Implementing an Algorithm for Spectrum Extraction of Circumstellar Objects with H Igh-Dispersion Spectroscopy

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.

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.

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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

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

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 ...... 53 4.2 Resampling method 2 ...... 54 4.3 Lorentzian fit to stellar PSF ...... 56 4.4 Polynomial fit to spectrum centre ...... 57 4.5 Tilted spectrum issue example ...... 58 4.6 Tilted spectrum resampling solution ...... 59

4.7 Spatial profile comparison ...... 60 4.8 Reference profile creation method ...... 61 4.9 Reverting resolution example ...... 62 4.10 Chi-squared minimization process ...... 64 4.11 Resampling via interpolation limitations ...... 66 4.12 Interpolation summation problem ...... 67 4.13 PSF shape after summation problem ...... 68

5.1 Schematic overview of CRIRES ...... 71 5.2 Upgraded/old detector mosaics ...... 73 5.3 Infrared composite of 훽 Pictoris ...... 75 5.4 Spectral location of 훽 Pictoris a & b ...... 78 5.5 CRIRES raw science data frames ...... 81 5.6 Initial reductions frame comparison ...... 85 5.7 Dithered and reduced spectral image ...... 85 5.8 Modelled telluric line spectrum ...... 87 5.9 Model 2D planetary spectrum ...... 88 5.10 Total spatial signal of models ...... 89

6.1 훽 Pictoris 2D spectrum example ...... 91 6.2 훽 Pictoris 1D spectrum example ...... 91 6.3 훽 Pictoris spatial signal example ...... 92 6.4 Results for 훽 Pic (2D spectra, RM1) ...... 93 6.5 Results for 훽 Pic (1D spectra, RM1) ...... 94 6.6 Results for 훽 Pic (spatial signal, RM1) ...... 95 6.7 Results for 훽 Pic (2D spectra, RM2) ...... 96 6.8 Results for 훽 Pic (1D spectra, RM2) ...... 97 6.9 Results for 훽 Pic (spatial signal, RM2) ...... 97 6.10 Results for 훽 Pic (2D spectra, RM2, w/o reverting resolution) ...... 98 6.11 Results for Model 1 (2D spectra) ...... 99 6.12 Results for Model 1 (1D spectra) ...... 100 6.13 Results for Model 1 (spatial signal) ...... 100 6.14 Results for Model 2 (2D spectra) ...... 101 6.15 Results for Model 2 (1D spectra) ...... 102 6.16 Results for Model 2 (spatial signal) ...... 102 6.17 Results for Model 3 (2D spectra) ...... 103 6.18 Results for Model 3 (1D spectra) ...... 104 6.19 Results for Model 3 (spatial signal) ...... 105

7.1 Spectrum cross-correlation ...... 108 7.2 Standard deviation of extracted spectrum ...... 110 7.3 Spline – function method model ...... 115 vii

List of Tables

Page

1 Horne’s optimal spectrum extraction algorithm ...... 35 2 Horne’s algorithm images and quantities ...... 36 3 Planetary spectrum extraction algorithm ...... 51 4 CRIRES detectors wavelength ranges ...... 79 5 CRIRES science data reduction pipeline ...... 82

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Chapter 1.

Introduction

The study of exoplanetary systems is a considerably recent field when compared to the whole of astronomy, one of the oldest natural sciences. As a result of their vast distances and faint brightness, detection of exoplanets has not been possible for most of history, and it is only with our most modern and powerful telescopes that their existence has been proven. Potential exoplanets were found as early as the 1980s but were often dismissed as either stellar activity (e.g. Gamma Ceph, Campbell et al. 1988) or probable brown dwarfs (e.g. HD 114762, Latham et al. 1989). It was not until 1992 that the first exoplanet was confirmed to have been found (Wolszczan & Frail 1992) around the millisecond pulsar PSR1257+12, and three years later the first detection of an exoplanetary system in orbit of the main-sequence star 51 Pegasi occurred (Mayor & Queloz 1995). These early detections relied on detecting a Doppler signal from the parent star, indicating that another object caused a variation in the stellar velocity. Since then, the number of detected exoplanets has only increased with each year, and, as of January 2019, there are now 3890 confirmed planets outside of our solar system, with an additional 2424 candidates awaiting further verification (according to NASA’s Exoplanet Archive1). A plot of all discovered exoplanets and their detection method can be seen in Figure 1.1 below.

While exoplanets have been found with a breadth of sizes, masses, and orbits over the years, the most common ones are those named hot Jupiters, due to their close proximity to their host star and Jupiter-like size. The first exoplanets discovered were all gas giants at highly eccentric orbits of just a few days, leading to some skepticism as to whether the Doppler shift was really caused by planets or not. These potential planets were so different from our concept at the time of how planetary systems should appear that many argued they could not possibly be planets (Black 1997). Only once very similar objects were discovered by another method, the transit method (Charbonneau et al. 2000, Henry et al. 2000), was the exoplanetary explanation accepted.

1 https://exoplanetarchive.ipac.caltech.edu/ 1

Chapter 1. Introduction

Figure 1.1: All confirmed discovered exoplanets sorted by the method of discovery, plotted logarithmically with planetary mass (in Jupiter masses) against orbital period (in days). Image data and plotting credit to NASA’s Exoplanet Archive1.

The research surrounding exoplanetary systems has often been combined with the study of circumstellar debris disks. These disks consist of dust and grains of various sizes and are typically found around very young stars, although can sometimes be present for older ones as well. Debris around other stars has not been known about for much longer than exoplanets, as the first disks were discovered in 1984 surrounding the stars Vega (Aumann et al. 1984) and Beta Pictoris (Smith & Terrile 1984) with use of the Infrared Astronomical Satellite, IRAS. These stars were found to have excess infrared emission, now attributed to dust orbiting the stars in disks of various distances (Aumann & Good 1990; Gillett 1986). With observations made by IRAS, it was later found that as many as 15% of main-sequence stars showed signs of infrared excess caused by dust heating up from absorption of starlight (Plets & Vynckier 1999).

In more recent times it has been found that large debris disks in the circumstellar region can be a good indicator that a stellar system is also a host of giant exoplanets. A study by Meshkat et al. (2017) concluded that the frequency of giant planets in a dusty system with a debris disk is far higher than those without. In such a system, it was found to be more than eight times likelier of also finding a giant planet (6.27 % chance with a disk versus 0.73 % without a disk). It can, therefore, be considered a good idea to search for exoplanets and debris disks in tandem, as the disks may provide information of any potential planets in the system, and circumstellar material has long been thought to be the leading cause of planetary formation (Raymond et al. 2011). One of the newest and most intriguing detection methods of exoplanets is direct imaging, an undertaking only made possible in the last decade. Such detections require the use of high contrast imaging coupled with special observing techniques in order to

Chapter 1. Introduction distinguish the exoplanet from the overwhelming scattered light from the parent star. The method is most commonly used to detect large planets in wide orbits, such as HR 8799 b, c, d, & e (Marois et al. 2008) and Beta Pictoris b (Lagrange et al. 2009a, b), however, recent results have yielded discoveries of Super-Earths located in the parent star’s habitable zone as well (e.g. Jenkins et al. 2015; Anglada-Escude et al. 2016; Kane et al. 2016). With the most recent developments in telescopic equipment, observational techniques, and computational methods, we are now able to take high-resolution images of exoplanetary system and analyse data with previously unmatched precision. We have been able to learn much about such systems, their potential debris disks, and the astronomical bodies that inhabit them. This includes sizes, masses, ages, orbital parameters, compositions, and other physical properties that may be of high value in understanding how exoplanetary systems behave and evolve (Batalha et al. 2013).

Out of all the physical properties, it can be argued that the spectrum of extrasolar planets and disks is among the most valuable to derive, as it is through spectral lines one can learn much about their chemical composition, including atmospheric conditions of the planet and what material can be found in the debris disk. These features are of great interest as the atmosphere of a planet can be closely linked to the appearance of the surface of the planet. By examining the spectra of planets, it is possible to find evidence of high-altitude winds and clouds (Snellen et al. 2010; Kreidberg et al 2014), the presence of geological, biological, or chemical processes, and traces of molecules such as water, oxygen, ozone, carbon monoxide and dioxide, and methane may be found as well (e.g. Madhusudhan & Seager 2009; Brogi et al. 2012, 2013; de Kok et al. 2013; Birkby et al. 2013). Spectroscopic and photometric studies of exoplanetary atmospheres are necessary to fully understand the physical properties which determine the habitability of a planet. Discovery of an Earth-like atmosphere is clearly an endeavour some time away, but knowledge of methods of how to detect the spectrum of gas giants in orbit around other stellar systems will be very valuable in the future. Only two exoplanetary detection methods – direct imaging and transit spectroscopy – allow for direct measurements of photons and spectral lines from the planets themselves, an aspect we discuss more in Chapter 2. This thesis will investigate a particular method for extracting the spectrum of an exoplanet (or a debris disk) surrounding a star by using direct imaging techniques. Although the theory behind finding the spectrum of the two objects is similar, an exoplanetary spectrum is more specifically focused on in this thesis and will thus be more heavily discussed and described. We will examine observations of the young stellar system Beta Pictoris with the goal of being able to detect circumstellar emission from the planet, Beta Pictoris b, as well as modelled planets of very high brightnesses. This will be achieved by modifying an optimal spectrum extraction algorithm, described in Section 3.1, developed by Horne (1986). This method will use direct imaging of the exoplanet to separate the stars and the planets or, alternatively, the stars and the disks

Chapter 1. Introduction spectrum from each other to further increase the contrast sensitivity of the fainter spectrum. Similar methods have previously been deployed to find the spectrum of an exoplanet (e.g. Brogi et al., 2012, 2013; de Kok et al. 2013; Rodler et al. 2012; Snellen et al. 2014; Bonnefoy et al. 2013, 2014; Janson et al. 2010; Macintosh et al. 2015; Birkby et al. 2017) and are constantly being refined to provide higher contrast images of the planetary system. Other techniques to perform exoplanetary spectroscopy exist as well, most commonly relying on transiting planets, where the light from the star passing through the atmosphere is used to infer spectral lines and chemical compositions. Each of these methods has their advantages and limitations, all of which are discussed more in the following chapter, Chapter 2, while in the following sections we examine some of the techniques necessary to perform such spectroscopic measurements.

Section 1.1. High Dispersion Spectroscopy and High Contrast Imaging

In recent years, the use of high dispersion spectroscopy (HDS) has proved to be highly useful in researching and characterizing extrasolar planets and their atmospheres. At a spectrographic resolving power of R ~ 100 000, molecular bands seen in the atmosphere of extrasolar planets or in circumstellar debris disks can resolve into individual lines numbering in the tens or even hundreds (see Figure 1.2), a feature which be used to separate the planetary or debris disk spectrum from that of nearly stationary telluric lines, produced by Earth’s atmosphere, and the stellar contribution, which invariably dominates the spectra of any observed stellar system (Snellen et al. 2015).

Figure 1.2: Model spectrum of carbon monoxide (CO) detected in the dayside spectrum of the exoplanet 휏 Böotis b, showing molecular bands resolved into dozens of spectral lines, only visible with high dispersion spectroscopy. Image credit to Snellen et al. (2013). 4

Chapter 1. Introduction

The resolving power 푅 of a spectrograph is given by the ratio in Formula 1.1,

휆 푅 = (1.1) Δ휆 where Δ휆 is the wavelength resolution, the smallest separation in wavelength two spectral lines may possess for them to be distinguishable from each other (i.e. both lines are resolved), at a given wavelength 휆 (Chromey 2010). As an example, at a wavelength of 1 휇푚, an 푅 = 100 000 spectrograph may resolve two lines separated by as little as 0.1 Å. In order to be able to separate the planetary spectrum from telluric lines found in Earth’s atmosphere and stellar spectral lines, the use of high-dispersion integral field spectrographs (IFS) is a fundamental requirement. Observations of exoplanetary systems require a very high signal-to-noise ratio (SNR) in combination with spectrographs of high angular and spectral resolution in order to achieve the necessary contrast ratios (10−7 − 10−10, Fischer et al. 2014) to perform spectroscopy on circumstellar objects. From a larger coverage in the spectral dimension, one also achieves a higher SNR, due to the number of resolved spectral lines. Unless the spectral resolution is high enough, it will be impossible to discern the exoplanetary absorption lines from spectral lines originating with other sources that contaminate the spectrum during the observations.

With HDS, the SNR of an exoplanetary system can be described by Formula 1.2 from Snellen et al. (2015),

푆푝푙푎푛푒푡 SNR = √푁 푙푖푛푒푠 (1.2) 2 2 2 √푆푠푡푎푟 + 휎푏푔 + 휎푅푁 + 휎퐷푎푟푘 assuming no hindrance from telluric line absorption. Here the planetary and stellar signal is given by 푆푝푙푎푛푒푡 and 푆푠푡푎푟 (in units of photons per resolution element), while 휎푏푔, 휎푅푁, and 휎푑푎푟푘 are the photon noise levels from the background, readout, and dark current, respectively. All three noise sources are, however, very low, as the observed stars are very bright, and the background is typically quite low. When investigating the SNR of HDS observations, the noise sources can, therefore, often be neglected as the signal from the star, 푆푠푡푎푟, will be the main factor in deciding the ratio. The factor

푁푙푖푛푒푠 describes the strength and number of individual spectral lines from the planet found in the observed wavelength range. When more spectral lines can be resolved, i.e. at higher dispersive capabilities, this factor will increase and grant a larger SNR between the planet and the star.

Chapter 1. Introduction

Many other studies of exoplanetary systems involving the use of HDS have also been performed fairly recently, with much success. Such observations of extrasolar planets have revealed carbon monoxide (CO) in the transmission spectrum of HD 209458 b (Snellen et al. 2015), CO in the dayside spectrum of 휏 Böotis b (Brogi et al. 2012; Rodler et al. 2012), 51 Pegasi b (Brogi et al. 2013), and HD 189733 b (de Kok et al. 2013), and atmospheric CO and water vapour on HD 179949 b (Brogi et al. 2014).

From a technical standpoint, even with the use of HDS, it may still prove too difficult to directly detect a planetary signal if it is too faint in comparison to the parent star. If there are simply not enough photons detected it will not matter how high the resolving power is when the planet cannot be distinguished from the stellar signal or even the background. One means of solving this problem is to employ the use of High Contrast Imaging (HCI) to observe the planet in order to improve on the contrast ratio between the signal from the star and planet or debris disk. Direct imaging at high contrasts is a fairly recent technical development, although there have been a few notably successful studies, producing both images and, eventually, the spectra of extrasolar planets. Planets such as Beta Pictoris b (Lagrange et al. 2009a, b, 2010) and HR8799 b, c, d, & e (Marois et al. 2008, 2010) are among those considered case studies for direct spectroscopic probes of exoplanetary atmospheres.

In combining HDS with HCI, we may be able to reach the necessary stellar/planetary contrast ratios for detailed spectroscopic studies of planetary atmospheres to become possible. Whilst HDS and HCI can individually reach raw contrast ratios between planetary and stellar signals down to the level of 10−5 each, combined they could, in theory, amplify this to contrasts of ~10−5 × 10−5 = 10−10 (Snellen et al. 2015). This ratio would be enough to detect Earth-like planets in Solar System-analogues. In practice, however, this estimate would be limited by a number of factors, including sky background noise and instrumentation. A more realistically achievable contrast ratio would be 10−3 × 10−4 = 10−7, one that has already been proved possible in both optical and infrared observations (e.g. Leigh et al. 2003; Brogi et al. 2012) and models (Snellen et al. 2015). In Figure 1.3 below, we show an example case of combining HDS and HCI, where the left panel is a model of a stellar point spread function (PSF), observed using HDS, the middle panel displays a case of HCI observations of an exoplanetary system with a star, planet, and the contrast ratio between them, while the last panel shows how a theoretical combination of the two methods may further increase the contrast sensitivity and detect even fainter planetary companions.

Chapter 1. Introduction

Figure 1.3: Model of the HDS + HCI observational method. The left panel shows the signal of a star observed with HDS, where it is possible to achieve contrast ratios of 10−4. The middle panels detail an exoplanetary system, observed with HCI where a planet is located at some angular distance and detectable if the signal contrast ratio is at least 10−3. The right panel shows the case of combining the two methods, where observations of planets with a brightness ratio of 10−7 can be achieved. Image credit to Snellen et al. 2015.

The reflected brightness of a gas giant in a stellar system much like our own would, at best, be roughly one to one-tenth of a billionth (10−9 − 10−10) as strong as that of the star in the system at visible wavelengths (de Pater & Lissauer 2015). With our current technology and instrumentation, this level of contrast ratio is impossible to attain, and we must make use of certain shortcuts to directly detect the faint planetary signal. This can come either from observational techniques, such as observing in the near- (1 – 3 휇푚) and mid-infrared (3 – 5 휇푚) where the planets have their blackbody emission peak and the contrast ratio is more favourable (Biller & Bonnefoy 2018), or targeting extrasolar planets of specific advantageous properties, such as those in wide orbits of 푎 > 5 AU where the stellar signal is not as bright, or massive, young, and thermally hot planets of 푇푒푓푓 = 400 − 2000 퐾 that are self-luminous (Fischer et al. 2014). For these types of gas giants, observed in the infrared, we may achieve star-planet contrast ratios as high as ~ 10−4 − 10−7, enabling direct spectroscopic measurements with current technology.

Section 1.2. Computational Spectrum Extraction Methods

The most fundamentally difficult limitation to overcome with direct imaging spectroscopy of exoplanetary systems lies in specifically detecting and differentiating the much weaker planetary signal from the significantly stronger and residually scattered stellar signal. While this process can be performed optically, i.e. distinguishing and blocking the stellar light from ever striking the CCD detector, this will require

Chapter 1. Introduction additional special observing techniques (see Section 2.2.3) or equipment currently only available on a select few telescopes (e.g. Coronagraphs, cf. Fischer et al. 2014). Instead, it may be easier to use post-processing methods to extract the planetary spectrum from images containing both the aforementioned one and a stellar signal. Algorithms that are able to recognize and separate the stellar signal from a planet or disk will likely become more advanced and widely used in the future as techniques such as HDS and HCI are developed further. This thesis will investigate just such a method, to see how well it performs the necessary steps to extract the planetary spectrum.

Computational spectrum extraction algorithms have been developed in tandem with CCD detectors and digital image processing for many decades now, leading to advanced methods able to optimally extract the spectra from noise-filled images and faint object sources. With the introduction of high dispersion, echelle spectrographs on many of the largest observatories in the world, techniques for the reduction of spectra produced by such instruments have been formulated many times (cf. Robertson 1986; Horne 1986; Marsh 1989; Piskunov 1995; Piskunov & Valenti 2002). Software for data extraction and analysis is constantly being updated and modernized as improvements are made to instrumentation and observing techniques.

The concept of the optimal spectrum extraction algorithm was introduced by Horne (1986), and many modifications to the method or other techniques built on it have been created since. Horne’s method (described more thoroughly in Section 3.1) involves constructing a spatial profile of the star for every pixel corresponding to the same wavelength in an image row or column. The pixels are then divided according to an estimated extracted spectrum at that wavelength, yielding a spectral reference image of the stellar spatial profile (or point spread function, PSF) for each wavelength which can be used to reduce the statistical noise of an extracted stellar spectrum while preserving the accuracy of the measured flux.

Studies on how to improve Horne’s method have been described by a number of authors. Marsh (1989) altered the algorithm such that it could handle those spectra with a large tilt that cross over many rows or columns in the detector image, something that Horne’s algorithm faltered on. Here, they applied polynomial fits along the spectrum which described the changes in the spatial profile across the image, modifying the extracted spectrum as necessary. Piskunov & Valenti (2002) created an additional algorithm for optimal extraction, based on the original formulae, where the spatial profile creation for each wavelength was handled differently. This method finds the best fit to the two-dimensional stellar spatial profiles through an iterative algorithm, which constructs stellar spatial profiles through linear interpolation and averaging of several wavelengths using an empirically determined mean profile for each wavelength.

Chapter 1. Introduction

Whilst the mentioned extraction methods have been shown to be very effective at extracting the spectrum of stars and other bright sources (e.g. Valdes 1992), approaches to exoplanetary spectra detection are far from refined. Let us assume we have a spectral image of a stellar system with one known planet at a given spatial separation, such as the one seen in the left panel of Figure 1.4 below. At each wavelength in the spectral direction, we will have a spatial profile of the stellar point spread function and a contribution from the planetary signal. An extraction algorithm for the planetary spectrum would have to remove the stellar contribution at every spectral position, leaving only the planetary spectrum for later summation and extraction of a one- dimensional spectrum.

Figure 1.4: The left part of the figure shows a spectral image of the 훽 Pictoris system. The spectrum of the star is shown as a dark line at the centre, with the spatial direction on the y-axis and the spectral direction on the x-axis. Each column at a particular wavelength in the spectral direction will contain a stellar spatial profile, i.e., the change of the signal from the star with angular position, blurred out over many milliarcseconds, shown in the right part of the figure.

Section 1.3. Project Overview

The goal of this thesis is to devise a new spectrum extraction algorithm and determine how well the method is able to extract the spectrum of an exoplanet in orbit around an extrasolar system. To perform this investigation, we use both observations of the star Beta Pictoris and a simple modelled planetary spectrum to examine the algorithm. The Beta Pictoris stellar system is host to both a debris disk and one known exoplanet, Beta Pictoris b, which have both been extensively observed and studied previously. As such, their position and separation from the star are known to high precision, greatly simplifying the search for the planetary spectrum in the combined spectra of the entire system. The observations of Beta Pictoris were made at the Very Large Telescope in the near-infrared (NIR) K-band part of the spectrum by using the CRIRES instrument. 9

Chapter 1. Introduction

This project will involve direct imaging methods of the stellar system, meaning there are other requirements and difficulties than for spectra extraction during transits. Detecting the circumstellar material requires special techniques, as well as high angular and high spectral resolution images, to achieve a high enough contrast sensitivity towards the star. By implementing and modifying an optimal spectrum extraction algorithm described in Horne (1986), we attempt to extract the spectrum of the system to improve the detection of circumstellar emission from both disks and planets. This can be achieved by separating the stars and the planets, or alternatively the stars and the disks, spectra into different components to further increase contrast sensitivity.

As with any method, there are problems that have previously been recorded with spectra extraction of directly imaged planets and disks that would have to be solved. By using the optimal extraction algorithm, we hope to solve some of those difficulties. The main limitation lies with reducing most or all of the light from the star, leaving only the light from the planet remaining. This can be achieved by creating a reference spatial profile of the stellar PSF as a function of wavelength, which is then subtracted from the actual stellar spectrum. Similar methods have been used previously to detect spectral lines from the disk (Brandeker et al. 2004) and the planet (Snellen et al. 2014) in orbit around Beta Pictoris.

In the future, state-of-the-art high-resolution spectrographs will further enable spectroscopic studies of exoplanets and their atmospheres with the potential of discovering signatures of life. These instruments will enable investigations of the chemical composition of atmospheres of exoplanets at currently unattainable sizes, orbital distances, and brightnesses. Many such spectrographs are planned for commissioning soon, including the CRIRES+ upgrade to the VLT (see Section 5.1.3) and the HIRES and METIS spectrographs for ESO’s upcoming European Extremely Large Telescope (E-ELT). When such instruments begin observations, it is important that methods already exist and are well-understood for how the spectrum of an exoplanetary atmosphere is extracted from a spectral image of the stellar system. This is the main motivation for this project, as we expect that these techniques will be highly sought after and necessary for future spectroscopic studies.

In the following chapters of this thesis, we describe the work that was done and all of the necessary information to understand the goals and methods for the project. In Chapter 2, we begin with a background discussion to some of the more common methods for detecting extrasolar planets, debris disks, and their respective spectra, as well as which advantages and limitations exist for the various methods.

Chapter 1. Introduction

In Chapter 3, the theory behind the optimal spectrum extraction algorithm studied for this thesis is described, how the stellar PSF can be used to subtract the stellar light from spectral images, and how to extract the exoplanetary spectrum.

In Chapter 4, we go into specific detail as to how the various steps of the algorithm are implemented, including formulae to establish the operations performed on the spectral images and figures which demonstrates how they affect the observational data. In addition, we account for some of the known problems and limitations with the algorithm taken into consideration.

In Chapter 5, information about the observational data and models treated and tested for our extraction algorithm in this thesis is provided. We also describe the instrumentation used to take the images, the extrasolar system (Beta Pictoris) that was studied, and how the images were processed and reduced to enable their use during the project.

In Chapter 6, the results of the spectrum extraction algorithm are presented for the various methods and cases of observational data we employ for the process.

In Chapter 7, we discuss our results and how well the algorithm performed, which potential uses there may be for it, which problems were encountered, and possible improvements that can be made in the future, along with plans for additional research into the subject.

In Chapter 8, the thesis is ended with a summary of the methods and results and any conclusions that can be drawn from these.

Chapter 2.

Detection of Circumstellar Objects and Spectra

In this chapter, we describe and discuss the most common methods for detecting exoplanets, debris disks, and their respective spectra. We will also go through the various advantages and limitations of each method.

Section 2.1. Exoplanet and Debris Disk Detection Methods

Section 2.1.1. Debris Disk Infrared Excess

Circumstellar debris disks were, unlike exoplanets, never objects that astronomers actively searched for. The first evidence of a debris disk only occurred during a routine calibration observation of the A0V main sequence star Vega (Aumann et al. 1984), when the infrared satellite IRAS observed a large infrared excess at wavelengths longer than 12 휇푚, seen in Figure 2.1. The emission excess was far higher than could be produced by the star itself and was originally attributed to a ‘shell’ of dust around the star. Soon after, the same excess IR emission was discovered in the Spectral Energy Distribution (SED) of three more main sequence star; Beta Pictoris, Fomalhaut, and Epsilon Eridani (Gillett 1986).

The excess emission is now known to be a result of cold dust absorbing and re-emitting stellar light in the infrared wavelengths (Plets & Vynckier 1999). Debris disks are typically too old to be a remnant of proto-planetary disks used for planetary formation, as they are only found in stars that are older than 10 Myr (Backman & Paresce 1993). This would be inconsistent with the small sizes of the dust (< 100 휇푚) (Paresce & Burrows 1987), which usually have short lifetimes of only a few million years due to Poynting-Robertson drag and collisions.

Chapter 2. Detection of Circumstellar Objects and Spectra

Figure 2.1: Infrared SED of the star Vega. The dashed line represents the expected flux density of a 500 K blackbody, while the solid line shows an 85 K blackbody spectrum fitted to the excess emission found at 휆 > 12 μm. Image credit to Aumann et al. (1984).

The circumstellar dust glows at low temperatures of ~ 30 − 100 K, corresponding to a peak in spectral radiance at a wavelength between 30 and 100 μm with an average at approximately 70 μm (Bryden et al. 2009), which lies in the far-IR where most debris disks have been detected. Since their first discovery, many different space telescopes have observed in the far-IR (IRAS, ISO, Spitzer, Akari, Herschel, Spica), so far finding several hundred main-sequence stars with an excess of IR emission (Rhee et al. 2007). To detect the emission, large catalogues of main sequence stars are used and observed, and the estimated stellar contribution in the infrared is compared to that a known nearby infrared source or a model of a stellar atmosphere. If the star shows a significant excess, typically of 3 times larger SED than expected, there may be a debris disk present that necessitates further study (Rhee et al. 2007; Bryden et al. 2009). The excess emission criterium is shown in Formula 2.1 below, where 퐹퐼푅 is the flux in the infrared,

퐹푝ℎ표푡 is the estimated total photospheric flux, and 휎퐼푅 is the estimated IR flux density error. Figure 2.2 below it shows the spectral radiance of a black-body dust grain glowing at two separate temperatures, simulating dust grain emission.

퐹퐼푅 − 퐹푝ℎ표푡 > 3.0 (2.1) 휎퐼푅

Chapter 2. Detection of Circumstellar Objects and Spectra

Figure 2.2: Black-body spectrum of dust grains glowing at temperatures of 30 K (blue line) and 100 K (red line). Dust grains found between these temperatures will have their peak emissions in the 30 − 100 μm range, precisely where the excess infrared emission has been found surrounding many stars, indicating the presence of such dust particles in debris disks.

Section 2.1.2. Doppler Effect Spectroscopy

The usage of Doppler spectroscopy to detect exoplanets is the oldest successful method for detecting extrasolar planets, and was for a long time the most effective one as well. The first exoplanet ever found around a main-sequence star, 51 Pegasi b, was discovered by this method (Mayor & Queloz 1995), and since then the total amount of discoveries number in the 600s (NASA Exoplanet Archive2). While no longer responsible for the highest amount of detected exoplanets, it remains the most reliable for large surveys of stellar systems.

The technique, also commonly called the radial-velocity method, uses the reflex motion of the parent star, incurred by the planet’s gravity, to measure the projected velocity of the star along the line-of-sight with regards to the observer. The shift in velocity back and forth around the two object’s centre of mass gives rise to a displacement of the spectral lines in the spectrum of the star due to the Doppler Effect. By measuring the displacement, we learn of the possible presence of the exoplanet and some of its properties (Fischer et al. 2014; Reiners et al. 2010). The star’s radial velocity can be calculated by means of the Doppler shift formula seen in Formula 2.2:

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Chapter 2. Detection of Circumstellar Objects and Spectra

Δ휆 푣 = 푅 (2.2) 휆0 푐

Here Δ휆 is the shift in the wavelength of the spectral lines, 휆0 is the wavelength of the source at rest, 푣푅 is the radial velocity of the object, and 푐 is the speed of light. As the planet moves around the parent star, the orbital motion of the star will regularly oscillate towards and away from the observer, and by measuring the wavelength shift at fixed intervals the radial velocity of the star can be calculated as a function of time. An example of this can be seen in Figure 2.3 below, where the orbital motion of the star 51 Pegasi was measured by Mayor & Queloz (1995), indicating the first extrasolar planet.

Figure 2.3: Radial velocity of the star 51 Pegasi as a function of periodic motion. The period of the star was found to be 4.23 days, meaning the planet orbits very close to the star, while the radial velocity of ± 60 m s-1 indicated that the planet was a massive gas giant due to the large velocity oscillations. Image credit to Mayor & Queloz (1995).

The precision with which the Doppler spectroscopy method can measure the radial velocity of a star has improved from ~ 10 m s−1 in 1995, to 3 m s−1 in 1998, and finally to 1 m s−1 in 2005 with the installation of the HARPS spectrograph at La Silla Observatory in Chile (Mayor et al. 2003; Fischer et al. 2014). This corresponds roughly to the ability to measure the Doppler effect of a sun-like star induced by a planet of 5 Earth masses at an orbital distance of ~ 0.2 AU, or a Neptune-size planet orbiting at ~ 2 AU. A visual example of this can be seen in Figure 2.4, where the detectable limits of a 1 m s−1 spectrograph are shown for planets of different masses and orbital distances, orbiting a 1 푀⊙ star.

Chapter 2. Detection of Circumstellar Objects and Spectra

Figure 2.4: Illustration of which types of planets are detectable with modern spectrographs using Doppler spectroscopy. Planets of masses and orbital radius above the line are detectable, while those below are not. Some planets from the Solar System are also shown to give an idea of which kinds of planets can be found. The largest gas giants are easily detectable, the ice giants almost so, while the rocky planets are far too small and orbiting too distantly.

While the method is effective at detecting planets and can even be used to reveal their period, semi-major axis, eccentricity, as well as a lower limit to their mass, it does not provide any information about the spectrum of the planet (Lovis & Fischer 2011; Fischer et al. 2014). One of the many other techniques of exoplanet detections must, therefore, be used to perform spectroscopy on the planet itself.

Section 2.1.3. Primary and Secondary Transit

The currently most effective method at detecting exoplanets is through transit photometry, where a planet transiting the parent star’s disk will dim the light from a star and cause an observable drop in its brightness. The method, first used to detect the planet HD 209458b in 1999 (Charbonneau et al. 2000; Henry et al. 2000), as seen in Figure 2.5 below, had only managed to find nine transiting planets by 2007, compared to almost 200 via Doppler spectroscopy (Charbonneau et al. 2007). Since then, it is now responsible for a majority of all discovered exoplanets, mostly through the enormous success of the Kepler Space Telescope, launched in 2009 (Borucki et al. 2010).

Chapter 2. Detection of Circumstellar Objects and Spectra

Figure 2.5: The light curve of the star HD 209458 showing a dimming of the relative flux of the star during a transit event in 1999, the first discovered extrasolar planet through the transit method. During the ingress and egress, the flux drops almost linearly, followed by a mostly constant transit of the stellar disk. Image credit to Charbonneau et al. (2000).

When the planet transits the star, the light curve is altered in the measured flux, noticeable for its approximately square-well shape indicating an object moving into, over, and out of the stellar disk. The fractional decrease of the stellar luminosity (Δ퐿) due to a transit is approximately proportional to the difference in radii of the planet

(푅푃) and star (푅∗), neglecting any other brightness variations such as limb darkening or sunspots, and is described by Formula 2.3 (de Pater & Lissauer 2015):

Δ퐿 푅 2 = ( 푃) (2.3) 퐿 푅∗

While there are a number of difficulties with the model regarding the probability of observing a transit (see Sections 2.3.1), it is possible for space-based telescopes to cover a large fraction of the sky and observe thousands of stars at once (e.g. 150 000 for Kepler (Borucki et al. 2010) and 12 000 for CoRoT (Barge et al. 2008)). An added benefit is that transits will always be periodic, making them easily distinguishable from other variabilities in stellar luminosity with precise enough measurements.

Chapter 2. Detection of Circumstellar Objects and Spectra

A second transit method for detecting extrasolar planets was reported a few years after the first (Charbonneau et al. 2005; Deming et al. 2005), called a secondary transit or eclipse. During such an event, the planet is blocked by the star and only the stellar light can be seen over the whole system. Given that the planetary brightness is much fainter than that of the parent star, the fractional decrease in luminosity will be much smaller than for a primary transit, but with the added benefit that the secondary eclipse will be equally periodic and occur roughly half of an orbital period after the first transit for a circular orbit. If a planet is suspected to transit a star and the orbital period is known, the secondary eclipse can be more easily investigated. An illustration of the difference between the two types of transits can be seen in Figure 2.6.

Figure 2.6: Illustration of the two possible types of transits/eclipses which can be seen for an exoplanetary system. During a primary transit, the planet blocks the star while allowing the stellar light to pass through the planet’s atmosphere. A secondary eclipse occurs when the star blocks the planet, and any scattered light from the planet’s atmosphere disappears from the flux of the entire system. Image recreated from work by S. Seager.

Section 2.1.4. Direct Imaging

Exoplanets are extremely faint in comparison to the much brighter stars they orbit, making them incredibly difficult to detect by direct means, which is also the reason why the first methods pioneered are indirect methods (Doppler spectroscopy, transit photometry). Directly imaging exoplanets is a comparatively newer method, with the first exoplanet directly observed being discovered orbiting the brown dwarf 2M1207 in the mid-2000s (Chauvin et al. 2004). Since then, only a few dozen more exoplanets have been directly imaged due to the limitations of the method (~ 44 as of January 20193).

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Chapter 2. Detection of Circumstellar Objects and Spectra

To directly image a planet, high angular and high spectral resolution detectors with adaptive optics are used to resolve them from the parent star and identify the relatively faint planetary signal. Compared to the planet, the stellar flux is many magnitudes brighter, making the two hard to separate if the planetary orbit or radius is too small. This method is, therefore, primarily only sensitive to large, hot, planets in wide orbits of 푎 > 5 AU (Fischer et al. 2014).

Figure 2.7: Modelled intensity comparison of planets and the Sun in the Solar System showing the energy distribution of Jupiter, Venus, Earth, and Mars. The optimal wavelengths for observations to improve the contrast ratio between a planet and the star is in the infrared, where the star begins to decrease in intensity. Particularly at ~ 20 μm the contrast ratio increases by 3 – 4 orders of magnitude compared to visual wavelengths. Image credit to Des Marais et al. (2002).

One technique used for improving the contrast sensitivity involves observing the system in the near-infrared or thermal infrared regions, as the flux ratio between the planet and the star is not as disadvantageous there as it is in the optical wavelengths, leading to an increase in contrast of approximately 3 orders of magnitude (de Pater & Lissauer 2015), as can be seen in Figure 2.7. Direct imaging of exoplanets for spectroscopic detections is, therefore, typically done in the 1 − 5 μm wavelength range. Even then, the imaging process requires a number of other observational and computational strategies to further reduce the starlight, remove artefacts and optical imperfections,

Chapter 2. Detection of Circumstellar Objects and Spectra and increase the contrast sensitivity even further (Lagrange 2014). With the current capabilities of instruments, observations are only targeting gas giants in wide orbits around young, nearby stars.

Even when extrasolar planets are observed with high-contrast imaging in the infrared, the planet is typically still too faint to resolve and is lost in the parent star’s scattered light. Other methods can instead be used where the light from the star is nearly or completely subtracted, for example by use of a theoretical point spread function (PSF). The PSF describes the shape of the signal from a star and planet, where the two objects will have their individual PSFs at separate locations and found on top of each other in the spectrum of the entire system. With specific techniques, discussed in Section 3.2, the stellar PSF can be used to construct a reference spectrum of the star, i.e. an expected theoretical stellar spectrum, which can later be used to remove the starlight and leave the reflected or thermally emitted light from the planet visible (Snellen et al. 2014; Brogi et al. 2012, 2013; Rodler et al. 2012; de Kok et al 2013). Direct imaging of exoplanets is the observational method studied in this thesis, where we investigate how an algorithm may be created that enables the scattered stellar light to be subtracted and direct spectroscopic analysis of the planet and its atmosphere be performed (see Section 3.1 and 3.2).

Section 2.2. Spectrum Observation Methods

Section 2.2.1. Primary Transit Spectroscopy

Ever since the first detection of an exoplanet, one of their most coveted physical properties is the spectrum of the planet. Through any potential spectral lines found, it is possible to determine much about the atmosphere and surface of the planet, including the presence of very interesting molecules such as water, oxygen gas, ozone, carbon monoxide, carbon dioxide, and methane. Hopefully, spectroscopy of exoplanets may eventually even lead us to the first signs of extra-terrestrial life. Therefore, many attempts at creating methods for exoplanetary spectroscopy have been made, with one of the most successful being primary transit spectroscopy, so far responsible for many dozens of extrasolar planetary atmospheres characterized (Seager & Deming 2010).

During the primary transit period, transmission spectroscopy can be performed on the atmosphere of a transiting exoplanet. Unlike for direct imaging spectroscopy, where photons scattered off the planetary surface may also be detected, transmission spectroscopy only reveals the spectrum of the actual atmosphere. As the planet passes over the stellar disk, the starlight travels through the atmosphere, and some specific

Chapter 2. Detection of Circumstellar Objects and Spectra wavelengths are absorbed by any molecules present while others are not. By measuring which wavelengths are able to penetrate the atmosphere, an absorption spectrum can be produced, revealing the chemical composition of the atmosphere. An example of this is shown in Figure 2.8 below. This method of spectra extraction has been used to find absorption lines from element such as sodium in the atmosphere of the planets HD189733b (Wyttenbach et al. 2015), WASP-49b (Wyttenbach 2017), and HD209458b (Charbonneau et al. 2002), the latter being the first detection of a chemical element or molecule in the atmosphere of an exoplanet.

Figure 2.8: Light curves for a transit event of the planet HD 209458b at 10 separate wavelength ranges, beginning at 293 nm (purple) and ending at 1019 nm (red), normalized to the shortest wavelength. The ten bandpasses all display amplitude depths of varying strengths, suggesting that some wavelengths are absorbed easier by planetary atmospheres, which can be used to infer molecular presences. Image credit to Knutson et al. (2007).

By measuring the light curve of the star during the primary transit over many different wavelengths, we can use the difference in the decrease of brightness between the varying spectral regions to infer a wavelength dependence on the atmospheric transmittance. The transmittance can then be used to create an absorption spectrum of the atmosphere of the exoplanet, revealing any chemicals present (Knutson et al. 2007).

Chapter 2. Detection of Circumstellar Objects and Spectra

Section 2.2.2. Secondary Eclipse Spectroscopy

In addition to the primary transit of an exoplanet, the secondary eclipse can also be used to perform spectroscopy on the planet and may complement the observations performed during the former. During the eclipse, the planet is completely obscured by the star and no light reflected or emitted from the planet will be seen in the spectra of the system. A light curve, much like one during a primary transit, can be constructed by observing the system at the moment of the eclipse and by measuring the decrease and increase in light when the planet is obscured and later re-emerges. A wavelength- dependent light curve will then show which specific wavelengths are dimmed during the eclipse, similar to what is seen in Figure 2.8, allowing for the identification of spectral lines in the atmosphere of the planet (Sudarsky, Burrows, & Hubeny 2003).

Two extrasolar planets in particular, HD189733b and HD209458b, have been extensively studied by means of their secondary eclipses with very promising results. Observations of the two planets with the Hubble Space Telescope (HST) and the

Spitzer Space Telescope (SST) has revealed the presence of molecules such as H2O, CO, CO2, and CH4 in the atmospheres of both HD189733b (Swain et al. 2008, 2009b; Tinetti et al. 2007; Charbonneau et al. 2008; Knutson et al. 2008) and HD209458b (Swain et al. 2009a; Madhusudhan & Seager 2009; Deming et al. 2013). Similar to the direct imaging method for detection of exoplanets and their spectra, the secondary eclipse method requires the planet to be, at the very least, present in the same region that is observed as the star, as the combined light of both objects must be visible before the eclipse. Much like for directly imaged exoplanets, the most favourable wavelengths to observe are the near- and mid-infrared, providing the highest contrast ratios between the planet and stellar flux (Burrows 2005). At these wavelengths, contrast may improve by a factor of ~ 10 − 100 as compared to visible light (Burrows, Sudarsky, & Hubeny 2006), as seen in Figure 2.9, making space-based telescopes observing in the infra-red, such as the SST and upcoming James Webb Space Telescopes (JWST), the optimal platforms for spectral analysis of transiting and eclipsing extrasolar planets.

Chapter 2. Detection of Circumstellar Objects and Spectra

Figure 2.9: Logarithm plot of the planet/star contrast ratio for the flux density of five large extrasolar planets at wavelengths from 0.5 − 30 μm. The ratio is most favourable in the > 10 μm regions, and optical light can be as low as three orders of magnitude fainter than the near- and mid-infrared. Image credit to Burrows, Sudarsky, & Hubeny (2006).

Section 2.2.3. HDS with Direct Imaging (Exoplanet)

As stated earlier, this thesis deals with the spectroscopy of exoplanets (and other circumstellar objects) directly imaged using high-dispersion instruments and high- contrast imaging telescopes. The largest issue when directly imaging exoplanets has already been discussed; the contrast ratio between the flux of the star and the planet. Regardless if one wants to simply detect the planet by a visual inspection of an exposure of the entire system or perform spectroscopy on the planet, the stellar light needs to be, at the very least, heavily reduced for the light from the planet to become distinguishable (Fischer et al. 2014). There are a number of additional ways that the SNR of the planetary signal and star/planet contrast ratio can be improved, such as observing the stellar system in the near-infrared (see Section 2.1.4), combining high- dispersion with high-contrast imaging, or usage of a coronagraph to block the stellar light before it reaches the detector (see, e.g., Kuchner & Traub 2002).

An observation to simply detect the planet and find its spatial position (e.g. Lagrange et al. 2009a, b, 2010; Marois et al. 2008, 2010) is treated somewhat differently than a

Chapter 2. Detection of Circumstellar Objects and Spectra two-dimensional spectral image of the system used to extract the spectrum of the exoplanet. Performing spectroscopy of the exoplanet requires the slit of the spectrograph to be oriented in such a way that it encompasses both of the planet and the star in a two-dimensional spectrum, where intensity as a function of wavelength is found in one dimension of the images and the spatial position in the other (Snellen et al. 2014). In Figure 2.10 below, it is shown how the two spectra of the objects are typically located in a high-dispersion spectral image of an exoplanetary system.

Figure 2.10: Example of a small section of a spectral image of an exoplanetary system. Here the spectral direction is located on the x-axis and the spatial position is located on the y-axis. In the centre, a very bright signal from the star exists, and a few pixels below in the spatial direction we find the planet, obscured by the scattered stellar light.

In such a spectral image, the star will have one very strong signal across the wavelength direction with the planet having a weaker one a few pixels away in the spatial direction, depending on the angular size of each pixel and orbital distance of the planet. In the case of the Beta Pictoris system, used for this thesis, the planet is located only 4 − 5 pixels below the star in an exposure similar to Figure 2.10 and should have a separate spectrum covering the length of the image obscured by the stellar light. In the infrared, the exoplanet is potentially stronger than the collective noise, and if the stellar profile is removed at every position along the image, the spectra of the planet should remain for extraction. In Figure 2.11 below, a model spectrum of the star and planet can be seen in both a surface plot of the entire spectral image and at one particular wavelength showing a spatial profile of the system.

Chapter 2. Detection of Circumstellar Objects and Spectra

Figure 2.11: Model spectral image of an exoplanetary system with a planet and a parent star. The left panel shows a surface plot of the entire image, comprised of many profiles along the spectral direction, increasing in flux towards the centre of the spectrum. Each profile along the spatial axis (referred to as a spatial profile from here on) contains the signal from the entire system at one particular wavelength. One of the profiles can be seen in the right panel, where the signal from the star is located at the centre, blurred out across several arcseconds. A second, fainter signal from the planet will be overlaid on top of the stellar signal which may be seen as a ‘bump’ in the profile. However, this model is highly exaggerated and the planetary signal will not be as strong as what is shown here.

Given that both of the objects have to be present in the slit during the observations, it would be highly difficult to separate the two spectra if the planetary orbit is very small. If the angular separation is too short, the light reflected or emitted from the planet may simply be added to the stellar light, and any reduction in the brightness of the star subtracts most or all of the planetary light as well. A stellar light reduction must remove as little of the planets photons as possible so as to not worsen the SNR more than necessary. As stated earlier, direct spectroscopic methods are currently only sensitive to planets in orbits wider than 푎 > 5 AU (Fischer et al. 2014; Lagrange et al. 2009a, b), although the further out the planets orbit, the better the contrast ratio will most likely be, as we expect young planets to be mostly self-luminous and reflect only a small amount of light. The cut-off point for how closely orbiting planets can be characterized is not well studied as of yet, but direct spectroscopy of the planet Beta Pictoris b, orbiting at ~ 9 AU (Lagrange et al. 2010) has been successfully performed previously (Snellen et al. 2014; Bonnefoy et al. 2013, 2014; Morzinski et al. 2015).

As described in Section 2.1.4, one of the most effective methods for removing stellar light in high-contrast direct images of exoplanetary systems is by utilizing the stellar

Chapter 2. Detection of Circumstellar Objects and Spectra

PSF to create a reference spectrum of the star. This spectrum is an attempt to model how the light from the system would appear in the spectral image without a contribution from the planetary spectral lines and can be constructed by various computational processes. One common method is the use of Angular Differential Imaging (ADI, Marois et al. 2006), a technique where the instrument field de-rotator is switched off as a sequence of images are taken with an altitude/azimuthal telescope, allowing for a rotation of the field of view while the instrument and optics stay aligned. This provides several images where the star and planet are rotating with regards to previous exposures instead of being perfectly aligned, and a reference PSF can be created for each image. The ADI method described by Marois et al. 2006 then takes the median of four of the closest PSFs with a large enough angular rotation in order to avoid subtracting the planetary signal as well. The optimized reference PSF can then be subtracted from the median of all images to reduce all of the stellar light.

This method has proved very useful in detecting and performing spectroscopy on extrasolar planets, including those in well-known systems such as HR 8799 (Marois et al. 2008, 2010) and 51 Eridani (Samland et al. 2017). Another method previously utilized to perform a stellar PSF reduction is Spectral Differential Imaging (SDI) (Smith & Terrile 1987; Racine et al. 1999; Marois et al. 2000; Sparks & Ford 2002). This technique takes advantage of the exoplanet’s large intrinsic molecular features that are often missing from the mostly flat parent star spectrum (Vigan et al. 2010). Two exposures are made of the system simultaneously at close wavelengths near one such feature and subtracted from each other, reducing parts of the stellar contribution. SDI is most effectively used when the exoplanet is colder than usual and display deep absorption lines from molecules such as H2O or CH4, and has previously successfully been utilized to detect and characterize exoplanetary companions (Biller et al. 2007; Apai et al. 2008; Close et al. 2014).

These are, however, not the methods we use to construct a reference stellar PSF and perform exoplanetary spectroscopy in this thesis. Instead, we have built on and developed an extension of the spectrum extraction algorithm for an astronomical object described in Horne (1986) (see Section 3.1). This method uses the pixel rows closest to each pixel in the object spectrum to construct a reference version of the stellar PSF (see Section 3.2) to remove the contribution from the star while leaving that of the planetary spectral lines. Similar versions of this method have been used previously to perform exoplanetary spectroscopy (Snellen et al. 2014), and a thorough description in detail is provided in Chapter 3.

Chapter 2. Detection of Circumstellar Objects and Spectra

Section 2.2.4 HDS with Direct Imaging (Disk)

While this thesis primarily focuses on exoplanetary spectroscopy, it is equally important to understand how to perform the analysis on a debris disk surrounding a star. It is expected that extracting the spectrum of such a disk can be done in a similar matter by using high-dispersion direct imaging. Debris disk observations share many similarities to those of exoplanets, as the disk is typically much fainter than the star and requires approaches that are akin to those described in Section 2.2.3. One advantage of observing debris disks over exoplanets is that the disks typically extend over many hundreds of astronomical units. For example, the Beta Pictoris circumstellar disk measures out to 1835 AU from the star in the north-eastern direction, and 1450 AU in the south-western (Larwood & Kalas 2000). While this could potentially suggest more easily performed spectroscopy than for closely orbiting exoplanets, there are other difficulties that must be addressed. One major limitation comes from the low reflectance of stellar light from the cold dust in the disks at very large orbits, making observations harder at large distances. The dust will instead glow with thermal emission, although this mostly occurs in inner parts of the disk, and not the extended halo at higher radii (Matthews et al. 2014). In Figure 2.12 it can be seen how the dust temperature and peak thermal emission wavelength changes with the radii of the debris disk. The different components of the disk may, therefore, be best observed at different wavelengths to yield the highest contrast ratio and SNR, with shorter wavelengths more pronounced at closer radii.

Figure 2.12: Illustration detailing the five different zones in an exoplanetary system where debris dust can be found. As the distance from the star increases, the dust glows at decreasing temperatures due to the lower amounts of sunlight reflected off the dust, and the peak emission occurs at increasingly longer wavelengths. Image credit to Su & Rieke (2013).

Chapter 2. Detection of Circumstellar Objects and Spectra

In addition, the most interesting sections of the debris disk to study are the planetary formation zones, where traces of molecules may be found that reveal the chemical composition of the early solar systems (e.g. Roberge et al. 2006; Dent et al. 2013; Brandeker et al. 2016). The further inside the stellar system we observe, the more can be understood about the system’s stellar properties, planetary formation, and evolution of the debris disk. While the thermal emission of the dust is much stronger at shorter radii, the stellar light is also more substantial and may block out the circumstellar emission. Much like for an exoplanet, it is, therefore, necessary to subtract the scattered light from the star, either with a PSF (Brandeker et al. 2004; Dent et al. 2013) or another method. It is expected that a reference PSF can be constructed in a similar way to those already described (Section 2.2.3), or the one used in this thesis (Section 3.2), though it will not be attempted. In the following section, the various advantages and limitations of each spectrum extraction method are discussed.

Section 2.3. Spectrum Observation Advantages and Limitations

Section 2.3.1. Primary and Secondary Transits

The main advantage of transit spectroscopy is the fact that a large number of stellar systems can be observed for long periods of time. Space-based telescopes can be pointed at the same population of stars for many years and potentially observe a multitude of transits for each exoplanet. By having more observations of transit occurrences available the results will yield more reliable data of the planetary flux than for methods where single systems are examined at only one particular time. Another major benefit to transit measurements as compared to direct imaging is that the stellar light does not need to be subtracted, as we observe the entire star’s spectrum to also see the transit depth in the light curve. It is typically quite easy to detect the transit in the spectrum of a star, as the shape of the transit event is nearly always a similarly distinguishable box-shape (Charbonneau et al. 2008).

Difficulties with primary transit spectroscopy do exist as well and can affect our ability to derive results from the transit event. Stellar activity, such as sunspots, has been known to affect the light curve of a star, either to the point of being mistaken for a transit event, or to changing the observed transit depth in the case of the activity being right along the transit path (Carter et al. 2011; Sing et al. 2011). In Figure 2.13, the effect a sunspot may have on the light curve of a transit event is shown.

Chapter 2. Detection of Circumstellar Objects and Spectra

Figure 2.13: Light curve during the transit of the planet GJ 1214b, showing a suspected sunspot affecting the measurements. The solid line details the fit to the expected light curve, while the circles show the actual measurements, which do not follow the model closely at certain parts. Image credit to Carter et al. (2011).

The largest limitation of the method with regards to spectroscopy is the fact that only a small fraction of the stellar light is blocked by the planet during transit, with an even lower amount actually passing through the annulus of the atmosphere surrounding the planet. The atmospheric scale height describes how the atmospheric density decreases with outwards distance and is used to determine the atmospheric height (Lecavelier des Etangs et al. 2008). The scale height depends on the temperature, mean molecular weight, and gravity of the planet and its atmosphere, signifying that a cold planet with a high gravity will contain an atmosphere rapidly diminish with altitude and not many absorptions will have time to occur. To further restrict the possibility of spectroscopic measurements, only some of that fraction of light will actually be absorbed by molecules in the atmosphere and re-emitted towards Earth. In addition, for some wavelengths the atmosphere will be completely transparent as the absorption cross-section of certain molecules will be wavelength-dependent (Venot et al. 2013).

There are additional limits to how many transiting planets can be observed that we can perform spectroscopy on simply due to the sheer geometric transit probability. The probability of a transit event occurring relative to the observer is determined by the geometrical properties of the planetary system. Only a very small fraction of exoplanets will transit their parent star in the line of sight to any observer, depending on the orbital eccentricity, orbital radius, and stellar radius. The transit probability can be described by Formula 2.4 for an exoplanet in an eccentric orbit (Winn 2010).

Chapter 2. Detection of Circumstellar Objects and Spectra

(푅∗ + 푅푝) 푝 = (2.1) 푎(1 − 푒2)

Due to the distance of exoplanetary systems, the formula will essentially only depend on three parameters; the stellar radius 푅∗, the orbital radius 푎, and the eccentricity 푒, and not the planetary radius. The transit probability formula can be seen illustrated in Figure 2.14 below, for a Sun-like star as a function of orbital radius. For a planet in an Earth-like orbit, the observed transit probability is less than 0.5 %, suggesting it would require observations of many stellar systems for long periods of time to observe such a transit. In addition, planets located in larger orbits than this will only transit once every few decades or longer, making observations highly impractical for any space- based telescope due to the very low probability and frequency. It can then be assumed that mostly planets with short orbital radii can be observed to transit.

Figure 2.14: Transit probabilities for planets orbiting a sun-like star at various radii in a circular orbit. We see that already at an orbit of 0.5 AU, the probability of observing a transit is less than 1 %, while at an orbit of 0.01 AU the probability is at 50 % due to the number of possible inclinations and eccentricities which allow for a transit event.

In addition to primary transits, secondary eclipse measurements and spectroscopy are best utilized when performed in collaboration with these observations. If an extrasolar planet will transit the star in the line of sight to an observer, there will also most likely be a secondary eclipse unless there is a particular orbital configuration which does not allow for it. Such a system would require the planet to have a significantly large

Chapter 2. Detection of Circumstellar Objects and Spectra inclination and eccentricity, which is highly unlikely for an exoplanet in a short orbit, i.e. the most common type of planet seen transiting. On the other hand, if the transit and eclipse are both seen at separate occasions, it will make constraining the orbital inclination and eccentricity easier if the precise time for the two events is well known (Pál et al. 2010).

Instead of observing a known-transiting exoplanetary system with the prospect of also discovering a secondary eclipse, it is usually more important to discover the timing of the event beforehand so as to not waste observation time if there is a long time in between the events. Eccentricity, periodicity, and inclination can be learned from radial velocity measurements that are best done first to determine the expected time of the secondary eclipse, if it even will occur.

A few other difficulties do exist for the method, many of them relating to the non- uniformity of the planetary surface and, subsequently, reflectance. If the planet is not a uniform disk, i.e. it reflects and absorbs stellar light differently across the planetary disk, the light curve will not necessarily be shaped in the same matter during the ingress and egress of the event (Majeau, Agol, & Cowan 2012), and a high deviation from the model case of secondary eclipses has been recorded for exoplanets previously (de Wit et al. 2012). An additional issue is the non-uniform temperatures of planets that decrease towards the limbs, making brightness measurements less accurate during the eclipse event and complicating the spectroscopic identification of spectral lines.

Section 2.3.2. Direct Imaging

Although much more difficult and limited in some matters, direct imaging spectroscopy of exoplanets can claim a number of advantages over primary and secondary transit methods. Since the photons observed are directly emitted or reflected from the planet, spectroscopic and photometric characterizations are highly more usable than those observed during transits. Direct imaging can provide high-quality images of extrasolar planets in multiple photometric bands that can be used to detect various molecules in the atmosphere, meteorological occurrences such as clouds or hazes in the upper atmospheric layers, and constrain other properties, e.g., temperature and surface gravity (Vigan et al. 2016; Zurlo et al. 2016; Bonnefoy et al. 2016).

Furthermore, with direct imaging, we can observe an entirely different sample of exoplanets than with other methods. Direct imaging is mainly used to image planets in high orbits of 푎 > 5 AU, far larger orbits than the transit and radial velocity method which, so far, are mostly only able to detect large planets in short orbits (Fischer et al. 2014).

Chapter 2. Detection of Circumstellar Objects and Spectra

While it is not currently the most reliable method, future space missions such as the JWST (Gardner et al. 2006) and WFIRST (Content et al. 2011, 2013) will greatly improve on direct imaging capabilities and provide images at wavelengths not accessible from ground-based telescopes. As of yet, there is no dedicated system for direct imaging, but once one is commissioned it is expected to rival the surveys performed by ground- based Doppler or transit missions in statistical significance. At the current pace of technological advancement, it is not unlikely that space-based telescopes using direct imaging and coronagraphy will be the first to discover an Earth-analogue orbiting in an extrasolar system.

Not only space-based missions are planned, however, as the European Extremely Large Telescope (E-ELT) is expected to begin observations in 2024. The E-ELT, an optical/near-infrared telescope with a 39.3-metre diameter primary mirror, is far larger and more capable than the VLT’s 8.2-metre mirror and will be used for exoplanetary sciences among other ventures. Additionally, the CRIRES+ upgrade to the CRIRES spectrograph (see Section 5.1.3) is planned for installation in 2019 and will further increase the contrast ratio of light gathering in extrasolar systems. When these instruments are completed, it is important that smart algorithms capable of reducing the stellar light and performing spectroscopy on the exoplanets automatically already exist that have been tested with our current capabilities. Investigating which methods work well or not will greatly speed up the process of exoplanetary spectroscopy in the future and is the main motivation for this project.

The largest technical drawback for direct imaging comes from the contrast ratio in the flux between the star and the planet. An exoplanetary system similar to our own solar system located 10 parsecs away would yield an approximate contrast ratio of ~ 10−9 at an angular separation of 0.5 arcsec between the star and a gas giant (Fischer et al. 2014). With our current instrumentation, combining high-dispersion spectroscopy with high-contrast imaging could potentially provide a flux ratio of 10−7; not enough to directly discern the planet from the star in the spectra. Instead, the stellar light must be subtracted in order for planetary spectroscopy to be performed. Perfectly subtracting the stellar light is a difficult task, and many techniques have been constructed to attempt it (see Section 3.2). An overview of the contrast ratios for the two combined techniques can be seen in Figure 1.3 in Chapter 1.

In order for high contrast imaging to be successful, several instruments and techniques can be deployed that allow for better contrast between planet and star. Some examples of these are adaptive optics, coronagraphy, differential imaging, and regular post- processing. Adaptive optics (AO) are systems used to prevent the atmospheric turbulence from affecting the propagation of light through the optics of the telescope and lower its spatial resolution at the diffraction limit. AO systems compensate for the

Chapter 2. Detection of Circumstellar Objects and Spectra common path defects of the optics and are imperative for the PSF to avoid deformation during observations that could potentially lower the contrast performance greatly. Coronagraphs are instruments mounted to telescopes that use optical methods to remove the stellar light from a star on-axis while letting the planetary light off-axis remain. A focal-plane mask is used that is similar to how a solar eclipse would work and blocks only the light from the star from being recorded by the CCD camera (Guyon et al. 2006). Differential imaging has already been discussed at length in Section 2.2.3, and other methods of post-processing will be described in Chapter 3.

As there is currently only one reliable method for detecting and performing spectroscopy on debris disks (detailed in Sections 2.1.1 and 2.2.4), it would be difficult to compare the advantages of the method to that of exoplanetary observations. Still, there are a few limitations to debris disk characterizations that warrant a mention. As previously discussed, the dust in the disks is detected by looking at the SED and observing an excess infrared emission at 30 − 100 휇푚 wavelengths. The reality is not this simple, in fact, as a number of dust properties will change the dust’s emissive properties. To begin with, the dust particles are not perfect blackbody emitters, and due to their size, shape, chemical composition, porosity, and cross-section distribution will instead emit light at higher temperatures (Matthews et al. 2014). Constraining the spatial distribution and grain composition is necessary to better understand the SED and may require observations at higher wavelengths of far-infrared and sub-millimetre to reveal the molecules present in the disks (Chen 2009).

Additional challenges exist with any ground-based observations that also must be accounted for with direct imaging spectroscopy. These can be atmospheric variations such as turbulence and seeing, absorption and scattering, and thermal sky emission, instrumental aberrations due to variations in thermal behaviour, optical paths, etc. Some of these will be discussed in Section 5.3, but many are well-known problems that are more thoroughly described elsewhere (e.g. Chromey 2010). In the following Chapter, we discuss the optimal spectrum extraction method, detailed in Horne (1986) and used as a basis for the planetary spectrum extraction algorithm constructed in this thesis.

Chapter 3.

Spectrum Extraction Theory

Section 3.1. The Optimal Spectrum Extraction Algorithm

Section 3.1.1. Algorithm Description and Overview

The spectrum extraction method used for this project is based on the optimal spectrum extraction algorithm presented in Horne (1986). This procedure was developed to deliver the maximum possible signal-to-noise ratio (SNR) while at the same time preserving spectrophotometric accuracy, a critical feature when performing directly imaged spectroscopy on extrasolar systems. When compared to conventional extraction methods, the optimal algorithm gives an improved SNR equivalent to a 70 % increase in exposure time, according to measurements performed in Horne (1986). The algorithm operates by applying weights to each pixel non-uniformly in the extraction sum so as to reduce the statistical noise in the extraction process. Extracting a standard spectrum by summing the sky-subtracted image over a range of pixels covering the object spectrum along the spatial direction will result in a noisier spectrum than necessary, as many pixels not part of the spectrum must be included in the summation process to preserve photometric accuracy. These pixels only contain a small amount of the light from the star (and planet) and thus contribute heavily to the statistical noise, but this issue is solved by the optimal extraction algorithm applying less weight to such pixels.

In this thesis, Horne’s algorithm is used as the basis for our spectrum extraction, although, since we must also reduce all or most of the stellar light, the procedure must be modified before a planetary spectrum can be extracted. We will nonetheless begin by a brief description of Horne’s algorithm. The optimal spectrum extraction algorithm covers nine different steps, of which the first four (Steps 1 – 4) are the standard extraction procedure, and the last five (Steps 5 – 9) are the additional steps to optimize the extraction. A brief summary of the formulae for the different steps in the extraction algorithm is shown in Table 1, while the images and quantities used in the formulae are described in Table 2 below.

Chapter 3. Spectrum Extraction Theory

Step Process Formula

1 Initial image processing 퐷 = (퐶 − 퐵)/퐹

2 Initial variance estimates 푉 = 푉0 + |퐷|/푄

3 Fit sky background 푆 = FIT푥[퐷; 푉]

4 Extract standard spectrum 푓 = ∑ (퐷 − 푆) 푥

Variance of standard spectrum var|푓| = ∑ 푉 푥

2 5 Construct spatial profile 푃 = FIT휆[(퐷 − 푆)/푓; 푉/푓 ]

Enforce positivity 푃 = MAX[푃; 0]

Enforce normalization 푃 = 푃/ ∑ 푃 푥

6 Revise variance estimates 푉 = 푉0 + |푓푃 + 푆|/푄

0 if (퐷 − 푆 − 푓푃)2 > 휎2 푉 7 Mask cosmic ray hits 푀 = { 푐푙푖푝 1 otherwise

Σ 푀푃(퐷 − 푆)/푉 8 Extract optimal spectrum 푥 푓 = 2 Σ푥 푀푃 /푉

Σ 푀푃 Variance of optimal spectrum 푥 var|푓| = 2 Σ푥 푀푃 /푉

9 Iterate Steps 5 through 8

Table 1: The optimal spectrum extraction algorithm presented in Horne (1986). All nine steps and the accompanying formulae are presented. Here, the subscript ‘푥’ stands for the spatial direction of the images while ‘휆’ stands for the spectral direction.

Image or quantity Description

퐶 Raw spectrum image 퐵 Bias image 퐹 Flat-field image 퐷 Reduced spectrum image 푄 Pixel gain (effective number of photons per pixel count)

Chapter 3. Spectrum Extraction Theory

푉0 Root-mean-squared readout noise 푉 Individual pixel variances 푆 Sky background image 푓 Extracted one-dimensional spectrum 푃 Spectrum spatial profiles 푀 Cosmic ray and bad pixel mask

Table 2: Description of images and quantities used in Horne’s algorithm.

The steps for dealing with the standard extraction are simple enough to understand, and here the standard spectrum is extracted through regular processes that are not particularly complicated. This begins by an initial image processing (Step 1), where the raw spectrum image 퐶푥휆 is first reduced pixel-by-pixel by a bias image, 퐵푥휆, then divided by a flat-field image 퐹푥휆, and any additional reductions that we may want to perform not included in Horne’s algorithm (dark current, optical defects, bad pixels, non-linearity correction, etc., see Sections 5.3.2 & 5.3.3). The raw spectrum image has two pixel coordinate directions, 푥 for the spatial direction and 휆 for the spectral (wavelength) direction. In a CCD image, each pixel will have a value proportional to the number of photons which were detected during the exposure. The reduced image,

퐷푥휆, is produced by means of Formula 3.1:

퐶 − 퐵 퐷 = (3.1) 퐹

This is followed by an initial statistical variance calculation, 푉푥휆, of the pixel values in the now reduced image 퐷푥휆, and later a sky subtraction of the sky background image 푆푥휆. The variances are necessary in order to create the weighted polynomial fits later used to represent the sky and spatial profiles. The sky background is derived by smooth interpolation of the sky data of each side of the stellar spectrum in the reduced image

퐷푥휆. The pixel variance and sky subtraction are calculated by Formula 3.2 and 3.3:

푉 = 푉0 + |퐷|/푄 (3.2)

푆 = FIT푥[퐷; 푉] (3.3)

The standard object spectrum can now be extracted from the sky-subtracted image (퐷 − 푆) by summation of the image along the spatial dimension (Formula 3.4). By performing this extraction, we can observe the spectral lines of the star along with any

Chapter 3. Spectrum Extraction Theory telluric (atmospheric) lines that remain. As an example, the standard extracted spectrum of Beta Pictoris can be seen in Figure 3.1.

푓 = ∑ (퐷 − 푆) (3.4) 푥

Figure 3.1: The standard extracted spectrum of the Beta Pictoris system at four wavelength ranges (see Table 4). However, we observe that essentially all of these spectral absorption lines are telluric lines, i.e., absorption lines from molecules found in Earth’s atmosphere, as stellar lines will not appear this sharp, and will instead be broadened by the motion of the star and the observer.

If we only were interested in the spectral lines of the star or any other very bright object, a standard spectrum extraction may well be efficient enough. However, since we are attempting to extract the planetary spectrum, as high of an SNR as possible is needed, and here the optimal extraction algorithm enters. Due to the high risk that the planetary signal is lost to noise, the stellar signal reduction, or any other necessary reductions, we need to retain as much of the signal as possible during the entire extraction process. The extraction algorithm described in Horne (1986) was specifically crafted to detect absorption lines from cool secondary stars/dwarf novae, meaning it will work very well for other faint targets as well, including exoplanets, and does not worsen spectrophotometric accuracy. This is of particular importance given that the goal of the planetary spectrum extraction is to identify molecular absorption spectral lines.

Chapter 3. Spectrum Extraction Theory

The optimal extraction extension to the standard extraction is summarized in Steps 5 – 9 in Table 1, beginning with the constructing of a spatial profile in Step 5. This is, in essence, a fit of the standard spectrum in the spectral direction to the initial pixel variance image. This profile is then normalized and positivity is enforced, as described in Formula 3.5 (a – c) below.

2 푃 = FIT휆[(퐷 − 푆)/푓; 푉/푓 ] (3.5a)

푃 = MAX[푃; 0] (3.5b)

푃 = 푃/ ∑ 푃 (3.5c) 푥

In the following Steps, 6 and 7, a new pixel variance image is created from the spatial profiles and the noise levels and gain, 푉0 and 푄, and cosmic rays are masked. This thesis will treat cosmic rays differently than Horne’s algorithm, and a more detailed description is found in Section 5.3. These steps are shown in Formula 3.6 and 3.7:

푉 = 푉0 + |푓푃 + 푆|/푄 (3.6)

0 if (퐷 − 푆 − 푓푃)2 > 휎2 푉 푀 = { 푐푙푖푝 (3.7) 1 otherwise

We have now produced all images necessary to optimally extract the spectrum. The optimal spectrum and its variance are calculated in Step 8 by means of Formula 3.8a and 3.8b, while Step 9 simply iterates the steps of the algorithm, and the spatial profile

푃푥휆, variance image 푉푥휆, cosmic ray mask 푀푥휆, and object spectrum 푓 can be determined again for each new iteration. While this extraction algorithm is the basis for the spectrum extraction algorithm constructed in this thesis, it must be altered to account for the removal of the scattered stellar light, blocking the signal from the planet. To achieve this, we instead construct a model point spread function as reference spatial profiles of the stellar signal to enable subtraction of the light, a method described thoroughly in Section 3.2.

Σ 푀푃(퐷 − 푆)/푉 푥 (3.8a) 푓 = 2 Σ푥 푀푃 /푉

Σ 푀푃 푥 (3.8b) var|푓| = 2 Σ푥 푀푃 /푉

Chapter 3. Spectrum Extraction Theory

Section 3.1.2. Curved Spectrum Problem

A well-known issue with spectroscopy with the use of a cross-dispersion instrument in conjunction with a CCD detector is the tilt or curvature that occurs in the images along the spectral direction of the image. The light entering the spectrograph is dispersed according to wavelength into a spectrum by means of a diffraction grating (or a prism), where the tilted effect arises. Most modern spectrographs used for astronomy have diffraction gratings instead of prisms as they are more efficient and preserve the SNR better. The grating consists of thousands of narrow and evenly spaced parallel lines arranged across a glass surface, where the light is split up into separate wavelengths and reflected onto the camera mirror and later CCD detector. Different wavelengths of light have different frequencies and as the photons are reflected off the grating, the spectrum can become tilted or curved due to varying atmospheric refraction, a tilt found on the gratings of the spectrograph, or camera distortions (Chromey 2010).

When extracting the spectrum of a star, a large number of rows not containing the signal from the object must be included in the summation of the sky rows in order to maximize the spectrophotometric accuracy. Each extra row included in the sum, however, will degrade the SNR as mostly noise is added from these rows. This is what the optimal extraction algorithm from Horne (1986) solves by adding a weighting factor to each pixel, proportional to the amount of signal in it. Pixels containing less of the object signal is given an individual weight smaller than those pixels containing a larger amount of the signal.

Horne’s algorithm is written in a way that is only able to cope with a small tilt of the object spectrum by fitting low-order polynomials along the pixel rows, making no assumptions about the spatial profile shape other than a smooth variation with wavelength. However, as detailed in Marsh (1989), the algorithm will not work for highly tilted spectra crossing many rows in the length of the images. In such a case, each row only contains a small fraction of the entire spectrum while at the same time requiring a high-order polynomial fit to the variation with wavelength. It is explained in Marsh (1989) that one cannot simply remove the tilt by measuring it and resampling the data by shifting pixels at each wavelength. Resampling the pixels to a new orientation will lead to a correlation between adjacent pixels and the extraction will lose statistical independence. The extraction will fail if the spectrum profiles become under-sampled, i.e. values will be divided equally between pixels if the shifting process requires the partial moving of pixels. Consider a case where a very narrow spectral profile that fits into a single pixel is used. If the profile were to be moved by half a pixel, it will be equally divided between two pixels, which lowers the amplitude of the profile. In addition, this operation gives rise to periodic oscillations in the spectrum

Chapter 3. Spectrum Extraction Theory along the columns, an effect heavily distorting the extracted spectra. An example of this is shown in Figure 3.2, where the oscillations caused by an aligning of a stellar spectrum are clearly visible.

Figure 3.2: Example spectrum of Beta Pictoris at ~ 2.3 μm after the spectral signal has been aligned to the centre of the spectral image to correct for the tilt. The periodic oscillations are clearly visible, causing the flux of the spectrum to incorrectly increase and decrease in strength, contaminating the spectrum and spectral lines.

The spectral tilt only affects the optimal extraction method for the case of a spectrum moving across of a large number of rows of > 30 rows. The images treated in this thesis have an average tilt of only ~2 − 10 pixel rows, meaning Horne’s extraction algorithm should still be usable. Despite this, there is an additional problem with the tilted spectrum, discussed more in Section 3.2.3, related to how it affects the subtraction of the stellar component from the combined signal from the entire system when attempting to extract a planetary spectrum.

Section 3.1.3. Use in Exoplanetary Spectroscopy

Horne’s optimal extraction algorithm is an exceptional guideline for how to perform any kind of spectroscopic measurements, including that of exoplanets or debris disks. The algorithm is designed to provide the maximum attainable SNR for any observations, a trait that is crucial when observing faint sources such as exoplanets and circumstellar disks. It will still need to be modified, however, since we are only interested in the spectra of the circumstellar objects, and not the star itself. The first four steps of the algorithm, Steps 1 – 4, are part of the standard extraction procedure,

Chapter 3. Spectrum Extraction Theory which will be included in this thesis as well. These operations do not affect the actual spectrum and are only used for improving the quality of the observational data images. They should be applied to any observational frames, regardless of which modifications to the data are performed later. This includes Step 7, the masking of cosmic rays and bad pixels, as this step also does not alter the object spectrum and only exists to increase the SNR and solve problems with the detectors, not the scientific data. How these steps are performed is described in Section 5.3.3.

The second part of Horne’s algorithm, Steps 5 – 9, deals with the optimal extraction method. Specifically, Step 5 is the most important one for our algorithm and for the extraction of the spectrum of an exoplanet or debris disk. As discussed in the previous section, this step involves constructing a spatial profile of the stellar spectrum at each wavelength by fitting the observational data to the variance of the images. The spatial profiles of the images are essentially the shapes of the images in the spatial direction, i.e. every pixel in a column at a specific wavelength. Whilst we will not follow the exact same method for constructing the profiles, it is argued that the use of spatial profile fitting may be beneficial to exoplanetary spectroscopy. Our hypothesis is that by fitting a model spatial profile to the actual data profiles, one can remove the stellar contribution from the observational images while leaving the planetary ones remaining for spectroscopic measurements. The planetary spectral lines are not part of the stellar spatial profile but are additional ones existing on top of the stellar signal, and would not be removed if the stellar data profiles are perfectly fitted and subtracted. How this is specifically achieved is discussed in the following section, with Figure 3.6 showing the theory behind fitting the spatial profile and subtracting the stellar signal.

Section 3.2. The Stellar Point Spread Function

Section 3.2.1. Defining the Point Spread Function

In this section, we begin with a definition of the Point Spread Function (PSF), as this concept is fundamental for the method used in this thesis. Firstly, one ought to keep in mind that all stars can be considered point-like sources due to their immense distance and relatively small radii in comparison with this number. However, stars captured on photographs typically appear as round disks of light, despite intuition telling us that they should present themselves as no more than a single, bright pixel. As an example, consider a Sun-like star located at a distance of 50 lightyears, similar to the Beta Pictoris system studied in this thesis (cf. Section 5.2). The angular diameter of the star as seen from Earth will be determined by Formula 3.9,

Chapter 3. Spectrum Extraction Theory

푑 푑 휃 = 2 arctan ( ) ≅ if 퐷 ≫ 푑 (3.9) 2퐷 퐷 where 푑 is the diameter of the star and 퐷 is the distance from the observer. For our example, it yields an angular size of ~ 7 × 10−10 radians, or 0.3 milliarcseconds. This is effectively a point-like object for any detector, as no modern instruments are able to achieve resolutions of this level. Despite this fact, as the light from the star reaches a telescope and detector on Earth, atmospheric turbulence, seeing, diffraction, and CCD sampling blurs the point-like source out over a longer angular spread. This effect causes the intensity of the signal to be distributed and fall off with increasing angular distance outwards from the centre of an image (Chromey 2010). The shape of the blurred signal is what is known as the ‘point spread function’, i.e. how the light from a point source is spread out across several pixels. In a regular, two-dimensional image, the blurring occurs radially outwards from the signal in both dimensions, giving the star a larger appearance the brighter it is. In a surface plot of the image, the star would resemble a two-dimensional Gaussian distribution, as seen in panel 1 of Figure 3.3 below. For a spectral image, however, the stellar light is divided into separate components, such that each column in the image contains light from the star at a specific wavelength. The PSF is still present for these types of images, although they manifest differently. Here, each column will have the signal spread out over many pixels in the angular (or spatial) direction in an almost Gaussian shape. A plot showing an example of the PSF appearance for a spectral image, much like those utilized for our algorithm, is seen in panel 2 of Figure 3.3.

Figure 3.3: Example of the stellar point spread function (PSF). The left panel shows the two-dimensional PSF of a star in a regular CCD image of a star, where the signal is blurred out in both of the angular directions. The right panel shows the PSF of a star in a spectral image, where the signal is only blurred out in the spatial direction at each wavelength. 42

Chapter 3. Spectrum Extraction Theory

Section 3.2.2. Role in Exoplanetary Spectroscopy

The PSF also plays a large role in how we devise a strategy for observing the reflected and emitted light from an exoplanet and perform spectroscopic measurements on it. Much like the parent star, the companion planet will emit a point-like signal that is blurred according to a PSF of very similar shape. In addition, the planetary component will be located at some angular, i.e. spatial, separation from the star both in reality and in the spectral images. Whilst they are two separate signals, the blurring of the stellar signal will cause the planetary signal to be added on top of the wings of the stellar PSF. This can be seen visually in the two panels of Figure 3.4, where the first panel shows the two separate signals at their given angular positions, and the second panel shows the two signals added together. However, this figure is a highly exaggerated case, as in reality, the planetary component will be much smaller in comparison to the star than what is shown.

Figure 3.4: PSF of an exoplanetary system with a star and a planet located at a separation of 0.3 arcseconds. The left panel shows the signals separated into individual components at their respective spatial positions. The right panel shows the two signals added together, where the planetary component can be seen as a ‘bump’ in the signal from the system, mostly overshadowed by the stellar signal. However, in this example, the signal from the planet is at a highly unrealistically 20 % strength of the stellar signal, whilst in reality, it will be closer to 10−3 − 10−4 of the stellar flux in the infrared.

Simply extracting the planetary spectrum at this position without any modifications to the data will not work, as the signal would be highly outweighed by the stellar spectrum. Instead, one must separate the two spectra into their individual components and analyze them separately in order for accurate measurements to be made.

Chapter 3. Spectrum Extraction Theory

To retain spectrophotometric accuracy, several pixels of data in a given column must be added together to encompass the entire signal from an object. The PSF spreads out the light over many pixels, although they are still part of the original signal and must be included in the spectrum extraction and analysis. This is where problems are encountered with the exoplanetary spectrum. Consider a situation where the signal from the planet is spread out over 10 pixels in both directions, yet the planet is only located 5 pixels away from the star. In such a case, any attempt to include the entire signal from the planet would simply result in the stellar component overwhelming the spectrum and any spectral lines from the planet will be lost in the starlight. This is demonstrated in Figure 3.5, which shows a model of this situation.

Figure 3.5: Example of the necessary extraction range for an exoplanetary spectrum. The exoplanet is located precisely at the red dashed line, but the entire signal from the planet is spread out over the marked area. To retain spectrophotometric accuracy, the entire signal should be included when extracting the planetary spectrum, and we must, therefore, sum the signal over this range covered by the marked area in the spatial direction. This will, however, mean that the planetary signal is completely obscured by the stellar component.

To accurately extract the exoplanetary spectrum, a method for separating the two signals into different spectra and subtracting the stellar component without heavily affecting the planetary one must first be devised. This is discussed in detail in the following section.

Chapter 3. Spectrum Extraction Theory

Section 3.2.3. Method for Subtracting the Stellar Light

As the two signals lie on top of each other, we must create a perfect fit to the stellar PSF in order to subtract it. The function has a similar shape to that of a Gaussian distribution, although it more closely resembles the lesser-used Lorentzian and Moffat profiles. It is not, however, perfectly similar enough to any known profile to enable their use in the fitting process and may change shape depending on wavelength. Instead, the shape of the stellar PSF must be determined empirically. There are a number of ways to achieve this (cf. Heasley 1999), and our algorithm will focus on fitting the PSF at each wavelength in the spectral images by looking at nearby PSFs and creating a mean spatial profile from them. This is similar to how Horne’s algorithm constructs spatial profiles and is demonstrated with a simple model in Figures 3.6 and 3.7 below:

Figure 3.6: Model version of the stellar light subtraction process. First, a reference profile is fitted to the stellar spatial profiles at each wavelength by an empirical method which does not include the planetary contribution. This is seen in the left panel above where the blue line is the total signal from the system while the red dashed line is the newly created reference profile. In the right panel, we have subtracted the reference profile from the total signal from the system, leaving only the planet behind for spectroscopic measurements. We must mention that this figure is accurate for emission lines, whilst for absorption lines that are more likely to be found, the remaining planetary signal will be negative. In such a case, while the planetary signal will be included in the mean, the absorption lines will not, and they remain for later extraction and analysis.

Chapter 3. Spectrum Extraction Theory

Figure 3.7: Model version of the reference profile creation method. The reference profile must be determined empirically, and here one cannot simply use each spatial profile for the reduction (since this includes the planet) or a mean of every profile (since the shape of the profiles changes with wavelength). We can instead create a mean reference profile of a few spatial profiles located in a row, since these will have a very similar shape, and there will be enough variation that the planetary signal is not fully reduced. In the model above, a reference profile of each column (spatial profile) is created by taking each pixel in said profile and creating a mean from the closest pixels in the same row. Here, the white pixels are the centre of the signal, weakening further out to greyer colours, whilst the red pixels are those we wish to create mean values for, and is achieved by taking the mean of the red and nearby blue pixels. The method is described more closely in Chapter 4.

The reason this method is viable originates from the fact that the star and the planet will have two entirely separate spectra with different spectral lines. When we create a mean reference spatial profile for each stellar PSF, the planetary signal will vary differently with wavelength than the stellar one will. If the reference profiles then are created from the mean of many columns, the planetary signal will not be included in every column, and the mean signal at the planetary location will be lower or higher than the actual signal, depending on whether we observe emission or absorption lines. For example, if an absorption line is present in a single pixel, and we create the mean from five columns, including the absorption profile and two surrounding it on each side, the mean pixel count at the position of the spectral line will be much closer to the average planetary signal, and when subtracting the reference profile from the actual one, the planetary absorption line will become heavily negative and easily visible. The question is then how many columns of spatial profiles should be used to create the mean, i.e. ‘reference’, profile that will be used to fit the stellar PSF. We cannot simply take the mean of every PSF in an image, as the profiles change shape with wavelength and won’t be a good fit for each column. Instead, ‘tailor-made’ reference profile for each PSF in the images is needed that are specifically created to

Chapter 3. Spectrum Extraction Theory best fit each individual shape of every image column. At the same time, too few nearby profiles cannot be used to empirically determine the reference profile, as it would risk including a high frequency of the planetary signal in the created profile. This method functions due to the specifically different spectrum of the star and planet, and the more columns are included in the mean profile, the more variation there will be between the two. In short, when creating a fit to the stellar PSF, some variation in the used profiles is needed, but not too much so as to cause further problems.

In addition, during the process to create a reference profile, more difficulties arise due to the known issue of tilted spectra. This has already been discussed in Section 3.1.2, although for the reference profile it must be taken into account once again. If the spectrum is tilted too heavily, taking the mean of several spatial profiles will become inaccurate, as pixels at different spatial positions will be averaged over. As discussed, the tilt cannot simply be removed by resampling pixels to the centre, since this contaminates the pixel counts. The altering of pixel counts can be somewhat solved through aligning the spectral tilt by only moving whole pixels. We explained the concept of how moving pixels shorter distances than by whole numbers affects the pixel count in Section 3.1.2, however, if pixels are simply moved one whole position over, e.g. from pixel coordinate (100, 100) to (100, 101), in the same column, the counts will not be affected. To shift columns directly on the observational images will nonetheless still not work since the tilt of the spectrum is constant across the length of the entire image. Consider a case where an image is of length 1000 pixels, with the tilt of the spectrum moving across 10 pixel rows. The change of the centre of the profile from one column to another will, therefore, only be on the order of 0.01 pixels, and once every 100 pixels would there be any pixels shifted. A model case of this is shown in Figure 3.8 below.

Chapter 3. Spectrum Extraction Theory

Figure 3.8: The top panel shows a spectral image of the Beta Pictoris stellar system, where the spectral tilt is clearly visible, moving 5 pixel rows across the length of the image. The bottom panel shows an attempt to align the spectrum to the centre by shifting columns up by whole pixel lengths. The resulting spectrum is very jagged and does not resolve the discussed problems with the reference profile creation process. It also introduces the periodic oscillations in the extracted spectrum as discussed in Section 3.1.2.

The method we have devised for solving both of these issues (creating a mean profile from a tilted spectrum and shifting pixels without affecting the pixel count) is to resample the image columns to a higher resolution, i.e. introduce more pixels in the spatial dimension, in order to enable shifting of pixels at the ‘sub-pixel’ level. If there are more pixels available at each spatial position, the spectrum can be aligned more correctly to the centre of each profile by shifting whole pixels at a much shorter scale than that of the original image resolution. This will allow us to move pixels in every column some amount instead of only at a few positions and is demonstrated in the four panels of Figure 3.9 below.

Chapter 3. Spectrum Extraction Theory

Figure 3.9: Four panels showing the attempted solution to the tilted spectrum problems investigated in this thesis. The top left panel shows a stellar spatial profile, where each blue circle represents a single pixel with the measured flux. The top right panel shows one method for how new pixels can be introduced between the original pixels to increase the resolution. New pixels are placed along the red dashed line, allowing for moving of pixels at the sub-pixel scale. The bottom left panel shows the spectral image displayed in the first panel of Figure 3.8, except where the resolution has now been increased by a factor of 100. The bottom right panel shows how the spectral image appears after the spectrum has been shifted by the same method as in Figure 3.8, although at the sub-pixel level. The jagged structure is noticeably missing and the spectrum is aligned to the centre of the image.

With these steps assembled into a computational algorithm, a reference stellar PSF image, consisting of many spatial profiles, can be produced and used in subtracting the stellar component from any image of an exoplanetary system. Exactly how this algorithm is constructed is detailed in the following Chapter 4, where each step necessary to extract the spectrum is carefully described.

Chapter 4.

Implementing the Spectrum Extraction Algorithm

Section 4.1. Extraction Goal and Algorithm Overview

In this chapter, the implementation process of our spectrum extraction algorithm is described. We discuss how each step of the algorithm is performed, why the operations on the data are made, and how they affect the observational frames. It can be considered that there are two separate goals with the extraction algorithm. The first is to empirically determine reference stellar spatial profiles that are of the same shape and amplitude as those seen in the object spectrum images, while the second is extracting a planetary spectrum and possibly detect spectral lines related to certain molecules within it.

Even if it is determined that the planetary signal is too weak to distinguish regardless of how well the algorithm works, it may still prove useful in accurately reducing the stellar light. In the future, instruments may provide observations at higher resolutions or higher dispersive capabilities that would allow for an, as of now, too faint planetary signal to be detected. In such a case, the stellar light component must still be subtracted as an exoplanet cannot be seen so close to a star, no matter the resolution of the instruments. Well-developed algorithms to reduce the starlight can be significantly helpful, if not as of right now, very possibly in the future.

Whilst the efforts to extract the spectrum of the exoplanet Beta Pictoris b may end up unsuccessful, the attempt still gives us a baseline for further studies. In addition to the exoplanet, models of observational data (see Section 5.4) are also utilized where the strength of the planetary signal is artificially determined followed by an attempted extraction through the use of this thesis’ algorithm. It can, through such models, be determined how bright an exoplanet must be in order for the algorithm to be effective, and such simulations are something we discuss more heavily later on in the discussion, Section 7.2.

Chapter 4. Implementing the Spectrum Extraction Algorithm

Next, a brief overview of the algorithm is made, firstly as a table detailing the various steps, equations, and formulae which comprise the algorithm, and secondly through comments on which operations each step involves and what they accomplish. We begin with Table 3 which presents an overview of the extraction algorithm, where 푆휆푥 is the data frame we wish to subtract the stellar light from:

Step Process Formula

1 Resample via repetition 푆휆푥2 = REPEAT[푆휆푥; 100]푥 OR

푆 = INTERP [푆 ; 푥 푘 ] Resample via interpolation 휆푥2 휆푥 푛+ 101 푛,푘=1,2,…,100

퐴 훾2 2 PSF Lorentzian fit 퐿(푥, 푥 , 훾, 퐴) = FIT [ ; 푆 ] 0 훾2 + (푥 − 푥 )2 휆푥2 표 푥 2 Lorentzian polynomial fit 푀(푥0) = FIT[푎푥 + 푏푥 + 푐; 퐿(푥, 푥0, 훾, 퐴)]푥0

3 Align spectrum to centre 푆휆푥2[휆, 푥] = 푆휆푥2[휆, 푥[푛] + 푀[푛]]

푆휆푥2 4 Normalize PSF data 푆휆푥2 = ∑푥 푆휆푥2 Create reference spatial 1 휆+푛

푃휆푥 = (∑ 푆휆푥2) profiles 2푛 + 1 휆−푛

5 Revert spectra tilt 푃휆푥[휆, 푥] = 푃휆푥[휆, 푥[푛] − 푀[푛]]

푥+99 Revert spectra resolution 푃휆푥 = ∑ 푃휆푥 푥=1,101,…

휆,푥 (푆 − 푃 × 퐴)2 6 Fit model to data with 2 휆푥 휆푥 휒 퐴 = MINIMIZE [∑ 2 , 퐴] 휆,푥=1 휎휆푥 Multiply model with correct 7 푃 = 푃 × 퐴 amplitude 휆푥 휆푥

Subtract model from data 푅휆푥 = 푆휆푥 − 푃휆푥

푥푝2 8 Extract planetary spectrum 푓 = ∑ 푅휆푥 푥푝1

Table 3: The eight steps of the planetary spectrum extraction algorithm attempted in this thesis. All steps are explained in further detailed in the following sections, while the table serves as a useful overview of the algorithm.

Chapter 4. Implementing the Spectrum Extraction Algorithm

As can be seen in the table, the extraction algorithm is comprised of eight steps of various techniques and operations to complete. The first four of these consists of creating a reference stellar spatial profile of our processed images at each wavelength in the spectral direction of the frames. The final four steps of the algorithm involve converting these spatial profiles to best fit the observational data frames and subtracting the stellar light, enabling extraction of the planetary spectrum.

The first step of the algorithm involves resampling the data frames to a higher resolution, either through repetition of data points or through linear interpolation of values between them. The second step of the algorithm is to measure the centre of the spatial profile of each wavelength and to fit a second-degree polynomial to the tilt of the spectrum from the measurements. The third step is to use the fitted polynomial of the tilt to align the spectrum to the centre of the frames by moving image columns up and down through interpolation. The fourth step of the process consists of normalizing the aligned profiles and empirically determining the shape of the stellar spatial profile by creating reference profiles from the mean of each individual column and those closest to it. The fifth step of the algorithm consists of reverting the data frames back to the original tilt and resolution through moving columns and summation of sub-pixels. The sixth step is to fit the reference profiles to the original data profiles through minimization of the Chi-Squared values of each data point, such that the reference profiles have the correct shape and amplitude. The seventh and final data treatment step is a simple subtraction of the reference frames from the observational data frames to reduce the stellar component while leaving the planetary signal intact. The eighth and final step is to extract the planetary spectrum by standard means, i.e. through the summation of the data in the spatial direction. In the following section, these step are further detailed with more explanations of how the operations are performed, which formulae are used, and example images to visually show how they affect the data frames.

Section 4.2. The Planetary Spectrum Extraction Algorithm

In this Section, we describe, in detail, the entire process during which each step of the extraction algorithm is carried out, both in writing and in showing the necessary formulae and figures. The steps and formulae are shown in Table 3, which may be useful to refer back to during the discussion of the process. We also mention that for the frames used in this thesis, only the 100 pixels located closest to the spectrum centre are used for the operations in order to decrease the computing time, although any number of pixels are effectively useable.

Chapter 4. Implementing the Spectrum Extraction Algorithm

Section 4.2.1. Step 1 – Resampling Data

The first step of the extraction algorithm, Step 1, is the resampling of the data frames into a frame of higher resolution in the spatial direction. For this step, two means of resampling the data frames are utilized in order to analyze whether either one produces better results. The first method is by simple data repetition, such that all pixels are repeated a certain number of times along each data column. With this method, it can effectively be considered that each pixel is divided up into a number of identical pixels, as is shown in Figure 4.1 below.

Figure 4.1: Model for the first resampling method, where each pixel is divided into a number of equal pixels. In this example, each pixel is repeated five times at each spatial position, increasing the resolution from 11 pixels in the spatial direction to 55 pixels.

We have elected to increase the resolution by 100 times, meaning that each pixel is divided into 100 sub-pixels, that can be shifted up or down during the spectrum alignment process. The data operation used for the resampling process for the first method is summarized as Formula 4.1. While this will increase the running time of the program significantly, it is done in order to minimize the potential artefacts that arise from the shifting of the pixels, a problem discussed earlier in Section 3.1.2.

푆휆푥 = REPEAT[푆휆푥; 100]푥 (4.1)

By shifting pixels on the sub-pixel level, we attempt to ensure that there are no large disparities between individual image columns, which can occur when whole pixels are shifted, and the object spectrum is not tilted over more than just a few pixels. An

Chapter 4. Implementing the Spectrum Extraction Algorithm example of this is shown in Figure 3.8 in Section 3.2.3, where it is shown how a high disparity between certain data columns will affect the aligned spectrum.

The second method for the resampling of the data is by use of linear interpolation, where new data points are constructed between each of the original pixel values in each image column. This yields new data arrays of seemingly the exact same shape as the original frames, only with more individual pixels across the entire column. A diagram of the model used for this method is shown in Figure 4.2, while the array operation is expressed in Formula 4.2, where new values are created through linear interpolation at positions 푥 푘 , 푛 is each position along the spatial axis, and 푘/101 is a position 푛+ 101 between each pixel location 푥푛.

Figure 4.2: Model for the second resampling method, where new pixel counts are interpolated between the original data points. The first panel shows an example of the pixels found in a spatial profile from the spectral image, while the second panel shows the same profile after 10 new values have been linearly interpolated and placed between every other pixel.

푆휆푥 = INTERPOLATE [푆휆푥; 푆휆푥 푘 ] , where 푛, 푘 = 1, 2, … , 100 (4.2) 푛+ 101 푥

The advantage of this method over simple repetition of pixels is that it avoids the highly ‘jagged’ nature of each pixel column that may also cause additional problems during the reference spectrum generation process. The downside is that none of the newly interpolated values are actual pixel counts, unlike for the first method where each pixel can simply be considered to be divided into a number of identical pixels. These pixel counts would, of course, be entirely different if the actual resolution of the

Chapter 4. Implementing the Spectrum Extraction Algorithm data frames taken by the detector were larger during the exposures and will have to be taken into consideration during a discussion of the results.

Both methods will be attempted and later evaluated to determine which one performs better during the spectrum extraction. In the resulting data frames, the first method will be represented by the label ‘Resampling Method 1’, or RM1, while the nomenclature for the second one will naturally be ‘Resampling Method 2’, or RM2.

Section 4.2.2. Step 2 – Polynomial Fit to Profile Centre

The second step of the algorithm, Step 2, is to fit a quadratic polynomial to the tilt of the spectrum in the data frames. In order to perform this step, we must first determine the central pixel of the spatial profile at each wavelength, i.e. at which image row the centre is located. The spatial profiles may not necessarily be centred perfectly on one specific pixel, and will, in fact, most likely have a centre located between two pixels. This is due to the tilt of the spectrum and will be discussed and accounted for shortly. To find the centre of each profile, a Levenberg-Marquardt algorithm and least-squares (LSQ) fitting is used to model a one-dimensional Lorentzian distribution to every column in the used sections of the data frames. A Lorentzian profile is one of the mathematical distributions most closely resembling a stellar spatial profile, and is described by Formula 4.3:

퐴훾2 푓(푥, 푥0, 훾, 퐴) = 2 2 훾 + (푥 − 푥0) (4.3)

where 퐴 is the amplitude, 훾 is the Full Width at Half Maximum (FWHM), and 푥0 is the centre, or mean, of the profile. Once a function has been fit to each of the 1024 columns in the data frames, an array showing how the centre of the spectrum is tilted across the image is obtained. An example stellar spatial profile and a Lorentzian distribution fit to the profile is shown in Figure 4.3 below:

Chapter 4. Implementing the Spectrum Extraction Algorithm

Figure 4.3: Example of a Lorentzian profile fitted to a particular stellar spatial profile. Notice that the profile is not a perfect fit, which is why the actual reference profile must be determined empirically.

Whilst this array may be enough to align the spectrum to the centre of the image, the LSQ fit will not always be entirely correct, particularly when strong absorption lines are present or defects are found on the object spectrum. It will, therefore, yield better results if a polynomial is fit to the array of the centre of each profile, to ensure that no mistakes have been made in the measurement of the centre. This can easily be achieved by performing a second-degree polynomial fit, as shown in Formula 4.4.

푓(푥) = 푎푥2 + 푏푥 + 푐 (4.4)

Since it is possible that some measurements of the centre of the profile may deviate enough that a single quadratic polynomial fit is still not close to the actual tilt of the spectrum, this process will be performed over several iterations. After each iteration, the fit is put through sigma clipping, and every value found to deviate from the polynomial fit by more than 3휎 will be masked and a new polynomial fit is made. After an iteration is made and no values are masked, a well-established second-degree polynomial representing the tilt of the spectrum is obtained. The measured centre of the spectral line and the polynomial fit after many iterations is shown in Figure 4.4 below, while Formula 4.5 and 4.6 details the data operation.

Chapter 4. Implementing the Spectrum Extraction Algorithm

Figure 4.4: Second degree polynomial fit to the centre of the spectrum at each spectral position. The blue dots are the measured centres through the Lorentzian profile fit while the red line is the polynomial fit to the dots which will be used to align the spectrum.

퐴 훾2 퐿(푥, 푥 , 훾, 퐴) = FIT [ ; 푆 ] (4.5) 0 훾2 + (푥 − 푥 )2 휆푥2 표 푥

2 푀(푥0) = FIT[푎푥 + 푏푥 + 푐; 퐿(푥, 푥0, 훾, 퐴)]푥0 (4.6)

In Formula (4.5) a Lorentzian profile is fitted to each spatial profile in the spectral images 푆휆푥2, and in Formula (4.6) we fit a second-degree polynomial to the measured centre of the Lorentzian profiles, i.e. the 푥0 value of each calculated profile.

Section 4.2.3. Step 3 – Align Spectrum to Remove Tilt

The third step of the extraction algorithm, Step 3, is the aligning of the object spectrum to the centre of the data frame in order to remove the tilt of the spectral lines. As discussed earlier (see Section 3.2), the object spectrum will need to be properly aligned to the centre of the image in order to create a workable reference stellar spatial profile from the surrounding data columns at each wavelength. Otherwise, the tilt of the spectrum will create difficulties when the spatial profiles are created from several image columns, as if the tilt is large enough the profiles will be constructed from pixels located at separate spatial positions. An example of this is shown below, in Figure 4.5.

Chapter 4. Implementing the Spectrum Extraction Algorithm

Figure 4.5: Model spectral image displaying the difficulties with creating a reference frame from a tilted spectrum. The white pixels in the figure is the central peak of the spectrum, while the grey pixels are those with lower amplitude. Consider a case where one attempts to create reference spatial profiles of a tilted spectrum, and the red-marked pixels above are the ones reference pixels are created for. For certain pixels, it is seen that the closest pixels in the same row have either larger or smaller values, meaning the reference pixels will be less than optimal.

We have also detailed why the alignment cannot be done immediately with the regular data frames, in Section 3.1.2, as this creates large artefacts in the extracted spectrum in the shape of ‘waves’ or oscillations that occur across the extracted spectrum. As stated in Marsh (1989), pixels cannot be partially shifted without affecting the pixel counts of the shifted column. This is why the columns will be shifted at each wavelength by whole pixels, i.e. by rounding the calculated centre of each profile found in Step 2 to the nearest integer and shifting values up or down in the columns the appropriate amount.

Another matter also previously discussed is how the resampling of the data frames to a higher resolution helps immensely during this process, as if the spectrum only crosses a few rows during the length of the image, only a small number of shifts will be made as most columns will be approximated to the same central row. This will essentially mean that no real aligning is performed, and the spatial profiles will not be correctly constructed. The general idea for how the shifting of the columns is performed is shown by an example in Figure 4.4, where the top panels show the shifting of the original frames, and the bottom panels show the process for a resampled frame. The operation performed on the data frames is shown in Formula (4.7).

Chapter 4. Implementing the Spectrum Extraction Algorithm

Figure 4.6: Model spectral image detailing how the aligning of the spectrum is performed. In the top left panel, a normal spectral image that has not been

resampled to a higher resolution (푆휆푥) is seen, where the spectrum is tilted and moves linearly across many pixels in the spatial direction. If the spectrum is aligned by moving whole pixels, much of the spectrum will still be located outside of the central row, as seen in the top right panel, leading to incorrect reference profiles and periodic spectrum oscillations. In the bottom left panel, the frames are resampled by dividing the pixels in the spatial direction into sub-pixels, which can be correctly aligned by whole pixel movement as seen in the bottom right panel.

(4.7) 푆휆푥2[휆, 푥] = 푆휆푥2[휆, 푥[푛] + 푀[푛]]

Formula (4.7) details the operation on the data frames, which involves changing the pixel coordinates in the spatial (푥) direction by adding the measured profile centres

푀(푥0) to the spatial coordinate position.

Section 4.2.4. Step 4 – Normalize and Create Spatial Profiles

The fourth step of the algorithm, Step 4, is the creating of the reference spatial profiles of the spectrum. To ensure that all the profiles used to create the references have the same amplitude, the first part of this step is to normalize the current data frames. This is performed in order for the profiles to all have the same approximate shape and amplitude, such that strong absorption lines in the spectrum will not be responsible for

Chapter 4. Implementing the Spectrum Extraction Algorithm incorrectly calculated reference profiles. The normalization can be achieved by dividing the profiles by their sum in the spatial direction, as shown in Formula 4.8:

푆휆푥2 푆휆푥2 = (4.8) ∑푥 푆휆푥2

Once we have resampled, aligned, and normalized data frames, they can be used to create the stellar reference spatial profiles. Here the same reference spatial profile at every wavelength in the original data frames cannot be used, as many of the profiles will not have the exact same shape, particularly those at wavelengths with strong absorption lines. An example of this is shown in Figure 4.7, where an average spatial profile is compared to one located at a strong absorption line, both normalized.

Figure 4.7: An average spatial profile of the Beta Pictoris spectrum compared to one located at a strong absorption line. The profiles located at absorption lines typically have higher wings than other profiles, due to their flatter shape.

Instead, a tailor-made reference spatial profile will be created for each wavelength in the spectral direction of the images. This can be accomplished by constructing the profiles from the mean of the values of each individual data column and those nearest to it. Here, we do not wish to use either too few or too many columns to create the profiles, as if too few are used it may result in the planetary signal being removed, and if too many are used the reference profile may not have the correct shape to subtract the stellar signal properly. We will, therefore, create reference profiles by three separate means; either from each given column and the closest two on each side (for a total of 5 columns), the closest five on each side (a total of 11 columns), or the closest fifteen

Chapter 4. Implementing the Spectrum Extraction Algorithm on each side (a total of 31 columns). These three variations can then later be examined for if any particular one performs better in the stellar signal subtraction. An expression for the creation of the reference spatial profiles is given in Formula 4.9,

1 휆+푛 (4.9) 푃휆푥 = (∑ 푆휆푥2) 2푛 + 1 휆−푛

where the reference data frames, 푃휆푥, are created by taking the mean of every pixel in

푆휆푥2 at position [휆, 푥] and the corresponding pixels between positions 휆 − 푛 and 휆 + 푛, where 푛 can be any chosen value. A model representation for how the pixel values of spatial profiles are calculated is shown in Figure 4.8 below.

Figure 4.8: Model spectrum showing the reference spatial profile creation method. The red-marked columns are spatial profiles that reference profiles are created for, and the blue columns are the columns which are used to create the empirically determined mean profiles.

Section 4.2.5. Step 5 – Revert Tilt and Resolution

Once satisfactory reference stellar spatial profiles have been created, a few more conversions of the frames must be made before we can subtract them from the reduced observational data. The first of these are made in the fifth step, Step 5, where the reference frames are converted back to the original spectrum tilt and image resolution. The first stage of these two processes is comparatively easy, as we need only to shift the columns back in the opposite direction from the shift that was performed in Step 3. Given that an array already has been obtained of how much each column is shifted,

Chapter 4. Implementing the Spectrum Extraction Algorithm the same method can be used in reverse as what is detailed and shown in Formula 4.7 and Figure 4.6, which is simply to shift the columns in the opposite direction, as is detailed in Formula 4.10 below.

푃휆푥[휆, 푥] = 푃휆푥[휆, 푥[푛] − 푀[푛]] (4.10)

The second procedure in this step is to reduce the resampled, higher resolution (e.g. 10000 × 1024) of the reference data frames to the original resolution (e.g. 100 × 1024). This is completed by the simple process of summing the values of the ‘sub-pixels’ made from the original pixels, i.e. summing up 100 pixels consecutively in each column. For Resampling Method 1, this works without problem since each sub-pixel is merely an equal, divided part of the original pixel, although, for Resampling Method 2 some difficulties arise. These are discussed in more detail in Section 4.3 and the process is assumed to be usable for now. The formula for the summation step is shown below in Formula 4.11, while an illustration of the operation is shown in Figure 4.9.

푥+99 푃휆푥 = ∑ 푃휆푥 , 푥 = 1, 101, 201 … (4.11) 푥

Figure 4.9: Model of the reverting of the frames to the original resolution. In the RM1 case (left panel), we simply sum all the values of the sub-pixels created by dividing each original pixel into a new value. In the RM2 case (right panel), we reduce the resolution by taking each original pixel location and sum all sub-pixel values halfway to the following and previous pixel found in the rectangles, such that all pixels are created with an equal number of larger and smaller pixel values than the original pixel.

Chapter 4. Implementing the Spectrum Extraction Algorithm

Section 4.2.6. Step 6 – Model Fit with Chi-Squared Method

The last step before constructing the final reference frames which will be subtracted from the observational data is Step 6; fitting the reference frames to the data by means of the Chi-Squared method. Recall that in the first part of Step 4 the frames are normalized, meaning that the current reference frames will have the correct shape, but not the correct amplitude. We will no longer be able to multiply with the same constant that was used to normalize the columns, as the values will be somewhat altered during the creation of the spatial profiles and the two will not be compatible. Instead, during this step, a chi-squared test is performed to fit the model stellar spectrum to the data. A chi-squared test is used to find how large the difference between the expected (modelled) and observed values is of a distribution of data. The equation for the test is shown in Formula 4.12.

푗 (푥 − 휇 )2 휒2 = ∑ 푖 푖 (4.12) 휎2 푖=1 푖

Here, 푥푖 is the observed values, i.e. the values of the original data frames 푆휆푥, 휇푖 is the model values, i.e. the reference frames 푃휆푥, and 휎푖 is the individual noise levels of each data point. By utilizing a minimization-algorithm, we can determine which multiplying factor would yield the most accurate amplitude for the model as compared to the observed values. This algorithm would minimize the result of the chi-squared test, i.e. minimize the difference between the model and the observed data, for a certain multiplying factor to the normalized frames. The operation performed on the frames is expressed in Formula 4.13.

휆,푥 (푆 − 푃 × 퐴)2 휆푥 휆푥 (4.13) 퐴 = MINIMIZE [∑ 2 , 퐴] 휆,푥=1 휎휆푥

The factor 퐴 is here the amplitude that must be multiplied with the reference frames, and the 휒2-test will find the optimal amplitude to use for perfectly subtracting the stellar signal. If, as predicted, the reference images contain a good model of the stellar signal, the chi-squared test will perfectly fit the reference frame to the reduced data frames with the exception of the planetary spectral lines. A somewhat exaggerated example of how the chi-squared would work in the optimal case is shown in Figure 4.10.

Chapter 4. Implementing the Spectrum Extraction Algorithm

Figure 4.10: Model showing an optimal case of the 휒2-test and minimization process. In the left panel, the stellar and planetary signal is seen as the blue line and the normalized reference profile as the orange dashed line. In the right panel, we have calculated the best amplitude to multiply the reference profile with and used it to fit the stellar signal.

Section 4.2.7. Step 7 – Create and Subtract Final Model from Data

The final processing of the images is performed in Step 7, where a complete reference image of the stellar spectrum is created from the profiles constructed so far and the stellar signal is subtracted from the processed data frames. This step is fairly simple, as it involves two quick operations, the first of which is to multiply each spatial profile of the reference frames with the correct amplitude calculated in Step 6. This is shown in Formula 4.14.

푃휆푥 = 푃휆푥 × 퐴 (4.14)

After this process has been completed, we should have produced full reference images of the stellar signal, and of the same image size as the data frames. A simple subtraction between the reference images and observational images should now yield the expected results, i.e. a frame containing only the background noise and planetary spectral lines.

This operation is shown in Formula 4.15, where 푆휆푥 is the original data frame found after the initial standard reductions described in Section 5.3 have been performed, 푃휆푥 is the completed reference frames, and 푅휆푥 is the frames after the stellar signal has been subtracted.

Chapter 4. Implementing the Spectrum Extraction Algorithm

푅휆푥 = 푆휆푥 − 푃휆푥 (4.15)

Section 4.2.8. Step 8 – Extract Planetary Spectrum

The final step of the algorithm, Step 8, is the actual extraction of the planetary spectrum. This step is performed in the same manner as any spectrum extraction from an observational data frame would be; through summation of the image data over a range of pixels containing the whole object spectrum in the spatial direction. Here, it is expected that the planetary signal will be quite weak, and not necessarily distinguishable from the background noise before the extraction. It is, therefore, important that the location of the planetary signal has been established beforehand, such that the correct image rows can be summed up. For Beta Pictoris b, the separation between the star and planet is known to be ~ 0.4′′ below the star, (Snellen et al. 2014). At the current pixel scale of 0.086′′/pixel, the planet will be located 4 – 5 pixels below the star.

The extraction must be careful so as to not include too much background noise or potentially include any stellar signal that may remain if the subtraction was not accurate enough. This is discussed more in Section 4.3.2 in a short while. For this reason, we will only sum over a few pixels in the spatial dimension, from 푥푝1 to 푥푝2, the approximate beginning and end of the planetary spatial profile signal, even if this risks degrading the spectrophotometric accuracy, which may occur if the sum does not range over a sufficient range of pixels. The summation operation is detailed in Formula 4.16 below and is the final operation in the spectrum extraction algorithm, after which an exoplanetary spectrum should be obtained.

푥푝2 푓 = ∑ 푅휆푥 (4.16) 푥푝1

Section 4.3. Problems and Limitations of the Algorithm

Section 4.3.1. Interpolation as a Resampling Method

The first limitation of the algorithm lies in the use of interpolation as a resampling method, where new data points are added between the original values. If it is determined beforehand that one wishes to increase the resolution of an array of values

Chapter 4. Implementing the Spectrum Extraction Algorithm by some factor, the method will only work as long as the increase in resolution equals the number of data points in the array. Consider a simple case, such as the one shown in the first panel of Figure 4.11, where an array consisting of only three data points is seen. If we want to increase the resolution of the array by a factor of 2, the interpolation must add three new values. It will, however, be impossible for it to place these three values between the original three whilst remaining linear. The process will instead alter any data points located before the first and final one (i.e. the middle point in our example scenario) such that the interpolated values can be placed linearly between each other, as shown in the second panel of Figure 4.11.

Since we do not wish to alter any of the original data values, we must, therefore, increase the resolution by the same factor as there are values in the original array, as this is the only result which does not change the original values. This is shown in the third and last panel of Figure 4.11 and is also part of the reason why only a small segment of the full observational data images is worked with (100 × 1024 instead of 512 × 1024) and why we increase the resolution by a factor of 100.

Figure 4.11: Model for how resampling to a higher resolution by means of interpolation works. In the first panel, three values (blue circles) are shown, where we want to add new values between them along the red-dotted line by interpolation. In the second panel, an attempt to increase the resolution by a factor of 2 has been made, i.e. by introducing 3 new data points. It will be impossible for the interpolation method to place them linearly between the three original values and will instead simply change the values between the first and last data point to linearly place new values (green circles) along the red-dotted line, which will lower the overall amplitude of the shape. In the third panel, we demonstrate that we must increase the resolution by a factor equal to the number of data points, or any multiple thereof, in order for the new values to be place linearly without changing the shape of the profile.

Chapter 4. Implementing the Spectrum Extraction Algorithm

During Step 5 of the algorithm, an additional separate problem arises in the case of using data frames created with Resampling Method 2, related to how the data columns are arranged during the summation process. The problem with the summation process in the RM2 case lies in how it alters the shape of the profile at its peak. Whilst every other data point will be summed with values linearly larger and smaller than itself, as seen in Figure 4.12 below, the largest data point in the centre of the profile will be summed with values smaller than itself on both sides towards the previous and following pixel. This leads to the central pixel value becoming smaller in relation to the other pixels and causes a broadening of the reference profile, particularly during the chi-squared minimization steps, where the amplitude is will become underrepresented and the wings overrepresented, as seen in Figure 4.13.

Figure 4.12: Example spatial profile showing the summation problem with resampling through interpolation. Here, we see five original data points and four interpolated values between every point (as well as two before and after the last points). Values would then be summed up inside the squares, where each square is a new pixel, although, as can be seen, the four pixels at the wings are summed with values larger and smaller than the original point, while the central value is only summed with values smaller than itself, leading to a broadening of the new profile.

Chapter 4. Implementing the Spectrum Extraction Algorithm

Figure 4.13: Example profile showing how the shape changes after the summation process is completed, where the blue line is the original shape and the orange line is after the summation. Since the profile needs to be as close to an exact match to the stellar signal as possible, this broadening will ensure that the subtraction will not be performed as expected.

For now, there is no direct solution to this problem except to simply not perform the summation step and later on, in Step 7, subtract the reference image (now size 10 000 × 1024) from the resampled data frames (i.e. RM2 frames of the same size). The results of both this method and to perform the summation regardless will be shown in the Results in Chapter 6.

Section 4.3.2. Spectrum Extraction Limitations

The main goal of our algorithm is to be able to extract an exoplanetary spectrum. However, a number of limitations to achieve this desired result are present, regardless of how well the method works theoretically. For instance, it may be found that the planetary signal is too weak to detect in the spectrum, no matter how perfectly the algorithm is able to subtract the stellar light. In the K-band, where the observations used in this thesis are made, the star Beta Pictoris and its planet, Beta Pictoris b, have absolute magnitudes of 푀훽 푃푖푐 = 3.45 and 푀훽 푃푖푐 푏 = 12.6 (Bonnefoy et al. 2013). This can be converted to a luminosity ratio by means of Formula 4.17,

Chapter 4. Implementing the Spectrum Extraction Algorithm

푀 −푀 퐿 퐿 − ∗ 푀 – 푀∗ = −2.5 log10 ( ) or = 10 2.5 (4.17) 퐿∗ 퐿∗

−4 which for 푀훽 푃푖푐 and 푀훽 푃푖푐 푏 equals 2.19 × 10 ≅ 1/4570. This means that the planetary signal is, in the Beta Pictoris case, more than 4500 times weaker than the stellar one. Whilst this is most likely too faint to directly see the planetary spectrum in the subtracted images and the extracted planetary spectrum images, it may still be possible to gain some information by other methods of analysing the data, which we discuss more of in Section 7.1.

Additional problems can also arise that cause the extraction step to fail to some degree. If the reference stellar spatial profiles are not created correctly, they could potentially contain a large amount of the planetary signal which would then be either somewhat or fully removed during the subtraction step, Step 7. The reference profiles may also not be fitted perfectly enough to remove all of the stellar signal, leaving some of it remaining which can possibly keep the planet obscured in the scattered starlight. These limitations are only some of the known ones as of yet, and more will be discussed later in Chapter 7, after the results of the spectrum extraction algorithm have been presented in Chapter 6. In the following chapter, we discuss the observational data and models utilized to test the spectrum extraction algorithm, including some information about the instrumentation (CRIRES) and the stellar system (Beta Pictoris) used for the spectral images.

Chapter 5.

Observational Information & Models

In this chapter, we discuss the observational instrumentation, target, data, and models used to assess the algorithm described in the previous chapter.

Section 5.1. The CRIRES Instrument

Section 5.1.1. CRIRES Main Characteristics

All of the observations of Beta Pictoris that are treated in this thesis were made by the ESO’s 8.2 metre Very Large Telescope (VLT) at Paranal, Chile, while using the Cryogenic high-resolution InfraRed Echelle Spectrograph (CRIRES) instrument. Since it was first commissioned in June 2006 (Käufl et al. 2004, 2006), CRIRES has greatly improved the availability of observations in the near-infrared (NIR) part of the electromagnetic spectrum due to its high spatial and spectral resolution. The instrument has made possible spectroscopic studies of difficult to detect phenomenon and objects, including direct detection of spectral lines of molecules in the atmosphere of extra-solar planets or in circumstellar disks, making it an excellent fit for this particular project.

At Paranal observatory, CRIRES is situated at the Nasmyth A focus of VLT Unit Telescope 1 (UT1), and consists of both the actual spectrograph to separate the light into different components used for analysis and the adaptive optics system called MACAO (Multi-Applications Curvature Adaptive Optics), allowing for the corrections of light distortion caused by atmospheric turbulence before the beams are directed towards the common focus at the telescopes interferometer. It gives an increase in sensitivity that significantly increases the efficiency of the telescope and maximizes the SNR and spatial resolution, qualities that are absolutely vital when observing faint objects such as exoplanets or debris disks.

Chapter 5. Observational Information & Models

CRIRES provides a nominal resolving power of 105 in the 1 − 5 μm range (more specifically 950 to 5200 nm), approximately corresponding to a radial velocity of 3 km s-1. The instrument provides three different slits with a length of 40 arcsec and possible widths of 0.0, 0.2, and 0.4 arcsec. The images taken with the camera have a plate scale of approximately 0.086 arcsec per pixel. The echelle grating uses a mosaic of four different Aladdin III InSb (indium-antimonide) detector arrays in the focal plane of 4 × 1024 × 512 pixel resolution in order to maximize the spectral coverage, providing four separate images at different wavelengths. The entire spectrograph is housed inside of a cryogenic vacuum chamber, cooling the optics to ~ 60 − 80 K and the detectors to ~ 25 − 30 K. Outside of the cryogenic environment sits the calibration unit, providing light sources for wavelength calibration and detector flat-fielding. A full schematic overview of the CRIRES detector array can be seen in Figure 5.1, while the following section will discuss why CRIRES is used for this thesis and which types of observations have been performed with it previously.

Figure 5.1: Schematic overview of the four CRIRES science detectors. Only the bottom half of the detector mosaics are used for obtaining images, resulting in spectral images of size 1024 × 512 pixels. Image credit to Käufl et al. (2004).

Section 5.1.2. Use in Exoplanetary Spectroscopy

As detailed in Section 2.1.4 & 2.2.3, direct imaging of extrasolar planets and direct spectroscopic detection requires particular high-dispersion spectral capabilities. The dispersive capacity of a spectrograph refers to how well the instrument is able to

Chapter 5. Observational Information & Models disperse the light and separate it into its component wavelengths. This is typically measured by the spectrographs spectral resolving power, 푅, defined in Formula 1.1 (Section 1.1), where Δ휆 is the spectral resolution; the shortest difference in wavelength distinguishable at a given wavelength 휆. The CRIRES instrument splits the incoming light very finely into the separate wavelengths, with the diffraction grating providing a nominal resolving power of 푅 = 105 when using a 0.2 arcsec slit. This yields a spectral resolution of 0.1 − 0.5 Å in the 1 – 5 μm wavelength range of the spectrograph, highly necessary both in order to resolve individual molecular lines and to distinguish the planetary lines from stationary telluric and stellar lines.

High-dispersion spectroscopy has often been recognized as potentially one of the most useful approaches to characterizing the atmospheres of extrasolar planets and the material found in debris disks, though only very recently have the first successful detections been made. Only a small number of infrared, high-dispersion spectrographs are currently in operation or planned and are able to achieve the needed resolving power to detect molecular absorption lines in the spectra of extrasolar planets (Snellen et al. 2015), including CRIRES (currently undergoing an upgrade, see Section 5.1.3), and the planned spectrographs METIS and HIRES for the E-ELT.

Given the rarity of these powerful instruments, CRIRES has been particularly successful so far in combining high-dispersion spectroscopy with high contrast imaging to characterize exoplanetary atmospheres and detecting molecular absorption lines. Accomplishments such as measuring carbon monoxide (CO) in the transmission spectrum of the planet HD209458b at 2.3 μm (Snellen et al. 2010), detecting CO in the thermal spectrum of tau Boötis b (Brogi et al. Nature 2012; Rodler et al. 2012), HD 189733b (de Kok et al. 2013; Rodler et al. 2013) and 51 Pegasi b (Brogi et al. 2013), and measuring absorption by water vapour in the spectrum of HD189733b (Birkby et al. 2013) have all been made utilizing CRIRES data. By using observational data treated by the CRIRES instrument in this thesis we can assess how well the spectrum extraction algorithm detailed in the previous chapter performs.

Observational strategies and computational reduction methods have been developed a great deal with regards to high-dispersion spectroscopy, yet improvements can always be made. With the upgraded CRIRES+ instrument in the near future, as discussed in the following section, spectroscopic detections are expected to improve a great deal, and high-performing and well-developed spectrum extraction methods will be immensely sought after to treat the data taken with a future, state-of-the-art spectrograph.

Chapter 5. Observational Information & Models

Section 5.1.3. Project Motivation; The CRIRES+ Upgrade

As of July 2014, CRIRES was removed from the UT1 telescope and is no longer operating while a project to upgrade the spectrograph is underway. The upgrade, titled CRIRES+, was originally scheduled for 2017, with first light now expected in the first quarter of 2019 (Dorn et al. 2014). CRIRES+ is one of the major motivations for this thesis, as when the upgrade is completed, the spectrograph will allow for even greater possibilities of directly imaging exoplanets and performing spectroscopy on them. As such, well-researched and established spectra extraction methods for these types of observations will be very valuable once a new generation of high-dispersion spectrographs become available to the scientific community.

The CRIRES+ upgrade will convert the instrument to a cross-dispersed spectrograph, giving an increase in wavelength simultaneously covered by a factor of ten. Expanding the wavelength range observed will allow for additional detection of multiple absorption lines simultaneously. In order to introduce the cross-dispersion, the spatial extent of the main slit is lowered to 10 arcseconds, down from the previous 40 arcsec, to balance the new implementations and current long slit availability. The new slit length is not expected to limit observations of moderately extended sources and it will maintain the optimal spectral resolution of 푅 = 105 (Dorn et al. 2014).

Figure 5.2: Comparison between the focal plane array of the upgraded and old detector mosaics for the CRIRES instrument, where the new detectors will increase the array size in the cross-dispersion direction by a factor of 2.7 whilst lowering the pixel size. Image credit to Dorn et al. (2014).

An additional major part of the upgrade is the installation of a new detector array to provide an increase in focal plane coverage. The new array, consisting of three HgCdTe (Mercury Cadmium Telluride) Hawaii 2RG detectors to replace the four InSb Aladdin ones, will yield a focal plane spanning 3 × 2048 × 2048 pixels (111 × 37 mm) with a pixel size of 18 μm, as compared to the old detector mosaic with a size of only 4 × 1024 × 512 (111 × 14 mm) at a pixel size of 27 μm, as can be seen in Figure 5.2,

Chapter 5. Observational Information & Models where the two mosaics are shown. The new mosaic area will yield an increase by a factor of 2.7 in the cross-dispersion direction, also providing a lower noise level and dark current, while at the same time yielding a higher quantum efficiency and cosmetic quality.

With the new upgrades, the CRIRES+ instrument will greatly improve on the sensitivity and quality of the observations of extrasolar planets and may in the future aid in detecting molecular absorption lines in nearby Earth-analogues. Once this becomes possible, either with CRIRES or other planned spectrographs, readily available data reduction software and spectrum extraction algorithms, providing instantaneous science and publication-ready data images, will aid in advancing the prospects of locating such molecular signals tremendously.

In the following section, we discuss and provide information about the target star for this thesis, Beta Pictoris, its companion planet, and why it is a good fit assessing the algorithm constructed in this particular thesis project.

Section 5.2. The Target System; Beta Pictoris

Section 5.2.1. Stellar and Planetary Information

The target star for the observations used in this thesis is Beta Pictoris, a well-known, young star system located in the Pictor constellation at a distance of ~ 19.75 parsecs (Brown et al. 2018). The stellar system has an age of 23 ± 3 Myr (Mamajek & Bell 2014), and has been studied extensively for almost 25 years, following the discovery of a large circumstellar debris disk in orbit around the star, the first one ever directly imaged in observations by Smith & Terrile (1984). As debris disks are typically very rare and are often found surrounding much older stars, the Beta Pictoris system is one of the most well-studied cases and is commonly regarded as a reasonable analogue for our own young solar system. The near edge-on orientation of the disk, extending several hundred, if not over 1000 AU (Larwood & Kalas 2001), allows for extensive studies of the early stages of stellar and planetary system evolution. In addition to a debris disk, it was long suspected that Beta Pictoris harboured an exoplanet as well, mainly due to evidence in the form of warping and perturbation of the inner parts of the disk, observed many times with the HST (Mouillet et al. 1997; Heap et al. 2000; Golimowski et al. 2006), and particular asymmetries seen in observations of the more external parts of the disk (Kalas & Jewitt 1995). These were most often attributed to gravitational perturbations caused by a large body, such as an exoplanet, supposedly in an inclined orbit around the star (Lagrange et al. 2012).

Chapter 5. Observational Information & Models

Despite the observed evidence, it was only as late as a decade ago that an extrasolar planet was discovered in orbit around Beta Pictoris by Lagrange et al. (2009a, b). The planet, Beta Pictoris b, was originally determined to be a gas giant with a mass of

푀훽 푃푖푐 푏 ~ 10 푀퐽푢푝 orbiting the star at a radius of 푎 ~ 8 − 13 AU, newly formed and still cooling down from the initial planetary formation process (Lagrange et al. 2010). In Figure 5.3, a composite image of the entire Beta Pictoris system can be seen in near- infrared light.

Figure 5.3: A composite image of the Beta Pictoris stellar system in infrared light with the stellar light mostly blocked out. The orbiting planet, Beta Pictoris b, is visible close to the centre of the image and the debris disk is seen extended outwards from the star. Image credit to ESO/A.-M. Lagrange et al.

The planet has been studied intensely since its discovery, further constraining the physical and orbital properties as methods and instruments have become more advanced. The planet is now known to be a super-Jupiter, of mass and radius significantly larger than Jupiter, with a planetary mass of 푀훽 푃푖푐 푏 = 12.9 ± 0.2 푀퐽푢푝 and a radius of 푅훽 푃푖푐 푏 = 1.46 ± 0.01 푅퐽푢푝 (Chilcote et al. 2017; Morzinski et al. 2015). The orbital parameters have been determined with many studies to an accuracy within one milliarcsecond, and which found a low-eccentricity orbit of 푒 < 0.17 with a very high inclination of 푖 = 88.5° ± 1.7°. The planet orbits with a semi-major axis of approximately 8 − 10 AU with an orbital period of 17 − 21 years (Chauvin et al. 2012; Bonnefoy et al. 2014; Wang et al. 2016).

Chapter 5. Observational Information & Models

Spectroscopic studies of the atmosphere of Beta Pictoris b in the infrared have shown that the planet has an extended, hot, dusty atmosphere with plenty of cloud-like formations (Bonnefoy et al. 2013). Still, analysis of the planetary atmosphere is in its early stages, and more advanced spectroscopic methods and higher resolution observations are needed to complete a full picture of the properties and molecular composition of the atmosphere. In the following section, we discuss why Beta Pictoris and its companion planet are studied for this particular thesis.

Section 5.2.2. Beta Pictoris as an Optimal Example

In this thesis, we study potential improvements that can be made to spectrum extraction algorithms for direct-imaging, high-dispersion spectroscopy of extrasolar planets. Only a small number of planets have ever been directly imaged, with an estimated 44 planets according to NASA’s Exoplanet Archive4. Of these, many are either not studied well enough as of yet or are known to be unfavourable for performing spectroscopic measurements on for other physical reasons. Several are rarely observed, and only a few have had more than one or two observing sequences as of yet, making observational data scarce and not particularly easily available. For most directly imaged planets, the orbital parameters are neither constrained well enough yet, and elements such as the semi-major axis and the orbital periods can be difficult to determine without many observations spanning several years. Only a very select few extrasolar planets have been directly imaged and studied for a long enough time that such properties are known to a reasonable precision. Some of the more well-examined such stellar systems are Fomalhaut, HR 8799, and Beta Pictoris, all with planets discovered in 2008 and observed many times since (Lagrange et al. 2009a, b; Marois et al. 2008; Kalas et al. 2008).

This thesis specifically examines the direct spectroscopic detection method for extrasolar planets using high dispersion and high contrast imaging. In order for this method to be viable, high SNRs of the planets are necessary, further complicating the planetary selection process for spectroscopic measurements. The exoplanets have two ways of emitting light; thermal emission and reflection from the parent star. The brightness of young exoplanets will almost entirely depend on their thermal self- luminosity, as it is expected that most of their brightness will come from the planets themselves, and not the reflected light from the stars (de Pater & Lissauer 2015). Circumstellar objects will receive a fraction of the incoming stellar light according to the definition of radiative flux, where the amount of photons from an object passing through a given area decreases with the inverse square of the distance (Formula 5.1),

4 https://exoplanetarchive.ipac.caltech.edu/ 76

Chapter 5. Observational Information & Models meaning a planet orbiting at 10 AU will only receive 1/100 the light of a planet orbiting at 1 AU. For these exoplanets, the method will therefore only be limited by how short the orbital distance to the star is, as if it is too close they will become completely indistinguishable from the star (Fischer et al. 2014).

퐿 퐹 = (5.1) 4휋푟2

All of these restrictions for choosing a planetary candidate to perform direct spectroscopy on leaves even fewer possibilities, and it can be determined that Beta Pictoris is an optimal choice for attempting the spectrum extraction method described in this thesis due to several of the aforementioned properties of the circumstellar environment around the star already substantially established. As we only attempt to improve on already existing measurements and methods, a well-studied example is an ideal place to begin. We already know much of what to expect from the system, such as the necessary information about the system to precisely know the exact position of the exoplanet and its separation from the parent star. In addition, Beta Pictoris has been abundantly observed with high dispersion spectrographs, from which much of the data is publicly available to the scientific community (see Section 5.3) and can be used for various types of studies of the system. Studying Beta Pictoris to assess the performance of the spectrum extraction algorithm, and which improvements can be made, allows us to better understand how such an algorithm can be used in the future for newly discovered exoplanets in order to probe the atmosphere for the molecular composition. In the following section, we discuss in-depth the technical details of the observational data used for this project.

Section 5.3. Observations and Standard Reductions

Section 5.3.1. Observational Data

The observations of the stellar system Beta Pictoris used in this thesis to test our spectrum extraction algorithm were performed at ESO’s VLT facility at Paranal Observatory in Cerro Paranal, Chile, while using the CRIRES instrument. The system was observed on the night between the 17th and 18th of December 2013 for almost one hour, from 00: 57 to 01: 47, when the star was located at a right ascension and declination of approximately ~ 05: 47: 17 & − 51: 03: 59 (J2000), respectively. A total of 44 exposures of 4 × 10 seconds each were taken, granting a total exposure time of 1760 seconds. The average airmass and seeing of the atmosphere throughout the night was between 1.3 − 1.5, and 1′′ – 1.3′′, indicating moderate to good conditions. 77

Chapter 5. Observational Information & Models

The observational data used for this project originates from an ESO observation program, with ID 292.C-5017(A) – “The fast spin-rotation of a young extra-solar planet”, carried out by Snellen et al. (2014). The program was allocated one hour of Director’s Discretionary Time (DDT), during which the Beta Pictoris system was observed. Any scientific data gathered at an ESO telescope is normally exclusive to the Principal Investigators (PIs) who submitted the proposals for the telescope time and performed the observations for a proprietary period of no more than one year. After this period, the raw scientific data products are made readily available to the public worldwide through the ESO Science Archive Facility5, where the raw, processed, calibration, and acquisition data can be found in the ESO Archive Browser6. This research has made use of the services of the ESO Science Archive Facility.

For these observations, the CRIRES slit of width 0.2 arcsec and length 40 arcsec was used, oriented such that the star and planet were both encompassed in the images. The orientation of the slit was rotated 30 degrees North through East, with the planet located approximately 0.4 arcsec South-West of the parent star, i.e. approximately ~ 4 – 5 pixels below the central row of the stellar spectrum in the images, given the detector’s pixel size of 0.086 arcseconds. The location of the exoplanet was determined in accordance with, at the time, close-at-hand high-contrast observations (Bonnefoy et al. 2013). In Figure 5.4 below, the approximate location of the planet in the stellar spectrum is shown.

Figure 5.4: Spectral image of the Beta Pictoris system, zoomed in to show the location of the star and planet in the spectrum. The star is located at the centre of the signal, while the planet is located 4 – 5 pixels (~ 0.4 arcsec) below in the spatial direction, as per the pixel size of 0.086′′.

5 http://archive.eso.org/cms.html 6 http://archive.eso.org/eso/eso_archive_main.html 78

Chapter 5. Observational Information & Models

The wavelength ranges of the spectrograph’s four detectors used for the observations were all in the near-infrared K-band, with the specific wavelengths detailed in Table 4 below.

Detector 1 Detector 2 Detector 3 Detector 4 Ref. 휆 훿휆 휆min 휆max 휆min 휆max 휆min 휆max 휆min 휆max

2325.2 2287.5 2300.2 2303.8 2316.1 2319.8 2331.1 2334.1 2345.4 11.5

Table 4: Wavelength ranges of the four detectors used for this thesis. All wavelengths are expressed in vacuum and in nm, with the exception of the last column, the mean dispersion of the detectors which is in units of 10−3 nm/pixel. The reference wavelength refers to the 512th pixel in the spectral direction of detector 3.

The 44 exposures taken were arranged to utilize an AB – BA dither pattern in order to provide for a proper reduction of sky background noise and potential instrumental defects. With this pattern, two images are paired and subtracted from each other, and subsequently combined for each image of the two-dimensional spectrum of the system. A further overview of the observational and calibration images is detailed in the following subsection.

Section 5.3.2. Observational and Calibration Image Overview

All raw spectrum images retrieved from the ESO Science Archive are provided in one consistent format where the recorded spectra from the four detectors are saved in extended FITS-files with each extension containing one of the four frames at different wavelength ranges where each frame has a size of 1024 × 512 pixels. These frames can be viewed and interacted with in programs such as SAOImage DS9, although the actual data processing and handling will be made in an integrated development environment (IDE) running on the Python 3.6 programming language, in this case, the Spyder software application.

In addition to the raw spectrum data frames from the observations, the ESO Science Archive also provide all of the necessary calibration images in order to properly reduce the scientific data. The detectors will have some systematic noise from dark current; electricity flowing through the CCD even when no light is striking the detector, and from pixel-to-pixel sensitivity variations, vignetting, and dust shadows; usually solved by flat fielding (Chromey 2010). Furthermore, the CRIRES detector arrays are subject

Chapter 5. Observational Information & Models to non-linearity effects in the case of high ADUs (Analog-to-Digital Units) of > 4000 in the conversion from measured electrons in the CCD to the pixel count, which will need to be corrected for. Pixels with higher ADU than this level will saturate the detector to the point where it cannot contain more charge, ‘spilling over’ electrons into nearby pixels in the same column and contaminating the data. To perform this correction, each pixel is fit according to the second-degree polynomial in Formula 5.2,

signal = 퐴 + 퐵 × DIT + 퐶 × DIT2 (5.2) where ‘signal’ is the signal conversion, A, B, and C are coefficient images, and DIT (Detector Integration Time) is the individual exposure time of the data frames. According to the CRIRES reduction pipeline, the first derivative of Formula 4.2 of the measured and true signal should be equal for short exposures, giving the solution for the correction of each individual pixel seen in Formula 5.3 and 5.4.

퐶 signal = 퐴 + signal + × signal2 (5.3) true 퐵2 true

4퐶(퐴 − signal) (−퐵2 + 퐵2 × √1 − ) 퐵2 (5.4) signal = 퐿(signal) = true 2퐶

To produce a reduced data frame which can be used to perform the spectrum extraction algorithm on from a raw science image, further calibrations are also required beyond those already mentioned. From the ESO Science Archive, we have acquired the following calibration frames; a number of dark current frames, a number of flat field frames, a coefficient map frame to perform the non-linear corrections, several frames from a Thorium-Argon arc lamp providing a wavelength calibration, bad pixel frames used to mask known defective pixels, and one-dimensional spectra for a model atmosphere above the Paranal Observatory for potential removal of telluric lines from the extracted spectrum. Examples of a raw science data frame is shown in Figure 5.5 below.

Chapter 5. Observational Information & Models

Figure 5.5: Raw science data frame recorded by one of the four CRIRES detectors. The signal from the stellar system is seen as the bright spectrum in the centre of the images. The frames contain a number of defects that will need to be corrected before they can be used for scientific analysis.

As can be seen in the raw data frame, there are a number of very bright, white pixels visible in Figure 5.5. These are either a result of defective pixels that have not or cannot record a pixel count, or extremely high-energy particles of cosmic origin that, by coincidence, strike the detectors during the exposure. These particles are often called cosmic rays and mostly consist of protons and helium nuclei (alpha particles). As the rays pass through the CCD detector, the electrons in the affected pixels will be excited and a significantly high count will be recorded. Depending on the incoming angle of the particle, more than one pixel may be contaminated, which can be seen as a straight line of high-count pixels in a track across the data frame. Typically, these events can be identified by a mere inspection of the CCD image, although if the particles strike on or near the object spectrum it may be difficult to distinguish it without inspecting each individual pixel. This may also contaminate the object spectrum heavily as spectra pixels hit by a cosmic ray will no longer be usable.

Several methods exist for eliminating these defects without damaging the remaining object spectrum. In reality, the best scientific approach would be to reject contaminated data and not attempt to ‘repair’ it (Horne 1986), which can be achieved by applying a mask to the data frames that simply ignores any such values. However, this leads to further problems with our algorithm. Since we resample the data frames to a higher resolution and shift columns according to the tilt of the spectrum, many pixels will be affected by the masked values during the extraction process, making the algorithm calculations unnecessarily more difficult to program, and a different approach will be taken by replacing any such affected pixels, described more in the following section. With the raw spectrum data frames, calibration frames, and an understanding of which reductions must be made, we can now describe in more detail how the reduction process is completed next.

Chapter 5. Observational Information & Models

Section 5.3.3. Standard Data Reductions

Before we can begin the implementation of the extraction algorithm and subtracting the stellar light contribution, a standard data reduction of the two-dimensional spectra images must first be performed. The data reductions of the observations will be performed in Python version 3.6 according to the steps in the standard ESO-CRIRES reduction pipeline7, as recommended by the CRIRES User Manual8 and used by the PIs of the data frames (Snellen et al. 2014). These reductions will be completed manually instead of with the CRIRES pipeline software to ensure that no reductions are made that will complicate the later extractions and stellar reductions, although the same steps are still followed throughout the process. The CRIRES reduction pipeline follows a recipe consisting of seven steps, which are detailed in Table 5.

Step Process Corresponding process

1 Dark subtraction 퐶휆푥 − 퐷휆푥

2 Correction for detector non-linearity 퐿(퐶휆푥)

3 Flat-fielding 퐶휆푥/퐹휆푥

휆+5 1 4 Cosmic rays / bad pixels correction 푆 = ((∑ 푆 ) − 푆 ) 휆푥 10 휆푥 휆푥 휆−5

Combination of nodding exposures 5 푆 (퐴) − 푆 (퐵) (dithering) 휆푥 휆푥

6 Spectrum extraction ∑ 푆휆푥 푥 7 Wavelength calibration −

Table 5: CRIRES science data reduction pipeline steps. These steps are detailed further below and deliver reduced data ready for scientific analysis of the object spectrum investigated.

We will not perform the spectrum extraction step of the pipeline, as this is treated with the specific algorithm detailed in Chapter 4, and the wavelength calibration is performed automatically. Save for these exceptions, the remaining steps are followed thoroughly.

7 ftp://ftp.eso.org/pub/dfs/pipelines/crires/crire-pipeline-manual-1.13.pdf 8 http://www.eso.org/sci/facilities/paranal/instruments/crires/doc/VLT-MAN-ESO-14500-3486_V93.pdf 82

Chapter 5. Observational Information & Models

Subtraction of the dark current is performed by first creating a master dark frame, 퐷휆푥, from the mean of several dark images taken throughout the observing time and subtracting the frame from the raw spectrum image, 퐶휆푥. Similarly, a master flat frame,

퐹휆푥, is created by the addition of the brighter sections of several flatfield images and later normalization, which will be divided from the raw data frames. Non-linearity corrections, 퐿휆푥, are performed according to the formulae shown in the previous section, Formulae 5.2, 5.3, and 5.4, where the coefficient images A, B, and C have been provided with the calibration data from the ESO Science Archive. The total operations performed on the raw spectrum images can now be written as Formula 5.5,

퐿(퐶휆푥 − 퐷휆푥) 푆휆푥 = (5.5) 퐹휆푥

where 푆휆푥 is the reduced science image, 퐶휆푥 is the raw observational image, 퐷휆푥 is the master dark frame, 퐹휆푥 is the master flat frame, and 퐿 is the non-linear correction. Every raw spectrum image is reduced by means of Formula 5.5 before the subsequent corrections are made.

The final step in the initial reduction process is the correcting of bad pixels and cosmic rays. As discussed in the previous section, we have elected to replace any such pixels with the mean of the closest pixels in the same row, so as to not impede the extraction algorithm later on, even though the standard procedure is to simply mask any such defective pixel. While the CRIRES calibration data provides a bad pixel mask for the detectors, this mask will not affect pixels containing cosmic rays or NaN pixels (Not a Number, i.e. the detector has been unable to measure a photon count). For this reason, it is easier to simply replace bad pixels, cosmic rays, and NaN values all at once by using a nearest-neighbour algorithm, where a determined set of pixels are replaced by the mean of the nearby pixels in the same row.

This set of pixels will consist of the those from the bad pixel mask provided by the calibration data, any pixel which displays a NaN value, and those pixels counts that are deemed to be the result of cosmic rays. To investigate for this, we implement an addition calculation that measures the count of each pixel, and if the count is found to be greater than the sum of a certain number of surrounding pixels, it is replaced by the mean pixel count of those it is compared to. The same principle is used to replace values from the bad pixel mask and NaN values. The operations performed to make these corrections are summarized in Formula 5.6a and 5.6b below, while Figure 5.6 shows an example data frame at before and after the initial reductions are made and all cosmic rays and other defective pixels have been filtered out.

Chapter 5. Observational Information & Models

휆+5

If 푆휆푥 = [0 or NaN] or 푆휆푥 > ((∑ 푆휆푥) − 푆휆푥) → (5.6a) 휆−5

휆+5 1 → 푆 = ((∑ 푆 ) − 푆 ) (5.6b) 휆푥 10 휆푥 휆푥 휆−5

In these formulae, 푆휆푥 refers to individual pixels in the reduced science images at position (휆, 푥) where, if it is found that the pixel is equal to 0, NaN, or larger than the sum of closest five pixels in the same row in both directions, it is replaced by the mean of those same closest pixels.

After all of the raw spectrum images have been properly reduced, we can combine images according to an AB-BA dithering pattern to further subtract the sky background noise. These observations took advantage of the nodding technique, a method where the object spectrum is moved along the detector slit between two positions, A and B, while keeping the slit parallel. One exposure can then be made at position A, after which the telescope is moved to position B where another is taken, followed by one more at the same position B, ending the sequence by moving it back to position A for one final exposure. This allows for two individual exposures to be paired and subtracted from each other and for the 퐴 − 퐵 and 퐵 − 퐴 images to later be combined if necessary. The new 퐴 − 퐵 and 퐵 − 퐴 data frames will then contain both a positive and a negative spectrum which can both be used for the extraction.

Chapter 5. Observational Information & Models

Figure 5.6: A raw, zoomed-in science data frame before (above) and after (below) the initial reductions and defective pixel filtering are made. Before the reductions are completed, the image is filled with cosmic rays, known detector defects, and dark current that are all removed during the process. The reduced images only contain a noise background and the object spectrum in the centre.

The final step in the CRIRES reduction pipeline is the wavelength calibration, to ensure that the pixels in the spectral direction are measured at their correct wavelength. This step is done with the aid of the ThAr arc lamp wavelength map provided by the calibration data and the wavelength calibration will be added automatically to the raw science frames. With all the initial reduction steps complete, we should now have reduced, calibrated, and dithered spectrum data frames that can be processed with the spectrum extraction algorithm described in the previous chapter. One of these data frames is shown in Figure 5.7 for one of the wavelengths of the detectors.

Figure 5.7: Example of a reduced spectral image of the Beta Pictoris stellar system for one exposure of 10 seconds. This frame includes the dithering process which produces a second, negative spectrum below the positive section that can also be used for analysis and reduces the total amount of frames by half.

Chapter 5. Observational Information & Models

Section 5.4. Model Data Frames

In addition to the Beta Pictoris data frames, we will also attempt the spectrum extraction for three artificial planets inserted into model data frames. The three models will be used to test the performance of the algorithm for brighter planets located further away from the star, where the scattered stellar light is not as prominent. As discussed in Section 4.3.2, the planet Beta Pictoris b is approximately 1/4500 as bright as the parent star in the K – band, which may be too faint to detect and extract the spectrum from, even with a near-perfect stellar light reduction. The pixel counts (i.e. the recorded ADU conversion) in the Beta Pictoris data frames are estimated to be 500 at the central spectrum peak, and the planet would, therefore, only exhibit a pixel count of ~ 0.1 in each column. Given that the noise in the data frames accounts for a pixel count of ~ 1 − 5, it is highly likely that the planet will not be detectable in the two- dimensional spectral images or in the extracted spectrum unless the stellar light is completely and perfectly reduced. As it is not expected that the algorithm will perform at such ideal levels, using modelled planets of higher flux is a useful technique for testing the algorithm theoretically.

We have constructed three different models of data frames containing an artificial planetary spectrum inserted into the reduced Beta Pictoris frames obtained in this chapter. The models will consist of a telluric absorption spectrum with H2O, CO, and

CH4 lines found in the K – band at separate wavelengths than the specific data frames where the model signal will be inserted, as is necessary for the algorithm to function. In the results chapter, we mainly present results obtained at one of the four wavelength ranges, specifically that of Detector 1 (2281 − 2301 nm), and the telluric line spectrum inserted into the Beta Pictoris frames obtained with this detector is shown below in Figure 5.8. Inserting an artificial planetary spectrum into the data frames is achieved in the following manner:

• Begin with a data frame of Beta Pictoris from one of the CRIRES detector, for example, Detector 1 (2281 − 2301 nm) and one frame from the succeeding one, in this case, Detector 2 (2304 − 2316 nm).

• Obtain all pixels containing the telluric spectral lines from Detector 2, and scale them down to the desired flux by dividing the pixel counts (e.g. 1/100 or 1/1000).

• Add the pixel counts from the spectrum of Detector 2 onto the pixels of Detector 1 at the desired angular separations (where 1 pixel separation represents 0.086 arcsec).

Chapter 5. Observational Information & Models

Figure 5.8: Telluric absorption lines typically found at wavelengths between 2304 and 2316 nm inserted into the Detector 1 wavelength range. These absorption lines will act as the reference planetary spectrum and must be taken from a different wavelength range than that of the star for the algorithm to function properly.

The flux of the three spectra models will be established to be at 1/1000 퐹훽 푃푖푐 (Model

1), 1/100 퐹훽 푃푖푐 (Model 2), and 1/100 퐹훽 푃푖푐 (Model 3) where 퐹훽 푃푖푐 the average stellar flux in the Beta Pictoris frames. This will yield a planetary signal that is 4.5, 45, and 450 times stronger than the Beta Pictoris b flux. The planets will all be placed at a separation of 0.6 arcsec below the star in the images, indicating a planet located at an orbital distance of 12 − 13 AU. An example of how the inserted planetary spectrum appears in the two-dimensional spectral images is shown below, in Figure 5.9, which depicts the highest flux model (Model 3) and where the planetary signal is distinct enough to discern.

Chapter 5. Observational Information & Models

Figure 5.9: Two-dimensional spectral image of the Beta Pictoris stellar system with

a secondary, artificial planetary spectrum of strength 1/10 퐹β 푃푖푐 (Model 3) inserted at − 0.6′′. The signal is somewhat distinguishable from the background and can be seen located between the two red arrows. A planet cannot realistically be found at such brightnesses, and in such a case it would affect the spectrum heavily.

While these are likely unrealistic flux levels to find at such an orbital distance in real exoplanetary systems, they will allow us to test how bright a planet must be in order to detect it in the reduced spectrum of a star, and if the algorithm works in theory regardless if it is able to detect Beta Pictoris b or not. In Figure 5.10 below, the total spatial profile of the three models is shown, i.e. the sum of every spatial profile found in the columns of the frames. Images which display the total signal of the system in the spatial direction are useful in order to detect the presence of signal of a possible second object in a stellar system, without having to analyze the extracted spectrum since it shows the total flux at each spatial position. We should, therefore, expect the flux to become somewhat larger for the planetary models and visible when summing all spatial profiles together.

The three models in Figure 5.10 shows how the planetary component affects the overall shape of the stellar PSFs, where Model 1 (1/1000 flux) will be essentially identical to the non-altered data frames, as the total planetary signal at its spatial location will only be approximately 1 % of the total flux at 0.6 arcsec, as the stellar flux at this separation is only one-tenth of the centre of the spectrum. For Model 2 (1/100 flux), we see a noticeable difference from Model 1, as the second modelled planet is ten times brighter, corresponding to an increase in total flux of 10 %. The third model (1/10 flux) will naturally be very visible even before the stellar light has been reduced, due

Chapter 5. Observational Information & Models to the increase in total flux of 100 % (i.e. double the flux) at the planetary position. The results from using the spectrum extraction algorithm on these three models will be included in the following results chapter, Chapter 6.

Figure 5.10: Total signal of the Beta Pictoris stellar system in the spatial direction with three separate planets inserted into the spectrum. The planet found in Model 1 is indistinguishable from the normal spectrum given that the signal is still too faint. The signal in Model 2 is almost equal to Model 1 despite the flux being ten times higher, although a small difference can be noticed at the planetary location. The planet found in Model 3 is seen to heavily affect the signal, creating a large increase in flux at the spatial location which extends to and increases the stellar flux due to the blurring of the planetary PSF. The location of the planet is marked with the red area, showing how far the PSF can extend the signal.

Results of the summation of the spatial signal can be useful to analyze to determine the effectiveness of the stellar reduction, as if the entire stellar signal is managed to be subtracted we would expect these images to be close to zero at all positions. Somewhat large negative or positive pixel values may indicate the presence of the planet and its spectral lines, or simply that there has been a problem with the reduction process and the stellar light is not properly subtracted. In the following chapter, the results of assessing the performance of the extraction algorithm are presented for the Beta Pictoris and model frames.

Chapter 6.

Results of Spectrum Extraction

In this chapter, we present the results of implementing the spectrum extraction algorithm for a number of different cases. These include extracting the spectrum of the planet Beta Pictoris b with Resampling Method 1 and 2, as well as the spectrum of three artificial planets inserted into the Beta Pictoris spectrum for RM1. The algorithm has been applied to data frames of all four wavelength ranges described in Chapter 5, although, as we have found very limited variation between separate exposures and wavelengths, only a few examples of each kind of result for one of the wavelength ranges (that of Detector 1, see Table 4) will be presented.

To begin with, images of the Beta Pictoris system before the algorithm has been implemented are displayed in order to have an example to compare with for their appearance before the stellar signal is reduced. This will include a two-dimensional spectral image of the system in Figure 6.1, an image of the extracted spectrum of the system in Figure 6.2, and an image of the sum of the total flux at specific spatial positions of the system in Figure 6.3.

These will display what can be expected of such an exoplanetary system before the stellar contribution is subtracted and is used for comparison with the later images after the algorithm implementation. In the following subsections, the results of attempting the spectrum extraction algorithm for the standard reduced images of Beta Pictoris (see Section 5.3) for the RM1 and RM2 cases will be shown in Sections 6.1 and 6.2, followed by the results with RM1 for artificial planets inserted in the Beta Pictoris spectral images of various fluxes (see Section 5.4) in Section 6.3.

Chapter 6. Results of Spectrum Extraction

Figure 6.1: Two-dimensional spectral image of the Beta Pictoris stellar system at 2.287 − 2.301 μm. The spectral dimension is located on the x-axis and the spatial dimension on the y-axis, while the colorbar on the right axis shows the total pixel count of each pixel. However, due to the tilted spectrum, the spatial position is only accurate at the left-most columns, and moves with the centre of the spectrum.

Figure 6.2: Spectrum of the Beta Pictoris stellar system at 2.287 − 2.301 μm, extracted by summation of the spectral image in Figure 6.1 in the spatial direction. Essentially all of the absorption lines in this spectrum are telluric lines from interactions in Earth’s atmosphere and are not from the star. Most of the lines are from water (H2O), carbon monoxide (CO), and methane (CH4).

Chapter 6. Results of Spectrum Extraction

Figure 6.3: Total flux of the Beta Pictoris stellar system in the spatial direction at 2.287 − 2.301 μm, extracted by summation of the spectral image in Figure 6.1 in the spectral direction. The figure shows the total pixel counts found at various spatial positions of the two-dimensional image. The total count at the peak is ~ 330 000 and is somewhat offset from the centre of the image due to the tilt of the spectrum.

Section 6.1. Spectrum Extraction of Beta Pictoris b with RM1

In this section, we present the results for the spectrum extraction of the exoplanet Beta Pictoris b while using Resampling Method 1 to increase the resolution of the original data frames. Images of the same kind as shown in Figures 6.1 – 6.3 will be presented, meaning the two- and one-dimensional spectrum and the extracted spatial signal. In Figure 6.4, the residual light of the system can be seen after the stellar light has been subtracted by using the mean of 5, 11, and 31 columns to create the reference profiles in Step 4 of the extraction algorithm. We find it is sufficient to display these three cases only for the first attempted extraction with RM1 to display the difference between them. In the following sections, only the results which yield the lowest residuals after the subtraction are presented. A perfect reduction would be indicated by no residual stellar light remaining with only the background noise and, possibly, some faint planetary spectral lines visible.

Chapter 6. Results of Spectrum Extraction

Figure 6.4: Residual spectral images of the Beta Pictoris system at 2.287 − 2.301 μm after reduction with RM1 by reference spatial profiles created from the mean of 5 (top panel), 11 (bottom left), and 31 (bottom right) columns. The colorbar details the counts of individual pixels. The frames are of size 20 × 1024 pixels, as it is only necessary to display the centre of the spectrum where the reduction occurs.

As seen in Figure 6.4, a perfect stellar subtraction has not been achieved, as some residuals from the star remain. These residuals appear as a few brighter and darker pixels, where the centre of the spectrum has not been reduced enough, and a few pixels outwards, in the wings, the reduction is too high and the pixel count becomes negative. This suggests that the reference profiles are broadened and had a low peak amplitude and high wing amplitude, a problem discussed in Section 4.3.1 for RM2 which appears to occur for RM1 as well.

However, an additional type of residuals also exists in Figure 6.4, particularly around absorption lines, where the opposite to other parts of the spectrum occurs and the centre of the lines are excessively reduced while the wings are insufficiently reduced.

Chapter 6. Results of Spectrum Extraction

It is also seen that there are no major differences in the residual pixel counts between the three frames, which all fall in the range of approximately ±20, where the noise is expected to have a pixel count in the range of 0 − 5. The residuals are somewhat more visible in the bottom right panel of Figure 6.4, indicating that the use of 31 profiles to create the mean reference profiles may be too many.

On average, the stellar light is reduced by a factor of 50 − 100 at the centre of the spectrum, while the wings are reduced by more than the original pixel count caused by the broadening effect. Due to the very faint flux of the planet and this effect, there is no sign of planetary spectral lines in the spectral images. Next, we present the extracted planetary spectrum at the approximate location of the Beta Pictoris b exoplanet in Figure 6.5 for the three reference profile creation methods. As expected from to the results seen in Figure 6.4, the noise is simply too high for any particular spectral lines to be visible, likely due to the profile broadening effect. A few negative spikes stand out from the noise, although not enough to conclude they are really absorption lines.

Figure 6.5: Extracted planetary spectrum at the Beta Pictoris b exoplanet location at 2.287 − 2.301 μm after the stellar reduction has been performed with RM1 by reference spatial profiles created from the mean of 5 (top panel), 11 (bottom left), and 31 (bottom right) columns.

Chapter 6. Results of Spectrum Extraction

Lastly, we display the result from the summation of the reduced data frames in the spectral direction, showing the total signal from the system at each spatial position. This is shown in Figure 6.6, and here it can be seen how the shape of the reference profiles have affected the shape of the stellar PSFs. Recall from Figure 3.6 how the theoretically expected spatial signal should appear after the stellar light reduction, where we should only see a baseline of noise and a faint signal from the planetary spectral lines. As expected, instead it is seen that the wings have a very negative total pixel count, while the centre is somewhat less negative. Although the centre of the spectrum should most likely be equally positive, the large negative pixel counts found at absorption lines have probably affected the total count as these images are a summation along every column which causes the sum of the centre of the spectrum to become negative as well. Regardless, the centre still has a larger amplitude than the wings, again indicating a broadening of the reference spatial profiles.

Figure 6.6: Signal from the Beta Pictoris system in the spatial direction at 2.287 − 2.301 μm after the stellar light reduction has been performed with RM1 by reference spatial profiles created from the mean of 5 (top panel), 11 (bottom left), and 31 (bottom right) columns. The irregularity found at the centre of the spectrum is most likely caused by the tilt of the spectrum.

Chapter 6. Results of Spectrum Extraction

Section 6.2. Spectrum Extraction of Beta Pictoris b with RM2

In this section, we present the same results as in the previous section, with the exception that the results are obtained by using interpolation as a resampling method with RM2. We also no longer present the results for three different reference profile cases, and only shows the results which had the lowest residual values.

We begin with the two-dimensional spectral images found in Figure 6.7, where the main difference between the two resampling methods is clearly visible. As discussed in Section 4.3.1, the residuals are much larger than for the RM1 case due to the broadening of the reference profiles during Step 5 of the algorithm. The stellar spectrum is now very clearly visible in all three images in Figure 6.7, with the residual flux estimated as approximately twice as large in the range of ±50 pixel counts.

Figure 6.7: Residual spectral images of the Beta Pictoris system at 2.287 − 2.301 μm after reduction with RM2 by reference spatial profiles created from the mean of 5 columns.

In Figure 6.8, we present the extracted spectrum of the system at the planetary location for the RM2 reduction case. The peaks in the spectrum resembling spectral lines are not caused by the exoplanet and are instead residual telluric absorption lines from the stellar position of the spectrum. These lines have not been properly subtracted by the algorithm and remain even at the planetary position. We also see that these residual lines are not present in Figure 6.5, detailing the extracted spectrum while using RM1, further evidence for the advantage of the first method.

Chapter 6. Results of Spectrum Extraction

Figure 6.8: Extracted planetary spectrum at the Beta Pictoris b location at 2.287 − 2.301 μm after the stellar reduction has been performed with RM2 by reference spatial profiles created from the mean of 5 columns.

Lastly, the results for extracting the spatial signal of the system are shown in Figure 6.9. As expected, the signal in the three images further substantiates the fact that the reference profiles are highly broadened and causes very large residuals, ensuring that it will be virtually impossible to discern the planetary signal given that they range from −10 000 to 2000 pixel counts.

Figure 6.9: Extracted spatial signal of the Beta Pictoris system at 2.287 − 2.301 μm after the stellar reduction has been performed with RM2 by reference spatial profiles created from the mean of 5 columns.

Chapter 6. Results of Spectrum Extraction

We have previously mentioned a different method for attempting the spectrum extraction using RM2 (see Section 4.3.1), which involves not performing the summation in Step 5 of the algorithm and instead subtracting the higher resolution (10000 × 1024 pixels) reference frames from the resampled original data frames of the same size. The results for this method are presented below in Figure 6.10, which shows the two- dimensional spectrum. We can immediately see that the residuals are lower than those found in Figure 6.7, and more closely resemble the results from using RM1, shown in Figure 6.4. This indicates that the resampling method works somewhat well up until the summation of sub-pixels, and if the issue found during this step could be solved, the method may be more viable.

Figure 6.10: Residual spectral images of the Beta Pictoris system at 2.287 − 2.301 μm after reduction with RM2 by reference spatial profiles created from the mean of 5 columns. These frames have not been resampled for a second time to revert to the original resolution, and are of size 10000 × 1024 pixels.

Section 6.3. Spectrum Extraction of Artificial Planets

In this section, we present the results for attempting the spectrum extraction algorithm for the three modelled planets detailed in Section 5.4. These are artificial planets placed in the Beta Pictoris spectrum somewhat further out than the actual planet (at approximately 0.6′′ below the star) and have strengths of 1/1000, 1/100, and 1/10 of the stellar flux, as compared to Beta Pictoris b, which has a strength of 1/4500 퐹훽 푃푖푐 at these particular wavelengths. As in the previous sections of this chapter, the results of the reduction and spectra extraction process will be presented as a two-dimensional

Chapter 6. Results of Spectrum Extraction spectral image, an extracted one-dimensional spectrum, and an extracted spatial signal for the different models. Since Section 6.2 showed that the second resampling method is less viable than the first, only results for the models using RM1 are presented, as we wish to find the most satisfactory results, and as such, there is no need to also present results already known to have more residuals and lower SNR.

We begin with the results for the Model 1 planet, an exoplanet with a flux level of

1/1000 퐹훽 푃푖푐 and ~ 4.5 퐹훽 푃푖푐 푏 in the K – band. In the figures below, we see the two- dimensional spectral image (Figure 6.11), the extracted spectrum (Figure 6.12), and the extracted spatial signal (Figure 6.13).

Figure 6.11: Residual spectral images of the Model 1 exoplanetary system at 2.287 − 2.301 μm after reduction with RM1 by reference spatial profiles created from the mean of 5 columns.

In Figure 6.11 above, no planetary spectral lines are particularly visible in the two- dimensional spectrum, most likely due to the continued weak flux levels, and they are easily lost in the noise. The small variation in pixel counts will likely only appear as a small change in noise that does not specifically indicate a planetary object.

Chapter 6. Results of Spectrum Extraction

Figure 6.12: Extracted spectrum of the Model 1 exoplanetary system at the location of the planet and at 2.287 − 2.301 μm after the stellar reduction has been performed with RM1 by reference spatial profiles created from the mean of 5 columns.

Much like for the original Beta Pictoris data frames, the spectrum does not reveal any distinct absorption lines in Figure 6.12. Although there are some wavelengths that are marginally larger than the noise and are noticeable, the results are too unclear to speculate too heavily, much as the results found in Figure 6.5.

Figure 6.13: Extracted spatial signal of the Model 1 exoplanetary system at 2.287 − 2.301 μm after the stellar reduction has been performed with RM1 by reference spatial profiles created from the mean of 5 columns.

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Chapter 6. Results of Spectrum Extraction

Figure 6.13 above shows the spatial signal of the reduced Model 1 images, where the span of the planetary signal due to the tilt of the spectrum is shown (the spectrum tilts towards negative angular separations). Since the artificial planet is placed much further out than Beta Pictoris b would be found, it is not as heavily affected by the broadened reference profiles, which are more pronounced towards the centre of the spectrum. In the figure, however, no sign of the spectral lines is seen, as the residuals are equally large as those for the Beta Pictoris b reduction results. The artificial planet is only 4.5 times brighter than Beta Pictoris b, while the residuals are much larger than the expected pixel count from the planet, the most likely explanation for its low visibility

For the results of the spectrum extraction using the second planetary model, the artificial exoplanet is ten times stronger than in Model 1, and has a flux of 1/100 퐹훽 푃푖푐, corresponding to ~ 45 퐹훽 푃푖푐 푏 in the K – band. The results of the stellar subtraction are shown in the figures below, where Figure 6.14 is the two-dimensional spectrum, Figure 6.15 is the extracted one-dimensional spectrum, and Figure 6.16 is the extracted spatial signal.

Figure 6.14: Residual spectral images of the Model 2 exoplanetary system at 2.287 − 2.301 μm after reduction with RM1 by reference spatial profiles created from the mean of 5 columns.

In Figure 6.14, the planetary spectral lines are still not distinct enough to be visible in the two-dimensional spectrum. We expect that the noise levels are simply still too large for the lines to be visible for individual pixels, and there is most likely a need to extract the one-dimensional spectrum for the lines to be seen.

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Chapter 6. Results of Spectrum Extraction

Figure 6.15: Extracted spectrum of the Model 2 exoplanetary system at the location of the planet and at 2.287 − 2.301 μm after the stellar reduction has been performed with RM1 by reference spatial profiles created from the mean of 31 columns. Potential absorption lines are marked with red lines.

The extracted spectrum for Model 2 in Figure 6.15 still has a large amount of noise in it, and it is difficult to discern too much information. We are able to detect a number of negative lines (planetary absorption lines will have negative pixel counts) at some particular wavelengths which may indicate molecular absorption lines, marked with red lines, although it is difficult to determine without examining the known spectral lines inserted into the spectrum (see Figure 5.8). In the following Chapter, a few methods for examining the spectrum for spectral lines will be discussed, including matching or cross-correlation with the known or expected spectrum of the planet (see Figure 7.1).

Figure 6.16: Extracted spatial signal of the Model 2 exoplanetary system at 2.287 − 2.301 μm after the stellar reduction has been performed with RM1 by reference spatial profiles created from the mean of 5 columns.

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Figure 6.16 above details the spatial signal found by reducing the Model 2 spectral frames, which does not reveal much more information than the spatial signal of Model 1 or Beta Pictoris b. We expect that the signal from the planet will simply not be visible in these images when the residuals are as large as seen here. We would first need to solve the problem with the profile broadening in order to possibly see the signal from the planetary absorption lines in the spatial sum.

Lastly, the results of the spectrum extraction for the third planetary model are presented, with the artificial exoplanet being ten times brighter than in Model 2 and

100 times brighter than Model 1 with a flux of 1/10 퐹훽 푃푖푐, corresponding to

~ 450 퐹훽 푃푖푐 푏 in the K – band. The spectrum from the planet is now clearly visible even before reducing the stellar component (see Figure 5.9). The results are presented in the same manner as the previous sections, with Figure 6.17 being the two-dimensional spectrum, Figure 6.18 the extracted one-dimensional spectrum, and Figure 6.19 the extracted spatial signal of the model system.

Figure 6.17: Residual spectral images of the Model 3 exoplanetary system at 2.287 − 2.301 μm after reduction with RM1 by reference spatial profiles created from the mean of 31 columns.

In Figure 6.17, the planetary spectral lines are now heavily visible below the residual stellar light, at a spatial position beginning at −0.6 arcsec and tilted downwards. Some of the lines seen at the planetary position are, however, residual telluric lines, and we need to examine the one-dimensional spectrum to separate the two.

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Figure 6.18: Extracted spectrum of the Model 3 exoplanetary system at the location of the planet and at 2.287 − 2.301 μm after the stellar reduction has been performed with RM1 by reference spatial profiles created from the mean of 11 columns. Potential absorption lines are marked with red lines.

Figure 6.18 above shows the extracted spectrum for Model 3, in which many spectral lines inserted into the model are potentially visible. Those lines which we expect appear due to molecular absorption will have negative pixel counts, while residual telluric lines will have positive counts. To identify which of the red-marked lines are real and which are noise, a comparison must be made between the extracted spectrum and a reference spectrum of known molecular features at these wavelengths, which is made in the discussion chapter. These results show that it is likely possible to identify atmospheric absorption lines with the algorithm although at, so far, highly unrealistic flux levels (see Discussion, Section 7.2).

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Figure 6.19: Extracted spatial signal of the Model 3 exoplanetary system at 2.287 − 2.301 μm after the stellar reduction has been performed with RM1 by reference spatial profiles created from the mean of 5 columns.

The final result is the spatial signal found in the reduced Model 3 frames, seen in Figure 6.19 above, which has a noticeably different shape from the previous spatial sums (Figure 6.13 & 6.16), particularly at the location of the planet. This is most likely from the strong absorption lines which would make the pixel counts more negative at the given position. Without the large residuals from the centre of the spectrum, it may be possible to see the signal from the planet in the extracted spatial sum.

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Chapter 7.

Discussion

In this chapter, we discuss our results, how well the algorithm performed for the different methods and data frames, and what could be improved for the future. To summarize our results, the spectrum extraction algorithm was used to obtain results for the exoplanetary system Beta Pictoris, as well as three modelled planets artificially placed in the data frames of the system. We have tested our algorithm with two resampling methods, RM1 and RM2 and reference spatial profiles from the mean of three separate numbers of stellar PSFs. For all of the combinations, a two- and one- dimensional spectrum and a spatial signal of the planet were obtained. We begin by discussing the results of the original data frames with the planet Beta Pictoris b, and how the various methods compare to each other.

Section 7.1. Algorithm Performance for Beta Pictoris b

The results for the Beta Pictoris b spectrum extraction was presented in Sections 6.1 and 6.2, where the two resampling methods are compared and we see results from all three mean profiles utilized for the RM1 case. The first conclusions we are able to make is that there is no apparent trace of the planetary signal or its spectrum in any of the three images presented for each method. It is not completely unexpected, however, since the planetary signal is faint enough to the point that it would most likely not be visible in any of the images. We calculate the SNR of the planetary signal to be approximately only ~ 0.1 at the planet’s position by comparing the expected flux of the planet to the noise level. A completely perfect reduction of the stellar light would perhaps allow for the detection of the spectrum, although we see that our algorithm has clearly not achieved this. Several residual effects are visible in the reduced frames, the most prominent of which is the broadening of the reference frames, causing the centre of the spectrum to be under-reduced and the wings to be over-reduced. This makes it very difficult to detect the planet, particularly in the one-dimensional spectrum, as we specifically would need the overall signal to be close to or effectively zero, with the spectral lines having somewhat more positive or negative pixel counts.

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The reason why the spectral lines may be visible at all lies in the fact that the exoplanet and star will have two entirely different spectra, and the same likely goes for the telluric absorption lines found in the images in comparison to the exoplanetary lines, which will also not be equivalent to each other. Since the exoplanetary spectrum will vary differently from the star (or Earth), the absorption or emission lines will not be found at the exact same positions for the separate objects. When a mean reference spatial profile is then created from many different stellar PSFs, the absorption lines of the exoplanet will significantly impact the planetary signal. For example, if an absorption line falls into a single pixel and the mean is created from many nearby pixels which do not contain a line, the mean will be closer to the average planetary signal and the subtraction will yield a large, negative spike in pixel count at the position of the line. In the extracted spectrum we would, therefore, expect the total signal of the system to be near zero after the subtraction, with a few positive or negative counts for certain columns, i.e. wavelengths, indicating either planetary emission or absorption lines.

If the signal of the entire system is not very close to zero for each column, or at least a smooth line at some flux above zero, it will be very difficult, if not impossible, to detect the spectral lines unless they are bright enough. As this was not the case for the subtracted Beta Pictoris b images, no absorption lines are particularly visible in the extracted spectrum. The extracted spatial signals of the system show us that the broadening of the profile during the reference profile creation and subsequently subtraction of the stellar signal has made the pixel counts heavily negative around the centre of the stellar signal. This will essentially mean that those spectral lines which would be slightly more negative or positive cannot be distinguished since we do not know how large the errors from the broadening are.

There are, however, other means of gaining knowledge about the system besides visually examining the spectrum. One method is to correlate the extracted spectrum with known or expected theoretical spectra to find if any spectral lines match each other despite the weak or indistinguishable lines. This is achieved by simply placing the two spectra alongside at the precise wavelengths and observing whether any visible lines correlate, and we could, for example, try this on the extracted spectra of the modelled data frames, such as Model 3. This model displays many spectral lines which can easily be identified by matching with the telluric absorption lines inserted into the model and is shown in Figure 7.1 below, where many of the lines are found after comparing it to the telluric spectrum. In addition, it is also possible to use cross-correlation, where the extracted and expected spectrum are multiplied according to a cross-correlation function in order to find how much larger the signal is at various wavelengths, such that if an observed spectral line is multiplied by an expected one, the signal will stand out much more and be easily visible. This method was used in Snellen et al. (2014) to detect carbon monoxide in the thermal spectrum of Beta Pictoris b in order to measure

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Chapter 7. Discussion the rotational spin and radial velocity of the planet. We expect that this may not be possible with the extracted spectrum in this thesis due to the issue with the broadened reference profiles as there are no particularly negative lines found in the spectrum in Figure 6.4, although it is not certain if any spectral lines would be visible even if the stellar subtraction worked as intended. Regardless, cross-correlation could be an important tool for identifying the possible presence of absorption lines.

Figure 7.1: Matching the extracted spectrum of the Model 3 frames with the known spectral lines inserted into the model. The top panel is the extracted spectrum shown in Figure 6.18, where large, negative pixel counts indicate an absorption line. The bottom panel is the inserted telluric spectrum (inverted for simplicity’s sake, as it is an absorption spectrum normally), placed such that the wavelengths exactly correspond to the those in the extracted spectrum. Large negative pixel counts have been marked with red-dashed arrows if they perfectly match one of the telluric lines in the bottom panel, and we find that approximately 12 of the spectral lines are visible in the extracted spectrum after the correlation process.

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Chapter 7. Discussion

In addition, it is possible to detect the presence of spectral lines without identifying any individual lines by examining the standard deviation of the reduced model images and comparing them to the standard deviation of the reduced images which do not contain any artificial planets (e.g. Figure 6.4). By normalizing the standard deviation of the model frames to the standard deviation of the non-model frames, any major difference between the two can be seen, suggesting the presence of spectral lines, even if they are not particularly visible as in Model 1 and 2. This is shown in Figure 7.2 below, where the standard deviation has been calculated at each position for the three models and divided by the standard deviation of the Beta Pictoris reduced frames without a contribution from an artificial planet. Additionally, the spectra used for these calculations have not been straightened to account for the spectral tilt, leading to a smearing of the signal, and the signal may become sharper if this effect is counteracted.

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Figure 7.2: The normalized standard deviation of the three models at each spatial position according to the Beta Pictoris frames with no artificial planet. If there was no planet present in the model frames, the normalized standard deviation would simply equal 1 at every spatial position. However, if there are model spectral lines present, they will have a larger standard deviation, and the normalization will yield higher values. We see that for all three models, the planetary lines are clearly visible despite the difficulty to detect them for Model 1 and 2. The use of 31 spatial profiles to create the mean profiles yields the highest deviations, which may indicate that the use of more profiles achieves better results during the subtraction process.

While the method used in this thesis could potentially be found ineffective at extracting the spectrum of faint exoplanets, there are many other types of circumstellar objects that could become a better fit for the algorithm. We have extensively discussed debris disks in Chapter 1 and 2, and these may be better targets for removal of the stellar light and extraction of their spectra than planets. Debris disks are quite different objects from planets in spectral images and have much larger sizes and spatial extensions, as well as very strong emission spectral lines that may be easier to identify than atmospheric absorption lines. In addition, objects such as brown dwarfs or binary stars are also of importance when investigating the circumstellar medium and would require similar methods for stellar light subtraction in order to extract their spectrum, while at the same time being much brighter than exoplanets and not as easily lost in the scattered starlight. It should, therefore, be a simpler task to extract the spectrum of these objects than for faint exoplanets which require far higher contrast ratios to detect. A further discussion of some alternatives for better uses of the algorithm and potential improvements to the method and instrumentation is made in Section 7.3.

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Section 7.2. Realistic Approach to Models

In this thesis, we also investigated how the algorithm performed for modelled planets of much higher flux than that of Beta Pictoris b. The three artificial planets utilized had brightnesses of 4.5, 45, and 450 times that of the actual exoplanet, and the results were significantly more decisive for the models, particularly for the brightest one. In this section, we discuss what can be determined from the use of models in exoplanetary spectroscopy, and whether the used models can tell us more about what can be realistically expected from results of actual exoplanets.

From our results, we have found that the algorithm will successfully perform its task regardless of the large residuals and imperfect stellar reduction as long as the exoplanet in question has a flux high enough compared to the parent star to outweigh the errors. The exoplanets spectral lines are detected for all models in the normalized standard deviations (Figure 7.2), and we are able to identify several potential spectral lines for Model 2 and 3. We found that for the first model, the spectrum is still considerably noisy and it is difficult to obtain much clear information. Several potential spectral lines are somewhat visible for Model 2, though we cannot say for certain before comparing it to the inserted spectrum. Results based on Model 3 did, however, produce a better spectrum of the artificial planet where the spectral lines are more easily accessible to the naked eye, and most of the inserted lines could be identified by correlating the potential lines with that of the known inserted spectrum. From this, it can be concluded that the algorithm performs quite well in theory, though further methods must be employed to identify the lines. We expect that the algorithm could be used for actual spectroscopy if it was able to operate on images of higher SNR, higher star/planet contrast ratios, and with better methods for creating the reference stellar PSFs.

Additionally, it is also important to discuss the feasibility of the artificial planets used in the models, and if it is realistic to assume that any of them could be found in actual exoplanetary systems, beginning with Model 1. Firstly, as an example, Beta Pictoris b has an absolute magnitude in the infrared K – band of 푀퐾 = 12.6 ± 0.1 (Bonnefoy et al. 2013), and the brightness of an exoplanet depends on two factors; the reflected light from the parent star and the self-luminosity of the planet. These two factors can be investigated separately to verify whether planets can be found at high enough luminosities for the algorithm to function more efficiently. The reflectance of an exoplanet depends mostly on the orbital distance and somewhat on the planetary radii. According to the inverse square law of radiative flux (Formula 5.1), a source of light’s apparent brightness (i.e. the flux) decreases with the square of the distance due to the light being spread out over a larger surface at higher radii. As such, a planet located at a larger orbital distance will reflect less of the light from the parent star and

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Chapter 7. Discussion measurements will become increasingly challenging as the planet is fainter. Naturally, one would want to observe planets located as close to the star as possible, as this is also where terrestrial planets of more interesting atmospheres than gas giants far out in the exoplanetary systems would be found.

However, two problems exist with this way of thinking. Firstly, as discussed in Section 2.3.2, the closer the planet lies to the star, the more problematic the observations will be. Direct imaging of exoplanets is with our current instrumentation limited to planets at orbital distances of 푎 > 5 퐴푈 (Fischer et al. 2014), due to the scattering of stellar light obscuring the planetary signal and rendering it indistinguishable from the star. Recall that Beta Pictoris b lies at an orbital distance of 푎 ≈ 9 퐴푈 (0.4 arcsec) and is still only separated from the star in our data frames by roughly 4 or 5 pixels. If the planet were to instead be located at approximately half the orbital distance the separation is reduced to no more than 2 – 3 pixels, where the measured stellar flux is much greater than further out in the wings. Even though the reflected flux is increased by a factor of 4, the contrast ratio may worsen due to the stronger scattered light.

The second problem lies with how much light is actually reflected off the planet’s atmosphere as compared to its thermal self-luminescence. The planet itself can emit light on its own through a number of natural processes which help in increasing the brightness. All planets glow with thermal emission generated by its internal heart, where younger and larger planets are typically warmer and emit more radiation as per Planck’s radiation law (de Pater & Lissauer 2015). In addition, specific recurring and sporadic events may temporarily increase the brightness of a planet, such as planetary aurorae or volcanic eruptions (although large enough activities ejecting much material into the atmosphere may instead mask the surface and lower the observed thermal emission), though it is essentially impossible to predict when such events will occur.

In the Beta Pictoris case, the thermal light can be easily calculated by looking at the flux at the stellar surface and at the planet’s orbital distance and comparing them to the brightness of the object objects with respect to Earth. The bolometric luminosity of Beta Pictoris is 퐿훽 푃푖푐 = 8.7 퐿⊙ and the radius is 푅훽 푃푖푐 = 1.8 푅⊙ (Crifo et al. 1997), which, with the use of Formula 5.1, yield a flux at the stellar surface of 퐹훽 푃푖푐 = 1.7 × 108 W/m2. The flux from the star at the orbital radius of Beta Pictoris b is calculated by the same means for a radius of 푎 = 9 AU, which we find to be only 147 W/m2. If the exoplanet perfectly reflected all light, i.e. it had an albedo of 1, and emitted nothing by itself, it would only be 1/1 150 000 times as bright as its parent star. Given that the planet is in reality 4 570 times fainter than the star, it means that only ~ 1/250 of the light from the planet comes from the reflected stellar light and the rest comes from its own thermal radiation. With regards to the planetary brightness, it will, therefore, be mostly irrelevant for these observations how close the planet is to

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Chapter 7. Discussion the star and it will essentially display the same flux. It will, however, worsen the planet/star contrast ratio the shorter orbital radius the planet is found at, as there is more scattered stellar light further in, and we would instead wish to detect planets located as far away from the star as possible, where there is little to nothing left of the stellar signal. Beta Pictoris b is quite a young planet, and the thermal light of a planet is mostly linked to its age, with younger planets being brighter (Fischer et al. 2014). We, therefore, expect that the brightness of an exoplanet such as Beta Pictoris b will not increase by much unless it is significantly younger (on the order of only a few million years), although it is possible to decrease the contrast ratio between the planet and its parent star by simply observing planets orbiting further out, which will be much more favourable for spectroscopic measurements. It can, however, be deemed possible, although improbable, to find planets of fluxes 4 − 5 times greater than Beta Pictoris b, as used in Model 1.

The results found for the second model were somewhat better than that of Model 1, and we were able to detect several potential spectral lines in the reduced spectrum. This indicates that if it is possible to discover objects of the brightness used for this model, we may be able to identify spectral lines from them in the future using our algorithm. We can say for certain that the brightnesses used for this model are not possible to find in exoplanets, but brown dwarfs or binary stars are also objects of interest and are more likely to be found at the flux levels used for Model 2.

The third model, with a flux of 1/10 that of Beta Pictoris, can immediately be discarded as far too unrealistic to find in an actual stellar system, as brightnesses of this magnitude would most likely indicate a binary system, where a secondary, fainter star is the source of the signal. Though this model obviously provided the best results, with most of the inserted spectrum being extracted and visible, we should not expect to achieve images of this quality regardless of how far instrumentation and techniques advance in the near future. It should neither be the results necessarily strived for, and finding evidence of a single spectral line in the atmosphere of an exoplanet could be considered a success considering how recently the field of direct imaging has emerged.

In the final section of this chapter, we discuss potential improvements to our algorithm and how future instrumentation could allow for the detection of the spectrum of even fainter planets.

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Chapter 7. Discussion

Section 7.3. Possible Future Improvements

In this section, we discuss how the algorithm may be refined in the future in order to enable more precise and detailed results for exoplanets of both lower brightnesses and shorter orbital distances. As already discussed previously, the algorithm will theoretically perform well, and the main problem which hindered us from obtaining satisfying results for the Beta Pictoris b data frames was the large residuals of the scattered stellar light that the algorithm was unable to completely remove. From the results, we have determined that the issue lies with how the algorithm creates the reference spatial profiles, where it appears that the reference profiles are broadened during one of the steps of the algorithm. While it is not entirely certain during which step this problem occurs, we believe that it is most likely from a step involving interpolation or the actual creation of reference profiles from the mean of several profiles in nearby columns. It is also possible that the spectral absorption lines found in the stellar spectrum affect the shape of the reference profiles. As mentioned in Section 4.2.4, the absorption lines have a different shape than an average position along the spectrum, where the wings have a somewhat higher flux for the lines. If the wings are too large for the reference profiles, during Step 6 & 7, when the reference profiles are fitted to the actual stellar PSFs by multiplying with the correct amplitude, the algorithm will attempt to find the best amplitude to multiply with, which will be determined to be somewhere between the shape of the reference profiles and real profiles. The wings will in such a case still be too large by some amount, while the centre will be too small, exactly the problem seen with the reduction process in Chapter 6. This effect would also explain why the residuals appear to be larger the more columns are used to take the mean from when creating the reference profiles, as if more profiles are included, there is also a larger possibility of a telluric absorption line being included.

In reality, there are most likely several factors that contribute to the broadening of the references profiles and subsequent less-than-optimal subtraction of the stellar PSFs. Empirically determining the shape of the stellar PSFs is a difficult process, and for this thesis, only one method was attempted for creating the reference profiles. There are many possible methods for estimating the shape of spatial profiles, and it is highly likely that another method accomplishes this task better. Next, we discuss some other possible ways of determining the reference PSF shapes that may be better suited for use in the extraction algorithm below, including both old methods and new ones.

A method previously investigated for similar spectra reduction and extraction techniques that we believe warrant further study and may help with our imperfect spectrum extraction is found in van Kerkwijk (1993), which details an optimal extraction method for echelle spectra. Here, the method shows how a fit to spatial

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Chapter 7. Discussion profiles of the star can be made, and it is expected that the technique described by van Kerkwijk may perform better than the method we have used since it does not rely on resampling and aligning the spectral images. Based on this method, we have devised a new way of creating reference stellar spatial profiles and made some preliminary tests on the Beta Pictoris data frames. The new method consists of drawing up the values found in pixels from many separate spatial profiles found in a row, as seen in Figure 7.3, and fitting a spline-function to the data.

Figure 7.3: Five spatial profiles found closely in a row drawn in the same plot. The data is based on the Model 3 planetary system, and the exoplanetary signal is seen at −0.6 arcsec, with the green dots being an absorption line of the model planet.

A spline-function can be used to represent a set of data by fitting several polynomials piecewise at certain sections and of differing degrees. For this method, testing has so far been conducted by fitting the spatial profile data according to cubic polynomials at an interval of three splines per pixel, and preliminary testing with this method has shown positive results with lower residuals in the extracted spectrum, although further development of the algorithm and spline-functions is necessary. In addition, a supplementary method which could possibly improve the shape of the reference profiles is to only create fits to the wings of the stellar PSFs, where the planetary signal will be found. If it is not necessary to create a reference profile that fits both the centre and wings of the spectrum, it is less likely that one of the two will negatively affect the shape of the other. If only the wings are fitted and the central few pixels are simply blocked from the reduced frames, we may have more success with the reduction and we expect that there will be fewer residuals in this case.

The issues may also be affected by which resampling method is chose to be employed. During the process of creating our algorithm, we tested two methods for resampling

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Chapter 7. Discussion the columns into higher resolutions, and we have already determined that one of them (RM1) performs significantly better than the other (RM2). There are, of course, other ways of increasing the resolution through resampling than by repetition or interpolation that have not been tested in this thesis that may perform more adequately and allows for better fitting of the reference profiles to the stellar PSFs. It may even not be entirely necessary to resample the frames at all if we are able to find another method of shifting the arrays to align the spectrum without causing the wave-like artefacts discussed in Section 3.1.2, and if such a method could be found we expect that the subtractions would be significantly better handled.

Lastly, it is also predicted that exoplanetary spectroscopic measurements will be improved upon in the near future, not just due to improved algorithms, but also from new and better instrumentation that is planned for the coming few years. Spectrographs with higher dispersive capabilities and higher resolutions will naturally function better than having to artificially increase the resolution and will allow for more accurate removal of the stellar light component. The most important aspect of direct imaging observations is the angular and spectral resolutions of the spectrograph, and it is most likely these two attributes which will determine how well the field of direct imaging evolves in the future.

In Section 5.1.3, we discussed the upgraded CRIRES+ spectrograph (Dorn et al. 2014), planned for commissioning in 2019, which will enable images of much higher resolution than those obtained for this thesis, and we expect that it will be easier to derive the desired results from the new images. CRIRES+ is not, however, the only high- dispersion spectrograph planned for the future. The upcoming E-ELT (European Extremely Large Telescope) will be the world’s largest optical / NIR telescope and will have a wide variety of instruments installed that will allow for exoplanetary spectroscopy. Instruments such as the Mid-infrared E-ELT Imager and Spectrograph (METIS, Brandl et al. 2018), the High Resolution Spectrograph (HIRES, Marconi et al. 2016), and the NIR spectrograph SIMPLE (Origlia, Oliva, & Maiolino 2010) will be able to explore exoplanetary systems, with it being the latter’s main mission to probe exoplanetary atmospheres. These three instruments can take full advantage of the E- ELTs giant 39-metre mirror and produce images of never before seen resolutions and observe far lower stellar/planet contrast ratios than any current instrument.

We have discussed the results and possible future improvements to the algorithm and instrumentation that may help us further develop methods for performing exoplanetary spectroscopy. In the following and final chapter of this thesis, we summarize what was learnt during this thesis, which results were obtained with the extraction algorithm, and what conclusions we can draw from them.

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Chapter 8.

Summary and Conclusions

In this section, we summarize the work performed in this thesis, the methods used and problems encountered when studying spectroscopy of extrasolar systems, the algorithm designed for extracting the spectrum of a circumstellar object, the results found when assessing the algorithm on observations and theoretical models, and the conclusions that can be drawn from our discussion of these. We summarize our findings as follows:

• When performing spectroscopy on circumstellar objects found in extrasolar systems, one of the most advantageous means of acquiring observations at the high contrast ratios which exist for stars and their orbiting objects is to employ and combine techniques such as high dispersion spectroscopy (HDS) and high contrast imaging (HCI). In addition, most circumstellar light is lost in the bright, scattered light from the star, which must first be heavily subtracted before any accurate measurements can be made. We investigate a method for reducing much of the starlight in order to extract the spectrum of an orbiting exoplanet.

• The method used for subtracting the stellar light from the spectral images takes advantage of the two separate spectra of the star and planet. The spectra consist of many spatial profiles located at specific wavelengths and are shaped according to the point spread function (PSF). The PSFs of the two objects are differently shaped and placed on top of each other. By empirically determining a fit to the stellar PSF, we can create reference spatial profiles at each wavelength and subtract the stellar spatial profiles without affecting the planetary spectral lines.

• Several difficulties exist with creating a perfect fit to the stellar spatial profiles, and to solve these, we have constructed an algorithm which creates the reference profiles and subtracts the stellar PSFs. This algorithm consists of eight steps, where the profiles are resampled to higher resolutions and the spectral tilt is aligned in order to properly determine the stellar PSF shapes. The profile shapes are empirically calculated from the shape of many profiles in a row, which enables the stellar subtraction while leaving the planetary spectral lines visible.

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• In order to assess the performance of the algorithm, we test it on spectral images of the stellar system Beta Pictoris as well as three artificial planets inserted into the same images. The observations are all made with the CRIRES instrument on the ESOs VLT in the infrared K – band, and the observational images are all initially reduced according to the pipeline provided by ESO. The models created consists of a telluric line spectrum also produced by CRIRES, scaled according to various flux strengths and inserted in the Beta Pictoris frames.

• When applying the algorithm to the spectral images of the Beta Pictoris system and the three model exoplanetary systems, we found that it could not accurately subtract the stellar component entirely, and left large residuals in the reduced frames. For the Beta Pictoris system and the faintest planetary model, we were unable to identify any spectral lines in the extracted spectrum of the reduced spectral images, whilst for the two brighter models, some molecular absorption lines are potentially visible and identifiable by correlating and matching them with the known spectral lines inserted into the spectrum.

• In our discussion of the results, we conclude that the algorithm will theoretically be able to extract the spectrum of circumstellar objects, and may work better for debris disks, brown dwarfs, or binary stars, although, for more accurate results, the algorithm must first be perfected to ensure that no residuals remain. We also discuss methods which may be able to perform the stellar subtraction more accurately and mention future instrumentation that will likely enhance observations of exoplanetary systems and allow for detailed spectroscopy.

In conclusion, the algorithm we have constructed is theoretically able to extract the spectrum of a circumstellar object, such as an exoplanet, and it is possible to identify the spectral lines by matching the spectrum with known absorption lines. The particular method we employed to subtract the stellar light was found to be partially inaccurate and produced large residuals in the reduced images that complicate the process of extracting the spectrum. The use of reference spatial profiles to fit the stellar light component alone appears to be a valuable technique for these types of subtractions, although, in order to improve on our algorithm, we must further investigate other methods for how the reference profiles can be created. Most likely, only with perfectly fitted reference profiles will the algorithm perform a stellar subtraction accurate enough to later be able to identify spectral lines observed in the atmospheres of extrasolar planets.

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