the search for transiting extrasolar planetsborders/thesis.pdf · the search for transiting...

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, ChairDepartment of Astronomy

William WelshDepartment of Astronomy

Calvin JohnsonDepartment 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 asby 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 theirexits 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 Planetsin the Open Cluster M52

byTiffany M. Borders

Master of Sciences in AstronomySan Diego State University, 2008

In this survey we attempt to discover short-period Jupiter-size planets in the youngopen 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 planetarytransits were apparent; however, some interesting variable stars were discovered. In total, 22variable stars were discovered of which, 19 were not previously known as variable. Ten of ourvariable stars were identified as eclipsing-type W Ursa Majoris contact binaries, 5 wereidentified 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. Acolor-magnitude diagram constructed from V and R photometry with fitted isochrones is alsopresented to help determine cluster membership of our variable stars. We find that 3 of our WUma stars lie within a region of high cluster membership probability. Radial velocity followup observations are needed to confirm cluster membership. Ifconfirmed, this would be highlyinteresting as W Uma stars are not excepted to be found in sucha 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 with Planets . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Planet-Metallicity Correlation . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Open Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 M52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 OBSERVATIONS OF M52 .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 DATA REDUCTION .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Overscan Correction and Trimming .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Bias Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Flat Fielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4 Correcting Bad Pixels . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.5 Header Corrections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.6 Image Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 ISIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.1 ISIS Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.2 Theinterp.cshRoutine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 17

4.3 Theref.cshRoutine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 18

4.4 Thesubtract.cshRoutine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 20

4.5 Thedetect.cshRoutine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 23

4.6 Thefind.cshRoutine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 24

4.7 Thephot.cshRoutine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 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 UMa Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 64

6.2.2 Slowly Pulsating B 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

Table 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 thecharacteristic 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 increasesstrongly withstellar metallicity. The solid line is a power law fit for the probabilitythat a star has a detected planet. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Figure 2.1 CMD with overlaid theoretical isochrones obtained from Cassisi etal. (2006) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Figure 4.1 Composite reference image from ISIS.. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Figure 4.2var.fitsproduced from ISIS . Most of the really bright spots are satu-rated stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 5.1 BLS example results from Kovacs et al. (2002) froma test set ofdata. This shows the time series in the upper panel, the normalized BLSfrequency spectrum and the folded time series in the lower panel. Thesignal parameters are displayed at the top wheren is the number of bins,P0 is the period,q is the fractional transit length,δ is the transit depth,andδ/σ is the SNR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 5.2 The top panel shows the RMS of the 4128 stars which appear on thevar.fitsand have 323 out of 423 observations. The middle panel showsthe RMS of the 3935 stars remaining after filters have been applied. Thebottom panel shows the 1238 stars remaining which are suitable for BLSstudy after filters were applied including an RMS< 0.015 magnitude cutoff. . . . . . 32

Figure 5.3 Binned phased plot for candidateID 1956. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Figure 5.4 Phase vs. unbinned delta magnitude of the points in transit for can-didateID 1956. Error bars have been added to convey the uncertainty inthe residual flux within the transit phase. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Figure 5.5 Residuals of candidateID 1956. Major time-axis tick marks arespaced by 2.4 hours. The time-axis is defined as the Heliocentric JulianDate (HJD(i)) subtracted from the Heliocentric Julian Dateof the firstobservation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Figure 5.6 Normalized signal residue versus trial frequency for candidateID1956. The SR peak corresponds to a period of 1.5096 days. . . . . . . . .. . . . . . . . . . . . . . . . 41

Figure 5.7 Binned phased plot for candidateID 2563. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

xi

Figure 5.8 Phase vs. unbinned delta magnitude of the points in transit for can-didateID 2563. Error bars have been added to convey the uncertainty inthe residual flux within the transit phase. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Figure 5.9 Residuals for candidateID 2563. Major time-axis tick marks arespaced by 2.4 hours. The time-axis is defined as the Heliocentric JulianDate (HJD(i)) subtracted from the Heliocentric Julian Dateof the firstobservation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 44


Figure 5.11 Binned phased plot for candidateID 1347. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Figure 5.12 Phase vs. unbinned delta magnitude of the pointsin transit forcandidateID 1347. Error bars have been added to convey the uncertaintyin the residual flux within the transit phase. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Figure 5.13 Residuals for candidateID 1347. Major time-axis tick marks arespaced by 2.4 hours. The time-axis is defined as the Heliocentric JulianDate (HJD(i)) subtracted from the Heliocentric Julian Dateof the firstobservation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Figure 5.14 Normalized signal residue versus trials frequency for candidateID1347. The SR peak corresponds to a period of 1.4552 days. . . . . . . . .. . . . . . . . . . . . . . . . 49

Figure 5.15 Binned phased plot for candidateID 1267. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Figure 5.16 Phase vs. unbinned delta magnitude of the pointsin transit forcandidateID 1267. Note that 1 “low” data point has been removed.Error bars have been added to convey the uncertainty in the residual fluxwithin the transit phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Figure 5.17 Phase vs. unbinned delta magnitude of the pointsin transit forcandidateID 1267 including “low” data point. Error bars have beenadded to convey the uncertainty in the residual flux within the transit phase. . . . . . . 53

Figure 5.18 Residuals for candidateID 1267. Major time-axis tick marks arespaced by 2.4 hours. The time-axis is defined as the Heliocentric JulianDate (HJD(i)) subtracted from the Heliocentric Julian Dateof the firstobservation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 54


Figure 6.1var.fitsframe with location of variable stars. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . 58

Figure 6.2 Composite reference image with location of variable stars. . . . . . . . . . . . . . . . . . . . . . . 59

Figure 6.3 CMD highlighting the location of variable stars detected. . . . . . . . . . . . . . . . . . . . . . . 60

Figure 6.4ID 0533 Lomb-Scargle period analysis. The peak of maximumpower corresponds to a P = 0.607 days. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 62

xii

Figure 6.5ID 0533 Lafer-Kinman period analysis. Two of the lowestr valuescorresponds to a period P = 0.607 days and P = 1.214 days. Lowerrvalues with larger periods can be ruled out based solely on the unphasedlight curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Figure 6.6 Phased light curves of suspected W UMa stars. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Figure 6.7 Light curve ofID 0533. Major time-axis tick marks are spacedby 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 ofID 0981. Major time-axis tick marks are spacedby 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








xiii



Figure 6.18 Phased light curves of suspected EA variables. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80









xiv

Figure 6.27 Phased light curve ofID 3096. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91




xv

ACKNOWLEDGEMENTS

First and foremost, my gracious thanks must be extended to myadvisor 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 yourinsight, patience, sense of

humor, endless advice, and for having a “test” for just aboutany 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 thankfulfor all the

tremendous amounts of help and patience you’ve provided forme 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 thefirst 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 internalstructure 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 itis, 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

distancea? 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 radiusR∗, the transiting planet radiusRp, and the

distance between both objects at the time of transita. The probability to observe a transit

assuming random orientation of the orbit is (Sackett 1999):

Probability =R∗ + Rp

a(1.1)

In the case of planetary transits, this probability becomesclose toR∗/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’sExtrasolar Planets Encycolpediaat 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 as51 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 1Saturn 0.05 41 0.7551 Pegasi b 9.1 3 1HD 209458 b 10.8 3 1.6

The diminution in brightness due to the transit of the planetis easy to determine. It is

simply the ratio of the apparent surfaces of the planet and the star:

∆F =

(

Rp

R∗

)2

(1.2)

Consequently, if the radius of the star can be estimated thenthe radius of the planet can be

deduced.

The duration of the transit depends firstly upon the period ofrevolution 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 durationTmax (when the planet crosses over the center of the stellar disk), in

front of a star of radiusR∗ and massM∗, for a planet orbiting with a periodP at a distancea

is (Lecavelier Des Etangs & Vidal-Madjar 2006):

Tmax =P × R∗

π × a≈ 13.0

( a

1AU

)1/2(

M∗

M⊙

)−1/2 (

R∗

R⊙

)

hours (1.3)

3

assuming a planet radius much smaller thanR∗. 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. Planetsthat 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 whichproduces 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 accountthe non-uniformity of the stellar flux

over the different parts of the stellar disk. It is in generalaffected 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 Brownet al. (2001) with the Hubble

Space Telescope. This observed profile can be very well fittedby 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 to90◦). 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 detectionprobability is expected (Sackett

1999). Other proposed ways to favor transit detection are toselect 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 factorof 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 accuratelyover an extended period, in the

4

Figure 1.1. Light curve of HD209458b from Brown et al. (2001)showing the characteristiclight curve of a planetary transit.

5

hope of being able to observe regular fluctuations as the stardims 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 thousandstars, for example, provide an

ideal environment for searching for transiting extrasolarplanets. 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 8Mjup 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 hostexoplanets 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 rangesMsini > 0.3Mjup and P<13 years and at least∼ 22% have planets in the

larger rangeMsini > 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 hotJupiters (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 rangeMSat < 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 factorsthat 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 ofa ∼ 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 etal. (2005) assumes that planets

can only be detected around single stars a binary fraction of50% 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 -M ETALLICITY 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 ofthe 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 below5% for solar metallicity objects

(Udry & Santos 2007).

The correlation between planet occurrence and metallicitycan be expressed as a

power law (Fischer & Valenti 2005):

P (planet) = 0.03 ×(

(NFe/NH)

(NFe/NH)⊙

)2

(1.4)

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 periodshorter 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 ironabundance [Fe/H] of the host star measured spectroscopically. The occurrence of observedgiant planets increases strongly with stellar metallicity. The solid line is a power law fit forthe 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 ofastronomical 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 anystar known to harbor an extrasolar

planet. Based on statistics from a sampling of planets in ourlocal 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 thatHST 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 separationd ∼ 5 AU. Short period planets,

those to which transit surveys are sensitive, would survivefor significantly longer.

1.4 OPEN CLUSTERS

As discussed in the previous sections, one way of overcomingthe 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 metallicityand harsh conditions may not support

planets (as discovered in the case of 47 Tuc). Other searcheshave undertaken a wide-field

search for transits in the Galactic plane since the Galacticplane 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 searchof 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 shouldhave 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-densityenvironment 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 M52The 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 andδ = 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 todetermine [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, basedon 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 fromthe 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 andNovember 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 1σ 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 1σ 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 theR 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 (′′)

2001 Aug 24 2452146.0 4.94 3.08± 0.582001 Aug 25 2452147.0 5.07 2.73± 0.262001 Aug 26 2452148.0 4.88 2.92± 0.272001 Sept 17 2452170.0 6.53 2.73± 0.262001 Sept 18 2452171.0 6.02 2.71± 0.152001 Sept 19 2452172.0 6.52 2.70± 0.162001 Sept 20 2452173.0 6.52 2.76± 0.182001 Oct 13 2452196.0 5.52 2.72± 0.222001 Oct 14 2452197.0 5.73 2.82± 0.192001 Oct 15 2452198.0 5.16 2.89± 0.282001 Oct 16 2452199.0 5.91 2.84± 0.202001 Nov 14 2452227.0 3.15 3.18± 0.432001 Nov 15 2452228.0 0.29 2.67± 0.192001 Nov 16 2452229.0 3.12 2.91± 0.332007 Dec 06 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 tomatch calibrated data of M52

12

Table 2.2. V Filter Observations of M52

Date Heliocentric Julian Day Duration (hr) Seeing (′′)

2001 Aug 25 2452147.0 0.24 2.73± 0.262001 Aug 26 2452148.0 0.20 2.92± 0.272001 Sept 17 2452170.0 0.18 2.43± 0.022001 Sept 19 2452172.0 0.42 2.70± 0.162001 Sept 20 2452173.0 0.83 2.76± 0.182001 Oct 13 2452196.0 0.39 2.72± 0.222001 Oct 14 2452197.0 0.42 2.82± 0.192001 Oct 15 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 BASTI2

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

0.2 0.4 0.6 0.8 1 1.2 1.4(V - R)

8

10

12

14

16

18

V

CMD of M52

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 objectwere reduced in the standard

fashion, using IRAF1 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 overscanregion 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 onan 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 ScienceFoundation.

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 subtractthe 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 areoverscan 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 theexposure times of the

observations and the beginning and end times recorded in thelog. 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 ouranalysis. 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 2.11, on our reduced images to identify variable candidates. We have

selected to use ISIS because it is one of the methods of choiceto search for variability in

crowded fields. The entire process requires running six scripts: interp.csh, ref.csh,

subtract.csh, detect.csh, find.csh, andphot.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 willprovide 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 ISIS SETUP

In order to run ISIS modifications need to be made to the configuration files in the

registerfolder. The configuration files include theprocessconfig, defaultconfig, and

phot configwhose parameters are displayed in Tables 4.1, 4.2, and 4.3. In processconfig,

some basic parameters about the directory structures must be inputted. The keyword IMDIR

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 theregisterdirectory and

is calleddates. 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 configandphot 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 storedMRJ DIR .. 1 Installation directoryREFERENCE a2m52r13rbtzf.fits Reference image for astrometryREF SUB ref.fits Reference image for subtractionINFILE ../register/dates Dates of the framesVARIABLES phot.data Coordinates of objects to make light curvesDEGREE 2 Degree of the polynomial astrometric transform

between framesCONFIG DIR ../register2 Where to find the configuration filesSIG THRESH 3.0 Threshold for variable detection in var.fitsCOSMIC THRESH 3 Parameter for cosmic ray rejectionREF STACK interp a2m52r13rbtzf.fits 5 Image for subtraction (only forsub imageN REJECT 2 If Nth brightest value in series too large, reject itMESH SMOOTH 3 Size of smoothing mesh for var.fits

4.2 THE interp.cshROUTINE

The interp.cshroutine 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 mapseach 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 transformthen 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 theprocessconfigfor 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 ofour 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.cshROUTINE

Theref.cshbuilds a composite reference frame to transform all images to the same

seeing and background level. REFSUB 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 (REFSTACK). 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.fitswhich is the placed in theimagesdirectory. We initially used a much larger set of

images to build theref.fitshowever, a number of the images were contributing to problems

found in theref.fits. Some of the images we initially selected did not get subtracted properly

when transformed in order to match the seeing and backgroundlevel of REFSTACK. By

looking at theconvr interp imagesproduced 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.fitsis among the most important step for this process. Figure 4.1shows our finalref.fits. It

should be noted that for our September images, which were processed separately due to

telescope complications, all parameters were kept the sameas our big run except theref.fits

was composed of only September images.

20

Table 4.2. ISIS Default Configuration File


nstampsx 15 Number of stamps along X axisnstampsy 15 Number of stamps along Y axissubx 1 Number of subdivision of the image along X axissuby 1 Number of subdivision of the image along the Y axishalf meshsize 12 Half kernel sizehalf stampsize 15 Half stamp sizedegbg 3 Degree to fit differential background variationssaturation 45000 Saturation value for eliminating pixelspix min 7 Minimum value for the pixels to fitmin stampcenter 100 Minimum value for objects to enter kernel fitngauss 3 Number of Gaussiansdeggauss1 8 Degree associated with 1st Gaussiandeggauss2 6 Degree associated with 2nd Gaussiandegguass3 4 Degree associated with 3rd Gaussiansigmagauss1 0.8 Sigma of 1st Gaussiansigmagauss2 1.67 Sigma of 2nd Gaussiansigmagauss3 4 Sigma of 3rd Gaussiandegspatial 3 Degree of the fit of the spatial variations of the Kernel

4.4 THE subtract.cshROUTINE

Once we have built a composite reference frame, we can apply image subtraction to all

images. To do this, theref.fitsimage 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 theimagesdirectory. 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)

Thekernel(u, v) represents a transform over a region of pixels(u, v) that when convolved

with theRef(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 inmany 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 tosolve:

Kernel(u, v) =∑

i

aiBi(u, v). (4.2)

21

Table 4.3. ISIS Phot Configuration File


subx 1 Number of subdivision of the image along X axissuby 1 Number of subdivision of the image along the Y axisrad1bg size 15 Inner radius of annulus for backgroundrad2bg size 20 Outer radiusnstars 5mesh 2saturation 45000 Saturation value for eliminating pixelsmin 7 Minimum value for the pixels to fitpsf width 100 Minimum value for objects to enter kernel fitngauss 23radphot 5 Radius of circle within the pixels will be fitted to estimate fluxnstarsmax 8nb aduel 0.5 Gain in units of ADU/electronsrmax 0.5first 1keep 5

The ai term is the contribution of the different basis functions describing thekernel(u, v). Bi

are the basis functions (a Gaussian) used to model the seeingdifferences with the form:

B(u, v) ≡ e−

(u2+v2)

2σn2 udnx

vdny

(4.3)

Solving the least squares problem yields the following matrix equation for theai coefficients:

Ma = V, (4.4)

with:

Mij =

∫

Ci(x, y)Cj(x, y)

σ(x, y)2dxdy

Vi =

∫

Ref(x, y)Ci(x, y)

σ(x, y)2dxdy

Ci(x, y) = I(x, y) ⊗ Bi(x, y),

where the variance is defined as:

σ(x, y) = k√

I(x, y) (4.5)

wherek is a constant set according to the gain of 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 tomodel 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) =∑

n

an(x, y) · Bn(u, v). (4.6)

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 kernelvariations 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) = a0 · B0(u, v) +∑

1,N

an(x, y) · B′

n(u, v), (4.7)

where

B′

n = Bn − B0 (4.8)

Provided thatBn vectors are normalized, theB′

n will all have zero sums exceptB′

0 which will

equalB0.

The most important parameters for the image subtraction arein theprocessconfigfile

in theregisterdirectory. The kernel size is represented byhalf meshsize, while the

half stampsizeis the area taken by the program around each object. It shouldbe 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 thenstampsx andnstampsy 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 thenstampsx andnstampsy values, we also increase the total number of stamps:

Total 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 bothnstampsx andnstampsy. 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 usedsubx andsuby 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 thatsubx and

suby set to 1 produces realistic photometric results not achieved with 3×3 or 2×2. 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 throughthedegspatialkeyword,

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:

[(degspatial+ 1) · (degspatial+ 2)]/2 (4.10)

coefficients, and needs a number of stamps that is at least 3 or4 times larger than this number.

The degree of differential background variations within a subimage can also be

changed, which is represented bydegbgparameter. 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

degbg= 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:saturationwith a value of 45000 counts,pix minwith a pixel value of 7, and

min stampcenterwith a pixel value of 100. Finally,sigmagauss1, sigmagauss2and

sigmagauss3represent the Gaussian sigmas of the kernel expansion; we have used values of

0.8, 1.67, and 4 pixels. Experimentation showed that the largestsigmagaussis not

particularly important.

4.5 THE detect.cshROUTINE

Once we have successfully applied this method to all the images, only variable stars

should have any significant correlated residual. Thevar.fitsimage 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 thevar.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 sincemost cosmics are removed in

earlier steps. The pertinent keyword here isN REJECTin theprocessconfigfile. 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 thedetect.cshscript produces two images:var.fitsandabs.fits

and are stored in theimagesdirectory. The smoothed, composite image of all these pixels is

var.fits, shown in Figure 4.2. Thevar.fitsrepresents the mean of absolute normalized deviation

from each of the convolution images while the imageabs.fitsis the mean absolute deviation.

Our originalvar.fitsconstructed using thedetectroutine 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 thevar.fits. For the purpose of

variable detection, December images were removed from thevar.fitsto search for variability.

It should also be noted that a number of residuals on thevar.fitshad 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 finalvar.fits. Note that

most of the really bright features on the image are from saturated stars.

4.6 THE find.cshROUTINE

After inspecting thevar.fits, one can select a threshold in order to identify the

variables. The parameter is represented by SIGTHRESH. 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 significantdetection. 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 ofvar.fitsbut can be easily eliminated by other

means. This script determines the location of the stars to beused for the photometry by

recording the coordinates of each of the mean of the absolutenormalized deviations on the

var.fitsthat are above a certain threshold. This routine outputs a file calledphot.data, which

contains the position of the variables, and is stored in theregisterdirectory.

25

Figure 4.2. var.fitsproduced from ISIS . Most of the reallybright spots are saturated stars.

26

4.7 THE phot.cshROUTINE

Light curves are produced using the ISIS routinephot.csh. The necessary

configuration file for this process isphot config. Most importantly, one must specify a value

for the radius of the annulus in order to estimate the background. This is set byrad1 bg,

which represents the inner radius, andrad2 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 forrad1 bg andrad2 bg respectively. Two other important parameters arerad phot

andrad aper, which we used values of 5 and 7 respectively. The keywordrad phot is the

photometric radius−the radius of the circle within which the pixels of the objectwill be fitted

in order to estimate the flux. Therad aperparameter represents the radius for flux

normalization. For all other values, we did not alter the originalphot configconfiguration 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 aphot.datafile from all

the stars found using the IRAF routine DAOFIND. After running phot.csh, 4128 light curves

for all the stars which appeared on thevar.fitswere 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):

ci = ctpl + ∆ctpl − ∆ci (4.11)

The magnitude is then calculated using the following equation:

mi = 2.5 ∗ log(

10mo−mtpl/2.5 + ∆ctpl − ∆ci

)

+ mo (4.12)

27

To convert the photometric error in flux to magnitudes we usedthe following relation:

σmi = 2.5 ∗ log

(

ci

ci + σci

)

(4.13)

The light curves have been plotted using a SM2 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 L EAST SQUARE ALGORITHM

We implemented the Box Least Square (BLS) algorithm by Kovacs et al. (2002)1 to

search for planetary transits. This method effectively fitsa 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 datapoints 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:

D =i1−1∑

i=1

wi(xi − H)2 +n

∑

i=i2+1

wi(xi − H)2 +i2

∑

i=i1

wi(xi − L)2 (5.1)

The boundaries of the transit arei1 andi2 within the phased binned data. The

observationsi 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) andxi 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 actuallyhas a higher value than H. L

and H are defined as:

L =s

r(5.2)

H = − s

1 − r(5.3)

1The BLS code is available for download at: http://www.konkoly.hu/staff/kovacs.html

29

wherer 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:

r =

i2∑

i=i1

wi (5.4)

s is given as the sum of the product of the weights and the data points:

s =

i2∑

i=i1

xi (5.5)

With these formulae, Kovacs shows that the minimization equation reduces to:

D =n

∑

i=1

wix2i −

s2

r(1 − r)(5.6)

Kovacs’ defines the BLS frequency spectrum by the amount of Signal Residue (SR)

defined as:

SR = MAX

{

s2(i1, i2)

r(i1, i2)[1 − r(i1, i2)]

}12

(5.7)

The SR is calculated over all trial periods with trial transits in the intervali1, i2. The

maximum value of SR minimizesD 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 probabilityof 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:

SDE =SRpeak− < SR >

sd(SR), (5.8)

where theSRpeak is the SR a the highest peak in the BLS spectra,< SR > is the average

signal residue, andsd(SR) is the standard deviation of the SR over the range of frequencies

tested. In other words, it looks at the “significance” of the peak to help determine the

likelihood of a planetary transit.

A transit that is theoretically visible is not necessarily detectable. Therefore, the SNR

(α) is used as a measure of the detectability of the transit. TheSNR(α) is defined as:

α =δ

σ

√nq, (5.9)

30

wheren is the number of data points,q is the fractional transit length,δ is the transit depth,

andσ 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 andα can

be used to filter out false detections. This can be especiallyuseful in the case where the SDE

might be high enough to suggest a likely transit but the noiseis 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 BLS IMPLEMENTATION

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 RMSfor each star was calculated as:

RMS =

√

1

Npts − 1

∑

i

(xi− < x >)2, (5.10)

wherexi is the magnitude at timei, Npts is the total number of data points, and< x > is the

average magnitude of the star. In order to remove any outlying data points a3σ rejection was

applied in the calculation of the RMS.

Figure 5.2 shows three different RMS vs. magnitude plots of our data set. The top

panel show the RMS of the initial data set. These stars have atleast 323 out of 423 total

observations and appear on thevar.fits. We chose to keep only stars with at least 323 total

observations so that at most a star is missing 100 observations. The middle panel shows the

RMS of the stars remaining after the following filters were applied: saturated stars were

removed, stars with broken residuals on thevar.fitswere removed, and stars with less than 323

total observations were not included. The bottom panel shows the remaining 1238 stars

suitable for the BLS study. These stars have passed all the previously indicated filters and the

RMS is< 0.015 mag.

The BLS input parameters used in this survey are summarized in Table 5.1.

The number of frequency pointsnf, the frequency stepdf, and the minimum

frequencyfmin, set the limits for the period range to be searched. The number of bins,nb,

was set to 100 (i.e. each bin covers 0.01 in phase). Setting the number of bins too low can

result in an overlooked transit. The disadvantage to setting the bins too high is computation

time. The minimum and maximum fractional transit lengths,qmi andqma respectively, were

selected because planetary transits of hot Jupiters are notexpected to have fractional transit

lengths less than 0.01 or greater than 0.2. Also included in our implementation of BLS (not

31

Figure 5.1. BLS example results from Kovacs et al. (2002) from a test set of data. This showsthe time series in the upper panel, the normalized BLS frequency spectrum and the foldedtime series in the lower panel. The signal parameters are displayed at the top wheren is thenumber of bins, P0 is the period,q is the fractional transit length, δ is the transit depth, andδ/σ is the SNR.

32

10 12 14 16 18 20 220.0001

0.001

0.01

0.1

1

RMS vs. Magnitude

10 12 14 16 18 20 220.0001

0.001

0.01

0.1

1

RM

S

10 12 14 16 18 20Magnitude

0.0001

0.001

0.01

0.1

Figure 5.2. The top panel shows the RMS of the 4128 stars whichappear on thevar.fitsandhave 323 out of 423 observations. The middle panel shows the RMS of the 3935 starsremaining after filters have been applied. The bottom panel shows the 1238 stars remainingwhich are suitable for BLS study after filters were applied including an RMS < 0.015magnitude cutoff.

33

Table 5.1. Input Parameters Used in BLS

Parameter Definition Value

nf Number of frequency points 200000df Frequency step (day−1) .00001

fmin Min frequency to be tested (day−1) .1nb Number bins in folded time series 100

qmi Min fractional transit length .01qma Max fractional transit length .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 SYSREMSearching 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 measurementsare 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 ofeach 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{ci; i = 1, ..., N} and{aj ; j = 1, ...M} that

minimize the global expression

S2 =∑

ij

(rij − ciaj)2

σ2ij

. (5.11)

First an estimate of the extinction coefficient is found by

ci =

∑

j(rijaj/σ2ij)

∑

j(a2j/σ

2ij)

. (5.12)

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

a(1)j =

∑

i(rijcj/σ2ij)

∑

j(c2j/σ

2ij)

. (5.13)

We then recalculate the best-fitting coefficients,c(1)i , and continue iteratively,

obtaining better approximations for both sets.

The effect is then removed by

r(1)ij = rij − c

(1)i a

(1)j . (5.14)

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 whenthese 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 andα > 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 andα is the measure of the detectability

of the transit. According to Kovacs et al. (2002) whenα exceeds a value of 6 you can expect a

significant detection of a transit. For our data set, whenα 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 anα threshold> 9. This is the also the sameα 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 toonly 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 andα.

Binned phase plots were created to show the average relativevariability 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 inspectionof 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 andα, 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 thatID 1261appeared to show variability in its light curve

characteristic of an eclipsing variable.ID 1261was thus added to our list of variable stars and

dismissed as a transit. AlsoID 3727 (not included in Table 5.2) was discovered to show

interesting variability from our BLS results. Because the period ofID 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 havepoints 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 inspectionthese 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 0.04961722 855,706 6.587 22.26 1.1271 6 -0.054 0.01421772 1422,722 6.481 14.742 1.7299 16 -0.021 0.03781612 383,672 6.377 14.274 1.0516 16 -0.028 0.03781956 994,781 6.269 11.524 1.0972 16 -0.013 0.03780776 1397,349 6.039 13.787 2.4569 19 -0.022 0.01423880 716,1464 5.936 20.370 2.2614 21 -0.016 0.04964012 454, 1520 5.751 13.789 1.9513 16 -0.031 0.03782563 1524, 997 5.295 10.308 1.5096 13 -0.024 0.03071347 1344,566 5.236 19.141 1.4552 13 -0.025 0.03071267 1806,535 5.149 16.867 1.3598 10 -0.060 0.02362808 924,1081 4.852 14.016 1.4033 20 -0.026 0.04732195 487,863 4.811 12.687 1.0913 10 -0.015 0.02362232 1451,877 4.621 10.391 1.135 23 -0.021 0.04022801 1783,1079 4.502 14.344 2.761 22 -0.032 0.05204035 1214,1524 4.501 18.038 1.3497 18 -0.031 0.04261051 464,456 4.464 19.890 1.1457 13 -0.007 0.03073827 385,1411 4.400 9.608 1.376 11 -0.031 0.0261261 243,533 4.376 19.224 1.524 12 -0.058 0.02842202 916,866 4.327 16.422 2.263 17 -0.016 0.04024635 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 0.03782563 1524, 997 5.295 10.31 1.509 13 -0.024 0.03071347 1344,566 5.236 19.14 1.455 13 -0.025 0.03071267 1806,535 5.149 16.87 1.359 10 -0.060 0.0236

The binned phase plot ofID 1956are 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 candidateID 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 1956where 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 candidateID 1956. The SR peak

corresponds to a period of 1.0972 days. The calibrated V magnitude ofID 1956 is 17.26 mag

and the calibrated (V-R) is 0.812.

The binned phase plot ofID 2563 is shown in Figure 5.7. The binned phased plot

shows evidence of variability during the transit phase. Thepoints 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 themean magnitude. The points

within the transit phase shown in Figure 5.8 are not on two discrete levels thus further

weakening the argument that candidateID 2563 is an actual transit. Figure 5.9 shows the

residuals ofID 2563where 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 ofID 2563 is

17.19 mag and the calibrated (V-R) is 0.850.

The binned phase plot ofID 1347are 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 thatID 1347 is an actual transit because it is not at two

discrete levels. Also, reducedχ2 statistics revealed that the 13 points within the transit bin are

consistent with transit magnitudes. The reducedχ2 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 1347where 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 ofID 1347 is 17.01

mag and the calibrated (V-R) is 0.875.

The binned phase plot ofID 1267are shown in Figure 5.15. The binned phased plot

shows evidence of variability during the transit phase. Theout-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 whileonly 1 point is coming from the

2nd night. This point is not at a lower discrete level with theother 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 pointsin transit for candidate ID1956. Error bars have been added to convey the uncertainty inthe residual flux within thetransit phase.

40

0 0.1 0.2 0.3

0.05

0

-0.05

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

0.05

0

-0.05

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

0.05

0

-0.05

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

Figure 5.5. Residuals of candidate ID 1956. Major time-axistick marks are spaced by 2.4hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from theHeliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.

41

0 0.5 1 1.5 2

0.4

0.6

0.8

1

Figure 5.6. Normalized signal residue versus trial frequency for candidate ID 1956. The SRpeak corresponds to a period of 1.5096 days.

42


43

Figure 5.8. Phase vs. unbinned delta magnitude of the pointsin transit for candidate ID2563. Error bars have been added to convey the uncertainty inthe residual flux within thetransit phase.

44

0 0.1 0.2 0.30.05

0

-0.05

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.20.05

0

-0.05

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.10.05

0

-0.05

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

Figure 5.9. Residuals for candidate ID 2563. Major time-axis tick marks are spaced by 2.4hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from theHeliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.

45

0.5 1 1.5 2

0.4

0.6

0.8

1

Figure 5.10. Normalized signal residue versus trial frequency for candidate ID 2563. TheSR peak corresponds to a period of 1.5096 days.

46


47

Figure 5.12. Phase vs. unbinned delta magnitude of the points in transit for candidate ID1347. Error bars have been added to convey the uncertainty inthe residual flux within thetransit phase.

48

0 0.1 0.2 0.3

0.05

0

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

0.05

0

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

0.05

0

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01


49

0 0.5 1 1.5 20.2

0.4

0.6

0.8

1

Figure 5.14. Normalized signal residue versus trials frequency for candidate ID 1347. TheSR peak corresponds to a period of 1.4552 days.

50


51

Figure 5.16. Phase vs. unbinned delta magnitude of the points in transit for candidate ID1267. Note that 1 “low” data point has been removed. Error bars have been added to conveythe uncertainty in the residual flux within the transit phase.

52

within the transit which appear at a lower level are actuallyonly 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 anSR peak corresponding to a

period of 1.3598 days. The calibrated V magnitude ofID 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 ID1267 including “low” data point. Error bars have been added to convey the uncertainty inthe residual flux within the transit phase.

54

0 0.1 0.2 0.3

0.2

0

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

0.2

0

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

0.2

0

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01


55

0.5 1 1.5 2

0.4

0.6

0.8

1

Figure 5.19. Normalized signal residue versus trial frequency for candidate ID 1267. TheSR peak corresponds to a period of 1.3598 days.

56

CHAPTER 6

VARIABILITY

The side benefit of a transiting extrasolar planet survey arethe number of variable

stars also discoved. We have identified 22 variable stars, 10were 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 these 7 only 3 (ID 0980, ID

2673, andID 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 compositeref.fitsin Figure 6.1 and on thevar.fitsin Figure 6.2

from ISIS.

Table 6.1 lists the variable star number, pixel coordinates(x,y), variable type, average

relative V-band magnitude< Vrel >, the color (V-R), period, the approximate depth of the

primary and secondary minima, and a cluster membership estimation based on its position on

the CMD. The (V-R) and V-band magnitudes reported are the calibrated values (see§2.1 for

calibration explanation). It should be noted that 4 out of the 22 variable stars were too faint in

our V frames, and so a color could not be determined.

Figure 6.3 shows the location of our variable stars on a CMD constructed from this

survey. The location of the variables on the CMD is used to estimate likelihood of cluster

membership, as well as the star’s distance from the cluster center. However, any conclusive

membership determination will require radial velocities or proper motion measurements. In

order to help better distinguish possible cluster members we have overlaid theoretical

isochrones from Cassisi et al. (2006) along with the isochrone shifted by 0.75 magnitude. It is

well known that an unresolved binary system comprising of two identical stars has the same

color but twice the luminosity of an equivalent single star and such a system will appear in the

CMD vertically displaced by 0.75 mag (since 2.5 log2 = 0.75).The region between these two

isochrones represents the region within which a variable star has the greatest probability of

being a possible cluster member. Four of our W UMa variables includingID 2513, ID 1834,

ID 1558, andID 2674and 1 SPBs variable lie within the region having the highest probability

of being a cluster member whileID 0681, ID 980, ID 2938andID 3727 lie just outside this

57

region. This is interesting because it is not expected that WUMa stars would be found in such

a young cluster since the time scale expected for the stars tocome into contact is larger than

the age of the cluster. It should be noted that the reliance onthe colors determined should be

taken with some caution as the colors can be affected by what part of the light curve

measurements the color measurements were taken on (this is especially the case for W UMa

stars where they are characterized by continuous changes intheir brightness).

Table 6.1. Variable Star InformationID (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 medium1558 441,654 EW 18.29 0.0755 0.9951 0.4617 0.2, 0.2 high/medium1834 943,744 EW 14.89 0.0165 0.6163 0.83 0.05, 0.05 high2513 1223,976 EW 14.73 0.0126 0.5503 1.44 0.06 high2673 1642,1030 EW 12.90 0.0035 0.3885 – – high2830 876,1087 EW 17.01 0.0278 0.6499 1.028 – low3727 76,1403 EW 13.56 0.0064 0.4973 0.4963 0.01, 0.02 low0681 708,324 EA 14.82 0.0069 0.6643 – – high0980 1067,440 EA 14.04 0.0037 0.5675 2.352 0.05 high1261 243,533 EA 16.54 0.0125 0.5732 3.159 0.25 low1284 318,543 EA 15.45 0.0078 0.8057 – 0.52 medium4109 1219,1554 EA 16.28 0.0375 – 1.9651 0.71, 0.05 –1855 1101,751 SPBs 13.53 0.0033 0.4351 – – high2409 833,944 Irr. 16.43 0.0111 0.8513 – – medium2773 1138,1065 Irr. 18.14 0.0363 0.6783 – – low3096 782,1183 Irr. 14.08 0.0075 0.395 2.23 – medium3928 1809,1480 Irr. 17.62 0.0214 0.8192 – – high/medium4540 1104,1718 Irr. 15.12 0.0111 0.4827 – – low4762 138,1810 Irr. 15.70 0.0135 1.007 – – low

6.1 PERIOD DETERMINATION

The periodicity search of our variable stars was carried outby 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 ofvariable stars.

60

0 0.2 0.4 0.6 0.8 1 1.2 1.4(V - R)

8

10

12

14

16

18

20

V

EW VariablesEA VariablesIrregular/UnclassifiedSPBs

CMD of M52

0980

06813096

4540

2513

1834

1284

2830

2773 2938

1558

4762

24091133

1261

3727

1855 2673

Figure 6.3. CMD highlighting the location of variable starsdetected.

61

P (ω) =1

2{ [

∑ni Xi cos ω(ti − τ)]2

∑ni Xi cos ω(ti − τ)

+[∑n

i Xi sin ω(ti − τ)]2∑n

i Xi sin ω(ti − τ)}, (6.1)

xi is the set of the measurements of a star’s light curve at timesti havingn observations.Xi is

the difference between each individual measurementxi and the average value of thex.

For a range of frequencies, a time offsetτ is computed for each value of the frequency,

by the equation

tan(2ωτ) =

∑ni sin 2ωti

∑ni cos 2ωti

(6.2)

Typically the frequency with the most power in the frequencyspectrum 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 successiveobservations are taken and added

together. This is expressed as,

S =n−1∑

i=1

|xi − xi+1| + |xn − x1| (6.3)

wherexi is theith 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,

r =S

Q− 2 (6.4)

where Q is the total range of observations (absolute value ofthe 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 ofr 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-Scargleand the

Lafler-Kinman results that were run on starID 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 lowestr values correspond to

62

0 0.5 1 1.5 2 2.5 3Period (days)

0

10

20

30

40

50

Pow

er

Figure 6.4. ID 0533 Lomb-Scargle period analysis. The peak of maximum powercorresponds to a P = 0.607 days.

63

0 0.5 1 1.5 2 2.5 3Period (days)

0

0.5

1

1.5

2

2.5

3

Pow

er

Figure 6.5. ID 0533 Lafer-Kinman period analysis. Two of thelowestr values correspondsto a period P = 0.607 days and P = 1.214 days. Lowerr values with larger periods can beruled 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 periodwas 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 VariablesEclipsing 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 wereoften 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 ourlight curves. For the phased plot

of ID 0533 only September observations were used. Two of the previously known variables,

ID 2673andID 1855, are not phased because their variability is less present inthe

non-September observations. It should also be be noted thatbecause 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 ofID 0533 are shown in Figure 6.7. Both primary and secondary

minima appear to be nearly identical in depth. The amplitudeof variation is about 0.2

magnitude from peak to peak. Cluster membership could not beestablished for this star as it

appeared too faint in the V band for color determination.

The light curve data ofID 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 asthere is no color determination

because it was too faint.

65

0 0.2 0.4 0.6 0.8 1

16.2

16.4

16.6

16.8

17

0533

0 0.2 0.4 0.6 0.8 1

16.216.316.416.516.6

0981

0 0.2 0.4 0.6 0.8 1

16.416.516.616.716.8

1107

0 0.2 0.4 0.6 0.8 1

15.3

15.4

15.5

15.6Mag

nitu

de

1133

0 0.2 0.4 0.6 0.8 1

16.2

16.4

16.6

1558

0 0.2 0.4 0.6 0.8 1

13.3

13.35

13.4

13.45

13.5

1834

0 0.2 0.4 0.6 0.8 1

13.213.2213.2413.2613.2813.3

2513

0 0.2 0.4 0.6 0.8 1Phase

15.315.3515.4

15.4515.5

15.55

2830

0 0.2 0.4 0.6 0.8 1

12.2

12.22

12.24

3727

Figure 6.6. Phased light curves of suspected W UMa stars.

66

0 0.1 0.2 0.3

16.816.616.4

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

16.816.616.4

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

16.816.616.4

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

16.816.616.4

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01

Figure 6.7. Light curve of ID 0533. Major time-axis tick marks are spaced by 2.4 hours. Thetime-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from theHeliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.

67

0 0.1 0.2 0.3

16.6

16.4

16.2

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

16.6

16.4

16.2

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

16.6

16.4

16.2

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

16.6

16.4

16.2

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


68

The light curve data ofID 1107 are shown in Figure 6.9. The peak to peak amplitude

of variation is about 0.3 magnitudes. Maxima appears to be ofsimilar heights, and minima are

of nearly identical depths. Cluster membership could not bedetermined because it was too

faint in V.

The light curve data ofID 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 thatID 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 ofID 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. Aswith 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 1558should 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 ofID 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 makingID 1834 and interesting star for follow up work.

The light curve data ofID 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 thatID 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 ofID 2673 are shown in Figure 6.14. A previous study by

Viskum et al. (1997) have identified 6.14 as aδ scuti variable. Viskum et al. (1997) reportID

2673is a main-sequence star near the hot border of the instability strip and could therefore be

69

0 0.1 0.2 0.3

17

16.5

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

17

16.5

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

17

16.5

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

17

16.5

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


70

0 0.1 0.2 0.3

15.6

15.4

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

15.6

15.4

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

15.6

15.4

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

15.6

15.4

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

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 theHeliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.

71

0 0.1 0.2 0.3

16.6

16.4

16.2

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

16.6

16.4

16.2

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

16.6

16.4

16.2

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

16.6

16.4

16.2

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


72

0 0.1 0.2 0.313.45

13.4

13.35

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.213.45

13.4

13.35

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.113.45

13.4

13.35

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.213.45

13.4

13.35

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


73

0 0.1 0.2 0.313.3

13.25

13.2

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.213.3

13.25

13.2

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.113.3

13.25

13.2

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.213.3

13.25

13.2

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


74

0 0.1 0.2 0.3

12.18

12.16

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

12.18

12.16

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

12.18

12.16

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

12.18

12.16

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


75

aδ Scuti variable. However, the periodicity in our light curvedoes 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 thatID 2673 is a W UMa variable. Based onID 2673’s position on the

CMD it is likely that it is a cluster member.

The light curve data ofID 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 toID

2830’sposition 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 ofID 3727 are shown in Figure 6.16. It should be noted thatID

3727was 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 usedto 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 thatID 3727 is a cluster member based on its position on the CMD.

6.2.2 Slowly Pulsating B StarsSlowly 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 variabilityis 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 of1855are shown in Figure 6.17.1855has been identified as a

variable in a previous study by Choi et al. (1999). Choi et al.(1999) proposes that1855is a

slowly pulsating B star with a pulsation period of 1.626 days. Choi et al. (1999) also reports

that1855is located near the SPBs instability strip. Based on1855’s position on the CMD it is

likely that it is a cluster member.

6.2.3 Detached Eclipsing BinariesThe 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 forǫ Aurigae) (Sterken

76

0 0.1 0.2 0.3

15.5

15.4

15.3

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

15.5

15.4

15.3

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

15.5

15.4

15.3

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

15.5

15.4

15.3

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


77

0.1 0.2 0.3

12.24

12.22

12.2

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

12.24

12.22

12.2

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

12.24

12.22

12.2

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

12.24

12.22

12.2

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


78

0 0.1 0.2 0.3

11.5811.56

11.54

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

11.58

11.5611.54

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

11.58

11.5611.54

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

11.58

11.5611.54

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


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 ofID

0980, ID 4109, andID 1261are shown in Figure 6.18.ID 0681would not be properly phased

because it was located near a bright star, which may have contaminated the light curve.ID

1284is 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 ofID 0681 are shown in Figure 6.19. The residual ofID 0681

appears strongly on thevar.fitshowever, 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 thatID

0681is a cluster member based on its position on the CMD.

The light curve data ofID 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 aδ 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 thatID 0980 is a cluster member

based on its location on the CMD.

The light curve ofID 1261 is shown in Figure 6.21. It should be noted thatID 1261

was not identified as a variable from our ISIS results but was identified from our BLS results.

Note thatID 1261does not show up on ourvar.fitsin 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 thatID 1261 is a

cluster member based on its position on the CMD.

The light curve data ofID 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 thevar.fits. Because only one eclipse was observed no period determination can be

made. Based onID 1284’sposition on the CMD there is a medium possibility is it a cluster

member. Given the large eclipse, it isn’t unreasonable thatthe CMD position is off the MS.

80

0 0.2 0.4 0.6 0.8 1

12.55

12.6

12.65

0980

0 0.2 0.4 0.6 0.8 1

15

15.1

15.2

15.3

Mag

nitu

de

1261

0 0.2 0.4 0.6 0.8 1Phase

16

16.5

17

17.5

4109

Figure 6.18. Phased light curves of suspected EA variables.

81

0 0.1 0.2 0.3

13.4

13.3

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

13.4

13.3

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

13.4

13.3

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

13.4

13.3

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


82

0 0.1 0.2 0.3

12.6

12.55

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

12.6

12.55

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

12.6

12.55

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

12.6

12.55

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


83

0 0.1 0.2 0.3

15.2

15.1

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

15.2

15.1

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

15.2

15.1

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

15.2

15.1

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


84

0 0.1 0.2 0.3

14.214

13.8

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

14.214

13.8

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

14.214

13.8

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

14.214

13.8

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


85

The light curve data ofID 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 observationID 4109 had some difficulties being

phased. The October 15th and 16th observations were removedfor the phase plot.

6.2.4 Irregular Variables or UnclassifiedSix of our variable stars have been identified as irregular orunclassified. 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 ofID 2409 are shown in Figure 6.24. Due to the variation in the

light curve it appears thatID 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 thatID 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 ofID 2773are 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 thatID 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 ofID 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 . Thenights 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 3096could be a possible quasiperiodic variable since the natureof the

variation changes with a little variation within a night, tovariation from night to night. There

is a medium likelihood thatID 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 ofID 3928 are shown in Figure 6.28. Variability appears to be

present but not clear or consistent.ID 3928could be a possible W UMa or EB variable.ID

86

0 0.1 0.2 0.3

17

16.5

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

17

16.5

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

17

16.5

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

17

16.5

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


87

3928appears to have a little out of eclipse variation period near2 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 CMDsuggest that there is a medium

likelihood is it associated with the cluster.

The light curve ofID 4540are shown in Figure 6.29. The residual ofID 4540 is very

strong on thevar.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 itappears thatID 4540might be a

quasi periodic variable but it classification remains unclear. Based onID 4540’s location on

the CMD there is little likelihood that it is associated withthe cluster.

The light curve data ofID 4762 are shown in Figure 6.30. Variability is present in the

September and October observations. The variability in theSeptember 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 whichmay be contaminating the

variability. The likelihood thatID 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

0 0.1 0.2 0.314.75

14.7

14.65

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.214.75

14.7

14.65

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.114.75

14.7

14.65

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.214.75

14.7

14.65

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


89

0 0.1 0.2 0.316.6

16.4

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.216.6

16.4

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.116.6

16.4

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.216.6

16.4

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


90

0 0.1 0.2 0.3

12.7812.7612.74

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

12.7812.7612.74

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

12.7812.7612.74

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

12.7812.7612.74

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


91

0 0.2 0.4 0.6 0.8 1

12.72

12.74

12.76

12.78

12.8

3096

Figure 6.27. Phased light curve of ID 3096.

92

0 0.1 0.2 0.3

16

15.8

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

16

15.8

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

16

15.8

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

16

15.8

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


93

0 0.1 0.2 0.313.8

13.7

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.213.8

13.7

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.113.8

13.7

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.213.8

13.7

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


94

0.1 0.2 0.3

14.2

14

Aug24,01

1 1.1 1.2 1.3

Aug25,01

2 2.1 2.2 2.3

Aug26,01

50 50.2

14.2

14

Oct13,01

51 51.2

Oct14,01

52 52.2

Oct15,01

53 53.2

Oct16,01

81 81.1

14.2

14

Nov14,01

81.9

Nov15,01

82.9 83 83.1

Nov16,01

23 23.2

14.2

14

Sept17,01

24 24.2

Sept18,01

25 25.2

Sept19,01

26 26.1 26.2

Sep20,01


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 planetssince 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 yetbeen confirmed within a star

cluster, these surveys have provided promising candidatesawaiting 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 anRMS< 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 apossible eclipsing system.

We obtained lightcurves for 4,128 stars using the ISIS imagesubtraction software, and

identified 22 variable stars, of which 19 were not previouslyknown 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 especiallyinteresting 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 theyare 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. CasoliandT. 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

Kovacs, G., Zucker, S., & Mazeh, T. 2002, A&A, 391, 369

Lecavelier Des Etangs, A. & Vidal-Madjar, A. 2006, Planetary transits: a first direct vision ofextrasolar 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 andObservations, 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 ofthe Pacific Conference Series, Vol. 294, Scientific Frontiers in Research on ExtrasolarPlanets, 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., Mallen-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 Planetsin the Open Cluster M52

byTiffany M. Borders

Master of Sciences in AstronomySan Diego State University, 2008

In this survey we attempt to discover short-period Jupiter-size planets in the youngopen 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 planetarytransits were apparent; however, some interesting variable stars were discovered. In total, 22variable stars were discovered of which, 19 were not previously known as variable. Ten of ourvariable stars were identified as eclipsing-type W Ursa Majoris contact binaries, 5 wereidentified 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. Acolor-magnitude diagram constructed from V and R photometry with fitted isochrones is alsopresented to help determine cluster membership of our variable stars. We find that 3 of our WUma stars lie within a region of high cluster membership probability. Radial velocity followup observations are needed to confirm cluster membership. Ifconfirmed, this would be highlyinteresting as W Uma stars are not excepted to be found in sucha young cluster.

the search for transiting extrasolar planetsborders/thesis.pdf · the search for transiting...

Documents