W URSAE MAJORIS VARIABLES FROM THE NORTHERN SKY VARIABILITY SURVEY A THESIS SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE MASTER OF SCIENCE BY ALAN A. GAVEL II ADVISOR: DR. ROBERT C. BERRINGTON BALL STATE UNIVERSITY MUNCIE, INDIANA DECEMBER 2018 For Sidney and Lucy with love i Contents List of Figures v List of Tables vii Acknowledgements ix Abstract x 1 Introduction 1 1.1 Binary Star Systems . .1 1.1.1 Orbital Parameters . .2 1.2 Eclipsing Binary Systems . .3 1.2.1 Light Curves . .4 1.3 Morphology of Binary Systems . .7 1.3.1 Roche Geometry . .7 1.3.2 Detached and Semi-detached Binary Systems . 11 1.3.3 Over-Contact Binary Systems . 13 1.4 Modeling of Eclipsing Binary Systems . 17 2 Data Acquisition 19 2.1 The Northern Sky Variability Survey . 20 2.2 Observations . 21 ii 3 Data Reduction 27 3.1 Data Reduction Overview . 27 3.1.1 Bias . 28 3.1.2 Dark Current . 28 3.1.3 Flat Fielding . 29 3.2 Data Reduction with IRAF . 30 3.2.1 CCD sections . 30 3.2.2 Image Headers and Task Parameters . 30 3.2.3 Instrument Parameters . 31 3.2.4 Overscan . 31 3.2.5 Combine Bias frames . 32 3.2.6 Combine Dark frames . 32 3.2.7 Combine Flat frames . 32 3.2.8 Process object frames . 33 3.3 Heliocentric Julian Date . 33 4 Data Analysis 35 4.1 Differential Aperture Photometry . 35 4.1.1 Choosing Apertures . 38 4.1.2 Coordinate List . 40 4.1.3 Measuring Instrumental Magnitudes . 42 4.1.4 Generating Light Curves . 43 4.2 Orbital Period . 46 4.2.1 Initial Analysis . 46 4.2.2 The Ephemeris . 47 4.3 Effective Temperature . 55 4.4 Modeling of W UMa Systems . 57 iii 5 W Ursae Majoris type variable star NSVS 3971593 60 5.1 WD model . 61 5.2 Summary for NSVS 3971593 . 63 6 W Ursae Majoris type variable star NSVS 7680691 72 6.1 New Orbital Period . 73 6.2 WD model . 74 6.3 Summary for NSVS 7680691 . 78 7 Conclusion 86 A IRAF Parameters 90 A.1 Editing Image Header Parameters . 90 A.2 Setting the Instrument . 91 A.3 Reduction . 92 A.4 Measuring FWHM . 93 A.5 Rectifying Images . 96 A.6 Creating a coordinate file . 97 A.7 Photometry . 98 A.8 Processing magnitude files . 102 A.9 Period Analysis with pdm . 102 Bibliography 104 iv List of Figures 1.1 Orbital Plane and Inclination . .3 1.2 Phased light curves . .5 1.3 Synthetic EA light curve . .6 1.4 Synthetic EB light curve . .6 1.5 Synthetic EW light curve . .7 1.6 Effective Potential . .9 1.7 Perpendicular distance . 10 1.8 Lagrange Points and Roche Surfaces . 12 1.9 Roche Lobes: Detached System . 14 1.10 Effective Gravitational Potential on x-axis . 15 1.11 Roche Lobes: Semi-Detached System . 16 1.12 Roche Lobes: Contact System . 16 2.1 Typical Image Frame . 20 4.1 Image frame of NSVS 3971593 . 36 4.2 Image frame of NSVS 7680691 . 37 4.3 Image with apertures and annuli . 39 4.4 Screen Display from phot task . 40 4.5 Differential light curve C2-C1 . 45 4.6 Folded light curves: NSVS 3971593 . 48 v 4.7 Folded light curves: NSVS 7680691 . 49 4.8 Find Minimum . 50 4.9 O − C Plot: NSVS 3971593 . 53 4.10 O − C Plot: NSVS 7680691 . 54 4.11 Color Plot: NSVS 3971593 . 57 4.12 Color Plot: NSVS 7680691 . 58 5.1 NSVS 3971593 q-search . 62 5.2 WD model fit sans spot: B bandpass . 66 5.3 WD model fit sans spot: V bandpass . 67 5.4 WD model fit sans spot: R bandpass . 68 5.5 WD model fit with spot: B bandpass . 69 5.6 WD model fit with spot: V bandpass . 70 5.7 WD model fit with spot: R bandpass . 71 6.1 ANOVA statistic plot . 74 6.2 Orbital Period Comparison . 75 6.3 NSVS 3971593 q-search . 77 6.4 WD model fit sans spot: B bandpass . 79 6.5 WD model fit sans spot: R bandpass . 81 6.6 WD model fit sans spot: V bandpass . 82 6.7 WD model fit with spot: B bandpass . 83 6.8 WD model fit with spot: R bandpass . 84 6.9 WD model fit with spot: V bandpass . 85 7.1 Morphological Representation NSVS 3971593 . 88 7.2 Morphological Representation NSVS 7680691 . 89 vi List of Tables 2.1 SIMBAD Data . 22 2.2 Observatory Data . 23 2.3 Observation nights for NSVS 3971593 . 25 2.4 Observation nights for NSVS 7680691 . 26 4.1 Orbital Periods . 47 4.2 Times of Minimum: NSVS 3971593 . 51 4.3 Times of Minimum: NSVS 7680691 . 52 4.4 Comparison Star Magnitude Data . 56 4.5 Color index and Effective Temperature . 59 5.1 PHOEBE Model Parameters: NSVS 3971593 . 65 6.1 PHOEBE Model Parameters: NSVS 7680691 . 80 A.1 Image header . 90 A.2 Parameters:hedit . 91 A.3 Parameters:setinstrument . 92 A.4 Parameters:ccdproc-section 1 . ..