New Mass and Orbital Constraints of J1407b
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New Mass and Orbital constraints of J1407b Bharath Chowdhary Nagam Technische Universiteit Delft New constraints on mass and orbital parameters of J1407b by Bharath Chowdhary Nagam in partial fulfillment of the requirements for the degree of Master of Science in Aerospace Engineering at the Delft University of Technology, to be defended publicly on Monday July 24, 2017 at 2:00 PM. Supervisor: Dr. Matthew Kenworthy(external) Dr. Daphne Stam(internal) Thesis committee: Ir. Prem Sundaramoorthy, TU Delft Samiksha Mestry M.Eng, TU Delft This thesis is confidential and cannot be made public until July 24, 2017. An electronic version of this thesis is available at http://repository.tudelft.nl/. Acknowledgement First and foremost, I thank the Almighty for giving me the strength, knowledge and opportunity to undertake this research and complete it satisfactorily. I sincerely thank Dr.Daphne Stam of TU Delft, who gave me this opportunity and referred me to Dr.Matthew Kenworthy of Leiden University. I also thank her for her numerous suggestions and insightful inputs in the end to make this thesis report more meaningful and attractive to read. I also sincerely thank Dr.Matthew Kenworthy, who , in spite of his very busy schedule, solely guided me in completion of this project. His advice and teachings will not only help me in just completing this course, but also for my entire career. I thank my Parents, who have supported me throughout my life to successfully become a graduate and a professional. Lastly, my friends in Delft , who provided me with great moral support and helped me in various difficult situations throughout my master’s. Thanks for all your encouragement and support! Bharath Chowdhary Nagam Delft, July 2017 iii Contents List of Figures vii List of Tables xi 1 Abstract 1 2 Introduction 3 2.1 Introduction to Exoplanets . 3 2.2 J1407b-An exoplanet with giant ring system . 4 2.3 Overview . 10 3 Earlier research on J1407 and its companion 13 3.1 About the star-J1407 . 13 3.2 Light Curve . 14 3.3 Possible explanations for the eclipse . 15 3.4 Modelling of the ring system . 16 3.5 Orbital Constraints. 19 3.5.1 Direct Imaging . 19 3.5.2 Photometry . 20 3.5.3 Radial Velocity . 20 3.5.4 휉 constraint . 21 3.5.5 Eccentricity Limit. 21 3.5.6 Mass and Period Limits . 24 3.6 Conclusion . 25 4 Introduction to Orbital Parameters and Observation Techniques 27 4.1 Definition of Orbital Parameters . 27 4.2 Visualisation of orbital parameters . 28 4.2.1 visualisation of inclination(i) . 28 4.2.2 visualisation of Ω . 28 4.2.3 visualisation of 휔 . 31 v vi Contents 4.3 Development of Algorithm. 31 4.4 Introduction to Direct Imaging . 35 4.5 Introduction to Transit photometry . 36 4.5.1 Importance of photometry. 37 4.6 Introduction to Radial Velocity(RV) . 38 4.7 Conclusion . 39 5 Inclination and Eccentricity Constraint 41 5.1 Introduction . 41 5.2 Eccentricity Constraints. 41 5.3 Inclination constraint . 43 5.4 Conclusion . 43 6 Direct Imaging 45 6.1 Observations of J1407. 45 6.2 Conclusion . 49 7 Photometry 51 7.1 Photometry data of J1407 . 51 7.2 Conclusion . 53 8 Radial Velocity 57 8.1 Radial Velocity data of J1407 . 57 8.2 Constraints for Circular Orbit . 57 8.3 Constraints for Elliptical Orbit . 59 8.4 Conclusion . 59 9 Results and Conclusion 63 9.1 Combined constraints for circular orbits . 63 9.2 Combined constraints for elliptical orbits . 63 9.3 Result . 65 9.4 Conclusion . 65 10 Recommendations 69 11 Appendix 71 11.1Appendix-a . 71 11.2Appendix-b . 71 Bibliography 75 List of Figures 2.1 Habitable zone of recently discovered exoplanets[1] ............... 4 2.2 Transit Method[2] .................................... 5 2.3 Dip in brightness flux of J1407[3] .......................... 5 2.4 J1407b (described by black circle) and its ring system described in series of colors of brown,cyan,blue,orange,gray, if present at the centre of earth-sun system , will tend to fill the entire gap between earth(yellow circle) and sun(red circle) and will even tend to extend beyond. ....................................... 6 2.5 Rings of J1407b [4] ................................... 7 2.6 Transit curve showing successive dips of flux in the HAT-P7 system[5] ... 7 2.7 Change in Radial Velocity of the star due to the gravitational tug of companion[6] ................................................ 8 2.8 Direct imaging of an exoplanet orbiting the star 1RXS J160929.1 – 210524 [7] 9 2.9 Number of Exoplanets detected by various methods[8] ............. 9 3.1 CTIO spectra of four standard stars[9] ....................... 14 3.2 superWASP photometry light curve of J1407[9] .................. 15 3.3 ASAS photometry light curve of J1407[9] ...................... 15 3.4 A basic ring model to fit superWASP data[9] .................... 16 3.5 Geometry of the ring model[3] ............................ 17 3.6 Ring model fit to the data[3] .............................. 18 3.7 Simulation of prograde and retrograde models[10] ................ 18 3.8 Eclipse duration for different models[10] ...................... 18 3.9 RV data of J1407[11] .................................. 21 3.10 period and mass limits for circular orbit of J1407b[11] .............. 22 3.11 period and mass limits for elliptical orbit of J1407b[11] ............. 23 3.12 Combined period and mass limits for circular orbit of J1407b[11] ....... 24 3.13 Combined period and mass limits for elliptical orbit of J1407b[11] ....... 25 4.1 Plot describing inclination(i) of arbitrary companion in the plane of sky ... 29 4.2 Plot describing Ω of arbitrary companion in the plane of sky .......... 30 4.3 Plot describing 휔 ..................................... 32 4.4 Plot describing function of 휔 .............................. 33 vii viii List of Figures 4.5 Position coordinates in the sky ............................ 34 4.6 Direct Imaging of HR8799 system[12] ....................... 36 4.7 Integrated image showing the path of Venus transit[13] ............ 37 4.8 Illustration of a transit curve[14] ........................... 37 4.9 Plot describing the change in Radial Velocity of a star versus time [15] .... 39 5.1 Eccentricity values satisfying the velocity constraint ............... 42 5.2 Critical eccentricity values from Kenworthy et al.(2015)[11] .......... 42 5.3 Critical inclination values which satisfies the modelled value of impact param- eter ............................................. 44 6.1 Constraints for circular orbit of J1407b[11] ..................... 46 6.2 Direct imaging constraint of J1407b(circular orbit) ................ 47 6.3 Position of Secondary Companion during various epochs of direct imaging .. 48 6.4 Direct Imaging constraints for elliptical orbits ................... 50 7.1 3.2 days phase folded results from van Werkhoven et al.(2014)[16] ..... 52 7.2 3.2 day period folding result for transit data of J1407b ............. 52 7.3 Photometry constraints of J1407b .......................... 53 7.4 Photometry data of PDS 110[17] ........................... 53 7.5 superWASP photometry light curve of J1407[9] .................. 54 7.6 Transit light curve of J1407 for the past 5 years[18] ............... 55 8.1 (a) represents the variation of RV of J1407 with time. (b) represents the FWHM of the star implying heavy stellar activity. (c) representing slope of bisector also is inline with the FWHM, implying high stellar activity. (d) represents the RV vs slope of bisector plot showing very high anti correlation. ............................. 58 8.2 RV Constraints for circular orbit ............................ 59 8.3 RV Constraints for elliptical orbit from Kenworthy et al(2015)[11] ...... 60 8.4 updated RV Constraints for elliptical orbit from the latest data of CORALIE observation ........................................ 61 9.1 Combined constraints for circular orbits ....................... 64 9.2 Combined constraints of RV, DI and photometry for elliptical orbits. The Mean mass for each case of 휔(in increasing order) are 7.32,9.10,9.56,10.04,10.43,1.74,14.48 and 24.98 Jupiter masses respectively. ............................. 67 11.1 RV constraint for circular orbits[11] ......................... 72 11.2 RV constraint result 휔 = 90 and n=9 ......................... 72 11.3 RV constraint result 휔 = 270 and n=11 ........................ 72 List of Figures ix 11.4 Direct imaging result for circular orbits ....................... 73 11.5 Direct imaging constraint[11] ............................. 73 List of Tables 3.1 Stellar Properties of J1407[9] ............................. 14 3.2 Disk model parameters[3] ............................... 17 9.1 Mean mass of J1407b for different cases of 휔 .................... 64 xi 1 Abstract Objective: The main objective of this research study is to combine the constraints from the value of impact parameter, transit, direct imaging and the radial velocity data to yield the final constraint of the mass and period of J1407b. Inclination constraints:In the previous research work of J1407 (kenworthy et al.(2015)[11]), it has been assumed that the orbit of J1407b is edge on(푖 = 90∘). However, since the impact parameter of J1407b is known from the modelling of the ring system (Kenworthy and Mamajek(2014)[3]), we use the modelled value of impact parameter to find the value of inclination as function of mass and period of J1407b for different values of argument of periastron. Combination of constraints : New data from Radial Velocity, Direct Imaging and Transit technique are combined to yield the final result of this research work as constraint limit for mass and period of J1407b for different values of argument of periastron. Result: The maximum mass of J1407b is limited to 63.5 Jupiter masses(푀) for all probable cases of argument of periastron.A table containing average expected value of mass of secondary companion for each case of argument of periastron is also presented. Recommendation: Out of all the exoplanet detection techniques, another set of observation by direct imaging technique will provide the most useful constraint in constraining further the mass limit of J1407b and ruling out the higher orbital period values.