij . (5.12) i (a2/σ2 ) P j j ij P 34
The extinction coefficient, ci, are star or position-dependant factors while the airmass term, aj, are frame-dependant factors. SYSREM can use random numbers as an initial guess for the airmass. This is because SYSREM finds linear trends in the data which are not necessarily airmasses so the airmass values have no special meaning for SYSREM. The value of the effective “airmass” is then
2 (rijcj/σ ) a(1) = i ij . (5.13) j (c2/σ2 ) P j j ij P (1) We then recalculate the best-fitting coefficients, ci , and continue iteratively, obtaining better approximations for both sets. The effect is then removed by
r(1) = r c(1)a(1). (5.14) ij ij − i j Additional linear trends can be fitted and removed with additional runs of SYSREM. We did not apply our SYSREM results to our light curves in the end. We found that a number of lightcurves with very large variations were creating problems by dominating the identification of low level systematics. However, even when these stars with large variations were removed the systematic effects that were found were at such a low level that even for our stars with the largest correction the correction was so small the removal of the effect was inconsequential. We found that our RMS was only improving for our dimmest stars with the largest change of 0.004%. SYSREM was used to help identify strange features in some of our stars but we did not apply the corrections to our stars.
5.4 TRANSIT SELECTION CRITERIA We selected criteria to help identify the most likely transit candidates. Each transit candidate was ranked according to SDE. An SDE threshold > 4 and α> 9 was used for this survey. Recall that the SDE determines the significance of the peak in the frequency spectrum to help determine the likelihood of a planetary transit and α is the measure of the detectability of the transit. According to Kov´acs et al. (2002) when α exceeds a value of 6 you can expect a significant detection of a transit. For our data set, when α was set to 6 and and using an SDE threshold > 4 it returned 257 planetary transits candidates so in order to narrow down our list we have used an α threshold > 9. This is the also the same α cutoff used by Mochejska et al. (2005) in one of a series of studies of open cluster stars. In this work, we search the data set for periods between 1.05 and 10 days. This is because the probability of finding planetary candidates in this period range is most probable. Another limit imposed to filter out any false positives was to only keep transits with a transit depth smaller than 0.08 mag because a potential planetary transit is unlikely to exceed this. 35 Also, any candidates that have a transit in only 1 transit phase bin (which corresponds to transit durations of 0.1 days for a 10 day period) were required to have a high SDE and α. Binned phase plots were created to show the average relative variability of the star over the course of the observations according to the trial period. Stars which show evidence of having two discrete levels in their brightness over the average phased observations were kept as potential transit candidates. We also looked at the binned phase plots of each transit candidate to determine whether or not the data points which fall in the transit phase were from more than one night. However, we did not reject candidates based only on this. For each transit candidate the light curve was also inspected.
5.5 PLANETARY TRANSIT RESULTS Using an initial criteria of an SDE threshold > 4, α> 9, and a period > 1.05 of the 1238 stars that were run on BLS we found 211 planetary candidates which required further inspection. While this number is very high it is not surprising given the low SDE threshold used. Each candidate required a second in-depth inspection of the binned phase plot and light curve to try to identify any false positives. After further inspection we found 21 transit candidates that were investigated further. Many of our initial candidates were rejected because of large amounts of variance about the mean magnitude, the points that fell into the transit bin were from only 1 night and also the candidate had a low SDE and α, and also if many points outside the transit bin were at the same depth as the points within the transit bin. The results of the planetary transit survey are listed in Table 5.2. This table contains the star ID number, the coordinates of the star on the var.fits, the Signal Detection Efficiency (SDE), the SR(α) which is the effective SNR, the period is the trial period corresponding to the global maximum, Nt is the number of points in the transit phase, depth is the depth of the transit in magnitudes, and qtran is the fractional transit length according to the BLS output. It should be mentioned that ID 1261 appeared to show variability in its light curve characteristic of an eclipsing variable. ID 1261 was thus added to our list of variable stars and dismissed as a transit. Also ID 3727 (not included in Table 5.2) was discovered to show interesting variability from our BLS results. Because the period of ID 3727 is much shorter than 1.05 days it was not included in our final BLS analysis, but it was added to the variability section of this thesis. From our list of 21 candidates 4 of these have been identified to have a box-shaped light curve characteristic of a planetary transits and have points from multiple nights within the transit. The properties of these best candidates are re-iterated in Table 5.3. To better check the authenticity of the BLS output, these candidates were investigated further. For each candidate 3 plots were examined: the binned phase plot, the frequency 36 spectrum, and the phased points within the transit. The output BLS spectrums are split into 1000 bins each with 100 points. The maximum SR in each bin was found and normalized according to the global maximum SR. After closer inspection these 4 candidates were dismissed, but a discussion of each is presented below.
Table 5.2. BLS Results
Star ID Coords. (x, y) SDE SR(α) Period(days) Nt Depth Qtran 4522 623,1712 7.429 15.84 1.5555 20 -0.024 0.0496 1722 855,706 6.587 22.26 1.1271 6 -0.054 0.0142 1772 1422,722 6.481 14.742 1.7299 16 -0.021 0.0378 1612 383,672 6.377 14.274 1.0516 16 -0.028 0.0378 1956 994,781 6.269 11.524 1.0972 16 -0.013 0.0378 0776 1397,349 6.039 13.787 2.4569 19 -0.022 0.0142 3880 716,1464 5.936 20.370 2.2614 21 -0.016 0.0496 4012 454,1520 5.751 13.789 1.9513 16 -0.031 0.0378 2563 1524,997 5.295 10.308 1.5096 13 -0.024 0.0307 1347 1344,566 5.236 19.141 1.4552 13 -0.025 0.0307 1267 1806,535 5.149 16.867 1.3598 10 -0.060 0.0236 2808 924,1081 4.852 14.016 1.4033 20 -0.026 0.0473 2195 487,863 4.811 12.687 1.0913 10 -0.015 0.0236 2232 1451,877 4.621 10.391 1.135 23 -0.021 0.0402 2801 1783,1079 4.502 14.344 2.761 22 -0.032 0.0520 4035 1214,1524 4.501 18.038 1.3497 18 -0.031 0.0426 1051 464,456 4.464 19.890 1.1457 13 -0.007 0.0307 3827 385,1411 4.400 9.608 1.376 11 -0.031 0.026 1261 243,533 4.376 19.224 1.524 12 -0.058 0.0284 2202 916,866 4.327 16.422 2.263 17 -0.016 0.0402 4635 941,1755 4.304 10.183 2.457 12 -0.0097 0.0284
Table 5.3. BLS Final Results
Star ID Coords. (x, y) SDE SR(α) Period(days) Nt Depth Qtran 1956 994,781 6.269 11.52 1.097 16 -0.013 0.0378 2563 1524,997 5.295 10.31 1.509 13 -0.024 0.0307 1347 1344,566 5.236 19.14 1.455 13 -0.025 0.0307 1267 1806,535 5.149 16.87 1.359 10 -0.060 0.0236
The binned phase plot of ID 1956 are shown in Figure 5.3. The binned phased plot shows evidence of variability during the transit phase. However, the out-of-transit phases do show variance about the mean magnitude. The points within the transit come from three different nights. Figure 5.4 shows the points within the transit phase. This plot shows that the variability is not on two discrete levels as would be expected for a transiting planet and thus 37 weakens the argument that candidate ID 1956 is an actual transit. It should be noted that there are 3 “low” points which are most likely caused by bad measurements from ISIS that BLS found to be in the transit phase. Figure 5.5 shows the residuals of ID 1956 where the points in transit are coming from the August 26th, November 14th, and November 16th observations. Figure 5.6 shows the normalized BLS spectrum for candidate ID 1956. The SR peak corresponds to a period of 1.0972 days. The calibrated V magnitude of ID 1956 is 17.26 mag and the calibrated (V-R) is 0.812. The binned phase plot of ID 2563 is shown in Figure 5.7. The binned phased plot shows evidence of variability during the transit phase. The points within the transit come from only two different nights weakening the likelihood a transit has been detected. The out-of-transit phases do not have a large variance about the mean magnitude. The points within the transit phase shown in Figure 5.8 are not on two discrete levels thus further weakening the argument that candidate ID 2563 is an actual transit. Figure 5.9 shows the residuals of ID 2563 where the points within the BLS transit are coming from the October 15th and November 14th observations. The BLS spectrum is shown in Figure 5.10 with an SR peak corresponding to a period of 1.5096 days. The calibrated V magnitude of ID 2563 is 17.19 mag and the calibrated (V-R) is 0.850. The binned phase plot of ID 1347 are shown in Figure 5.11. The binned phased plots do show evidence of variability during the transit phase. The points within the transit are however only from only 2 different nights. The unbinned phased plot of the transit shown in Figure 5.12 weakens any argument that ID 1347 is an actual transit because it is not at two discrete levels. Also, reduced χ2 statistics revealed that the 13 points within the transit bin are consistent with transit magnitudes. The reduced χ2 of the 13 points within the transit bin also reveal that the points are also consistent with each other. Therefore, the points within the transit are being contributed from points with large errors. Figure 5.13 shows the residuals of ID 1347 where the points within the transit bin are coming from the October 16th and November 14th observation. The BLS spectrum is shown in Figure 5.14 with an SR peak corresponding to a period of 1.4552 days. The calibrated V magnitude of ID 1347 is 17.01 mag and the calibrated (V-R) is 0.875. The binned phase plot of ID 1267 are shown in Figure 5.15. The binned phased plot shows evidence of variability during the transit phase. The out-of-transit phases do not have a large variance about the mean magnitude. The points within the transit are from only 2 nights. The unbinned phased plot of the transit shown in Figure 5.16 is at a lower discrete level than the other 3 transiting candidates and the transit is also on the larger side. However, 8 of the points within the transit phase are coming from 1 night while only 1 point is coming from the 2nd night. This point is not at a lower discrete level with the other 8 points. Thus, the points 38
Figure 5.3. Binned phased plot for candidate ID 1956. 39
Figure 5.4. Phase vs. unbinned delta magnitude of the points in transit for candidate ID 1956. Error bars have been added to convey the uncertainty in the residual flux within the transit phase. 40
-0.05 0 0.05 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 -0.05 0 0.05 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 -0.05 0 0.05 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
Figure 5.5. Residuals of candidate ID 1956. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 41
1
0.8
0.6
0.4
0 0.5 1 1.5 2
Figure 5.6. Normalized signal residue versus trial frequency for candidate ID 1956. The SR peak corresponds to a period of 1.5096 days. 42
Figure 5.7. Binned phased plot for candidate ID 2563. 43
Figure 5.8. Phase vs. unbinned delta magnitude of the points in transit for candidate ID 2563. Error bars have been added to convey the uncertainty in the residual flux within the transit phase. 44
-0.05 0 0.05 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
-0.05 0 0.05 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
-0.05 0 0.05 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
Figure 5.9. Residuals for candidate ID 2563. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 45
1
0.8
0.6
0.4
0.5 1 1.5 2
Figure 5.10. Normalized signal residue versus trial frequency for candidate ID 2563. The SR peak corresponds to a period of 1.5096 days. 46
Figure 5.11. Binned phased plot for candidate ID 1347. 47
Figure 5.12. Phase vs. unbinned delta magnitude of the points in transit for candidate ID 1347. Error bars have been added to convey the uncertainty in the residual flux within the transit phase. 48
0 0.05
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
0 0.05
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
0 0.05
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
Figure 5.13. Residuals for candidate ID 1347. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 49
1
0.8
0.6
0.4
0.2 0 0.5 1 1.5 2
Figure 5.14. Normalized signal residue versus trials frequency for candidate ID 1347. The SR peak corresponds to a period of 1.4552 days. 50
Figure 5.15. Binned phased plot for candidate ID 1267. 51
Figure 5.16. Phase vs. unbinned delta magnitude of the points in transit for candidate ID 1267. Note that 1 “low” data point has been removed. Error bars have been added to convey the uncertainty in the residual flux within the transit phase. 52 within the transit which appear at a lower level are actually only coming from only 1 night. It should be noted that 1 “low” point has been removed in Figure 5.16 but this point is included in Figure 5.17. It is very unlikely that this is an actual transit. Figure 5.18 shows the residuals of ID 1267 where the points within the transit bin are coming from the October 15th observation. The BLS spectrum is shown in Figure 5.19 with an SR peak corresponding to a period of 1.3598 days. The calibrated V magnitude of ID 1267 is 17.36 mag and the calibrated (V-R) is 0.845. 53
Figure 5.17. Phase vs. unbinned delta magnitude of the points in transit for candidate ID 1267 including “low” data point. Error bars have been added to convey the uncertainty in the residual flux within the transit phase. 54
0 0.2
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
0 0.2
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
0 0.2
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
Figure 5.18. Residuals for candidate ID 1267. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 55
1
0.8
0.6
0.4
0.5 1 1.5 2
Figure 5.19. Normalized signal residue versus trial frequency for candidate ID 1267. The SR peak corresponds to a period of 1.3598 days. 56
CHAPTER 6 VARIABILITY
The side benefit of a transiting extrasolar planet survey are the number of variable stars also discoved. We have identified 22 variable stars, 10 were identified as eclipsing-type W Ursa Majoris contact binaries, 5 were identified as detached binaries of the Algol type, 1 was identified as a slowly pulsating B star, and 6 were irregular and require further investigation before they can be classified. Previous studies by Viskum et al. (1997) and Choi et al. (1998, 1999) identified 7 variable stars in the cluster. Of these7only3 (ID 0980, ID 2673, and ID 1855) has been confirmed as variable in our survey. All 7 of these known variable stars are in our field of view but, 2 are saturated (ID 1901, ID 2752) on our frames and the other 2 (ID 2195, ID 2256) show no variability in their light curves. A total of 19 new variable stars have thus been discovered. The position of these stars have been identified on the composite ref.fits in Figure 6.1 and on the var.fits in Figure 6.2 from ISIS. Table 6.1 lists the variable star number, pixel coordinates (x,y), variable type, average relative V-band magnitude
Table 6.1. Variable Star Information
ID (x,y) Type < Vrel > RMS (V-R) P (days) Approx. Depth Memb. 0533 1547,256 EW 16.54 0.0710 – 1.214 0.2, 0.2 – 0981 1541,433 EW 16.41 0.0562 – 0.6896 0.2 0.2 – 1107 828,481 EW 16.59 0.1038 – 1.4826 0.3, 0.3 – 1133 1235,489 EW 17.28 0.027 0.9481 1.2318 0.1, 0.1 medium 1558 441,654 EW 18.29 0.0755 0.9951 0.4617 0.2, 0.2 high/medium 1834 943,744 EW 14.89 0.0165 0.6163 0.83 0.05, 0.05 high 2513 1223,976 EW 14.73 0.0126 0.5503 1.44 0.06 high 2673 1642,1030 EW 12.90 0.0035 0.3885 – – high 2830 876,1087 EW 17.01 0.0278 0.6499 1.028 – low 3727 76,1403 EW 13.56 0.0064 0.4973 0.4963 0.01, 0.02 low 0681 708,324 EA 14.82 0.0069 0.6643 – – high 0980 1067,440 EA 14.04 0.0037 0.5675 2.352 0.05 high 1261 243,533 EA 16.54 0.0125 0.5732 3.159 0.25 low 1284 318,543 EA 15.45 0.0078 0.8057 – 0.52 medium 4109 1219,1554 EA 16.28 0.0375 – 1.9651 0.71, 0.05 – 1855 1101,751 SPBs 13.53 0.0033 0.4351 – – high 2409 833,944 Irr. 16.43 0.0111 0.8513 – – medium 2773 1138,1065 Irr. 18.14 0.0363 0.6783 – – low 3096 782,1183 Irr. 14.08 0.0075 0.395 2.23 – medium 3928 1809,1480 Irr. 17.62 0.0214 0.8192 – – high/medium 4540 1104,1718 Irr. 15.12 0.0111 0.4827 – – low 4762 138,1810 Irr. 15.70 0.0135 1.007 – – low
6.1 PERIOD DETERMINATION The periodicity search of our variable stars was carried out by two different period search routines using the Lomb-Scargle and Lafler-Kinman methods. Both techniques are sensitive to different kinds of periodic signals and compliment each other well. The Lomb-Scargle period search used in this study was based on the work of Lomb (1976) and Scargle (1982). This method is essentially a fitting of sine and cosine terms of various frequencies that correspond to possible periodicites. The Lomb-Scargle normalized power spectrum provides a measure of the spectral power in the signal as a function of frequency (ω =2π/T ) and is defined as, 58
Figure 6.1. var.fits frame with location of variable stars. 59
Figure 6.2. Composite reference image with location of variable stars. 60
CMD of M52
EW Variables 8 EA Variables Irregular/Unclassified SPBs 10
1855 2673 12 3727 0980
V 0681 14 3096 1284 2513 4762
4540 2409 16 1834 1133 1261 1558 18 2830
2773 2938 20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 (V - R) Figure 6.3. CMD highlighting the location of variable stars detected. 61
1 [ n X cos ω(t τ)]2 [ n X sin ω(t τ)]2 P (ω)= i i i − + i i i − , (6.1) 2{ n X cos ω(t τ) n X sin ω(t τ) } P i i i − P i i i − xi is the set of the measurementsP of a star’s light curveP at times ti having n observations. Xi is the difference between each individual measurement xi and the average value of the x. For a range of frequencies, a time offset τ is computed for each value of the frequency, by the equation n sin 2ωt tan(2ωτ)= i i (6.2) n cos2ωt Pi i Typically the frequency with the most power inP the frequency spectrum corresponds as the frequency of variability or an alias of the period. The Lomb-Scargle routine will be more sensitive to variability that is closer to sinusoidal. The Lafler-Kinman search relies on the fact that for time series data folded on to the correct period there will be a minimization of brightness differences between observations of adjacent phases. In this method a trial period is chosen and the data are folded in phase and then ordered. The absolute differences between successive observations are taken and added together. This is expressed as,
n−1 S = x x + x x (6.3) | i − i+1| | n − 1| i=1 X th where xi is the i data point, in order of phase for that particular trial period. S is determined for all the different trial periods. If the trial period tested is correct then the summation will become a minimum. An iterative process is used to refine the detected period. The discriminant function is expressed as,
S r = 2 (6.4) Q − where Q is the total range of observations (absolute value of the difference between the maximum magnitude and the minimum magnitude). The minimum of the discriminant function versus trial period is the location of the period. The frequency spectrum shows a distinct drop or minimum near the value of r near the period. The Lafler-Kinman routines tends to be more sensitive to the point-to-point correlations that arise in a light curve. The validity of the period from either technique can be checked by simply folding the data and examining the resulting phased plot. Figure 6.4 and Figure 6.5 show an example of the Lomb-Scargle and the Lafler-Kinman results that were run on star ID 0533. These techniques were run with trial periods from 0 to 3 days with a spacing of 0.0001. The peak of maximum power for the Lomb-Scargle results corresponds to a P = 0.607 days. The lowest r values correspond to 62
50
40
30 Power 20
10
0 0 0.5 1 1.5 2 2.5 3 Period (days) Figure 6.4. ID 0533 Lomb-Scargle period analysis. The peak of maximum power corresponds to a P = 0.607 days. 63
3
2.5
2
1.5 Power
1
0.5
0 0 0.5 1 1.5 2 2.5 3 Period (days) Figure 6.5. ID 0533 Lafer-Kinman period analysis. Two of the lowest r values corresponds to a period P = 0.607 days and P = 1.214 days. Lower r values with larger periods can be ruled out based solely on the unphased light curve. 64 periods of P = 0.607 days and P = 1.214 days for the Lafer-Kinman period analysis. Since the Lomb-Scargle technique could not distinguish between primary and secondary eclipses, the period returned half the likely true period. Once the period was doubled the data were folded correctly to P = 1.214 with a primary and secondary eclipse. The phased light curve be see in Figure 6.6.
6.2 VARIABILITY RESULTS
6.2.1 W UMa Variables Eclipsing binary stars of W Ursae Majoris type are characterized by continuous brightness changes due to eclipses and due to changing aspects of tidally distorted stars. The minima in the light curves are of almost equal depth, indicating similar surface temperatures of the components. The periods are short, almost exclusively ranging from about 7 hours up to 1 day (Sterken 1997). W UMa stars are best explained by the assumptions that both stars are in contact, and that the more massive component is transferring energy to the less massive one via a common envelope, thus equalizing the surface temperatures (Sterken 1997). Ten of our variable stars have been identified as probable W UMa variables. The phased plots of our W UMa stars are shown in Figure 6.6. All December 2007 observations and were removed from the phased light curves as the data were often too noisy and offset from the rest of the observations. Also, because our September observations were processed alone they are offset from the rest of the observations in our light curves. For the phased plot of ID 0533 only September observations were used. Two of the previously known variables, ID 2673 and ID 1855, are not phased because their variability is less present in the non-September observations. It should also be be noted that because W UMa variables often show nearly identical eclipse depths, the Lomb-Scargle search is sensitive to a period that phases only one eclipse per orbit. The routine is not sensitive to the differences between eclipses and finds each eclipse to be the same event therefore, the periods needs to be doubled in this case. The light curve data of ID 0533 are shown in Figure 6.7. Both primary and secondary minima appear to be nearly identical in depth. The amplitude of variation is about 0.2 magnitude from peak to peak. Cluster membership could not be established for this star as it appeared too faint in the V band for color determination. The light curve data of ID 0981 are shown in Figure 6.8. The amplitude of variation is about 0.2 magnitudes from peak to peak with primary and secondary eclipses being almost identical depth. ID 0981 is particularly interesting because of the asymmetric shape of the light curve. Cluster membership could not be established as there is no color determination because it was too faint. 65
0533 0981 1107 16.2 16.2 16.4 16.4 16.3 16.5 16.4 16.6 16.6 16.5 16.7 16.8 16.6 16.8 17 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1133 1558 1834 15.3 13.3 16.2 15.4 13.35 15.5 16.4 13.4 13.45 Magnitude 15.6 16.6 13.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 2513 2830 3727 13.2 15.3 12.2 13.22 15.35 13.24 15.4 12.22 13.26 15.45 12.24 13.28 15.5 13.3 15.55 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Phase Figure 6.6. Phased light curves of suspected W UMa stars. 66
16.4 16.6 16.8
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
16.4 16.6 16.8
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
16.4 16.6 16.8
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
16.4 16.6 16.8
23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.7. Light curve of ID 0533. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 67
16.2 16.4 16.6 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 16.2 16.4 16.6 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 16.2 16.4 16.6 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
16.2 16.4 16.6 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.8. Light curve of ID 0981. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 68 The light curve data of ID 1107 are shown in Figure 6.9. The peak to peak amplitude of variation is about 0.3 magnitudes. Maxima appears to be of similar heights, and minima are of nearly identical depths. Cluster membership could not be determined because it was too faint in V. The light curve data of ID 1133 are shown in Figure 6.10. From the structure and nightly variations in the light curve, it is likely that the variable is a W UMa variable. The amplitude of the eclipse seems to change from the August and October observations. In the phased plot, the depth of the eclipse appears to be changing. The period is slightly larger than that would be expected of a W UMa but not too far off. It is possible that ID 1133 is a cluster member based on its position on the CMD. It is located approximately 5′ from the cluster center. The light curve data of ID 1558 are shown in Figure 6.11. Variations from night to night are present but the light curve changes noticeable from night to night. This may be due to spotting of the surface which is common among this type. As with ID 1133 the minima appears to be changing. The peak to peak variations are around 0.2 mag. The phased plot shows a lot of scatter. Based on its location on the CMD it is a possible a cluster member but it also located in a region of lots of scatter. It should also be noted that the color determination for ID 1558 should be taken with some caution as larger amplitude W UMa stars are more likely to be more effected by what part of the light curve measurements the color data are taken on. The light curve data of ID 1834 are shown in Figure 6.12. Both primary and secondary minima appear to be similar in depth. The peak to peak variations are very small, approx 0.05 magnitudes. While the phasing of the data looks slightly like the period could be incorrect multiple trials with the data show that this period is the most likely period. The close spatial position to the cluster center (approximate 3′) and the high membership probably based on its located on the CMD indicates that this object could be a cluster member. M52 is young to have a member W UMa making ID 1834 and interesting star for follow up work. The light curve data of ID 2513 are shown in Figure 6.13. The light curve indicates it is likely a W UMa variable. The amplitude of variation is small with peak to peak light variations of approximately 0.06 magnitudes. The light curve shows and increase in amplitude on the August 26th and September 19th observations. It is likely that ID 2513 is a cluster member based on its location on the CMD and its close spatial position (approximately 1′) to the cluster center. The light curve data of ID 2673 are shown in Figure 6.14. A previous study by Viskum et al. (1997) have identified 6.14 as a δ scuti variable. Viskum et al. (1997) report ID 2673 is a main-sequence star near the hot border of the instability strip and could therefore be 69
16.5
17 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 16.5
17 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 16.5
17 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
16.5
17 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.9. Light curve of ID 1107. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 70
15.4
15.6
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
15.4
15.6
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
15.4
15.6
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
15.4
15.6
23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.10. Light curve of ID 1133. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 71
16.2 16.4 16.6 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 16.2 16.4 16.6 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 16.2 16.4 16.6 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
16.2 16.4 16.6 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.11. Light curve of ID 1558. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 72
13.35 13.4 13.45 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 13.35 13.4 13.45 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 13.35 13.4 13.45 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
13.35 13.4 13.45 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.12. Light curve of ID 1834. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 73
13.2 13.25 13.3 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 13.2 13.25 13.3 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 13.2 13.25 13.3 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
13.2 13.25 13.3 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.13. Light curve of ID 2513. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 74
12.16 12.18 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
12.16 12.18 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
12.16 12.18 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
12.16 12.18 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.14. Light curve of ID 2673. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 75 a δ Scuti variable. However, the periodicity in our light curve does not seem characteristic of a δ scuti star which is characterized by short pulsations (periods less than 0.3 days). We propose that it is more likely that ID 2673 is a W UMa variable. Based on ID 2673’s position on the CMD it is likely that it is a cluster member. The light curve data of ID 2830 are shown in Figure 6.15. The continuous light curve variations indicate that the star is likely a W UMa variable. Because the binary appears to have a period very close to 1 day, the depth of the eclipse is difficult to determine. Due to ID 2830’s position on the CMD it is has a lower probability of being a cluster member however, it does have a close spatial position (approximately 3′) to the center of the cluster. The light curve data of ID 3727 are shown in Figure 6.16. It should be noted that ID 3727 was not identified as a variable from our ISIS results but was identified from our BLS results. The variability in the light curve seems to indicates two eclipses which is more likely to be a contact binary than a transiting planet. Also, the period is low for a transiting planet. The peak to peak amplitude variations are very small only 0.02 magnitudes for the primary eclipse and 0.01 for the secondary. The variability is more clearly present in our September observations and only the September observations were used to phase the data. The position of ID 3727 is near the edge of many frames, which probably effected our our August 24th observations. The period used to phase the data was found from BLS as 0.49635 days. It is unlikely that ID 3727 is a cluster member based on its position on the CMD.
6.2.2 Slowly Pulsating B Stars Slowly pulsating B stars (hereafter SPBs) were first introduced by Waelkens (1991) as a distinct group of variables with spectral types ranging from B2 to B9. The SPBs are situated in the main sequence, with masses ranging from 3 to 7M⊙. They have periods from 0.5 - 3 days and low amplitudes less than 0.1 mag. Their variability is interpreted in terms of non-radial pulsations of higher-order g-modes (g-mode oscillations are found deep in the solar interior) (Dziembowski et al. 1993). The light curve data of 1855 are shown in Figure 6.17. 1855 has been identified as a variable in a previous study by Choi et al. (1999). Choi et al. (1999) proposes that 1855 is a slowly pulsating B star with a pulsation period of 1.626 days. Choi et al. (1999) also reports that 1855 is located near the SPBs instability strip. Based on 1855’s position on the CMD it is likely that it is a cluster member.
6.2.3 Detached Eclipsing Binaries The Algol type eclipsing binaries (EA) are a subgroup of eclipsing binaries with well defined eclipses and the light remains rather constant between the eclipses. Orbital periods range from extremely short (a fraction of a day) to very long (27 years for ǫ Aurigae) (Sterken 76
15.3 15.4 15.5 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 15.3 15.4 15.5 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 15.3 15.4 15.5 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
15.3 15.4 15.5 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.15. Light curve of ID 2830. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 77
12.2 12.22 12.24 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 12.2 12.22 12.24 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 12.2 12.22 12.24 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
12.2 12.22 12.24 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.16. Light curve of ID 3727. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 78
11.54 11.56 11.58
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 11.54 11.56 11.58
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 11.54 11.56 11.58
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
11.54 11.56 11.58
23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.17. Light curve of ID 1855. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 79 1997). Eclipse depth can range from very shallow (0.01 magnitudes) if partial, to very deep (several magnitudes) if total. The two eclipses can be comparable in depth or can be unequal (Sterken 1997). Another classification of eclipsing binaries is EB, which also have well defined eclipses and some variation between eclipses. Five of our variables have been identified as EA variables. The phased plots of ID 0980, ID 4109, and ID 1261 are shown in Figure 6.18. ID 0681 would not be properly phased because it was located near a bright star, which may have contaminated the light curve. ID 1284 is not phased because only one eclipse was observed and therefore no period could be determined. Unfortunately, because the times were not properly recorded in our image headers calculations of the eclipse ephemerides for all our EA variables are too inaccurate to be made. The light curve data of ID 0681 are shown in Figure 6.19. The residual of ID 0681 appears strongly on the var.fits however, it is located near a bright star which appears to be contaminating the light cuve. ID 0681 is a strong candidate for an eclipsing system with a possibility of a totality but more data would be needed to verify this. It is possible that ID 0681 is a cluster member based on its position on the CMD. The light curve data of ID 0980 are shown in Figure 6.20. This system has been observed in the literature by Viskum et al. (1997) and has been identified as being located on the main sequence within the stability strip. This star was initially identified as a δ Scuti, but its light curve clearly indicates that it is an eclipsing variable. The depth of the primary eclipse is about 0.5 magnitudes. Nothing is seen at the expected position of the secondary eclipse. However, it could be possible that the period is actually 4.704 days and the secondary and primary eclipse are of equal depth. It is very likely that ID 0980 is a cluster member based on its location on the CMD. The light curve of ID 1261 is shown in Figure 6.21. It should be noted that ID 1261 was not identified as a variable from our ISIS results but was identified from our BLS results. Note that ID 1261 does not show up on our var.fits in Figure 4.2 The variability is clearer in the September data that was not run in BLS. The returned period from BLS was 1.524 days but with the September data the period is clearly closer to 3.159 days. The depth of the eclipse is 0.25 magnitudes suggests that it is not a planetary transit. It is not likely that ID 1261 is a cluster member based on its position on the CMD. The light curve data of ID 1284 are shown in Figure 6.22. The depth of the eclipse is 0.52 magnitudes. The total eclipse lasts for almost 5 hours. This variable shows up very strong on the var.fits. Because only one eclipse was observed no period determination can be made. Based on ID 1284’s position on the CMD there is a medium possibility is it a cluster member. Given the large eclipse, it isn’t unreasonable that the CMD position is off the MS. 80
0980
12.55
12.6
12.65 0 0.2 0.4 0.6 0.8 1 1261 15 15.1 15.2 Magnitude 15.3 0 0.2 0.4 0.6 0.8 1 4109 16 16.5 17 17.5 0 0.2 0.4 0.6 0.8 1 Phase Figure 6.18. Phased light curves of suspected EA variables. 81
13.3 13.4
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
13.3 13.4
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
13.3 13.4
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
13.3 13.4
23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.19. Light curve of ID 0681. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 82
12.55
12.6 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
12.55
12.6 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
12.55
12.6 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
12.55
12.6 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.20. Light curve of ID 0980. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 83
15.1 15.2
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
15.1 15.2
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
15.1 15.2
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
15.1 15.2
23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.21. Light curve of ID 1261. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 84
13.8 14 14.2
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 13.8 14 14.2
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 13.8 14 14.2
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
13.8 14 14.2
23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.22. Light curve of ID 1284. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 85 The light curve data of ID 4109 are shown in Figure 6.23. This binary system shows a light curve of type EA. From the phase plot in Figure 6.18 it appears from the light curve that there is one primary eclipse and one very low amplitude secondary eclipse. The secondary eclipse is seen at 0.5 phase which is 0.3 phase away from the primary eclipse indicating that the system is eccentric. The light curve of the primary eclipse does seem to change depth slightly from the nights it was observed. Because the times of the October 15th and 16th observations were not recorded in the header and an estimated time was used based on an observation log recorded during the time of observation ID 4109 had some difficulties being phased. The October 15th and 16th observations were removed for the phase plot.
6.2.4 Irregular Variables or Unclassified Six of our variable stars have been identified as irregular or unclassified. Phase plots of these irregular variables were not all included as an optimal period could not be determined. A period search was attempted using both Lomb-Scargle and Lafler-Kinman codes, but no adequate period was found. The light curve data of ID 2409 are shown in Figure 6.24. Due to the variation in the light curve it appears that ID 2409 is a likely W UMa variable candidate but this system could not be phased properly. The variations do not appear consistent. The approximate amplitude of variation is around 0.05. It is likely that ID 2409 is a cluster member based on its position on the CMD and location to the center of the cluster (approximately 2′). The light curve data of ID 2773 are shown in Figure 6.25. The night to night variations indicate that this star is variable and possibly a W UMa variable. Attempts were made to phase the data but no clear period could be determined. The light curve varies with a period probably near a day. There is a small likelihood that ID 2773 is a cluster member based on its position on the CMD. However, it is located near the cluster center (approximately 0.4 ′). The light curve data of ID 3096 are shown in Figure 6.26. The light curve does not provide clear evidence as to the classification of this star. The closest result which phases the data is shown in Figure 6.27 with a period of P = 2.227 days . The nights phased include August 25th, October 13th, 14th, 15th, and November 13th, 15th. The amplitude is about 0.02 magnitudes. There appears to be a significant amount of scatter in this light curve and in the phased plot. ID 3096 could be a possible quasiperiodic variable since the nature of the variation changes with a little variation within a night, to variation from night to night. There is a medium likelihood that ID 3096 is associated with the cluster based on its location on the CMD. It is located (approximately 2′) from the cluster center. The light curve data of ID 3928 are shown in Figure 6.28. Variability appears to be present but not clear or consistent. ID 3928 could be a possible W UMa or EB variable. ID 86
16.5 17
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
16.5 17
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
16.5 17
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
16.5 17
23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.23. Light curve of ID 4109. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 87 3928 appears to have a little out of eclipse variation period near 2 days. The September observations seem to indicate an eclipsing system but the October observations appear to be unclear. It is possible that this could be a quasiperiodic variable. ID 3928 is spatially located away from the center of the cluster but its location on the CMD suggest that there is a medium likelihood is it associated with the cluster. The light curve of ID 4540 are shown in Figure 6.29. The residual of ID 4540 is very strong on the var.fits. However, because it is located so close to charge bleeding extending from the brightest central star in the field it is likely that the light curve is somewhat contaminated. Based on the variability in the light curve it appears that ID 4540 might be a quasi periodic variable but it classification remains unclear. Based on ID 4540’s location on the CMD there is little likelihood that it is associated with the cluster. The light curve data of ID 4762 are shown in Figure 6.30. Variability is present in the September and October observations. The variability in the September 17th and October 16th observations indicate there is a possible eclipse. It should be noted that this star fell on a column of bad pixels in all of our October observations which may be contaminating the variability. The likelihood that ID 4762 is associated with the cluster is low since it lies offset on the CMD and its spatial position is far from the center of the cluster. 88
14.65 14.7 14.75 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
14.65 14.7 14.75 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
14.65 14.7 14.75 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
14.65 14.7 14.75 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.24. Light curve of ID 2409. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 89
16.4
16.6 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
16.4
16.6 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
16.4
16.6 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
16.4
16.6 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.25. Light curve of ID 2773. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 90
12.74 12.76 12.78
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 12.74 12.76 12.78
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 12.74 12.76 12.78
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
12.74 12.76 12.78
23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.26. Light curve of ID 3096. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 91
3096 12.72
12.74
12.76
12.78
12.8 0 0.2 0.4 0.6 0.8 1 Figure 6.27. Phased light curve of ID 3096. 92
15.8
16
0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01 15.8
16
50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01 15.8
16
81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
15.8
16
23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.28. Light curve of ID 3928. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 93
13.7
13.8 0 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
13.7
13.8 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
13.7
13.8 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
13.7
13.8 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.29. Light curve of ID 4540. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 94
14
14.2 0.1 0.2 0.3 1 1.1 1.2 1.3 2 2.1 2.2 2.3 Aug24,01 Aug25,01 Aug26,01
14
14.2 50 50.2 51 51.2 52 52.2 53 53.2 Oct13,01 Oct14,01 Oct15,01 Oct16,01
14
14.2 81 81.1 81.9 82.9 83 83.1 Nov14,01 Nov15,01 Nov16,01
14
14.2 23 23.2 24 24.2 25 25.2 26 26.1 26.2 Sept17,01 Sept18,01 Sept19,01 Sep20,01
Figure 6.30. Light curve of ID 4762. Major time-axis tick marks are spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. 95
CHAPTER 7 CONCLUSION
The probability for a planet to transit the host star is relatively small, so that large data sets are needed to have a reasonable chance of finding a planet. Open clusters potentially provide an ideal environment for finding extrasolar planets since they have a relatively large number of stars. There have been many survey searching or planetary transits in star clusters (see Weldrake (2007) for a review). While no planets have yet been confirmed within a star cluster, these surveys have provided promising candidates awaiting follow-up observations, as well as cluster parameters and variables stars. Detecting transiting planets involves finding a faint signal in noisy data which is a very challenging task. Only large planets in short orbits can be detected using ground-based surveys. We have searched for planetary transits with a period range between 1.05 and 10 days using the BLS method searching 1,238 stars which have an RMS < 0.015 magnitude, finding no likely transit candidates. While no planetary transits have been found in our survey this does not rule out the possibility that there are not planets in M52. If, however, a planetary transit candidate were found additional photometric observations in multiple filters would be needed to check for transit consistency in order to rule out a possible eclipsing system. We obtained lightcurves for 4,128 stars using the ISIS image subtraction software, and identified 22 variable stars, of which 19 were not previously known as variable. Ten of our variable stars were identified as eclipsing-type W Ursa Majoris contact binaries, 5 were identified as detached binaries of the Algol type, 1 was identified as a slowly pulsating B star, and 6 were irregular and require further investigation before they can be classified. A color magnitude diagram was constructed from V and R photometry with fitted isochrones from Cassisi et al. (2006). Our color magnitude diagram was used to help establish cluster membership for our variable stars. We find that 3 of our W UMa stars lie within region of high cluster membership probability. This is especially interesting because it is not expected that W UMa stars would be found in such a young cluster. Radial velocity follow up observations would be required to confirm whether or not they are actual cluster members. 96 REFERENCES
Alard, C. 2000, AAPS, 144, 363
Alard, C. & Lupton, R. H. 1998, APJ, 503, 325
Bonatto, C. & Bica, E. 2006, A&A, 455, 931
Bouchy, F., Pont, F., Santos, N. C., Melo, C., Mayor, M., Queloz, D., & Udry, S. 2004, A&A, 421, L13
Brown, T. M., Charbonneau, D., Gilliland, R. L., Noyes, R. W., & Burrows, A. 2001, APJ, 552, 699
Burke, C. J., Gaudi, B. S., DePoy, D. L., Pogge, R. W., & Pinsonneault, M. H. 2004, APJ, 127, 2382
Carroll, B. W. & Ostlie, D. A. 2006, Institute for Mathematics and Its Applications
Casoli, F. & Encrenaz, T. 2007, The New Worlds (The New Worlds, by F. Casoliand T. Encrenaz Berlin: Springer, 2007. ISBN:978-0-387-44906-7)
Cassisi, S., Pietrinferni, A., Salaris, M., Castelli, F., Cordier, D., & Castellani, M. 2006, Memorie della Societa Astronomica Italiana, 77, 71
Charbonneau, D., Brown, T. M., Noyes, R. W., & Gilliland, R. L. 2002, APJ, 568, 377
Choi, H. S., Kim, S.-L., & Kang, Y. H. 1998, Inf. Bull. Variable Stars, 4545, 1
Choi, H. S., Kim, S.-L., Kang, Y. H., & Park, B.-G. 1999, AAPS, 348, 789
Davies, M. B. & Sigurdsson, S. 2001, MNRAS, 324, 612
Dziembowski, W. A., Moskalik, P., & Pamyatnykh, A. A. 1993, MNRAS, 265, 588
Fischer, D. A. & Valenti, J. 2005, APJ, 622, 1102
Gilliland, R. L., Brown, T. M., Guhathakurta, P., Sarajedini, A., Milone, E. F., Albrow, M. D., Baliber, N. R., Bruntt, H., Burrows, A., Charbonneau, D., Choi, P., Cochran, W. D., Edmonds, P. D., Frandsen, S., Howell, J. H., Lin, D. N. C., Marcy, G. W., Mayor, M., Naef, D., Sigurdsson, S., Stagg, C. R., Vandenberg, D. A., Vogt, S. S., & Williams, M. D. 2000, APJL, 545, L47
Guillot, T. 2005, Annual Review of Earth and Planetary Sciences, 33, 493
Harris, W. E. 1996, VizieR Online Data Catalog, 7195, 0
Kov´acs, G., Zucker, S., & Mazeh, T. 2002, A&A, 391, 369
Lecavelier Des Etangs, A. & Vidal-Madjar, A. 2006, Planetary transits: a first direct vision of extrasolar planets (Planet Formation), 147 97 Lineweaver, C. H. & Grether, D. 2003, APJ, 598, 1350 Lomb, N. R. 1976, APSS, 39, 447 Marcy, G., Butler, R. P., Fischer, D., Vogt, S., Wright, J. T., Tinney, C. G., & Jones, H. R. A. 2005, Prog. Theor. Phys, 158, 24 Marcy, G. W. & Butler, R. P. 2000, PASP, 112, 137 Mochejska, B. J., Stanek, K. Z., Sasselov, D. D., & Szentgyorgyi, A. H. 2002, APJ, 123, 3460 Mochejska, B. J., Stanek, K. Z., Sasselov, D. D., Szentgyorgyi, A. H., Adams, E., Cooper, R. L., Foster, J. B., Hartman, J. D., Hickox, R. C., Lai, K., Westover, M., & Winn, J. N. 2006, APJ, 131, 1090 Mochejska, B. J., Stanek, K. Z., Sasselov, D. D., Szentgyorgyi, A. H., Bakos, G. A.,´ Hradecky, J., Devor, V., Marrone, D. P., Winn, J. N., & Zaldarriaga, M. 2005, APJ, 129, 2856 Sackett, P. D. 1999, in NATO ASIC Proc. 532: Planets Outside the Solar System: Theory and Observations, 189 Scargle, J. D. 1982, APJ, 263, 835 Sterken, C. 1997, jrasc, 91, 139 Stetson, P. B. 2000, PASP, 112, 925 Street, R. A., Horne, K., Collier Cameron, A., Tsapras, Y., Bramich, D., Penny, A., Quirrenbach, A., Safizadeh, N., Mitchell, D., & Cooke, J. 2003, in Astronomical Society of the Pacific Conference Series, Vol. 294, Scientific Frontiers in Research on Extrasolar Planets, ed. D. Deming & S. Seager, 401–404 Tamuz, O., Mazeh, T., & Zucker, S. 2005, MNRAS, 356, 1466 Tingley, B. 2003, A&A, 403, 329 Udalski, A., Paczynski, B., Zebrun, K., Szymanski, M., Kubiak, M., Soszynski, I., Szewczyk, O., Wyrzykowski, L., & Pietrzynski, G. 2002a, acta, 52, 1 Udalski, A., Zebrun, K., Szymanski, M., Kubiak, M., Soszynski, I., Szewczyk, O., Wyrzykowski, L., & Pietrzynski, G. 2002b, acta, 52, 115 Udry, S. & Santos, N. C. 2007, ARAA, 45, 397 Viskum, M., Hernandez, M. M., Belmonte, J. A., & Frandsen, S. 1997, AAPS, 328, 158 von Braun, K., Lee, B. L., Seager, S., Yee, H. K. C., Mall´en-Ornelas, G., & Gladders, M. D. 2005, PASP, 117, 141 Waelkens, C. 1991, AAPS, 246, 453 Weldrake, D. T. F. 2007, ArXiv e-prints, 709 ABSTRACT OF THE THESIS
The Search for Transiting Extrasolar Planets in the Open Cluster M52 by Tiffany M. Borders Master of Sciences in Astronomy San Diego State University, 2008
In this survey we attempt to discover short-period Jupiter-size planets in the young open cluster M52. Ten nights of R-band photometry were used to search for planetary transits. We obtained light curves of 4,128 stars and inspected them for variability. No planetary transits were apparent; however, some interesting variable stars were discovered. In total, 22 variable stars were discovered of which, 19 were not previously known as variable. Ten of our variable stars were identified as eclipsing-type W Ursa Majoris contact binaries, 5 were identified as detached binaries of the Algol type, 1 was identified as a slowly pulsating B star, and 6 were irregular and require further investigation before they can be classified. A color-magnitude diagram constructed from V and R photometry with fitted isochrones is also presented to help determine cluster membership of our variable stars. We find that 3 of our W Uma stars lie within a region of high cluster membership probability. Radial velocity follow up observations are needed to confirm cluster membership. If confirmed, this would be highly interesting as W Uma stars are not excepted to be found in such a young cluster.