STOCKHOLM UNIVERSITY MASTER OF SCIENCE THESIS Implementing an Algorithm for Spectrum Extraction of Circumstellar Objects with H igh-Dispersion Spectroscopy Author: Supervisor: Marcus Karlsson Dr. Alexis Brandeker [email protected] Stockholm Observatory Department of Astronomy February 15, 2019 ABSTRACT In this thesis project, we study the field of high-dispersion spectroscopy and methods for extracting the spectrum of circumstellar objects such as exoplanets from the combined signal of a stellar system. One of the only techniques for detecting absorption lines in exoplanetary atmospheres is to directly image a planet and record the reflected light. However, exoplanets are incredibly faint compared to the parent star and are often completely obscured in any images of the system. We utilize techniques such as high-dispersion spectroscopy (HDS) and high contrast imaging (HCI) in order to capture the planetary signal and develop methods for reducing only the stellar light while leaving the planet relatively untouched. We investigate a method for removing the scattered starlight by utilizing the separate spectra of the star and the planet, where the signal from the objects will be spread out according to a point spread function (PSF) and laid on top of each other. By empirically determining the shape of the stellar PSF, reference profiles can be created for each wavelength and subtracted from the entire signal, revealing the planetary spectrum. To achieve this, we have constructed a spectrum extraction algorithm, written in Python 3.6, for use on the spectra of directly imaged exoplanetary systems. Additionally, we discuss many of the problems which may arise when reducing cross-dispersed echelle spectra and attempt to solve them with the algorithm. To assess our algorithm, we utilize spectral images of the system 훽 Pictoris, taken with the high-dispersion spectrograph CRIRES, and three model exoplanetary systems of varying brightness. When extracting the spectrum of the planets, we find that the method employed for constructing the reference stellar PSFs is partially flawed and leaves a substantial amount of residual stellar light in the reduced images. This leads to difficulties with identifying any spectral absorption lines and an alternative method is likely necessary. Nonetheless, the algorithm is found to successfully extract the spectrum and identify spectral lines of an exoplanetary atmosphere if the planet is sufficiently bright, although only for theoretically unrealistic luminosities. We expect that our algorithm can be improved upon with more well- researched methods for reducing the starlight and by using data recorded with spectrographs of even higher dispersive capabilities, such as CRIRES+, METIS, or HIRES. ii Acknowledgements First and foremost, I’m incredibly grateful to my supervisor, Alexis Brandeker, for providing me with numerous ideas, suggestions, and answers that were immensely helpful during the length of this project. The work performed in this thesis has been some of the most interesting I’ve ever engaged with, and it would not have been possible with his support. I additionally wish to extend my gratitude to Per Calissendorff for his helpful advice on the data reduction processes used for the project. I must also thank the lecturers and teachers assistants at the Department of Astronomy at Stockholm University for the very informative courses during the master’s programme that helped me complete my thesis work. This includes Angela Adamo, Claes-Ingvar Björnsson, Simon Eriksson, Claes Fransson, Matthew Hayes, Markus Janson, Katia Migotto, Stephan Rosswog, and many more, I’m sure. I’d like to acknowledge the assistance of the ESO Archive for providing the observational data used in this thesis and their practical suggestions for how to perform certain data operations. Based on observations collected at the European Southern Observatory under ESO programme 292.C-5017(A). Based on data obtained from the ESO Science Archive Facility under request number 377577. iii Contents Page Abstract ii Acknowledgements iii List of Figures vi List of Tables viii 1 Introduction 1 1.1 High Dispersion Spectroscopy and High Contrast Imaging . 4 1.2 Computational Spectrum Extraction Methods . 7 1.3 Project Overview . 9 2 Detection of Circumstellar Objects and Spectra 12 2.1 Exoplanet and Debris Disk Detection Methods . 12 2.1.1 Debris Disk Infrared Excess . 12 2.1.2 Doppler Effect Spectroscopy . 14 2.1.3 Primary and Secondary Transit . 16 2.1.4 Direct Imaging . 18 2.2 Spectrum Observation Methods . 20 2.2.1 Primary Transit Spectroscopy . 20 2.2.2 Secondary Eclipse Spectroscopy . 22 2.2.3 HDS with Direct Imaging (Exoplanet) . 23 2.2.4 HDS with Direct Imaging (Disk) . 27 2.3 Spectrum Observation Advantages and Limitations . 28 2.3.1 Primary and Secondary Transits . 28 2.3.2 Direct Imaging . 31 3 Spectrum Extraction Theory 34 3.1 The Optimal Spectrum Extraction Algorithm . 34 3.1.1 Algorithm Description and Overview . 34 3.1.2 Curved Spectrum Problem . 39 3.1.3 Use in Exoplanetary Spectroscopy . 40 3.2 The Stellar Point Spread Function . 41 3.2.1 Defining the Point Spread Function . 41 3.2.2 Role in Exoplanetary Spectroscopy . 43 3.2.3 Method for Subtracting the Stellar Light . 45 iv 4 Implementing the Spectrum Extraction Algorithm 50 4.1 Extraction Goal and Algorithm Overview . 50 4.2 The Planetary Spectrum Extraction Algorithm . 52 4.2.1 Step 1 – Resampling Data . 53 4.2.2 Step 2 – Polynomial Fit to Profile Centre . 55 4.2.3 Step 3 – Align Spectrum to Remove Tilt . 57 4.2.4 Step 4 – Normalize and Create Reference Profiles . 59 4.2.5 Step 5 – Revert Tilt and Resolution . 61 4.2.6 Step 6 – Model Fit with Chi-Squared Method . 63 4.2.7 Step 7 – Create and Subtract Final Model from Data . 64 4.2.8 Step 8 – Extract Planetary Spectrum . 65 4.3 Problems and Limitations of the Algorithm . 65 4.3.1 Interpolation as a Resampling Method . 65 4.3.2 Spectrum Extraction Limitations . 68 5 Observational Information & Models 70 5.1 The CRIRES Instrument . 70 5.1.1 CRIRES Main Characteristics . 70 5.1.2 Use in Exoplanetary Spectroscopy . 71 5.1.3 The CRIRES+ Upgrade . 73 5.2 The Target System; 훽 Pictoris . 74 5.2.1 Stellar and Planetary Information . 74 5.2.2 훽 Pictoris as an Optimal Example . 76 5.3 Observations and Standard Reductions . 77 5.3.1 Observational Data . 77 5.3.2 Observational and Calibration Image Overview . 79 5.3.3 Standard Data Reductions . 82 5.4 Model Data Frames . 86 6 Results of Spectrum Extraction 90 6.1 Spectrum Extraction of 훽 Pictoris b with RM1 . 92 6.2 Spectrum Extraction of 훽 Pictoris b with RM2 . 96 6.3 Spectrum Extraction of Artificial Planets . 98 7 Discussion 106 7.1 Algorithm Performance for 훽 Pictoris b . 106 7.2 Realistic Approach to Models . 111 7.3 Possible Future Improvements . 114 8 Summary and Conclusions 117 References 119 v List of Figures Page 1.1 Confirmed exoplanets by discovery method . 2 1.2 Model spectrum of CO . 4 1.3 Model of the HDS + HCI method . 7 1.4 Example spectrum of 훽 Pictoris . 9 2.1 SED of the star Vega . 13 2.2 Dust grain blackbody spectrum . 14 2.3 Radial velocity of 51 Pegasi . 15 2.4 Radial velocity detection limits . 16 2.5 Light curve of HD 209458 . 17 2.6 Primary/secondary transit illustration . 18 2.7 Solar system intensity comparison . 19 2.8 Light curve of HD 209458 by wavelength . 21 2.9 Planet/star contrast ratios . 23 2.10 훽 Pictoris spectral image illustration . 24 2.11 Model 2D-spectrum of exoplanetary system . 25 2.12 Debris dust zones illustration . 27 2.13 Sunspot effect on transit light curve . 29 2.14 Transit probabilities of planets . 30 3.1 Standard spectrum of 훽 Pictoris . 37 3.2 Periodically oscillating spectra . 40 3.3 2- and 1-dimensional PSF example . 42 3.4 Extrasolar system model PSF . 43 3.5 Spread of planetary signal in PSF . 44 3.6 Model stellar light subtraction process . 45 3.7 Model reference profile creation . 46 3.8 Aligning tilted 2D spectrum . 48 3.9 Solution to tilted spectrum problem . 49 4.1 Resampling method 1 . ..