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Observation and analysis of transits of TRAPPIST-1 systems

Auteur : Thimmarayappa, Darshini Promoteur(s) : Gillon, Michaël Faculté : Faculté des Sciences Diplôme : Master en sciences spatiales, à finalité approfondie Année académique : 2017-2018 URI/URL : http://hdl.handle.net/2268.2/5544

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Observation and analysis of transits of TRAPPIST-1 systems

Master Thesis in Space Sciences Research Focus

Author: Supervisor: Darshini Thimmarayappa Dr. Michaël Gillon

Academic 2017-2018 ii Acknowledgements

I owe my deepest gratitude to Dr. Michaël Gillon, for always inspiring me, motivating me and teaching me at every step of my thesis. He always believed in me from the day I walked into his door asking to be a part of this up to now. I also thank him for his constant availability to clear all my doubts and for always keeping his door open for me. His advises and numerous readings of my drafts helped produce a better thesis. I think he’s the best mentor that I could have asked for. I am also deeply grateful to Mr Artem Burdanov, Miss Elsa Ducrot for helping me out whenever I had doubts about my work and for fruitful discussions of the results. I would like to thank them for their patience and for clearing my doubts in spite of their busy schedule. I would also like to thank Miss Sandrine Sohy who helped solve all my queries related to programming. I would like to thank Mr Amaury Triaud for giving me this opportunity to use the data for my reduction and also for many of his suggestions and remarks on the results obtained in my thesis. I thank all the staff members of the space science department and my friends for helping me throughout the course and for this wonderful experience. Last but not the least, I would like to thank my parents Mr. Thimmarayapaa T and Mrs. Pushpavathi for showing constant support from India and for encouraging me throughout. I owe them my deepest gratitude as it would not have been possible for me to come to from India and pursue my masters.

iii iv Abstract

My chosen topic for this thesis is the newly discovered TRAPPIST-1 with its seven revolving around the nearby ultracool dwarf . The main need to focus on the TRAPPIST-1 system is to refine the of the seven planets, to constrain their composition and also their dynamics. In order to do that we use the measured tran- sit timing variations (TTVs) to constrain their masses, and hence refine the transit parameters through analysis. Measured TTVs are used to detect a change in the of each caused by gravitational pull of the planets in a resonant chain, this causes the planets to accelerate and decelerate along its in a packed planetary system and therefore change the orbital period. We also reduce the photometric data obtained from the Liverpool over the time span of 2017/05/31 to 2017/10/28. The photometric data obtained consists of 19 light curves and each of these light curves were analyzed individually and then a global analysis was performed on all the transits pertaining to a single planet. The individual and global analysis was performed with the recent version of the adaptive Markov Chain Monte-Carlo (MCMC) code developed by M. Gillon. For the reduction of the data, we first performed differential to measure the flux of our target star with respect to a standard star in the field of view and eventually from this we obtain the dip in the value of the measured flux of a star during a planetary transit. Individual analysis is performed for each light curve to obtain the astrophysical and instrumental effects observed at the photometric variation level and finally we perform global analysis for a set of light curves obtained for the same planet. Both individual and global analysis is done in a preliminary chain of 10,000 steps and a secondary chain of 100,000 steps. In the global analysis, we improve the accuracy of the system parameters, de-trended light curves along with photometric representations which are also included in the report.

The global analysis result for TRAPPIST-1b gave us a transit duration of 0.025 ±0.00050 days with its 1 σ limit of the posterior PDF, similarly we have a value of 0.029±0.00076 days for TRAPPIST-1c and a value of 0.0388±0.00075 days for TRAPPIST-1e. These values are in good agreement with the values obtained from the Spitzer analysis. These timings will be useful to constrain further the dynamics of the TRAPPIST-1 system and the masses and compositions of its planets. We also compare the results with the already reduced Spritzer results, to check the accuracy of the results obtained from the Liverpool telescope. Some of our results are presented in the paper "The 0.6-4.55m broadband transmission spectra of TRAPPIST-1 planets" (Ducrot et al. 2018, under review).

v vi Contents

Introduction 1 Habitability of planets and the habitable zone ...... 3 Classification of exoplanets ...... 4

1 Transiting planets: treasures in the sky 7 1.1 Transit method ...... 8 1.2 Physical parameters ...... 10 1.3 Limb darkening ...... 11 1.4 Transmission and emission spectroscopy ...... 13 1.5 Transiting planets with the James Webb space telescope (JWST) . . . . . 15

2 Ultracool dwarfs and their planets 17 2.1 Description of ultracool dwarfs ...... 17 2.2 Ultracool dwarfs and planets ...... 18 2.3 The SPECULOOS project ...... 18 2.4 Prototype survey for SPECULOOS on TRAPPIST ...... 20

3 The TRAPPIST-1 system 23 3.1 The host star TRAPPIST-1 ...... 23 3.2 The TRAPPIST-1 planetary system ...... 24 3.3 Characterization of TRAPPIST-1 planets: present and future ...... 25 3.4 On the scientific importance of TRAPPIST-1 ...... 26

4 Concept and goal of this thesis 29

5 Reduction method 1- Observations 31 5.1 Liverpool telescope ...... 31 5.1.1 :O ...... 31 5.2 Reduction methods ...... 32

vii viii CONTENTS

5.2.1 Observations ...... 32 5.2.2 Data reduction ...... 33 5.2.3 Differential photometry ...... 34

6 Reduction method 2- Data analysis 37 6.1 Introduction to Markov-chain Monte Carlo (MCMC) method ...... 37 6.1.1 Individual analysis ...... 41 6.1.2 Global analysis ...... 42

7 Results 43 7.1 Differential photometry ...... 43 7.1.1 Differential light curves obtained for TRAPPIST-1 system with IO:O camera ...... 45 7.2 Individual analysis ...... 64 7.2.1 Parameters obtained from Individual analysis for TRAPPIST-1b . . 65 7.2.2 Parameters obtained from Individual analysis for TRAPPIST-1c . . 67 7.2.3 Parameters obtained from individual analysis for TRAPPIST-1d . . 69 7.2.4 Parameters obtained from individual analysis for TRAPPIST-1e . . 70 7.2.5 Parameters obtained from individual analysis for TRAPPIST-1g . . 71 7.2.6 Parameters obtained from individual analysis for TRAPPIST-1h . . 72 7.3 Global analysis ...... 73 7.3.1 Parameters obtained from global analysis for TRAPPIST-1b . . . . 73 7.3.2 Parameters obtained from global analysis for TRAPPIST-1c . . . . 75 7.3.3 Parameters obtained from global analysis for TRAPPIST-1e . . . . 76 7.3.4 Transit depth variations ...... 77

8 Discussion and conclusion 79

Introduction

There are 400B in ,but could the be the only one with an inhabited planet ? May be ! May be the origin of and intelligence is exceedingly improbable or may be civilizations arise all the time and wipe themselves out as soon as they are able. Or here and there , peppered across space, may be there are worlds, something like our own, on which other beings gaze upon us and wonder like we do about who else in the dark. Life is a comparative rarity, you can survey dozens of world and only find only in on one of them there is life.....But we continue to search for inhabited, life looks for life. - (Carl Sagan series - http://saganseries.com/)

We humans, with our curious minds have always wondered about the two questions that connect us to our existence. "Where do we come from? " and "Are we alone? ". As the quote by Carl Sagan clearly summarizes, we want to find out if our existence or life is limited only to the and if our Earth is a special and a unique place. The quest to answering the two questions cited above could be back to 1584 , when the Italian philosopher Giordano Bruno wrote in his book ’De L’infinito Universo E Mondi’

There are countless and countless all rotating round their suns in exactly the same way as the seven planets of our system.

With hundreds of billions of stars in the observable , we try to reason that the other stars could also have planetary systems like ours and could host life. The search for planets in other solar systems have since given rise to a new field of study called , focused on the detection and detailed characterization of these extrasolar worlds. The direct detection of exoplanets is very challenging as the star’s is much higher than the (one) of the planet and the angular separation between the two bodies would be a few seconds of arc at the most as seen from Earth. Many alternative detection methods have been developed which makes use of indirect techniques to discover the planets. These techniques are discussed in the upcoming chapters. The first detection of an around a Sun like star was achieved through method in 1995 [1] around the star 51 Peg. It was not only a scientific achievement but it also gave us a glimpse of satisfaction as this very discovery might bring us closer to the answer. The planet 51 Peg b has a similar to and acts as a prototype to the Hot-Jupiter class of planets. It orbits its parent star every 4 days which is much closer than the distance at which orbits the Sun (approximately 7 times closer). This discovery and many more have reassured us that

1 2 INTRODUCTION we should be at some point capable of reaching sensitivities that can discover Mercury-, Earth- , - and Jupiter- like planets in other planetary systems. Over the , many missions and astronomers contributed to the discovery of a lot more exoplanets and as of today there are more than 3500 exoplanets (Figure 1) in an average of 2000 systems. Since then the field of exoplanetology i.e. the search and characterization of extra Solar planets has grown tremendously to become one of the most dynamical field of .Today the large number of exoplanets only indicate the existence of a huge mixture of planets with different orbits, mass and a huge diversity in various other aspects. These detections have shown that a maximum of 5% of the solar type stars can harbor a Jupiter like planet ,an amount of ≈ 10% can host an eccentric and (or) short orbit giant planets [2], up to 50% can host a compact system of super-Earths [3]. Surprisingly, planets slightly (up to ten times) more massive than Earth were found to be very frequent in shorter orbits than Mercury around Sun-like stars [4, 5]. Some of these "super-Earths" may be mini-versions of and , others more massive versions of "our" terrestrial planets. For even smaller planets, a preliminary inference is that about 10% of the solar-type stars should have an Earth-sized planet with a similar orbit like that of the Earth [6, 7]. Population of stars which are more massive than the Sun is still uncharted territory. They have low mass planets but according to Jones et al. [8], giant metal rich planets are more easily formed around these massive stars. M dwarf category of stars take up about ≈ 70% of all stars in the Milky Way galaxy [9] . giants appear to be rarer in these star systems. These M dwarfs host 3 times more small planets than solar-type stars and contain more heavy element mass composition at short orbital periods compared to solar type stars. An example of a system in M dwarf category is GJ876b (one of the first ones to be discovered) and it’s found around a nearby M3- type dwarf [10]. In this thesis we will concentrate on an M type star - Trappist-1. There are many more discoveries to come in the field of exoplanetology so it’s not viable to place all our assumptions on the facts obtained up until now as these criteria only apply to a particular system of planets. All the previous discoveries add a great deal to knowing the types of planets, migration mechanism, planet-planet interactions and the planet-star interactions, orbital periods and minute details of planetary formation . This is just the beginning as there are many potentially habitable planets (conditions for a planet to be considered habitable is discussed below). Planets which are suitable for atmospheric characterization and more diverse planets yet to be discovered. As mentioned earlier, direct imaging of exoplanets is very difficult for obvious reasons (many giant planets with large separation have been imaged) and many indirect techniques have been developed to detect exoplanets. See figure 1 for the number of exoplanets discovered with different techniques. We can clearly see the enormous growth in the number of planets discovered each year by both direct and indirect methods, initially radial velocity technique was the most dominant technique used for exoplanet detection and the after the introduction of other effective methods like transit techniques the number of planets detected by radial velocity method fell down. Direct imaging and microlensing techniques are also quite popular and is indicated in the figure 1 below. Also from the figure we can see that the transit method is one of the most employed method for exoplanet detection now, in my thesis I have used the results obtained from the transit technique and the procedure used to obtain the results along with the other interpretations made 3 from the data will be discussed throughout this document.

Figure 1 – Histogram of the number of planets detected over the course of years. Different colours indicate different method of detection [11]

Habitability of planets and the habitable zone

Keeping the Earth’s biosphere as the reference, habitable zone is defined as the bound- ary condition put forth for a with necessary atmospheric conditions to maintain liquid water which is the basic form of ingredient of all the forms of life 1 on Earth. For a Sun-Earth like system, the inner edge of the zone is subjected to runaway greenhouse effect (it is a process where a small change in surface temperature and the atmospheric opacity leads to a large increase in the strength of the greenhouse effect on a planet until all its ocean water is all evaporated. It mainly occurs when the planet absorbs more energy from the sun or a star than it can radiate back into space [12]) due to the enormous amount of heat supply from the star. This is believed to have been the case for Venus [13]. Also at the outer edge, CO2 clouds that are formed reflect the sun rays due to high albedo and eventually cool down the surface which results in a decreased greenhouse effect. Earth is a habitable planet due to its thick that protects us from all the harmful electromagnetic radiation from both the sun and the universe, this makes the pressure and temperature as conditions which are well suited for the existence of liquid

1. we define life as self sustained chemical system capable of undergoing Darwinian evolution 4 INTRODUCTION water. The atmosphere is protected from the sun’s wind due to an intrinsic magnetic field present around the Earth and also the rotation of the planet is in direct link with the Hadley’s cell (it’s the global scale tropical atmospheric circulation, hot equatorial air lead by the Sun rises towards the poles to cool down and return back to the equator. The primary cause of this being the trade winds and the hurricanes). If a planet is too close to the star it’s too hot to sustain liquid water on its surface and its close proximity to the host star houses many harmful radiation. In some cases it even causes an erosion of the atmosphere [13] . Slower rotation implies enhanced atmospheric circulation that leads to longer hot days and cool nights. Presence of liquid water is another main characteristic needed along with its composition. Tectonic plate activities are also a must as it releases CO2 into the atmosphere and plate tectonics along with water provides a suitable environment for the sustainability of life. The planet must also be of the appropriate size in order to maintain habitability and prevent the atmosphere from eroding due to an impact. They also seize all their tectonic plate activities as they cool down fast where as super Earth (Mass varies from 1 to 10) like objects can keep theirs active. Based on these considerations, we can classify habitable planets in four different classes [13] .

— Class 1 habitable planets- These planets are Earth like, with stellar and geophysical resemblances. — Class 2 habitable planets- These planets previously had Earth like conditions e.g. . Future conditions not suitable for advanced life forms. — Class 3 habitable planets- The planets here contain a sub-surface ocean below the ice layer with a silicate rich core in contact with it. — Class 4 habitable planets- These planets also contain sub surface water but they have no contact with silicates or rocks (Core) and they have large content of water on them. For exoplanets, we focus only on terrestrial planets orbiting in the HZ (class 1), as our only means to remotely assess the habitability of an exoplanet is to perform a spectroscopic study of its atmosphere. For Classes 2 to 4, only in situ exploration could detect traces of life.

Classification of exoplanets

As the number of detections of exoplanets have increased over the years. It is now possible to categorize them as we have a lot of data to do so. There still hasn’t been a substantial classification of exoplanets as their diversity is quite varied and large. Given below is the classification of exoplanets according to their mass. [14]

— - They are massive planets with a mass of at least 10 Earth masses and have a thick atmosphere of and . — Mesoplanet- These planets vary among the size range between and Mer- cury(between the range of 1,000 km to 5,000 km in diameter) — Mini Neptune- Planets of mass below 10EM⊕, with a thick hydrogen-helium at- mospheres. 5

— Super Earth- They are terrestrial planets more massive than Earth with an upper limit of size 2r = R⊕ — Sub earths- They are less massive than Earth and do not have a substantial at- mosphere due to low and weak magnetic fields. They are very difficult to identify due to their size (produce a weak signal). — PMO ( object)- This category of planets includes dwarf planets capable enough to maintain hydro static equilibrium but are not capable enough to clear their orbit.

Classification by orbital regime [14],

— Circum-binary planet- They orbit the two stars or a binary system instead of one. — - A Jupiter like mass planet with an eccentric orbit with me- dian eccentricity of 0.23. If this planet is present in a system, it would restrict the presence of Earth like systems as they will be removed due to gravitational interaction. — - A Jupiter like (0.36–11.8 ) object that orbits very close to its host star(0.015 - 0.5 AU) with a temperature range of 1000 to 2000 K. They are the most easily detected planets by the transit and radial velocity methods. These planets should be tidally locked and have circular orbits and are of low . It is also believed that these planets migrated from beyond the frost line to form stable orbits. — - Just like Hot , these planets also have a short orbit(less than 1 AU) and are relatively easy to be detected by transit techniques. As the name suggests their mass is similar to that of Neptune. — Terrestrial inner planets- Dense rocky planets with a central metallic core and a silicate mantle. — planet- Planets orbiting a pulsar or a rapid moving .

There are many more categories of exoplanets, the list is quite long with planets being dis- covered now and then but we have mentioned a few important and well known categories above.

Small stars come with many advantages, the planets that orbit them have a small period so it’s easier to obtain many observational data. Their transit depths are deeper due to its host size and irradiation[15] . Their population is quite large compared to the other types of stars (probability of finding a small planet is 3 times compared to sun like star) and they are easily detected by the transit methods and some are even suitable for atmospheric characterization. One such suitable example is the newly discovered TRAPPIST-1 system. This system has become the prime target for many astronomers and the upcoming mission James Webb Space Telescope (JWST). In this thesis, I target the TRAPPIST-1 planets (all except TRAPPIST-1f) and the main goal is to improve the planets transit parameters. Observations for this are taken with the Liverpool telescope. The instrument is a part of the Research Institute of Liverpool, John Moores University in north west England. It’s fully robotic with a 2m Cassegrain reflector telescope. Observations are taken over a time range from May to November 23rd (Chapter 4) and there are 19 individual light curves for the all planets included. We first subject the images to 6 INTRODUCTION preliminary calibration and photometric stacking. Differential light curves (Chapter 4) are obtained after the stacking process and suitable comparison stars are used here to obtain the curve. After this we perform individual and global analysis (Chapter 5) of all the differential light curves to obtain the parameters of the system. At the end, we summarize the results (Chapter 6) obtained from all the analysis and make inferences (Chapter 7).

Chapter 1

Transiting planets: treasures in the sky

In this chapter, we are going to discuss in detail about the transit method of detection which is the main focus of this thesis.

Transiting exoplanets are the only kind of exoplanets for which radius and mass can be accurately determined. This gives a peek through the composition and the structure of these planets. They are also the candidates suitable for atmospheric study without having to spatially resolve them from their host star, figure 1.1 . Orbits of transiting exoplanets have a special geometrical configuration relative to the Earth, this makes them well-suited for detailed characterization [16]. So we can exploit current technologies to study these planets, not just to detect the basic physical parameters but also to characterize the atmosphere. This kind of study lets us master the subject of exoplanetology through which we can uncover the secrets of the temperate terrestrial planets to giant planets and beyond. In this thesis we concentrate on applying the transit method on detecting and observing the parameters of such terrestrial planets around small ultra cool stars. This method gives us an adequate enough signal-to-noise ratio (SNRs) in order to read the atmospheric signatures on the spectroscopic data. Good examples of such targets are low mass M-dwarf stars with their low that pushes the habitable zone more closer to them.

As of today more than 3000 transiting planets within 2000 or so systems have been discovered. Majority of this discovery was due to the NASA’s Kepler space mission [17, 18], other search missions like WASP [19] and HAT [20] have also played a role in this. Discovery of many exoplanets leads to more foundational information when targeting an unknown system as it gives us a preliminary prediction of what the system could look like. It gives us an on properties like chemical composition, atmospheric properties and various other physical properties (after follow up observations ) of the known systems. In this chapter we will discuss the basic concepts involved in the transit method and techniques employed for it. We will also see the how to obtain the physical parameters from the light curve and learn about limb darkening effects. Detail description of transmission and emission spectroscopy along with the methods employed by JWST for atmospheric characterization could describe the system entirely.

7 8 CHAPTER 1. TRANSITING PLANETS: TREASURES IN THE SKY

Figure 1.1 – Picture of a transiting system, time-series spectroscopy and spectro photom- etry is associated to temporal resolution of the combined light of the system.Transmission spectrum for the atmospheric limb is obtained through transit depth seen during the pri- mary eclipse and during secondary eclipse we can obtain the day side emission spectra.The combined flux modulation can also be studied for the atmospheric circulation properties, picture taken from [16].

1.1 Transit method

Relative to the observer’s line of sight, if we observe a planet crossing the host star in front of it, there will be a dip in the apparent brightness of the star as the planet blocks a consistent amount of light each time it crosses the star. This is called the primary eclipse or transit. The same process occurs again in the ongoing completion of the same orbit, but this time it occurs half an orbit later and the star blocks the planet, although the dip in the brightness is not the same. This is called or secondary eclipse. The transit dip in brightness can be obtained from the equation below [21]

2 RP ∆F 2 = (1.1) R∗ F

Where, — F is the flux measured from star — ∆F the change in flux during transit 2 — RP is the planets disc 2 — R∗ is the star’s disk For a giant planet transit, there will be a dip of ' 1% in the light curve of the host star. while for a terrestrial planet transit will cause a dip of ' 10−2%. Sometimes the best way to understand the properties of a system is the analytical approach, given below are the equations that describe the transit curve completely, equations (1.2), (1.3) and (1.4) give out the geometry of the transit and it’s given in terms of transit depth, shape and the transit duration (figure 1.2). Transit shape is laid out in terms of the total transit tT ( from the first to the fourth contact point in the figure 1.2) and the inner transit (from 1.1. TRANSIT METHOD 9 the second to the third point in the figure 1.2). Given below is the equation to the transit depth [21] 2 Fnotransit − Ftransit RP ∆F = = 2 (1.2) Fnotransit R∗

Here, — ∆F is the transit depth or change in flux during transit — F is the total observed flux of the star

R l (1− p )2−( a cosi)2 R∗ R∗ R∗ 0.5 tF arcsin(( a )[ 1−(cosi)2 ] ) = R l (1.3) (1+ p )2−( a cosi)2 tT R∗ R∗ R∗ 0.5 arcsin(( a )[ 1−(cosi)2 ] ) Above equation is of the transit shape,it’s the ratio of the inner transit to the total transit[21]. Here,

— R∗ is the radius of the star — a is the semi major axis — Rp is the radius of the planet — i is the inclination P R (1 + Rpl )2 − ( a cosi)2 t = arcsin(( ∗ )[ R∗ R∗ ]0.5) (1.4) T π a 1 − (cosi)2 This equation gives the total transit time and here P is the orbital period. By fitting the transit light curves as we can see we obtain ∆F , tF and tT , from these values we get b (impact parameter), i (inclination) and a/R∗. let us see the further steps taken to obtain these parameters. From equation 1.2 we can obtain the planet star ratio as

R √ P = ∆F (1.5) R∗

From (1.5) and the transit shape equation (1.3) we get the impact parameter b, it is defined as the distance between the planet and star center during mid transit.

√ 2 tF π √ 2 sin P 2 (1 − ∆F ) − ( 2 tT π )(1 + ∆F ) a sin P 0.5 b = cosi = [ t π ] (1.6) sin2 F R∗ P 1 − ( 2 tT π ) sin P Directly by interchanging the impact parameter b in (1.6), we can also obtain the incli- nation (i) which is stated as follows,

R i = cos−1 (b ∗ ) (1.7) a

From the transit duration (1.4) we can get √ a (1 + ∆F )2 − b2(1 − sin2 tT π ) = [ P ]0.5 (1.8) 2 tT π R∗ sin P 10 CHAPTER 1. TRANSITING PLANETS: TREASURES IN THE SKY

Stellar density ρ∗ is obtained from the above equation and the Kepler’s third law given below (1.9) with Mp << M∗ [21].

a3 G(M + M ) = P ∗ (1.9) P 2 4π2

√ M∗ 2 2 2 2 tT π ρ∗ M 4π (1 + ∆F ) − b (1 − sin P ) 3/2 = = [ ][ t π ] (1.10) R∗ 3 2 2 T ρ P G sin P R

Here,

— ρ is the solar density — M∗ is the mass of the star — M is the mass of the Sun — G is the gravitational constant — P is the orbital period

1.2 Physical parameters

From the transit light curve we can obtain the parameters ρ , a , t , RP and a as observ- ∗ R∗ T R∗ ables or by interpretation but how do we determine M∗, R∗, Rp and i. Given below are a few methods to obtain the above mentioned physical parameters

— Host star parameters such as Teff (effective temperature), log g can be obtained from spectroscopic observations and stellar atmospheric modeling and after this M∗ and R∗ are obtained by choosing from appropriate stellar evolutionary models.

— By using interferometric observations we can get a direct measurement of stellar angular diameters θ∗, which is transformed into R∗ on the basis of a trigonometric parallax and this is independent of models.

— The stellar density ρ∗ which is obtained from the light curve provides a direct constraint on R∗, and it’s also a sensitive indicator of its evolutionary state. stel- lar density ρ∗ is also added as an input in determination of M∗ from the stellar evolutionary models

— We can also use the empirical laws M∗ (Teff , Fe/H, ρ∗) calibrated on eclipsing binaries

— measurements of ρ∗ can be used to obtain M∗ and R∗. 1.3. LIMB DARKENING 11

Figure 1.2 – Transit geometry depicted with indication of ∆F ,total and interior transit. [21]

1.3 Limb darkening

Limb darkening appears as a factor to consider while analyzing our data in order to avoid errors. Given below is the cause for limb darkening and the measure taken to correct it. It’s an effect seen in stars where the center of the star appears brighter when compared to the edge of the star. Such an effect occurs because the solar atmosphere has a change in the temperature with the considered depth and this because the temperature is dependent on altitude in the . A deeper look into the center shows the deepest and warmest layers that emit the most light, this is at a higher temperature and with intense radiation. 12 CHAPTER 1. TRANSITING PLANETS: TREASURES IN THE SKY

This on the contrary makes the surface closer to the atmosphere more cooler and dimmer. For this the temperature decreases with the altitude in the and the edge of the star appears thus dimmer than the center. The spherical geometry of the star means that the further it is from the center of the stellar disk, the higher the altitude of the emission source and as the temperature decreases with the altitude in the stellar atmosphere, the edge of the star appears thus dimmer than the center. Limb darkening effect is stronger at bluer wavelengths. From the figure 1.3 we can see the transit is having a very round shape in the blue optical region where as on the other hand the bottom of the transit is nearly flat for NIR wavelengths. To account for limb darkening effects we include the quadratic limb darkening law( given below) in the MCMC code (seen under chapter ’Data analysis’) in order to model it. In the equation below C1 and C2 are the two limb darkening coefficients used in the quadratic law, µ is the Limb-darkening coefficient, IO is the central intensity and I is the intensity seen along the line of sight.

I 2 = 1 − C1(1 − µ) − C2(1 − µ) (1.11) IO

Figure 1.3 – Limb darkening effects seen at different wavelengths [11] 1.4. TRANSMISSION AND EMISSION SPECTROSCOPY 13 1.4 Transmission and emission spectroscopy

Transmission spectroscopy involves observing a planet as it crosses its host star(1.4 ) and this measurement gives us the combined or the total brightness (star plus the transiting planet) of the system over time i.e. the transit light curve [22]. The planet blocks a fraction of the stellar flux emerging from the host star. The amount of flux blocked by the planet is the sky projected area of the planet relative to the area of its host star and this dip in the brightness is given as the transit depth. The transit depth varies from planet to planet according to their size. The bigger the planet more is the transit depth obtained. The transmission spectrum consists of the measured transit depths as a function of wavelength, the main idea behind the procedure of transmission spectroscopy is that the transit depths obtained are dependent on wavelength. At certain wavelengths where the atmosphere is more opaque due to absorption by certain atoms or molecules it is observed that the planet blocks more flux [22]. The variations in the flux mentioned above are observed in binned wavelength sections and the resulting light curves are each assigned a transit model and the resulting transit depths obtained from these curves are the ones that constitute the transmission spectrum.

Figure 1.4 – Indication of the transit and occultation geometry, Rs is the stellar radius (we use R∗) Rp is the planetary radius, d is the separation of the two centers with respect to the plane of the sky and H is the .

The name for the technique comes from from the fact that these occurring variations come from the transmission of stellar flux through the planet’s atmosphere and hence the name [23]. Also when monitoring a transit event photometrically, we can see that a planet crossing the visible hemisphere of the host star causes a dip as big as 1% for a Jupiter sized planet around a sun like star, 0.1% for a Neptune sized planet or ≈ 0.01% for an Earth sized planet [22]. From the obtained transmission spectra and by knowing the atmospheric scale height (H) we can get the size of the variational features in the transmission spectrum. By using the ideal gas law and assuming hydrostatic equilibrium 14 CHAPTER 1. TRANSITING PLANETS: TREASURES IN THE SKY we have scale height written as [23],

k T H = b eq (1.12) µg

— kb is the Boltzmann constant — Teq is the planet’s equilibrium temperature — g is the — µ is the mean molecular mass The amplitude of the variations seen in the transmission spectrum is then given as [23]

2nRP H δλ ≈ 2 (1.13) R∗

Here n is the number of scale heights that is crossed at wavelengths with high opacity. Planets of high temperature, lower stellar radius and low surface gravity give a better transmission signal, this also applies for M stars with their smaller host star size (Ultra cool dwarfs). Emission spectra is the observation spanning the secondary eclipse, whenever a planet passes out of view behind the star we can measure the planet’s thermal emission and obtain its associated spectral features (these are due to atmosphere’s changing opacity relative to wavelength and the size of these variations depend on the temperature pressure profile of the atmosphere). Emission spectra is estimated from the difference between the total light received just before or after eclipse (star + planet day-side) and that during the eclipse (star only). Emission spectra gives information of the deeper atmospheric layer at high pressure in addition to atmospheric composition. For an emission spectra obtained from short period planets the cause for the dominant source of flux is the re-radiation of incident stellar flux [22].

Figure 1.5 – Exoplanet transmission spectroscopy, picture shows the fraction of light being absorbed by the chemical constituents in the atmosphere [24] 1.5. TRANSITING PLANETS WITH THE JAMES WEBB SPACE TELESCOPE (JWST)15 1.5 Transiting planets with the James Webb space tele- scope (JWST)

JWST the upcoming and most awaited telescope should do wonders for exoplanetology, as many candidates should be well suited for atmospheric characterization with it. So let’s see below the features that JWST provides for Transiting planets JWST has 6.2 and 50 times the collecting area when compared to the (HST) and Spitzer. JWST will produce relatively high resolution (up to 1700) spectra with a broader wavelength region (1 to 10 µm) compared to other instruments. It’s going to reach distances that no instrument has gone before. It will also provide a S/N ratio in the near and mid IR region for exoplanet i.e. transmission and emission spectra of planets lower than 10 Earth masses ([25]). It will also provide details 109 about the molecular features of CH4, CO, CO2, H2O, and NH3 . These chemical abun- dances reveal the element abundances of the observed objects along with their formation history. The instruments used here are well equipped for transit spectroscopy.

— NIRISS (Near Imager and Slitless Spectrograph) with SOSS (single object slitless spectroscopy) mode uses a grism to produce a slitless spectra and operates in the range of 0.6 – 2.8 µ m simultaneously with R = 700 — NIRCam (Near Infrared Camera) operates over a range of 2.4 – 5.0 µm with R = 1100 to 1700. — MIRI LRS (low-resolution spectroscopy) gives slitless mode of operation with a R of 100 for a region between 5-12 µm — NIRSpec (Near-Infrared Spectrograph) with its wide slit compensates for telescope jitter and all the 6 gratings with a 0.6 – 5 µm prism is used for time series transit spectroscopy

Super-Earth and Earth-sized planetary atmospheres will also be characterized with JWST. Their weak features will be supported with other transmission or emission spectra to ob- tain results. Most important of all TRAPPIST-1 planets will be observed a number of times for their transmission spectra with NIRISS or NIRSpec or for their emission spec- tra. MIRI at λ > 5 µm is to reveal atmospheric and thermal features. M dwarfs are also targeted for characterizing their Earth sized planets and high expectations have been put on them for achieving the transmission signals for many warmer Earth-sized planets with varied composition (Morley et al. 2017). JWST MIRI observation for TRAPPIST-1b (Teq = 400 K ) is to be of 300 ppm with respect to its star at the wavelength range of 10 – 15 µm. This emission at S/N 5 is to be detected within five secondary eclipses (at 12.8 µm and 15 µm filters) and also a dozen of other scheduled observations are to be performed for the other TRAPPIST-1 planets (TRAPPIST-1 d and e) 16 CHAPTER 1. TRANSITING PLANETS: TREASURES IN THE SKY Chapter 2

Ultracool dwarfs and their planets

2.1 Description of ultracool dwarfs

Ultra cool dwarfs (UCDs) belong to the stellar or sub-stellar objects (, is an object whose mass is smaller than the minimal mass required to sustain stable hydrogen fusion, which is about 0.07M ) [12, 1] whose effective temperature is lower than 2,700 −3 K and have luminosities ≤ 10 L . They belong to spectral class M7 [26] and extend up to brown dwarfs including spectral classes of type L,T and Y. Their spectral energy distribution is rather intricate and peaks in the near and mid IR due to their effective tem- peratures. Accounting for its physical parameters and stellar conditions the atmosphere contains molecular like H2O, CO, T iO, V O, CH4,NH3, CaH and F eH. Condensed refractory species like mineral-metal-condensates, salts and ices [15] are present too. They make up for about 15% of the astronomical objects found around the Sun [27] . These objects have core as high as as 1000 g/cm3 [13] and have dense interiors with a high value that can host metallic hydrogen which leads to a fully convective and well mixed interior composition of the star. The smallest UCD stars live for about a trillion years [28] which is a result of the combined effect of a fully convective structure and low fusion rates (electron degeneracy pressure keeps the object from ). Comparing the current age of UCDs to the age of the universe we can tell that these particular systems of stars are young and more advantageous when it comes to finding Earth sized planets around them and some of the planets even emit flares and radio waves (M9 ultracool dwarf LP 944-20 [29]) indicating magnetic properties. Observing programs at Arecibo and the are the indicators of such a drawn con- clusion [29]. Category of Ultra cool dwarf stars were first introduced in 1997 by J Davy Kirkpatrick, Todd J Henry and Michael J Irwin [30], their count has been increasing ever since and over the past few years we have even included some systems nearest to the sun as well. The systems nearest to the Sun are the L dwarf plus T dwarf binary Luhman 16AB at 2.0 pc and Y dwarf WISE 0855-0714 at 2.3 pc [31]. Ultra cool dwarfs of the L and T kind have a more tackle-able environment than the M kind as its low Teff hinders the coupling of the photospheric gas to its internally-generated magnetic field leading to a reduced relative strength and incidence of optical (H-alpha, Ca II) and X-ray non thermal emission. Also results from core theory tells that due to low masses and the small size of their protoplanetary discs [32, 33] they are able to host a dominant Earth size terrestrial planets in their system. Their sizes should range from Mercury to Earth

17 18 CHAPTER 2. ULTRACOOL DWARFS AND THEIR PLANETS sized. TRAPPIST-1 is a very suitable example of such an ultra-cool dwarf system and is in agreement with the core accretion theory result [34].

2.2 Ultracool dwarfs and planets

As Ultra-cool dwarfs are small objects it becomes easier and more prominent to identify a transit of an Earth like object around it. Among the small population of planets discovered around UCDs, the 7 TRAPPIST-1 planets, planet MOA-2007-BLG-192Lb of ≈ 3ME and planet OGLE-2016-BLG-1195Lb of ≈ 1.3ME are a few of them. The latter two planets are detected by microlensing technique [35] and are examples of planets more massive than Earth which are formed in a region of a lower mass protoplanetary disc. The TRAPPIST-1 planets belong to a compact system of terrestrial planets around their host star. The planetary detection agrees with the observational evidence pointing towards a in the surrounding of young UCDs [36]. These UCDs with their small mass persist longer than Solar type stars [37] and they are also known to have accretion jets, evidence of disk formation and formation which are indications of pre- planetary formation [38, 39, 40, 41]. He et al. (2017) wrote that the percentage of a short period planet being present is below 67 ± 1% in the radius range of 0.75 and 3.25 R ⊕ and within a 1.28 d orbit, but at present this population is quite low. Planetary models for UCDs show that they should be able to host terrestrial planets but have disputes regarding their composition and mass. Montgomery and Laughlin (2009) came to a conclusion that the system could contain more massive planets than Mars with volatile rich composition and Raymond et al. (2007) predicted systems of short-period metal-rich terrestrial planets that are not habitabily suitable with a mass less than Mars where as Benz (2017) predict Earth-sized planets, that are volatile rich (condition being- protoplanetary discs orbiting low-mass stars are long lived). These theories along with observational evidence of finding short-period low-mass planets around solar type stars in nearly co planar systems [42] gives the conclusion that system with terrestrial planets can be around UCDs and they would be a tidally locked red system like TRAPPIST-1.

2.3 The SPECULOOS project

Low luminosity and small size lead to a large planet to star flux ratios and this makes the detection of spectroscopic features in the atmosphere of the transiting planet more easy compared to the other systems. From Cantrell et al. [27], we have SNR (Signal to Noise Ratio) expectations from JWST for Earth sized planets around M0-M9 dwarf stars at a distance of 10pc. Upon considering a lower limit of SNR=10 for the atmospheric compo- sition we can get the upper limits of distance for various UCD stars of different spectral types. Number densities of UCD stars near the Solar neighbourhood along with their distance limits yield a target number for UCD as 800 (different systems to be observed) [15]. On the whole there are about a 1000 opportunities of observation near our solar neighbourhood for systems that can be suited for atmospheric characterization and that may include terrestrial planets. Among the 1000, 800 are stars and 200 are brown dwarfs. Having such a good number only means that we have to find suitable instruments in order 2.3. THE SPECULOOS PROJECT 19 to observe it. UCDs hold advantages when it is comes to a transit search survey as they are small in size which makes the terrestrial planets to have a transit depth in the range of a few 0.1%up to > 1%. They also have a period of a few days due to the proximity of their habitability zones, this helps a great deal in photometry as the observation can be frequent and lucrative. Finally a target of 1000 systems can be achieved rather easily due to the of the UCD system and the observations can be performed within a few years. This and observation of each target individually is the main scientific goal of SPECULOOS (Search for habitable Planets EClipsing ULtra-cOOL Stars). This initiative is lead by the University of Liege (Belgium) in collaboration with the Cavendish Laboratory of the University of Cambridge (UK), Massachusets Institute of Technology (MIT), the Institute of Astrophysics of the Canaries (IAC), the Cadi Ayad University of Marrakech and the King Abdulaziz University (Saudi Arabia) [15]. SPECULOOS Southern Observatory is situated in the southern hemisphere at ESO Paranal Observatory, Chile Atacama. It’s composed of 4 Ritchey-Chretien (F/8) robotic with a diameter of 1m each and comes with a 2k*2k CCD camera Peltier-cooled with a pixel size of 13.5 µm and a pixel scale of 0.35", FOV is 12’*12’. They are very sensitive to the very near IR region (700 to 1000 nm) [43] and operate with the median seeing condition of < 1.2". The light curves obtained from the instrument are of the photometric precision of 0.1%. As mentioned earlier for a target of at least 500 systems, time required would be 5 years considering 12000 nights of observation with all the four telescopes. HZ are explored and marked with continuous individual observation of 4 telescopes on one target over a period of 10 nights. As mentioned UCD systems have low amplitude transits with a short duration of the transit time so more importance must be given to continuous monitoring of the object and this is what is being done here at SPECULOOS. The photon count is increased by continuous monitoring and photometric detection threshold is enhanced and after the transit ephemeris is established observations are taken over by a more precise photmetric instruments like VLT or Spitzer. SPECULOOS also has a northern twin, installation and other formalities are in progress and it’s set to be operational in 2019. 20 CHAPTER 2. ULTRACOOL DWARFS AND THEIR PLANETS

Figure 2.1 – Top- and Bottom-Io, the first two telescopes of the SPECULOOS southern observatory [43]

2.4 Prototype survey for SPECULOOS on TRAPPIST

Initially it was speculated that SPECULOOS observations could be limited because of the following reasons, first late M-dwarfs are active objects [44] which would hinder the observation of low amplitude transits and second, due to the emission of OH that causes airglow and a number of absorption bands coming from the water molecule and OH radical in the IR region inducing high levels of red noise in the photometric observations. Considering these factors a survey was to be done and TRAPPIST-South (TRAnsiting Planets and Small Telescope) [45] was chosen for it. It contains an optical tube of the Ritchey-Chretien type with a 0.6 meter telescope and has a focal length of 4.8m. It comes with a German equatorial mount with direct drive system motors. There is no periodic error and the speed is up to 50 deg/sec and the tracking accuracy without auto guider is about 1 arc sec/10 min also the camera is a back illuminated Peltier-cooled commercial camera with an array size of 2048 x 2048 pixel having a pixel scale of 0.64 arc sec/pixels, Field of view of 22x22 arcmin and has a quantum efficiency of 96% at 750 nm [45]. One of TRAPPIST-South telescopes goal is to obtain the limitations of 2.4. PROTOTYPE SURVEY FOR SPECULOOS ON TRAPPIST 21 the SPECULOOS and this survey was extended towards TRAPPIST-South’s twin, the TRAPPIST-North telescope. On the whole, a total 40 UCDs were observed out of which some indicated (20%) low frequency flares which have an initial riSe in intensity and a decay, 30% had rotational modulation with a value up to 5% amplitude while the rest had flat curves indicating stability.

TRAPPIST-South UCD light curves were injected with synthetic transit cures of terres- trial planets, these intense simulations concluded that the two factors of obstruction were no longer a threat and the extra noise of 10% is due to high humidity conditions and nominal sub-mmag conditions can be reached and as an added benefit to prove this con- clusion, TRAPPIST-1 planets were discovered (one of TRAPPIST-South UCD targets). This shows the magnificent capacity of SPECULOOS.

: Right-TRAPPIST-South telescope with its dome Left-TRAPPIST-South telescope,ESO Paranal Observatory Chile [31] . 22 CHAPTER 2. ULTRACOOL DWARFS AND THEIR PLANETS Chapter 3

The TRAPPIST-1 system

3.1 The host star TRAPPIST-1

TRAPPIST-1, the name comes from the discovering telescope TRAPPIST [46, 47] or 2MASS J23062928-0502285. It was discovered in 2000 pertaining to the search of Ultra- cool dwarfs according to the photometric criteria [48] by 2MASS. Its an isolated Ultra-cool lying in the main sequence with a spectral class of M8.0 ± 0.5 (TRAPPIST-1 best fit that of the M8-type standard LHS 132 spectrum [34]). It’s emission peaks in the near-infrared, at around 1 micron and is at a distance of 12.0 ± 0.4 from earth as indicated by the trigonometric parallax [34], the mass of this star is about 8 percent of sun and has an age limit more than 500 million years. Other main characteristics of the star is indicated below (3.1) [34]. The Cerro Tololo Interamerican Observatory Parallax Investigation (CTIOPI) project indicated a trigonometric parallax of π = 82.6 ± 2.6 mas for the host star which means that the star is at a distance of 12.1 ± 0.4 [49] parsecs. The star is a very low mass main sequence star which is consistent with the non-detection of the 6,708 Å lithium absorption line by high-resolution optical spectroscopy. This is in agreement with its thick disc kinematics [50]. Furthermore observing its photometric stability, slow rotation and moderate activity the stars estimated age was at least 7.6 ± 2.2 Gyr [34].

Magnitudes V=18.8, R=16.6, I=14.0, J=11.4, K=10.3 Distance [pc] 12.1 ±0.4

Mass M∗[M ] 0.089±0.006

Radius R∗[R ] 0.121±0.003 +1.2 Density ρ∗[ρ ] 50.7−2.2 Effective temperature Teff [K] 2516±41

Luminosity L∗[L ] 0.000522 ±0.000019 [Fe/H] [dex] 0.04 ±0.08 Table 1: TRAPPIST-1 parameters [34] [51]

23 24 CHAPTER 3. THE TRAPPIST-1 SYSTEM 3.2 The TRAPPIST-1 planetary system

As we know the TRAPPIST-1 star (moderately active M8±0.5 dwarf star) system houses 7 transiting planets with similar size estimates as our Earth around an UCD host star at a distance of 39 light years [52]. Among the seven planets TRAPPIST-1e, f, and g are in the habitable zone and are the targets for atmospheric bio signatures classification with JWST. Given below is a figure (3.1 ) that contains the transit light curves of all the seven planets observed by Spitzer at 4.5µm and their orbits. The TRAPPIST-1 planets are in a unique near-resonant chain with orbital periods (1.51, 2.42, 4.04, 6.06, 9.21, 12.35 and 18.76 days) as near-ratios of small integers [52]. Planets are in mutual interaction and proof of this can be seen in the Transit Time Variation (TTV) signals that last from a few tens of seconds to a little more than 30 minutes [45, 53, 54]. Analyzing these TTV signals initial mass estimates with upper limit on is derived (e < 0.085). Stellar irradiation is similar in range of the inner (Mercury = 6.7 SE, SE = Solar irradiation at 1 au) and lies within ≈ 4.3 to ≈ 0.14SE. TRAPPIST-1h lies in the snow line of the system as it has an equilibrium temperature of 170 K (assuming a null albedo). The planetary system is co planar when seen edge on with orbital inclinations close to 90◦, this indication combined with the near resonant chain structure tells us that the planets had formed further away the star and that they migrated inward by interaction with the disc [55, 56]. All the physical and model parameters for the planetary system are given below (3.2) with their 1σ error limits of the posterior Probability density function (PDF) derived from the global MCMC analysis.

Figure 3.1 – Left-Photometric measurements obtained by Spitzer for planets TRAPPIST- 1b-h, this is corrected for the measured TTVs Right-Representation of the orbits of the 7 planets, the grey annulus and the two dashed lines represent the zone around the star where abundant long-lived liquid water could exist [50] 3.3. CHARACTERIZATION OF TRAPPIST-1 PLANETS: PRESENT AND FUTURE25

Figure 3.2 – Updated properties of the TRAPPIST-1 planetary system. The values given are the median values with their 1σ error limits of the posterior PDFs given from the global MCMC analysis [52]

3.3 Characterization of TRAPPIST-1 planets: present and future

The TRAPPIST-1 system is a very good candidate for atmospheric characterization due to the small size of their host star, low luminosity and infrared brightness (K = 10.3) along with this their transiting configuration makes it possible to study their atmospheric properties. Although the disadvantage being that we know very little about their atmo- spheric composition as they are the first transiting planets detected transiting a UCD. The theoretical predictions put forth cover the whole atmospheric range from the H/He dominated atmospheres to H/He depleted atmospheres [57, 58, 59, 60, 61] also cloud free H/He dominated atmospheres give signatures of H2O and/or CH4 in the near IR region, this condition was not satisfied by TRAPPIST-1b and TRAPPIST-1c and was ruled out by observations from HST/WFC3 [62]. This still means that there could be a presence of cloudy or dense atmosphere with H2O or N2 or CO2 domination. Observations made like the one above were done for TRAPPIST-1d, e, f and g planets too and further obser- vations in the IR region will probe higher mean molecular weight atmospheres and later after this we will be able to see detailed characterization by JWST [63] .

To know about the atmospheric stability and habitability status of the planet, charac- terization of high-energy radiation environment of planets is necessary. With regard to this XMM-Newton observations of TRAPPIST-1 led us to know that despite its lower bolometric luminosity TRAPPIST-1 is a strong a variable X-ray source having a similar 26 CHAPTER 3. THE TRAPPIST-1 SYSTEM

X-ray luminosity as the Sun [63] . Hubble space telescope measured the Ly- line and found it to be much fainter than what was supposed to be brought about by the X-ray emission, this may indicate a moderately active compared to the corona and the transition region [64]. Even though the Ly-α line is relatively faint, it can still be used search for signs of planetary hydrogen escape (could indicate presence of water reservoirs by the presence of photo dissociated water molecules in the upper atmosphere [65]). A good precision of the mass estimates of the planets constraints their composition [66], it is a pre requisite for atmospheric observation and for a deeper understanding of these plan- ets. An assessment of the percentage of on the total energy budget can be brought about by the measure of orbital eccentricities, it can also tell us an estimate of its geological activity (counterbalance of atmospheric erosion through volcanism). Current estimates of mass and low density for TRAPPIST-1 f indicate a volatile-rich composition. Small eccentricities represent tidal heating for all planets (TRAPPIST-1 f and h have a higher tidal heat flux than Earth [67]).

3.4 On the scientific importance of TRAPPIST-1

Given below are the few reasons to indicate as to why we must focus on the TRAPPIST-1 system. — Assuming earth like atmosphere, it is possible that the planets TRAPPIST-1e, TRAPPIST-1f and TRAPPIST-1g could harbour liquid water in the form of oceans on their surface (1D cloud-free climate model [30]). — The stellar irradiation of the planets cover a range of 4.3 to ≈0.13 SEarth. In fact TRAPPIST-1c, TRAPPIST-1d and TRAPPIST-1f have irradiation very close to that of Venus, Earth and Mars. Although 3D climate model indicates a run away greenhouse effect for the planets, nevertheless if some water is retained, irradiance makes it possible for it to be still contained on the planet(For planets TRAPPIST- 1b, c, and d only)[52]. — If internal energy is favoured for TRAPPIST-1h, it could harbour liquid water on its surface and a very strong green house effect due to a H − 2 could also result in liquid water on the planet. — Based on mutual separations between the planets, the system appears to be stable (statistical methods [52]) — TRAPPIST-1b and TRAPPIST-1c lie close to the inner edge of the habitable zone unlike TRAPPIST-1d and with their low equilibrium temperature they can hold a few habitable regions. — It is accessible by ground based and space based telescopes as its distance is ap- proximately 39 light years away. It is also suitable for atmospheric characterization which uncovers more details about the system and its atmosphere. — The last three planets (e,f and g) lying in the habitable zone makes it more exciting as the atmospheric analysis from James Webb telescope could reveal breath taking results of the life sustaining elements present in them. — TRAPPIST-1 as a system itself could set a platform for other exoplanet searches that indicate candidates that can possibly host life. This particular system is the best possible candidate to study what life emerging conditions might look like outside our solar system. 3.4. ON THE SCIENTIFIC IMPORTANCE OF TRAPPIST-1 27

— Reduced flare activity over the years due to a slightly older star (more than 500 million years) has improved conditions. 28 CHAPTER 3. THE TRAPPIST-1 SYSTEM Chapter 4

Concept and goal of this thesis

In my thesis, the main goal is to study the TRAPPIST-1 star along with its seven planets and analyze their data. As we know the era of discovering planets outside our solar sys- tem has arrived and now with instruments like James Webb telescope, the atmospheric characterization of the chosen planets will also be easier than ever. James Webb telescope is regarded the best for atmospheric characterization due to its orbit, its aperture size and its infrared sensitivity (chapter 1, section 1.5). Now that we have the instruments to characterize the system we must put extra thought on which system to pick and as discussed before, one of the most targetable system for bio signature detection on a hab- itable terrestrial planet would be a terrestrial planet transiting around an ultracool dwarf star like TRAPPIST-1. These star systems are of small in size and prevent dampening of the planetary signals, this allows the system to be accessed more which only means that more information about the system is revealed and also their low luminosity (0.0005 L ), infrared brightness (k=10.3) and the small size (0.12 R ) makes it one the most preferred systems for atmospheric classification with current and future astronomical facilities [15]. In order to perform atmospheric studies on TRAPPIST-1 and to understand the sys- tem thoroughly we need precise physical values of the mass and the constraints on their compositions. As we know that the results obtained from first observations are variable and do not succeed in providing the whole picture, many such observations from different instruments must be considered and my results from the Liverpool telescope aims to play a small role in solving this problem. Also measurement of accurate eccentricities can lead to a better judgment on the planets habitability condition and in turn constraints the effect of tidal heating and the total energy budget. The more precise our measurements are for the system the more accurate our dynamic solution for the system could be. In order to get accurate values the data obtained from Liverpool telescope were subjected to differential photometry, this is important as it gives a variation of the flux in the host star and this variation in our case is primarily caused due to the transit of the planets around its host star. Later the light curves obtained were subjected to individual analysis in order to obtain the astronomical effects and instrumental effects at a photometric level. Individual analysis was run through an initial chain of 10,000 steps to obtain the CF (correction factor) and to account for red and white noise. CF obtained here is later accounted for in the next step and is added to the photometric error bars. Then the second chains of 100,000 steps is run to ensure the convergence and the well mixing of the MCMC simulation. Followed by the individual analysis we have the global analysis,

29 30 CHAPTER 4. CONCEPT AND GOAL OF THIS THESIS here we combine all the observational data obtained for a particular planet in order to perform the MCMC analysis. Just like before MCMC analysis is run twice and we must also ensure that Gelman-Rubin statistic less than 1.11 which is an indication of converged chains. Global analysis gives the physical parameters and the best fit models for the planet. Values obtained from both individual and global analysis are indicated in chapter 7. Trappist-1 measurements from my deductions and the conclusions drawn from my studies can also form the basis of similarities of many other such planetary systems that are to be discovered from the upcoming missions like SPECULOOS.

Chapter 5

Reduction method 1- Observations

5.1 Liverpool telescope

This instrument is a part of the Astrophysics Research Institute (ARI) of Liverpool John Moores University in north west England. It’s fully robotic with a 2m Cassegrain reflector telescope, it also comes with Ritchey-Cretien hyperbolic optics on an alt-azimuth mount. The telescope is placed in a novel clamshell designed enclosure, the enclosure opens in two halves from the top which helps the instrument get a better view of the sky and along with this, it makes it easier to lock the target for observation. This instrument is located in the canary islands at international ’Observatorio del Roque de los Muchachos’.

The main scientific goal of this instrument is to [68],perform simultaneous observations with regard to ground and space based instruments, perform rapid robotic reaction to certain unpredicted phenomenon and do follow up observations on the same, monitoring variable objects and finally perform small scale surveys. Principal investigator of the project resulting in these Liverpool/IO:O data is Mr Amaury Triaud, I thank him for this opportunity to let us explore the data.

The main optical instruments on this telescope which is concerned with this thesis is:

5.1.1 IO:O

It’s an optical imaging component of the Infrared optical line of instruments. It has a detector array size of 4096x4112 pixels with a pixel size of 15.0 x 15.0 microns. The pixel scale is ≈ 0.15 arcsec/pixel (unbinned), FOV is 10 x 10 arcmin.

The filter used for our observation is the SDSS-Z filter and all images that were obtained are subjected for bias subtraction, trimming of the overscan regions, and flat fielding [68] .

31 32 CHAPTER 5. REDUCTION METHOD 1- OBSERVATIONS

Figure 5.1 – IO:O Camera mounted on the Liverpool telescope [76]

5.2 Reduction methods

Let us discuss below the preliminary steps performed in this thesis to obtain the light curves. It begins with with the observational data which is obtained to reduce, the pho- tometric steps performed and concludes with obtaining the light curves with the suitable comparison stars.

5.2.1 Observations

As mentioned, the observational data for my thesis is obtained from The Liverpool tele- scope. The observational run comprises of totally 19 runs of data with 17 transit light curves. All the observations were taken from the 2m Liverpool telescope between May to October of 2017. It was taken from the IO:O CCD camera of 4096x4112 pixels on the SDSS z0 filter, the field of view is 10 x 10 arcmin with a binning scheme of 2’x 2’ and a pixel scale of 0.3 arcsec/pixel with an integration time of 20 seconds. This same pattern was maintained for all the 19 observational runs.

Details of all these observations along with the planet in transit is given in the table below. Data from 2017/10/03 was not further considered for individual and global analysis as the was saturating the CCD field. The moon was 2 degrees from the object with an illumination of 96% for this particular observation. This resulted in the data being unsuited for high precision photometry. 5.2. REDUCTION METHODS 33

Date of Observation Camera with filter used Planet(s) in transit

2017/05/31 IO:O camera with SDSS-Z Filter TRAPPIST-1b 2017/06/17 IO:O camera with SDSS-Z Filter TRAPPIST-1e 2017/07/01 IO:O camera with SDSS-Z Filter TRAPPIST-1c 2017/07/14 IO:O camera with SDSS-Z Filter TRAPPIST-1d 2017/07/20 IO:O camera with SDSS-Z Filter TRAPPIST-1b 2017/07/22 IO:O camera with SDSS-Z Filter TRAPPIST-1d 2017/07/23 IO:O camera with SDSS-Z Filter TRAPPIST-1b 2017/07/29 IO:O camera with SDSS-Z Filter TRAPPIST-1b 2017/08/04 IO:O camera with SDSS-Z Filter TRAPPIST-1c TRAPPIST-1b 2017/08/15 IO:O camera with SDSS-Z Filter TRAPPIST-1h 2017/08/17 IO:O camera with SDSS-Z Filter TRAPPIST-1e 2017/08/20 IO:O camera with SDSS-Z Filter TRAPPIST-1g 2017/09/07 IO:O camera with SDSS-Z Filter TRAPPIST-1c 2017/09/19 IO:O camera with SDSS-Z Filter TRAPPIST-1c 2017/09/21 IO:O camera with SDSS-Z Filter TRAPPIST-1d 2017/10/05 IO:O camera with SDSS-Z Filter TRAPPIST-1e 2017/10/03 IO:O camera with SDSS-Z Filter NA 2017/10/21 IO:O camera with SDSS-Z Filter No Transit 2017/10/28 IO:O camera with SDSS-Z Filter TRAPPIST-1c Table 3: Observational dates for TRAPPIST-1 along with the camera used and the planet in transit

5.2.2 Data reduction

The data obtained from the Liverpool telescope are subjected to instrumental corrections and then are made available to the user through the data archive. All this is done through an automated pipeline that already exists for Liverpool.

— Bias Subtraction- Bias occurs due to a constant voltage applied to the CCD detec- tor, to correct for this we have to analyze the over scans of the sides of the image and after this a single constant bias is applied over the whole image. — Over scan Trimming- Overscan regions are trimmed off the image leaving a 2048x2056 array image. — Dark Subtraction- The dark current is developed in the detector which leads to count of ‘photons’ in the CCD even when there is no exposure to light. This is due to the fact that there will be generation of thermal electrons. This is usually called reverse bias leakage current. In order to avoid this error, the dark frames are taken without any passage of light on the detector by covering the shutter and making sure we have used the same exposure time as our science images and 34 CHAPTER 5. REDUCTION METHOD 1- OBSERVATIONS

subtract this factor from the images to calibrate them successfully. For Liverpool, this is not usually done as the dark current is usually negligible (0.002 electron / pixel / second) at the operating temperature(-110 C). — Flat Fielding- Flat field correction is to correct for the differential gains in the pixel intensity. Flats are automatically obtained every evening and morning and master flat is created(median of stacked images) and this data is stored in the library and operated when in need for the right filter and binning configurations multiplied with the image data. — Bad Pixel Mask- No cosmic ray rejection or bad pixel mask is applied for correction.

After the preliminary reduction the images are subjected to photometric reduction and differential photometry. Our main goal is to monitor the flux change in our target object and this is done by using the photometric data obtained through the CCD. Since it records flux of all the objects in the FOV we can perform differential photometry to extract the instrumental of the target object and its comparison stars. The flux is measured through aperture photometry, where at first, the pixel counts are summed with the object being centered on the aperture from which the product of nearby average skycount per pixel and the number of pixels within the aperture is subtracted. Raw flux = Σ(counts in aperture)−sky ×n, where n is the number of pixels inside the aperture. The signal obtained in the image for a target will cover a number of pixels according to the PSF (Point Spread Function). Photometry is performed, this results in obtaining images that are calibrated, then the brightest stars are detected in each image, the FWHM is measured, the images are aligned based on their measured dx and dy differences, then they are stacked, then the stars are detected in the stacked images, then aperture photometry is performed on each image to measure the fluxes from each star.

5.2.3 Differential photometry

The principle is to measure the flux of an of your choice relative to a standard star in the field of view that has a constant brightness. This is important as we measure the variation of the flux which is our prime goal when it comes to observing a transit that causes a fluctuation in the brightness. Here we determine the ratio of the flux of TRAPPIST-1 and the sum of flux of all the other comparison stars that are chosen. The comparison stars are decided upon by looking through the stacked image to find other target stars that are closer to your star and are of the similar flux value. To help us do this, we use the ’ALADIN’ [54] software that indicates the flux value of your target and comparison stars.

Comparison stars are chosen because most of the observational variables drop out as both the comparison and target stars are observed using the same filters, same instrument and are also viewed through the same optical path. By doing this we get the differential mag- nitude as the difference of the instrumental magnitude of the target and the comparison stars. Later using this we can easily plot the light curve. The light curve plotted will give the result of the ratio described earlier versus the time. The light curve is indicated with errors bars for each measurement which shows the uncertainty (can come from bias correction, flat fielding) in the measurements. The automated pipeline is run in order 5.2. REDUCTION METHODS 35 to obtain the differential light curve, the best fit light curve is obtained by adjusting the aperture, the ensemble of comparison stars and aperture size number used. 36 CHAPTER 5. REDUCTION METHOD 1- OBSERVATIONS Chapter 6

Reduction method 2- Data analysis

After obtaining the light curves we must subject it to MCMC analysis to obtain the best fit transit curve along with the physical and model parameters. Before performing this, we convert each universal time(UT) of mid-exposure to the BJDTDB time system and the correction factor is introduced from an online program created by J. Eastman and distributed at ’http://astroutils.astronomy.ohio-state.edu/time/utc2bjd.html’. Individual attention is given to each light curve (out of the 18 light curves obtained) to obtain the final model for the light curve by changing the baseline parameters (seven parameters each included for time, FWHM, sky, airmass and many more) until we reach a reduced BIC (Bayesian Information Criterion) value. The BIC is generally used for model selection among a set of models and the model with the lowest BIC is chosen. BIC = ln(n)k−2ln(L)ˆ where

• Lˆ is the maximized likelihood function. • n is the number of data points in the chosen dataset. • k number of estimated parameters by the model. Values which are obtained from the posterior probability distribution function (PDF) of the parameters through an adaptive Markov-chain Monte Carlo (MCMC) code are explored and then global analysis for all transits pertaining to a single planet is performed to improve determination of system parameters.

6.1 Introduction to Markov-chain Monte Carlo (MCMC) method

To obtain the best fit model with a reduced BIC, we use the latest version of the Markov- chain Monte Carlo code [69]. In this method, the data is subjected to using random variations with observational data using Bayes rule. Bayes rule describes the probability of an event based on prior knowledge of conditions that might be connected to the event. It connects the odds for different events before and after conditioning another event. Baye’s Theorem is given as

p(D|H,I)p(H|I) p(H|D,I) = (6.1) p(D|I)

37 38 CHAPTER 6. REDUCTION METHOD 2- DATA ANALYSIS

Here p(D|I) is a normalization factor, D is our observing data and I are the priors. We multiply the Probability of observing our data D at the conditions that connect to the event and the priors if they are true to the prior probability of our conditions to give the probability of this same condition (p(H|D, I)), given the prior and data. This gives the probability of a given set of observational data leading to a certain set of model parameters. MCMC is a very popular method for obtaining the information about distributions and for estimating posterior distributions in Bayesian inference [70]. It constructs a chain of states with the given model parameters, after the chain is obtained, we calculate the uncertainties from all the states and the medians of the model parameters. The uncertainties for the first 20% is not taken as it’s in the burn in phase that’s to be excluded. Sampled model parameters for the posterior probability function is taken after the burn in phase or after convergence. Each of these model parameters are randomly generated and constrained by their probability distributions, this is what Monte Carlo of the name implies and Markov chain strictly depends on the previous state of the unique model parameter set and no further correction for this is allowed. On the overview, the Monte-carlo part is used to estimate the different properties of a particular distribution by analyzing random samples of that distribution. One particular stand-out feature of MCMC is that it can generate random samples of a distribution without having any information other than just how to determine the density of the drawn samples. The markov-chain part is used to generate random samples in a special sequence [71] Markov’s condition is given by,

p(Hn = xn|Hn−1 = xn−1, ....H0 = x0) = p(Hn = xn|Hn−1 = xn−1) (6.2) where,

• Hn is the new state at time n. • Hn−1 is the present state at time n − 1

The properties (xn) of the new state are estimated by the present state. A model is derived from a set of parameters (every state) and it is then compared to the data. We then vary those parameters and determine the likelihood. These parameters are also called the Jump parameters which are discussed below.

In the code the Markov’s condition is implemented as.

Pn,j = Pi−1,j + fσPj G(0, 1) (6.3) where

• P is the set of parameters. • j indicates the current parameter. • i is the incremental step. th • Pn,j indicates the j parameter.

• fσPj G(0, 1) is the amount by which the new state will differ from the old one. 6.1. INTRODUCTION TO MARKOV-CHAIN MONTE CARLO (MCMC) METHOD39

• G(0, 1) is the Gaussian distribution of mean 0 and standard deviation 1. • New state n is determined by the old state i − 1.

We then derive a model µ from the new set of parameters Pn and a χ2 statistic is used to compare the model and and the data ν.

The χ2 formula is give by

2 2 l (νk − µk) χn = Σk=1 2 (6.4) σνk

Where (νk − µk) is the difference between the data point and the model. νk is the data 2 point with the Gaussian error bar σνk. From these we determine a merit function,

2 2 2 (Pn,j − P0,j) Qn = χn + Σj 2 (6.5) σP0,j where (Pn,j − P0,j) is the prior which might be from any previous information of the end solution. The merit function is thus of the sum of the chi2 (agreement between model and data) and a prior term (agreement between model and priors). Its minimization is equivalent to the maximization of the posterior probability of model = prior probability times likelihood.

We compare the new state Pn to the present state Pi−1 and choose either one to continue the chain using the Metropolis-Hastings algorithm. This comparison will yield an estimate of a probability density function for the set of parameters under consideration. This algorithm will choose between the two states based on the merit function. The way this algorithm works is as follows,

• Depending on the value of the parameter r ( It is the relative probability of the new −0.5 2 2 model parameters vs the previous ones ) = e (Qn − Qi−1), the choice is made whether to accept Pn or Pi−1. r is the relative probability of the new model parameters vs the previous ones. 2 2 2 2 • if r > 1(Qn 6 Qi−1) , the step is accepted as Qi = Qn with Pi = Pn. New value for 2 2 nand i is proposed. Qi changes to Qi−1 and Pi changes to Pi−1. 2 • if r < 1(Qn), a number between 0 and 1 is drawn from an uniform distribution defined u. 2 2 • if r > u, then the step is accepted as Qi = Qn with Pi = Pn. New value for nand i is 2 2 proposed. Qi changes to Qi−1 and Pi changes to Pi−1. 2 2 2 • if r < u, the step is not accepted and it is denoted as Qi = Qi−1 with Pi = Pi−1. Qi−1 and Pi−1 are not changed. Metropolis-Hastings algorithm will converge to a stationary posterior distribution whose resolution will depend on the step size. Step size determines the number of steps needed to reach the final posterior distribution. If the step size is chosen to be very small, then it would take a lot of time to explore the 40 CHAPTER 6. REDUCTION METHOD 2- DATA ANALYSIS

space Pj far from the equilibrium state(or the most likely value). If the step size is chosen to be large, then we obtain the condition r < u most of the time and the new states would be rarely accepted. f in (6.3) will scale the step size such that the exploration is done efficiently. The value of f is initially chosen to be high which makes the step size large and since the acceptance rate will be very low, the value of f will decrease and continue to search in smaller space around Q2. This process is known as burn in. The chain will then settle and r < 1 criteria will be mostly dominate. The evolution of f is determined by running several chains at once and calculate the mean of it after all the chains converge to a similar distribution. The convergence is confirmed through the Gelman Rubin test (The Gelman–Rubin diagnostic evaluates the MCMC convergence by analyzing the difference with regard to many Markov chains, the convergence is then assessed by comparing the estimated between-chains and within-chain variances for each model parameter. Large differences between these variances are not supposed to occur as they indicate non convergence.)[72] which compares the variances of the between-chains and the within-chains for every model parameter, small differences between the variances indicate convergence whereas large differences indicate non-convergence. In the end we obtain the posterior probability function mentioned earlier, this can be marginalized.

Model parameters (Jump parameters, they are the main parameters that can be randomly perturbed at each step of the Markov chain analysis) are used to fit the data in order to run the MCMC analysis. Given below are the general jump parameters used:

— M∗ — Stellar Radius R∗ — Effective temperature Teff — Metallicity [Fe/H]. — For each planet we take the transit depth (dF) and the mid-transit time (To). — Linear combinations of quadratic limb darkening coefficients with respect to its bandpass c1 = 2 × u1 + u2 and c2 = u1 − 2 × u2

Jump parameters used for my thesis are mentioned below under individual and global analysis. Also the period here is fixed as it cannot be derived from a single transit data, the reference period is taken from Delerez et al. [73]. The code uses jumps parameters in a specific combination of parameters to speed up the convergence by reducing the correlations. Quadratic or a linear trend is assumed to model phase effect, drift on detector pixels, long term variability of the stars that affects parameters like dx, dy, dt of the point spread function and coefficients are adjusted at each step for the affected parameters. As all the noise is not accounted for most of the time, we obtain the correlated noise called the red noise. To consider this noise, we need uncertainties on model parameters. Un- correlated noise or the white noise which measured could obtain the standard deviation for residuals of observed to calculated flux(σ1), expected standard deviation for residuals of M bins and N points is

s σ1 M σN = √ (6.6) N M − 1

σN is larger due to the involvement of correlated noise, to compensate this we include 6.1. INTRODUCTION TO MARKOV-CHAIN MONTE CARLO (MCMC) METHOD41

βr. To estimate βr and photometric results, we run the first MCMC simulation and the second run is used for the model parameters with their uncertainties.

For the individual analysis the baseline parameters are adjusted according to the various external parameters (high airmass, FWHM of the pixel, X and Y positions of the target PSF). To obtain the reduced value of BIC and a transit like feature in the light curve, posterior probability distribution function (depth, impact parameter, mid-transit timing) is explored for the curves with the adaptive Markov-chain Monte Carlo code. The light curve parameters which are obtained are cross checked for consistency from [73]. The algorithm is run twice to see the convergence and the well mixing of the MCMC simulation i.e. Gelman rubin test and after all this we would have finally obtained our best fit model which will further be considered for the global analysis.

6.1.1 Individual analysis

Individual analysis is done for each observational run and it is taken as the transit model [28] multiplied by the photometric baseline model. The main aim here is to obtain the astrophysical and instrumental effects observed at the photometric variation level. Before we begin analyzing the light curves, we must convert each universal time (UT) of mid- exposure to the BJDTDB time system. Here for each individual analysis Quadratic limb darkening law is considered for the star and the baseline parameters are adjusted individ- ually taking the external parameters into consideration ( bright sky, drifting of stars...). Another main thing to look into is the minimization of the Bayesian Information Criterion (BIC) value which has to be reduced at the end of analysis, for this reduction we consider a large number of baseline models and the final selected model must have the least BIC value. we use a certain set of jump parameters that are perturbed for every MCMC run. The parameters used are the same that are mentioned in the section above. For the analysis, period is not considered as a jump parameter but is rather fixed as it cannot be determined with just one transit. Also Planets are assumed to be circular (e=0) and a prior is considered on the impact parameter as a few transits are incomplete. As mentioned above we consider many different baseline models in order to obtain a reduced BIC value and the five main baseline parameters that I have considered in this thesis are time, airmass, FWHM, SKY and X-Y model order, BIC must also be monitored here. Each one is considered appropriately according to the conditions involved like the presence of clouds, bright sky and the drifting of stars. Considering all the jump parameters mentioned above with the baseline parameters the MCMC algorithm is first run in 1 chain of 10,000 steps to obtain the CF(Correction factor). The CF obtained accounts for both the lower and upper limit of red (correlated noise in the data) and white noise and this is applied to the photometric error bars in order to compensate for it. Along with CF, we also get the reduced BIC value obtained at the end of the first chain and this must be crossed check with different baseline models to get the best reduction value of BIC. After this the MCMC algorithm is run for 2 chains of 100,000 steps, here the convergence and the well mixing of the MCMC simulation is checked using the Gelman rubin test. The convergence is then observed and the final median values of jump parameters along with the 1−σ limits of the posterior PDFs obtained must be consistent with the reference values (to check accuracy of the results obtained). 42 CHAPTER 6. REDUCTION METHOD 2- DATA ANALYSIS

6.1.2 Global analysis

To improve system parameters we perform the global analysis, this includes running the MCMC simulation with all the transits obtained for a particular planet at once. In order to do this we consider the same stellar parameters that were considered before in the individual analysis and along with this, limb darkening law, and circular planet assumptions are also maintained the same. In the global analysis along with considering the previously used jump parameters we also take into account the transit timing variation of each transit wrt to the mean transit ephemeris which is derived from the individual analyses. Like individual analyses, the MCMC algorithm is run with one chain of 10,000 steps initially and the with two chains of 100,000 steps and at the end of the second chain we must obtain a GelmanRubin statistic value less than 1.11(chains are converged) for every jump parameter, which is what we have obtained for all our tests. At the end of the global analysis, we must obtain all the physical parameters and the best fit models for the planet. These are indicated in the next chapter which summarizes the results obtained from this analysis. The physical parameters obtained here are deduced from the jump parameters that were perturbed at each step of the MCMC. The parameters for this section along with the best fit transit model for each planet is included under global analysis section in the ’results’ chapter. At the end of this analysis we also obtain parameters like Rp, a and i from the stellar and the transit parameters. Irradiation and the equilibrium temperatures is also computed.

Chapter 7

Results

In this chapter, we present the results obtained from differential photometry, individual and global MCMC analysis. Given below are the light curves (obtained with or without the transit of a planet), model and the system parameters. All the procedural steps mentioned above is being employed here and results are indicated under the relevant section.

7.1 Differential photometry

Differential light curves obtained are presented below and are sorted according to the date of observation and planet in transit. Suitable comparison stars and aperture size were chosen for the curve by comparing different combinations of comparison stars and aperture size. There were a total of 19 light curves observed through the IO:O camera and 18 of them include a transiting planet. The data taken from IO:O camera are taken with a 4096x4112 pixel CCD camera with an integration time of 20 seconds and SDSS-z filter. Standard data reduction is performed through an automated pipeline for IO:O data (section 4.2.2). Table below is a log of all the observational data with their respective camera and filter used. There are also certain remarks present to indicate the goodness of the results. Observational data of 2017/10/03 was excluded as the moon was very close on that particular day, the moon was 2 degrees from the object with an illumination of 96%. Due to this reason the system was quite difficult to view and had to be excluded. As we notice in the remarks section that for many of the observational days, there were clouds present and other factors like bright sky and drift of the stars also play a role in the analyzing the light curve. All these factors lead to a bad precision in the light curve.

43 44 CHAPTER 7. RESULTS

Date of Observation Remarks Planet(s) in transit

2017/05/31 precision of the light curve is good TRAPPIST-1b 2017/06/17 clouds, bad precision of the light TRAPPIST-1e curve 2017/07/01 good precision of the light curve TRAPPIST-1c 2017/07/14 bright sky and drifting of stars, TRAPPIST-1d bad precision 2017/07/20 dip during the transit, clouds TRAPPIST-1b 2017/07/22 clouds, bad precision TRAPPIST-1d 2017/07/23 good precision of the light curve TRAPPIST-1b 2017/07/29 good precision of the light curve TRAPPIST-1b 2017/08/04 good precision of the light curve TRAPPIST-1c TRAPPIST-1b 2017/08/15 transit time variation present TRAPPIST-1h 2017/08/17 good precision of the light curve TRAPPIST-1e 2017/08/20 transit depth higher than 0.78 % TRAPPIST-1g 2017/09/07 good precision of the light curve TRAPPIST-1c 2017/09/19 good precision of the light curve TRAPPIST-1c 2017/09/21 good precision of the light curve TRAPPIST-1d 2017/10/05 good precision of the light curve TRAPPIST-1e 2017/10/03 moon was quite close, light curve N/A cannot be obtained 2017/10/21 bad precision, clouds no transit 2017/10/28 good precision of the light curve TRAPPIST-1c Table 1: Log of the data obtained from IO:O camera with SDSS-z filter for TRAPPIST-1 with Liverpool telescope. 7.1. DIFFERENTIAL PHOTOMETRY 45

7.1.1 Differential light curves obtained for TRAPPIST-1 system with IO:O camera

2017/05/31, Object in transit is TRAPPIST-1b

Note- Precision of the light curve is good and a transit depth of 0.7% for TRAPPIST-1b is visible at the expected time (center around 2457905.715 HJD).

Figure 7.1 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 46 CHAPTER 7. RESULTS

2017/06/17,Object in transit is TRAPPIST-1e

Note-Precision of the light curve is bad due to clouds and transit depth is more than 0.7% for TRAPPIST-1e.

Figure 7.2 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 7.1. DIFFERENTIAL PHOTOMETRY 47

2017/07/01,Object in transit is TRAPPIST-1c

Note- Precision of the light curve is good and a transit depth of 0.6% for TRAPPIST-1c is clearly seen.

Figure 7.3 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 48 CHAPTER 7. RESULTS

2017/07/14,Object in transit is TRAPPIST-1d

Note-precision of the light curve is not quite good due to the bright sky, this is reflected in the graph of elev versus sky, electron count is higher than 2000 and along with this the stars are drifting, seen in the curve dx versus dy and no transit is visible by eye.

Figure 7.4 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars. The orange line indicates the expected transit mid-time. 7.1. DIFFERENTIAL PHOTOMETRY 49

Figure 7.5 – Top-Bright sky is indicated by the background electrons(2500) and Bottom- Drifting of stars 50 CHAPTER 7. RESULTS

2017/07/20,Object in transit is TRAPPIST-1b

Note-precision of the light curve is good,but there is a dip in the transit at HJD 2457955.58 due to clouds and a transit depth of < 1% is visible for TRAPPIST-1b

Figure 7.6 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 7.1. DIFFERENTIAL PHOTOMETRY 51

2017/07/22,Object in transit is TRAPPIST-1d

Note-precision of the light curve is not quite good due to the presence of clouds and the transit depth is more than 0.367% for TRAPPIST-1d.

Figure 7.7 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars. The orange line indicates the expected transit mid-time. 52 CHAPTER 7. RESULTS

2017/07/23,Object in transit is TRAPPIST-1b

Note-precision of the light curve is good and a transit slightly shallower than 1% is visible for TRAPPIST-1b.

Figure 7.8 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 7.1. DIFFERENTIAL PHOTOMETRY 53

2017/07/29,Object in transit is TRAPPIST-1b

Note-precision of the light curve is good and a transit depth of < 1% is visible for TRAPPIST-1b

Figure 7.9 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 54 CHAPTER 7. RESULTS

2017/08/04,Object in transit is TRAPPIST-1c and TRAPPIST-b

Note-precision of the light curve is good and a transit depth of approximately 0.6% for TRAPPIST-1c and transit depth of < 1% is visible for TRAPPIST-1b

Figure 7.10 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 7.1. DIFFERENTIAL PHOTOMETRY 55

2017/08/15,Object in transit is TRAPPIST-1h

Note-precision of the light curve is good but there is a transit time variation present and a transit depth of 0.3% for TRAPPIST-1h is clearly seen

Figure 7.11 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 56 CHAPTER 7. RESULTS

2017/08/17,Object in transit is TRAPPIST-1e

Note-precision of the light curve is good and a transit depth of < 1% is visible for TRAPPIST-1e

Figure 7.12 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 7.1. DIFFERENTIAL PHOTOMETRY 57

2017/08/20,Object in transit is TRAPPIST-1g

Note-precision of the light curve is not quite good due to high airmass and a transit depth of ≈ 1% for TRAPPIST-1g is seen.

Figure 7.13 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 58 CHAPTER 7. RESULTS

2017/09/07,Object in transit is TRAPPIST-1

Note-precision of the light curve is good and a transit depth of 0.687% for TRAPPIST-1c is clearly seen

Figure 7.14 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 7.1. DIFFERENTIAL PHOTOMETRY 59

2017/09/19,Object in transit is TRAPPIST-1c

Note-precision of the light curve is good and a transit depth of 0.687% for TRAPPIST-1c is clearly seen

Figure 7.15 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 60 CHAPTER 7. RESULTS

2017/09/21,Object in transit is TRAPPIST-1d

Note-precision of the light curve is good and a transit depth of 0.367% for TRAPPIST-1d is clearly seen

Figure 7.16 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 7.1. DIFFERENTIAL PHOTOMETRY 61

2017/10/05,Object in transit is TRAPPIST-1e

Note-precision of the light curve is good and a transit depth of 0.519% for TRAPPIST-1e is clearly seen

Figure 7.17 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 62 CHAPTER 7. RESULTS

2017/10/21, Target-TRAPPIST-1 there was no Object in transit

Note-precision of the light curve is bad due to the clouds and there was no transit observed on this day

Figure 7.18 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 7.1. DIFFERENTIAL PHOTOMETRY 63

2017/10/28,Object in transit is TRAPPIST-1c

Note-precision of the light curve is good and a transit depth of 0.687% for TRAPPIST-1c is clearly seen

Figure 7.19 – Top-Differential light curve binned for 0.005 days (black points with error bars) and unbinned points are shown in blue, Bottom-Raw light curves with green line indicated for the planet and blue is for the comparison stars 64 CHAPTER 7. RESULTS 7.2 Individual analysis

A total of 15 light curves with their photometric data is considered for individual analysis. Data acquired on 2017/06/17, 2017/07/20, 2017/09/19, 2017/07/14 and 2017/07/22 are not considered due to the bad precision of the data. Stellar parameters are considered as jump parameters and a prior is assumed which is a normal Gaussian distribution corresponding to the Spitzer results of Delrez et al [73] on the impact parameter(b) as a few transits are incomplete, more information on this is under the section(5.1.1). Appropriate baseline mentioned below were chosen to obtain the reduced BIC value for that particular data in order to obtain the best fit model. Period is fixed as it cannot be derived from a single curve. Quadratic law is assumed for stellar limb darkening and Spitzer results from Delerez et al. [73] is also given for each planet in order to compare the results obtained with the reference data. MCMC algorithm is run twice, once for 1 step of 10,000 chains and the second time for 2 steps of 100,000 chains, GelmanRubin statistic were less than 1.11 for all these analysis.

Baseline parameters used here account for the variation of the external parameters like the bright sky and drift of stars. These baseline parameters are accounted for whenever necessary. The model parameters are indicated in the table along with their 1-σ limits of the posterior PDFs and de-trended light curves are also indicated for each transit data. 7.2. INDIVIDUAL ANALYSIS 65

7.2.1 Parameters obtained from Individual analysis for TRAPPIST-1b

Planet in transit TRAPPIST-1b Transit depth(dF) with error 0.007277 ±0.000075 Impact parameter(b(R*)) with error 0.157±0.075 Transit midpoint(T0) with error 7322.51654 ±0.00012 Table 4: Transit parameters inferred from Delrez et al. [73] for TRAPPIST-1b

Date of Observation 2017/05/31 2017/07/20 2017/07/23 2017/07/29 2017/08/04 Planet in transit TRAPPIST-1b TRAPPIST-1b TRAPPIST-1b TRAPPIST-1b TRAPPIST-1b Camera used IO:O camera IO:O camera IO:O camera IO:O camera IO:O camera Filter used(SDSS-Z) z’ z’ z’ z’ z’

Baseline parameters Time 0 0 0 0 0 Airmass 0 0 0 0 0 FWHM 0 0 0 0 0 Sky 0 1 0 0 0 X-Y model order 0 0 0 0 0 Optimization BIC(before CF) 301 820 231 201 53 CF(Correction fac- 1.58 1.98 1.09 1.07 1.99 tor) Jump parameters Transit depth(dF) 0.0056 0.0080 0.0067 0.0082 0.0071 Error on Transit -0.0007 -0.0009 -0.0004 -0.0005 -0.0002 depth +0.0006 +0.0007 +0.0007 +0.0004 +0.0003 Impact parame- 0.158 0.146 0.155 0.168 0.136 ter(b(R*)) Error on Impact -0.078 -0.064 -0.068 -0.069 -0.063 parameter +0.072 +0.065 +0.071 +0.078 +0.065 Transit mid- 7905.72 7955.57 7958.59 7964.65 7970.69 point(T0) Error on midpoint -0.00079 ±0.00025 ±0.00054 ±0.00047 ±0.00027 +0.00076 Table 5: parameters obtained from individual analysis

Figure 7.20 – De-trended light curve (cyan = unbinned, black = binned per 7.2min) + best-fit transit model (red) for 2017/08/04 . 66 CHAPTER 7. RESULTS

Figure 7.21 – De-trended light curves, (cyan = unbinned, black = binned per 7.2min) + best-fit transit model (red) (Top-2017/05/31, bottom-2017/07/20).

Figure 7.22 – De-trended light curves (cyan = unbinned, black = binned per 7.2min) + best-fit transit model (red), top-2017/07/23 and bottom-2017/07/29. 7.2. INDIVIDUAL ANALYSIS 67

7.2.2 Parameters obtained from Individual analysis for TRAPPIST-1c

Planet in transit TRAPPIST-1c Transit depth(dF) with error 0.006940 ±0.000068 Impact parameter(b(R*)) with error 0.148±0.088 Transit midpoint(T0) with error 7282.80879 ±0.00018 Table 6:Transit parameters inferred from Delerez et al. [73] for TRAPPIST-1c

Date of Observation 2017/07/01 2017/08/04 2017/09/07 2017/09/19 2017/10/28 Planet in transit TRAPPIST-1c TRAPPIST-1c TRAPPIST-1c TRAPPIST-1c TRAPPIST-1c Camera used IO:O camera IO:O camera IO:O camera IO:O camera IO:O camera Filter used(SDSS-Z) z’ z’ z’ z’ z’

Baseline parameters Time 0 0 0 0 0 Airmass 0 0 0 0 0 FWHM 0 0 0 0 0 Sky 0 0 0 0 0 X-Y model order 0 0 0 0 0 Optimization BIC(before CF) 140 265 220 369 268 CF(Correction fac- 1.07 1.02 1.06 1.01 1.63 tor) Jump parameters Transit depth(dF) 0.00716 0.00621 0.00817 0.00550 0.00803 Error on Transit -0.00049 -0.00038 -0.00046 -0.00052 -0.00033 depth +0.00051 +0.00036 +0.00077 +0.00051 +0.00023 Impact parame- 0.154 0.183 0.160 0.180 0.161 ter(b(R*)) Error on Impact -0.078 -0.086 -0.083 -0.082 -0.084 parameter +0.079 +0.081 +0.086 +0.077 +0.085 Transit mid- 7936.7080 7970.6550 8004.5120 8016.6190 8055.3660 point(T0) Error on midpoint -0.00042 -0.00045 -0.00052 -0.00043 -0.00026 +0.00039 +0.00050 +0.00046 +0.00064 +0.00025 Table 7: parameters obtained from individual analysis

Figure 7.23 – De-trended light curve (cyan = unbinned, black = binned per 7.2min) + best-fit transit model (red) for 2017/10/28. 68 CHAPTER 7. RESULTS

Figure 7.24 – De-trended light curves, Top-2017/07/01,bottom-2017/08/04

Figure 7.25 – De-trended light curves (cyan = unbinned, black = binned per 7.2min) + best-fit transit model (red), top-2017/09/07 and bottom-2017/09/19. 7.2. INDIVIDUAL ANALYSIS 69

7.2.3 Parameters obtained from individual analysis for TRAPPIST-1d

Planet in transit TRAPPIST-1d Transit depth(dF) with error 0.003566 ±0.000070 Impact parameter(b(R*)) with error 0.08 +0.10 0.06 Transit midpoint(T0) with error 7670.14227 ±0.00026 Table 8:Transit parameters inferred from Delerez et al. [73] for TRAPPIST-1d

Date of Observation 2017/09/21 Planet in transit TRAPPIST-1d Camera used IO:O camera Filter used(SDSS-Z) z’

Baseline parameters Time 0 Airmass 0 FWHM 0 Sky 0 X-Y model order 0 Optimization BIC(before CF 561 CF(Correction factor) 1.72 Jump parameters Transit depth(dF) 0.0047 Error on Transit depth -0.00048 +0.00047 Impact parameter(b(R*)) 0.062 Error on Impact parame- -0.039 ter +0.061 Transit midpoint(T0) 8018.4390 Error on midpoint -0.0008 +0.0022 Table 9: parameters obtained from individual analysis

Figure 7.26 – De-trended light curve (cyan = unbinned, black = binned per 7.2min) + best-fit transit model (red) for 2017/09/21 70 CHAPTER 7. RESULTS

7.2.4 Parameters obtained from individual analysis for TRAPPIST-1e

Planet in transit TRAPPIST-1e Transit depth(dF) with error 0.004802 ±0.0094 Impact parameter(b(R*)) with error 0.240 +0.056 -0.047 Transit midpoint(T0) with error 7660.37910 ±0.00040 Table 10: Transit parameters inferred from Delerez et al. [73] for TRAPPIST-1e

Date of Observation 2017/08/17 2017/10/05 Planet in transit TRAPPIST-1e TRAPPIST-1e Camera used IO:O camera IO:O camera Filter used(SDSS-Z) z’ z’

Baseline parameters Time 0 0 Airmass 0 0 FWHM 0 0 Sky 0 0 X-Y model order 0 0 Optimization BIC(before CF) 530 231 CF(Correction factor) 1.01 1.55 Jump parameters Transit depth(dF) 0.0043 0.0048 Error on Transit depth ±0.00080 ±0.00064 Impact parameter(b(R*)) 0.245 0.233 Error on Impact parame- -0.056 -0.055 ter +0.056 +0.054 Transit midpoint(T0) 7983.650 8032.443 Error on midpoint -0.0015 -0.0011 +0.0013 +0.00090 Table 11: parameters obtained from individual analysis

Figure 7.27 – De-trended light curves,(cyan = unbinned, black = binned per 7.2min) + best-fit transit model (red), Top Right-2017/06/17,Top left-2017/08/17 and Bottom- 2017/10/05. 7.2. INDIVIDUAL ANALYSIS 71

7.2.5 Parameters obtained from individual analysis for TRAPPIST-1g

Planet in transit TRAPPIST-1g Transit depth(dF) with error 0.00764 ±0.00011 Impact parameter(b(R*)) with error 0.406 +0.031 -0.025 Transit midpoint(T0) with error 7665.35084 ±0.00020 Table 12: Transit parameters inferred from Delerez et al. [73] for TRAPPIST-1f

Date of Observation 2017/08/20 Planet in transit TRAPPIST-1g Camera used IO:O camera Filter used(SDSS-Z) z’

Baseline parameters Time 0 Airmass 0 FWHM 0 Sky 0 X-Y model order 0 Optimization BIC(before CF) 234 CF(Correction factor) 0.97 Jump parameters Transit depth(dF) 0.00702 Error on Transit depth -0.00015 +0.00016 Impact parameter(b(R*)) 0.455 Error on Impact parame- -0.036 ter +0.07 Transit midpoint(T0) 7986.531 Error on midpoint -0.0017 +0.0017 Table 13: parameters obtained from individual analysis

Figure 7.28 – De-trended light curve (cyan = unbinned, black = binned per 7.2min) + best-fit transit model (red) for 2017/08/20 72 CHAPTER 7. RESULTS

7.2.6 Parameters obtained from individual analysis for TRAPPIST-1h

Planet in transit TRAPPIST-1h Transit depth(dF) with error 0.00346 ±0.00014 Impact parameter(b(R*)) with error 0.392 +0.039 -0.043 Transit midpoint(T0) with error 7662.55467 ±0.00054 Table 14: Transit parameters inferred from Delerez et al. [73] for TRAPPIST-1h

Date of Observation 2017/08/15 Planet in transit TRAPPIST-1h Camera used IO:O camera Filter used(SDSS-Z) z’

Baseline parameters Time 0 Airmass 0 FWHM 0 Sky 0 X-Y model order 0 Optimization BIC(before CF) 348 CF(Correction factor) 0.972 Jump parameters Transit depth(dF) 0.00266 Error on Transit depth -0.0009 +0.0015 Impact parameter(b(R*)) 0.370 Error on Impact parame- -0.039 ter +0.016 Transit midpoint(T0) 7981.669 Error on midpoint -0.004 +0.005 Table 15: parameters obtained from individual analysis

Figure 7.29 – De-trended light curve (cyan = unbinned, black = binned per 7.2min) + best-fit transit model (red) for 2017/08/20 7.3. GLOBAL ANALYSIS 73 7.3 Global analysis

Global analysis is performed for each planet with more than one transit to improve the determination of the system parameters. 5 transit curves with photometric data for TRAPPIST-1b, 5 transit curves with photometric data for TRAPPIST-1c and 2 transit curves with photometric data for TRAPPIST-1e were considered. Just like individual analysis, we performed a preliminary run of 1 chain of 10,000 steps to obtain the CF, this is added to the error bars of each light curve and a secondary run of 2 chains of 100,000 steps to obtain the model parameters. Impact parameter ’b’ is also maintained as a prior here, the transit timing variation(TTV) for each transit observed with respect to the mean transit ephemeris obtained from the individual analyses is taken as a jump parameter. The resulting model parameters are indicated below.

7.3.1 Parameters obtained from global analysis for TRAPPIST-1b

Parameter Value

Star TRAPPIST-1 = 2MASS J23062928-0502285

Luminosity, L∗ 0.000523 ±0.000038L

Mass, M∗ 0.088 ±0.005M

Radius, R∗ 0.121 ±0.002R

Density, ∗ 50.01 ±0.030

Effective temperature, Teff 2,511 ±0.0037K Metallicity, [Fe/H]dex +0.036 ±0.07

Limb darkening co efficient, µ1,2 0.186 ±0.014and0.499±0.0059K planet TRAPPIST-1b No of transits observed 5 Orbital period, P 1.51087 days

Mid-transit time, tO -2,450,000 (BJDTDB) 7,322.51765 ±0.000 2 Transit depth (RP /R∗) 0.710 ±0.040%

Transit impact parameter b 0.156 ±0.071R∗ Transit duration, W 0.025±0.00050days , i 89.56 ±0.41deg Orbital eccentricity, e 0 (fixed)

Radius, Rp 1.112 ±0.035REarth 0.48 Scale parameter, a/R∗ 20.530.22 Semi-major axis, a 0.01149 ±0.00024AU Irradiation, Sp 3.96 ±0.29SEarth

Equilibrium temperature, Teq 393.003 ±0.070K Table 17: Median values and their 1 − σ limits of the posterior PDFs. 74 CHAPTER 7. RESULTS

Figure 7.30 – Left: Period-folded photometric measurements corrected for the measured TTVs, Blue dots-unbinned measurements, open circles-binned measurements(for visual clarity) and Blue line- best-fit transit model Bottom:Corresponding residuals 7.3. GLOBAL ANALYSIS 75

7.3.2 Parameters obtained from global analysis for TRAPPIST-1c

Parameter Value

Star TRAPPIST-1 = 2MASS J23062928-0502285

Luminosity, L∗ 0.000518 ±0.000036L

Mass, M∗ 0.088 ±0.006M

Radius, R∗ 0.121 ±0.002R

Density, ∗ 50.10 ±0.034

Effective temperature, Teff 2,506 ±0.0035K Metallicity, [Fe/H]dex +0.042 ±0.08

Limb darkening co efficient, µ1,2 0.186 ±0.014and0.499±0.0072K planet TRAPPIST-1c No of transits observed 5 Orbital period, P 2.4218 days

Mid-transit time, tO -2,450,000 (BJDTDB) 7,282.808 ±0.000 2 Transit depth (RP /R∗) 0.648 ±0.071%

Transit impact parameter b 0.158 ±0.083R∗ Transit duration, W 0.029±0.00076days Orbital inclination, i 89.67 ±0.16deg Orbital eccentricity, e 0 (fixed)

Radius, Rp 1.06 ±0.051REarth 0.66 Scale parameter, a/R∗ 27.970.65 Semi-major axis, a 0.0157 ±0.00037AU Irradiation, Sp 2.088 ±0.14SEarth

Equilibrium temperature, Teq 334.908 ±0.062K Table 18: Median values and their 1 − σ limits of the posterior PDFs.

Figure 7.31 – Left: Period-folded photometric measurements corrected for the measured TTVs, Blue dots-unbinned measurements, open circles-binned measurements(for visual clarity) and Blue line- best-fit transit model Bottom:Corresponding residuals 76 CHAPTER 7. RESULTS

7.3.3 Parameters obtained from global analysis for TRAPPIST-1e

Parameter Value

Star TRAPPIST-1 = 2MASS J23062928-0502285

Luminosity, L∗ 0.000519 ±0.000036L

Mass, M∗ 0.089 ±0.005M

Radius, R∗ 0.120 ±0.002R

Density, ∗ 50.93 ±0.029

Effective temperature, Teff 2,510 ±0.0038K Metallicity, [Fe/H]dex +0.038 ±0.07

Limb darkening co efficient, µ1,2 0.186 ±0.014and0.499±0.0060K planet TRAPPIST-1e No of transits observed 2 Orbital period, P 6.0990 days

Mid-transit time, tO -2,450,000 (BJDTDB) 7,660.379 ±0.000 2 Transit depth (RP /R∗) 0.477 ±0.032%

Transit impact parameter b 0.239 ±0.054R∗ Transit duration, W 0.0388±0.00075days Orbital inclination, i 89.736 ±0.062deg Orbital eccentricity, e 0 (fixed)

Radius, Rp 0.90 ±0.032REarth 1.0 Scale parameter, a/R∗ 52.061.0 Semi-major axis, a 0.02922 ±0.00059AU Irradiation, Sp 0.609 ±0.042SEarth

Equilibrium temperature, Teq 246.101 ±4.4K Table 19: Median values and their 1 − σ limits of the posterior PDFs.

Figure 7.32 – Left: Period-folded photometric measurements corrected for the measured TTVs, Blue dots-unbinned measurements, open circles-binned measurements(taken for visual clarity) and Blue line is the best-fit transit models Bottom:Corresponding residuals 7.3. GLOBAL ANALYSIS 77

7.3.4 Transit depth variations

We can see from below the temporal evolution of transit depths derived from the global analysis of Liverpool data and we can say that their chi square values are in harmony with the normal distribution. Some scatter in the transit depths is visible for planets b and c which could originate from the evolution of stellar photospheric heterogeneities (spots or faculae), or from systematic errors.

Figure 7.33 – Individual transit depth measurements(with its errors) for each of the events captured with Liverpool for Trappist-1b,1c,1e. The horizontal dark line shows the median of the global MCMC posterior PDF (with its 1σ as the shaded region) 78 CHAPTER 7. RESULTS Chapter 8

Discussion and conclusion

In this document we have presented 19 new light curves with 18 of them that have a transit present in them. All these observations were made with the Liverpool telescope in the time period of 2017/05/31 to 2017/10/28. At first the data was subjected to differential photometry to obtain the light curves and after this individual analysis was performed using an MCMC code. Individual analysis is further then followed by global analysis, here we obtain the revised values for the existing physical parameters. All these observations performed gives a student like me a very good insight to the vast domain of exoplanetology and particularly the system TRAPPIST-1. The data reduced is important to understand the system and to even aid the detailed atmospheric characterization of its planets with JWST. Ground based telescopes have a few limitations when it comes to providing accurate results. For examples, atmospheric turbulence, distortion and limitations from the earths atmosphere play a big role in the quality of the data obtained. Comparing the results obtained from the Spitzer data (3.2) and the data reduced from Liverpool telescope, the accuracy of the results can be obtained. Comparing the global analysis results for TRAPPIST-1b we can say there is a minor difference in the transit depth, impact parameter and the radius.

Planet in transit TRAPPIST-1b(Spitzer TRAPPIST-1b (Liverpool results) results) Transit depth(dF) with error 0.00727±0.000075 0.00710±0.000040 Impact parameter(b(R*)) with error 0.157±0.075 0.156±0.071

Radius (Rp(REarth)) with error 1.127 ±0.028 1.112 ±0.035 Transit duration (W)in days with error 0.025 ±0.00083 0.025 ±0.00050 Table 20: Comparison of transit parameters obtained from Spitzer and Liverpool for the planet TRAPPIST-1b

For TRAPPIST-1c there is a bigger difference in the transit depth values and the impact parameter.

79 80 CHAPTER 8. DISCUSSION AND CONCLUSION

Planet in transit TRAPPIST-1c (Spitzer TRAPPIST-1c (Liverpool results) results) Transit depth(dF) with error 0.00694 ±0.000068 0.00648 ±0.000071 Impact parameter(b(R*)) with error 0.148±0.088 0.158±0.083

Radius (Rp(REarth)) with error 1.10 ±0.028 1.06 ±0.051 Transit duration (W)in days with error 0.029 ±0.00097 0.029 ±0.00076 Table 21: Comparison of transit parameters obtained from Spitzer and Liverpool for the planet TRAPPIST-1c

TRAPPIST-1e, the accuracy of the results obtained is quite good and only the radius value diverges by a little from the Spitzer obtained value.

Planet in transit TRAPPIST-1e (Spitzer TRAPPIST-1e (Liverpool results) results) Transit depth(dF) with error 0.0048 ±0.0094 0.0047 ±0.0032 Impact parameter(b(R*)) with error 0.240 +0.056 -0.047 0.239 ±0.054

Radius (Rp(REarth)) with error 0.915 ±0.025 0.90 ±0.032 Transit duration (W)in days with error 0.0388 ±0.00027 0.0388 ±0.00075 Table 22: Comparison of transit parameters obtained from Spitzer and Liverpool for the planet TRAPPIST-1e

Since the difference is small value when compared with the Spitzer results for the TRAPPIST-1 planets, we can say that the results deduced from our data can be considered good and along with this we must also consider the limitations from the ground based telescopes to be a factor for the occurrence of the difference in these values. The results obtained here were also used to construct the broadband transmission spectra of the TRAPPIST-1 planets over the 0.6-4.5 µm spectral range (Ducrot et al. 2018, under review), the spectra was checked with stellar contamination models in order to assess the influence of the heterogeneity of the star’s photosphere on the atmospheric characterization of the planets. It was mainly used to constrain the limb darkening coefficients considering the fact that each planet samples a different chord of the stellar photosphere, but this was not possible as the global analyses failed to converge not allowing the constraint on the limb darkening coefficients.

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