Universit`A Degli Studi Di Napoli “Federico Ii

UNIVERSITA` DEGLI STUDI DI NAPOLI “FEDERICO II”

Scuola Politecnica e delle Scienze di Base Area Didattica di Scienze Matematiche Fisiche e Naturali

Dipartimento di Fisica “Ettore Pancini”

Laurea Triennale in Fisica

Characterization of exoplanets via photometric transit with the Transiting Exoplanet Survey Satellite

Relatori: Candidato: Prof. Giovanni Covone Luca Cacciapuoti Dott. Elisa Quintana Matr. N85/857 Dott. Veselin Kostov

Anno Accademico 2018/2019 “...to explore new worlds, to seek out new life and new civilizations, to boldly go where no man has gone before.” -Star Trek

1 Contents

1 Stars and planets 6 1.1 Formation of stars ...... 6 1.1.1 The HR diagram ...... 7 1.2 Stellar parameters ...... 8 1.2.1 Coordinates and distance ...... 8 1.2.2 Brightness: apparent and absolute magnitude ...... 10 1.2.3 Color and temperature: the blackbody radiation . . . . . 10 1.2.4 Mass ...... 11 1.3 Formation of planetary systems ...... 12 1.3.1 Inner and outer planets ...... 12

2 Exoplanets detection 15 2.1 A brief history of discoveries ...... 15 2.2 Detection methods ...... 16 2.2.1 Direct imaging ...... 16 2.2.2 Microlensing ...... 17 2.2.3 Radial velocity ...... 17 2.3 Transit ...... 18 2.4 Light curves of transiting planet ...... 18 2.4.1 The shape of a transit ...... 19 2.4.2 A geometric model: observables ...... 19 2.4.3 The unique solution ...... 20 2.4.4 Smooth curve: limb darkening ...... 21 2.5 Eclipsing binaries and Variable stars...... 21 2.6 Multiple transits ...... 22

3 The Transiting Exoplanet Survey Satellite 24 3.1 Beyond Kepler ...... 24 3.2 Mission Overview ...... 25 3.3 The observatory ...... 26 3.3.1 Charged Coupled Device & Point Spread Function . . . . 27 3.4 Sky observing ...... 28 3.5 Target Selection: TIC & CTL ...... 28 3.6 The ground network ...... 29

2 3.7 TESS data products ...... 30 3.7.1 Target Pixel Files ...... 30 3.7.2 Full Frame Images ...... 31 3.7.3 Light curves ...... 32

4 A candidate exo-system: TESS Object of Interest 175 33 4.1 Target star: L98-59 ...... 33 4.2 The software tools lightkurve and exoplanet ...... 34 4.2.1 A ﬁrst display of LCs from TPFs ...... 34 4.2.2 Periodograms ...... 36 4.2.3 Period analysis with exoplanet ...... 36 4.2.4 Aperture Photometry & Diﬀerence Imaging ...... 37 4.3 TOI 175 transits ...... 38 4.4 Background signal analysis ...... 40 4.5 Suspected Eclipsing Binary ...... 42 4.6 Planets parameters ...... 43 4.7 Conclusions about the exo-system ...... 46

5 Conclusions 47

Bibliography 47

3 Introduction

What if today someone comes to us claiming Earth is a unique place in the whole Universe? One may agree with such a statement because life, as we know it, seems to be an earthly peculiarity so far. Some others, though, would argue that it’s at least unlikely that no other planet with the same characteristics and life-hosting potentiality exists. This question has been partially answered for the first time in 2014 when the NASA Goddard Space Flight Center’s team for Kepler mission (Bolmont, Raymond, von Paris, Selsis, Hersant, Quintana & Barclay, 2014) discovered an Earth-sized planet orbiting in the so called habitable zone (HZ) around the M-dwarf star Kepler-186. We have to keep in mind, though, that a planet orbiting in the HZ is not yet to be defined as habitable itself. Further studies are to be done to accept this classification. These studies regard the atmosphere of said exoplanets and will be ARIEL and JWST’ mission (Kempton et al.,, 2018). TESS work on candidates for these two mission will be of fundamental importance. Kepler-186f, as it’s been named, was just the first of many Earth-sized planets discovered from then on. This type of planets fall in a wider ensemble known as “exoplanets”. An exoplanet is a planet orbiting a star outside the Solar System. A modern estimate of the number of exoplanets we know nowadays amounts to around four thousands bodies. Why is it so important to study them? One could backfire the question asking things like ”How Beethoven’s Fifth Symphony is important?” or ”Is Da Vinci’s Monna Lisa that important?”. There are people to whom studying the secrets of the Universe looks of huge importance without even having to think about it. Someone would say the quest for the quest’ sake. But why shall this quest be embraced by everyone? I here itemize some unsolved questions that could be answered through exoplanets studies: • Are planetary systems like ours common in the universe? Is there any trend among these systems in the universe? • How frequently do rocky planets establish in the so called habitable zone? How frequent life could be in our universe? • How is pre-biotic material, which supports bacterial life, distributed in proto-planetary discs? • The quest for habitable planets also means looking for the conditions in which life can rise. Where did we come from? Is there life beyond Earth?

4 • What if one day we will have handled the technology to move from our birthplace? We could use a precise archive of possible destinations. Even though some of these reasons look far in space and time, this kind of research could be of inestimable value for our early posterity. This thesis aims to introduce the extra solar planets argument, the linked detection methods and a modern mission in the ﬁeld. Chapter 1 is a general introduction on stars and planets: their formation and describing parameters which will come in handy during the explanations in the remaining chapters. Chapter 2 presents the methods for exoplanets detection with particular focus on the transit method, introducing the concept of light curve. Chapter 3 consists of a review of the Transiting Exoplanet Survey Satellite (TESS) mission launched in early 2018. Chapter 4 contains the analysis of a recently discovered planetary system around TESS Object of Interest 175 (TOI 175) conducted alongside an international TESS research team. Conclusions aim to present the bright future in this ﬁeld of research.

5 Chapter 1

Stars and planets

1.1 Formation of stars

Star formation takes place in gigantic dust and gas clouds which go by the name of Interstellar Medium (ISM). The whole process of formation is triggered by gravitational collapse: when ISM clouds mass exceeds a maximum value called Jeans mass, the materials start converging. Some considerations can be easily made by looking at Jeans mass formula Carroll & Ostlie (1996):

3 1 5 k T 2 3 2 MJ = . (1.1) GµmH 4πρ The equation shows how the critical mass has a super-linear dependence on 1 temperature T and a radical one on ρ . In a formation event, the collapsing region gets denser and denser as material particles are squashed in a smaller region. This would normally cause an increase in temperature but the cloud is transparent to this IR radiation so that the collapse is nearly isothermal in this first stage. The increase in density forces the Jeans mass to diminish so that some sectors begin an individual collapse in a so-called fragmentation process. At this phase gravity is the only force acting upon the system, according to Newton’s second principle: d2r GM = − . (1.2) dt2 r2 Solving the second order differential equation (Carroll & Ostlie, 1996) one can find the so-called free-fall timescale:

1 3π 2 t = (1.3) ff 32Gρ However, the order of magnitude of the free-fall time is 105 years, which is not the actual amount of time required for star forming processes and this is because hydrostatic equilibrium is eventually reached when temperatures grow, slowing the process. When the cloud is way too dense for the radiation to pass through,

6 Figure 1.1: The image shows protostar HOPS-383 in the Orion nebula. The left side images are taken by the Kitt Peak National Observatory in 2004 while the right ones are courtesy of Spitzer mission in 2008. the internal temperature begins to rise, until it becomes predominant in the process, eq. 1.1. In this situation of nearly hydrostatic equilibrium the rate of collapse near the core of the cloud slows and we refer at the dense object at the center of the collapse as a protostar. The initial spin of the cloud will translate into a much larger one as the collapse goes on and this will ﬂatten the cloud into a debris accretion disk. After the protostar is formed and accretion continues, so much gas is gathered by it that temperatures become so high (107K) that hydrogen fusion can be triggered. When a star burns hydrogen into helium it is said to be in the main sequence. This stage lasts for over the 90% of a star lifetime.

1.1.1 The HR diagram The HR diagram [Carroll & Ostlie (1996)] plots magnitude and surface temperature of stars. It is based on a star spectrum. The spectrum of a star is a range of frequencies in which the star emits or absorbs light. The bright lines of a spectrum are an index of which elements are radiating away while the dark ones enable us to understand which elements absorb certain wavelengths blocking light in that range. In 1890s Harvard’s professor Edward C. Pickering and his assistant Williamina P. Fleming classified spectra of stars with capital letters according to the strength of the hydrogen lines in them. Latter kinds of classification were made by one of Pickering’s assistants, Annie Jump Cannon, who listed them according to the surface temperature. This sorting is now known as the Harvard’s classification and it consists of seven types: O, B, A, F, G, K, M, from the hottest and brightest O-giants to the faintest and coolest M-dwarf stars. New classes have been

7 Figure 1.2: The HR diagram. subsequently added such as L, T and Y. A number is also given for a division in sub classes from 0, hottest, to 9, coolest ones.

1.2 Stellar parameters 1.2.1 Coordinates and distance Seen from Earth, stars appear to be distributed on a sphere that surrounds the globe. We call it celestial sphere. Thanks to this illusion astronomers developed systems of coordinate to point at a source in the sky.

• Horizontal coordinates: also known as Altitude-Azimuth, these are perfect coordinates to point out the position of the target in the sky from the observer point of view. They consist of altitude, the angle between the object and the observer’s horizon, and azimuth, the angle of the object around the horizon, usually measured increasing eastwards. These coordinate system, though, is time varying. • Equatorial coordinates: this system is important because the position of a target does not vary over time (even if small deviations occur due to Earth precession) as it is given with respect to celestial equator, ﬁg.1.3. It consists of right ascension, which measures the angular distance of an object eastward along the celestial equator from the vernal equinox to the hour circle passing through the object, and declination, that measures the angular distance of an object perpendicular to the celestial equator, positive to the north, negative to the south. On the other hand, one can determine a deep map of the sky observing and computing star distances. More then one sophisticated space mission have been

8 Figure 1.3: Equatorial system of coordinates performed to measure high precision distances, e.g ESA’s Gaia, but the fundamental concept has always been the same: parallax. If you point at something with your finger only looking with the right eye and then switch you will notice that you are not pointing precisely at the target anymore. This is because of the distance between your eyes, the so-called baseline. Nonetheless, knowing the baseline and the separation between the two formed images (obtained as comparison with much further objects), one can easily calculate the distance to the target using trigonometry. We do the same with stars and we use Earth or a satellite’s orbit as baseline and the furthest light sources of the sky as fixed objects (see fig. 1.4). The method has been improving during the centuries and today we have measurement precise down to micro-arcseconds. baseline 1AU 1pc d = = = (1.4) parallax p p00

Figure 1.4: Parallax method using Earth orbit as basis. The star appears to be at diﬀerent position with respect to ﬁxed stars.

9 1.2.2 Brightness: apparent and absolute magnitude The Greek astronomer Hipparcus invented a way to classify stars based on how bright they appear. He assigned a value, the apparent magnitude, m = 1 to the brightest stars in the sky and m = 6 to the faintest ones. A difference of one magnitude between two sources implies a constant ratio between their brightnesses. In 1856 Norman R. Pogson formalized the system. Two stars having 5 magnitudes of difference are defined as 100 times different in brightness 1 so that one leap in the magnitude scale corresponds to 100 5 which is about 2.5. Nowadays the range has been extended from Sun’s magnitude m = −27 to the faintest object about m = 30. The brightness of a star is measured in terms of its flux which is the total amount of light per unit area and time emitted from the source. The flux we receive depends on both the intrinsic luminosity L of a star and its distance r from Earth: L F = (1.5) 4πr2 This is called inverse square law for light and it states that the radiant flux is inversely proportional to the square of the distance. Astronomers also assign stars absolute magnitude, M, defined as the apparent magnitude a star would have if located at 10pc. The link between a star’s distance and difference in apparent and absolute magnitudes is given by:

m−M d 2 100 5 = (1.6) 10pc

1.2.3 Color and temperature: the blackbody radiation When a object, such as a chimney stick, is taken to high temperatures, it bright- ens. Actually any object with a non-zero temperature emits light in a range of frequencies so that the hotter a body, the higher its frequency. Hence, hot stars tend to radiate blue light while cooler ones emit in the red portion of the spectrum. A blackbody, or ideal emitter, is an object that absorbs all of the light incident upon it. Stars, to a ﬁrst approximation, are blackbodies. This type of bodies have a well deﬁned spectrum, i.e the distribution of energy in function of wavelength. This distribution is well described as: 2hν3 1 Bν (ν, T ) = 2 hv (1.7) c e kT − 1 where B is the energy density, h is Planck constant, c is the speed of light, ν is the frequency, T is the temperature and k is Boltzmann constant. The distribution of energy always exhibits a peak at a certain frequency according to Wien’s displacement law:

−3 T λmax = 2, 89 ∗ 10 mK (1.8) The physical interpretation of the peak is that the most of the light coming from the observed star has that corresponding wavelength: so the wavelength

10 Figure 1.5: Blackbody radiation graph. peak value gives us stars eﬀective temperature via (1.8). Besides, temperature and luminosity of a body are mathematically linked by Stefan-Boltzmann law:

2 4 L = 4πr σTeff (1.9)

Here T is defined as an effective temperature, i.e. the surface temperature of the star. Once we know a star’s luminosity and its effective temperature we can point at it on the HR diagram, identifying its spectral class.

1.2.4 Mass The mass of a star is the most striking of its features. It depends on the quantity of materials at the time of the formation process. Mass is so important that the whole life of a star can be deduced by its mass. A very massive star, e.g over 10 M , has a much shorter life then a solar mass star as it tends to burn its hydrogen faster to balance the enormous force of gravity. The ﬁnal stages of massive stars are also very diﬀerent, ending in degenerate bodies such as neutrons stars or black holes. There are various ways to compute stars masses and they are based on gravitational interaction with other bodies such as in binary systems.

• Visual binary: if the angular separation of the two stars is greater then the resolution limit imposed by local seeing conditions, one can directly observe the system. If the system is somewhat perpendicular to the line of sight one may calculate the position of the stars common center of mass: m r + m r 1 1 2 2 = 0 (1.10) m1 + m2

from which, deﬁning r = r2–r1, we can derive:

−m2r r1 = (1.11) m1 + m2

11 m1r r2 = (1.12) m1 + m2

and their ratio gives:r2/r1 = m1/m2. Given that r2/r1 = a2/a1, ai being the semi-major axis, one can calculate the ratio of masses knowing the ratio of orbits. Thus, using Kepler’s third law: 4π2a3 P 2 = (1.13) G(m1 + m2) the sum of masses can be determined. Having two equations with two masses, we can ﬁnd the single ones. • Spectroscopic binaries: if the plane of the binary has a parallel component along the line of sight one can measure the periodical Doppler shift in the spectra of the star determining their velocities. Since period and velocities are simply computable from the spectrum one can determine the semi- major axis and apply the same procedure as for the visual binary system.

1.3 Formation of planetary systems

Formation of planets takes place during the protostar or pre-main-sequence stages. There are two main hypothesis on how the planetary systems form. The first process is based on the gravitational instability of some region of the debris disk surrounding the star. It is basically the same concept of star formation due to density gradients: some denser regions begin to attract material from their surroundings concentrating on a center that will be the planet nucleus. According to this model a new, localized accretion disk could form around the building planet and it could be the moon birthplace. This hypothesis, though, suffers from more then one problem. The mechanism results to be too slow for planets like Neptune to form and it does not explain features like the asteroid belt. A second, generally favored, bottom-up model is the accretion one. Dust particles, sized in micrometers in the accretion disk, fig1.6, may start to collide and stick together to form bigger bodies called planetesimals. These bodies can actually grow as they can gravitationally pull surrounding particles, an estimate of the minimum distance among these elements is called Hill radius. The accretion disk in which these phenomena take place is virtually divided in two regions: the one closer to the star where temperature are high and the one besides the so-called snow line.

1.3.1 Inner and outer planets According to the model diﬀerent kinds of planets form within and beyond the snowline. • High temperatures and radiation pressure do not allow the formation of gaseous planets such as Jupiter in the inner region while enabling heavier dust particles to go through the process and form rocky planets with well

12 outlined internal structures. Secondary bodies such as moons tend to form around the biggest planets and this is the reason why the Solar System inner planets only have three moons: Deimos and Phoebe orbiting Mars and our Moon. • Beyond the snow line, the limited action of radiation pressure and low temperatures, which result in low kinetic energy of gas particles, allow giant gaseous to form. These planets are way diﬀerent from their inner neighbours. Outer planets are surrounded by many moons or minor bodies systems. For instance, Uranus has twenty-seven satellites and Saturn has a complex ring system. The inner structure is not as well deﬁned as rocky planets, they are thought to consist of an outer layer of molecular hydrogen surrounding a layer of liquid metallic hydrogen, with probably a molten rocky core.

Figure 1.6: Observation of proto-planetary disk around HL Tauri (right), position of a planet within another observed disk. Credits: Atacama Large Mil- limeter Array

The definition of planet is somewhat arbitrary, too. It can not be defined for its dimension as there are moons bigger then Mercury and it can not said to be one for having moons because some of them have none, like Venus. One attempt is to define a planet as a body able to free its orbit from debris. This definition exclude bodies like Ceres and Pluto, known as dwarf planets. On the other hand, planet formation being probably based on the same principles of stars’ one, what is the upper limit for a planet dimension beside which it should be considered a star? This occurs from 13MJ on, where deuterium burns so that the body produce energy of its own. The International Astronomical Union defines a planet as follows: “A celestial body that (a) is in orbit around a star, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit. Even though the previous nebular

13 hypothesis is widely accepted, certain problems are encountered. To build up planetesimals the material of the protostar accretion disk has to lose momentum. How does it happen? Besides, the formation of giant gaseous planets presents a time scale problem as it would be necessary more then ten million years to form their core while accretion disk tend to disappear earlier. And finally, why do planets like Jupiter are near their parent star in extra solar systems? Did our Jupiter migrated? Or did the extra-solar ones? Why? The most thrilling part is that such unanswered questions could be finally solved looking from a different perspective at planetary systems: the discovery of exoplanets and entire “exosystems” will certainly play a central role in answering these questions.

Figure 1.7: Cycle of formation: the loose cloud gets denser, it produces pro- tostars and accretion disks inside of which planets build up. Lately, when the stars experience late stages of their lives, mass losses and freeing of elements make the cycle begin again.

14 Chapter 2

Exoplanets detection

2.1 A brief history of discoveries

An exoplanet is a planet that orbits a star outside the Solar System. The first 1 suspected exoplanet was unknowingly detected on October 24th, 1917 by Adriaan van Maanen. Van Maanen was hunting the first ever detected polluted white dwarf also known as “van Maanen 2”. Scientists believed the heavy elements detected in these type of stars were attracted there from ISM but in 1987 (Zuckerman & Becklin, 1987) reported an excess of IR light coming from the white dwarf Glicas 29-38 and associated this fact to a dusty disk of material surrounding it. Further studies (Farihi, Becklin & Zuckerman, 2001) brought to a new theory involving exoplanets as debris source after being disrupted by the white dwarf’s gravity. The first verified detection (nasa.gov, nasa.gov) took

Figure 2.1: Van Maanen’s star spectrum is contained in an envelope at Carnegie Observatories [www.nasa.gov]. place when a planetary system of three terrestrial-mass planets was discovered orbiting Lich, or PSR B1257+12, a pulsar in Virgo’s constellation (Wolszczan & Frail, 1992). The next important step was the discovery of an exoplanet orbiting

1https://www.nasa.gov/feature/jpl/overlooked-treasure-the-ﬁrst-evidence-of-exoplanets

15 Figure 2.2: List of detected exoplanets as of late 2018. The detection method is also showed [Nasa’s Exoplanet archive]. a main-sequence star, 51 Pegasi, in 1995 (Mayor & Queloz, 1995). Dimidium, also known as 51 Pegasi b, is an “hot jupiter”, a Jupiter-sized object closely orbiting its parent star. Given the diversity of the possible exoplanets and their combination with diﬀerent type of parent stars, various detection methods are used. Anyway, our ability to detect them has highly increased. As of 1st November 2018, there are 3,874 conﬁrmed planets in 2,892 systems, with 638 systems having more than one planet.

2.2 Detection methods

We now shortly describe the most successful methods to detect exoplanets (Wei, 2018), and then we will focus our attention on the transit method.

2.2.1 Direct imaging Infrared radiation coming from the planet can be detected. This only works for very near, big and hot planets which orbit far from their parent star so that their radiation is not overwhelmed. Coronographs are also used to ﬁlter most of the light from the star. This approach presents obstacles in deriving planet parameters. One could roughly calculate its radius using its thermal radiation, brightness and the distance from Earth. An example of experiment that aim to detect exoplanets via direct imaging is GIP 2 (Gemini Planet Imager), in Chile.

2http://planetimager.org/

16 Figure 2.3: Direct image of 51 Eridani b with the Gemini Planet Imager.

2.2.2 Microlensing Gravitational microlensing occurs when the gravitational field of a star acts like a lens, magnifying the light of a distant background star. If the foreground lensing star has a planet, then that planet own gravitational field can make a detectable contribution to the lensing effect. Comparing this method of detect- ing extrasolar planets with other techniques such as the transit method, one advantage is that the intensity of the planetary deviation does not depend on the planet mass as strongly as effects in other techniques do. This makes microlensing well suited to finding low-mass planets. It also allows detection of planets further away from the host star than most of the other methods. One disadvantage is that followup of the lens system is very difficult.

Figure 2.4: An illustration of the results microlensing detection. The bell- shaped function shows the magniﬁcartion of the light due to foreground star. The narrow subsequent peak is the eﬀect of the exoplanet.

2.2.3 Radial velocity This method uses Doppler spectroscopy: the change of the spectrum lines can be used to calculate the star velocity due to the planet gravitational pull. This velocities can also be as little as few meters per second. This was the most used detection method until 2012. Using this approach one can calculate the ratio

17 of the masses of the two considered bodies. First, we can compute the orbit radius:

∆λ vsin(i) 2πr sin(i) = = s (2.1) λ c cP Then, once the period P is measured, knowing Kepler’s third law:

4π2a3 P 2 = , (2.2) GM∗ we can calculate the semi-major axis, and from:

aMp rs = 1,, (2.3) M∗ + Mp we are allowed to calculate the mass ratio. Knowing the stellar mass using scale relations, we can also compute planet mass. Both velocity and mass calculations gives lower limits as result due to the unknown inclination of the orbit.

2.3 Transit

If the planet orbit is somewhat along the line of sight of the observing instrument, the planet will transit its parent star. The light coming from the star will be somewhat blocked depending on the planet parameters. This last method is the most used of the last years, Kepler and TESS missions use photometric transit to explore for new exoplanets. One of the reasons why this method is preferred is that it provides a large number of planet relative-to-star parameters such as radius, semi-major axis of the orbit and the period.

Figure 2.5: Illustration of transit eﬀect on stellar ﬂux.

The curve in the upper ﬁgure goes by the name of light curve.

2.4 Light curves of transiting planet

We will analyze the peculiar graph associated to a transit from which one can derive planet parameters.

18 2.4.1 The shape of a transit A transit could basically be divided in four “contacts”. • First contact: the planet is entirely outside the star silhouette. The edges of the two bodies virtually touch each other. The planet orbits inward the star outline, hence its flux decreases. • Second contact: the other edge of the planet passes by the edge of the star: the smaller body is now entirely inside the bigger one’s profile. • Third contact: the planet begins its egress from the star outline so the incoming flux begin to rise again. • Fourth contact: the planet is now fully beyond the star shape and the flux is 100% of the initial one. The various stages are well recognizable using light curves, graphs which display flux values over time ones. Flux is often normalized and expressed in erg per second while time is given in Barycentric Julian Date. Let’s analyze the main features of a light curve and the information we can gather from them.

2.4.2 A geometric model: observables There is a unique solution of the planet and star parameters from a planet transit light curve with two or more transits if the planet has a circular orbit and the light curve is observed in a band pass where limb darkening is negligible. The existence of this unique solution is very useful for current planet transit surveys (Seager & Mall´en-Ornelas,2003). Seager and Ornelas geometric model is based on some assumptions: • The planet orbit is circular;

• M∗ is much bigger then M∗ and the planet is totally dark compared to the star; • The stellar mass-radius relation is known; • The light comes from a single star, rather than from two or more blended stars. • The eclipses have flat bottoms which implies that the companion is fully superimposed on the central star’s disk; • The period can be derived from the light curve. To find the unique solution to the transit problem, five equation have to be solved. The first three of them are geometrical ones based on the curve shape and are related to the successive observables. Transit depth: using this observ- able one can infer the ratio between planetary and star radius. According to the inverse square law (2.5), being the luminosity of the target star nearly constant

19 during the orbital period of the planet, the diﬀerence in ﬂux is proportional to the ratio of the radii: ∆F R 2 = p (2.4) F R∗ The ratio between the interval of time during which the planet shape is fully covering the star one and the total transit:

R h (1−( p )2−( acosi )2 i(1/2) arcsin R∗ R∗ R∗ tf a 1−cos2i = R (2.5) h (1+( p )2−( acosi )2 i(1/2) tT R∗ R∗ R∗ arcsin a 1−cos2i where the total transit duration:

Rp ! P R h(1 − ( )2 − ( acosi )2 i(1/2) t = arcsin ∗ R∗ R∗ (2.6) T π a 1 − cos2i

We need two other equations to ﬁnd a unique solution: Kepler’s third Law: 4π2a3 P 2 = (2.7) G(m1 + m2) The stellar mass-radius relation, where k is a constant whose value depends on the stellar sequence (main, giant etc.):

x R∗ = kM∗ (2.8)

2.4.3 The unique solution

We ultimately wish to solve for the five unknown parameters M, R, a, i, and Rp from the five equations (2.4) - (2.8). We can start computing four parameters by those. The ratio of the radii in case of normalized flux, trivially from (2.4): √ R ∆F = p (2.9) R∗ The impact parameter b from (2.5): a b = cosi (2.10) R∗ The ratio between stellar radius and orbital semi-major axis: " √ #1/2 a (1 − ∆F )2 − b2(1 − sin2 tT π ) = P (2.11) 2 tT π R∗ sin P The density of the star: " #" √ #3/2 ρ M /M 4π2 (1 − ∆F )2 − b2(1 − sin2 tT π ) ∗ = ∗ = P (2.12) 3 2 2 tT π ρ (R∗/R ) P G sin P

20 From the previous parameters, we can ﬁnally infer the physical parameters, via the mass-radius relation. From equation (2.8) we have:

1−3x M∗/M M∗/M 3 = 3 = (2.13) (R∗/R ) k

Replacing this in the (2.12) we obtain the mass:

1 M h ρ i 1−3x ∗ = k3 ∗ (2.14) M ρ

And the stellar radius: x R h ρ i 1−3x ∗ = k1/x ∗ (2.15) R ρ The semimajor axis can be computed as:

" #1/3 P 2GM a = ∗ (2.16) 4π2

Finally, the planet radius is:

x R R √ h ρ i 1−3x √ p = ∗ ∆F = k1/x ∗ ∆F (2.17) R R ρ

2.4.4 Smooth curve: limb darkening In reality, the stellar luminosity is not constant across the stellar disk. The stellar disk is brighter at its center than at its edges. The photons received from the centre of the stellar disk come from deeper into the stellar atmosphere than those received from the edge of the disk. A photon coming from deeper into the stellar atmosphere has a higher temperature and thus appears brighter at the associated wavelength. Thus, at the corresponding wavelength, the stellar center appears brighter than the stellar limb, hence the expression ”limb darkening”. We should take limb darkening into account in determining planets parameters. Mandel Agol (2002) give a list of analytic functions to model transit light curves which include limb-darkening (quadratic and non-linear laws). The function to be used depends on the size (radius) of the planet relative to the star and on the position of the planet on the stellar disk. The exact analytic formulae are given in (Mandel & Agol, 2002).

2.5 Eclipsing binaries and Variable stars.

These kind of curve could of course be produced by more then one phenomenon. One of the ﬁrst steps in transit analysis is rejecting false positives. These may be of diverse kinds (Ciardi, Pepper, Colon, Kane & Astrophysical Community, 2018).

21 • Eclipsing binary system: if the system is composed of a bright star, e.g an F dwarf, and a less bright one, e.g an M dwarf,the light curve of the system resembles one caused by a Jupiter-sized planet. One way to solve the ambiguity lays in the periodicity of the curve. A planet does not glow while an M dwarf does so the curve will present a ﬂux diminishing both when the secondary transits the primary and when the latter eclipses the former one. • Variable star: its signal is fairly diﬀerent from a transit but a star intrinsic variability or systematical noise can distort the gathered data. This is a major problem when working with small planets. To improve the quality of the data one can use ground-based follow up but these are very expensive.

Figure 2.6: Eclipsing binary light curve example.

2.6 Multiple transits

Most of the observed stars have entire planetary systems orbiting around them- selves. When more then one planet orbits a star, different light curves will be detected as time passes by as we will describe in the last Chapter given that the studied object TOI 175 belongs to this class. What about the possibility for a planet to transit more then one star in our frames? Let’s say we are observing a star at a 10 pc distance and it has a bright neighbour 1’ away. Using trigonometry we figure out that linear distance between the stars is of the order of tens of thousands of AU. This means that, for the planet to transit both star, it should have an orbit with that same order of magnitude. Applying Kepler’s third law: 4π2a3 P 2 = (2.18) G(M + m) we find that, for a solar mass star and a ten thousands AU semi-major axis orbit, the orbital period is of the order of tens of thousands of years itself, this

22 is in net conﬂict with the observed transits, having the order of days.

23 Chapter 3

The Transiting Exoplanet Survey Satellite

TESS stands for “Transiting Exoplanet Survey Satellite” and it is the most recent mission designed to discover exo-planets. This mission is led by the Massachussets Institues of Technology. The NASA’s Goddard Space Flight Center (GSFC) provides project management, systems engineering, and safety. TESS is the ﬁrst NASA satellite mission launched under a contract with SpaceX 1, who provided a Falcon 9 rocket to launch the satellite.

Figure 3.1: TESS during the ﬁnal stages of its assembly. Credits: NASA/Orbital ATK.

3.1 Beyond Kepler

Thanks to Kepler’s data, a key statistics of expected transits has been inferred. First fact to be considered (Christ, Montet & Fabrycky, 2018) is that TESS

1Space Exploration Technologies Corp. is a private American aerospace manufacturer and space transportation services company headquartered in Hawthorne, California

24 increases the time baseline from four to ten years allowing us to gather much more data from the same systems. This enables us to study long-term dynamics of planetary systems and discover new transits whose periods were prohibitively long for Kepler. How is TESS going to handle its populations differently? • Kepler’s field of view (FOV) comprehended about 0,28% of the sky, the instrument gathered data from a limited area in Cygnus’ constellation. TESS’ FOV enables us to observe over 85% (fig.3.4) of the sky 3.2. • TESS’ four wide field cameras are giving us a way different perspective. They are designed to monitor a much larger and nearer area then Kepler’s ones did. Tess is observing near and bright F5 to M5 main sequence dwarf stars which are better candidates for ground-based follow-up as they present much deeper and more frequent transits (fig.3.3). • TESS and Kepler filters are different. Kepler used a filter way more on the blue side of the spectrum while the filter on TESS is a red one. The choice is due to the spectral types of the target stars. The range, however, is wide (600-1000 nm bandpass) as we need to gather the most light possible, independently of the frequencies.

Figure 3.2: Comparison of observed sky sector: TESS, in blue and Kepler, in yellow [HEASARC: NASA’s Archives].

3.2 Mission Overview

TESS will observe from a unique elliptical high Earth orbit (HEO) that will provide an unobstructed view of its ﬁeld to obtain continuous light curves and a more stable platform for precise photometry than the low Earth orbit. The

25 Figure 3.3: Comparison of the magnitudes of observed stars: note that the position of TESS ones is way up, which means brighter stars [HEASARC: NASA’s Archives].

ﬁnal orbit is elliptical with a period of 13.7 days and perigee and apogee of 17 Earth and 59 Earth radii respectively, so that eclipses of the Earth and Moon through the FOV are avoided. The large orbit keeps the satellite above the Earth radiation belts and provide a nearly constant thermal environment for the stable -75 degrees C operation of the CCDs.

Figure 3.4: TESS will cover 85% of the sky, leaving out only the equatorial sector and overlapping at poles [HEASARC: NASA’s Archives].

3.3 The observatory

The spacecraft for TESS is the Orbital LEOStar-2/750 bus equipped with a Ka transmission band and two solar panels wings. The transmitter is a 0.7 diameter antenna with a 100Mb per second data rate. TESS is equipped with with four

26 wide-field cameras each having 24x24 degrees FOV while the focal plane array includes four CCDs, produced by Lincoln Lab at MIT, with total dimension 2048 squared pixels, each covers 21”.These detectors work in a 600 to 1000 nm range, having a depletion region which can gather about 200’000 electrons before saturation. A thermostat will keep a 10 electrons per pixel noise. Each of the four cameras (fig.3.5) point the sky with different angles so that a total 24x96 squared degrees stripe sector is obtained. The lens assembly consists of four spherical lenses with a 1.4 focal ratio design and a 10.5cm diameter.

Figure 3.5: TESS’ camera [tess.mit.edu].

3.3.1 Charged Coupled Device & Point Spread Function Modern telescopes’ detectors are charge coupled devices. These are built using semi-conductors. Squares of light sensitive material form a grid on a SiO2 layer which is based on a much thicker p-doped silicon layer. When a photon passes through the pixel, it frees electron in the p-Si layer which migrate and are stored into the depletion zone underneath the sensitive material by a voltage bias. The stored electrons are moved toward an output pin using voltage differences between pixels. The exiting current is proportional to the incident radiation. The point spread function (PSF) (fig.3.6) describes the response of an imaging system to a point source or point object. It can be thought of as the extended blob in an image that represents an unresolved object. This broadening is due to both the optics in the telescope and the astronomical seeing. In order to gather light from an unresolved source 3 pixels grid are conventionally used. TESS actually enables different numbers of pixels according to the position on the detector with a 1.88 pixels mean value which implies 99.7% of a star flux within 2.4 pixels (Oelkers & Stassun, 2018).

27 Figure 3.6: Point Spread Function underneath pixel grid ﬁles.

3.4 Sky observing

TESS will survey 26 sectors, 13 per hemisphere, covering about 90% of the sky. The 13 sectors will be observed for 1 year each, beginning in the south. Each sector will be observed for two orbits (27.4 days total), hence the spacecraft will point to the next sector. The sector is composed of a 20x96 degrees using the 4 wide-ﬁeld cameras. Within each of these large sky stripes TESS will impress full frame images (FFIs) at 30 minute cadence and gather data from about 15,000 target stars on a 2 minute cadence. The sectors highly overlap at pole regions to simplify latter ground based follow-ups and provide data for following missions such as JWST (Ricker et al.,, 2014).

3.5 Target Selection: TIC & CTL

The creation and maintenance of the target catalog (Stassun et al.,, 2018) has been a task of the TESS Target Selection Working Group. The resulting list is known as the TESS Input Catalog (TIC) and it was generated unifying many existing catalogs. The ﬁnal TIC contains data for 596 million objects, including 470 million point sources, 125 million extended sources, and 1 million special objects. A subset of TIC objects was then created to identify more then 200,000 targets for the 2 minutes cadence, high-priority observations. This catalog is known as Candidate Target List (CTL). The CTL was obtained by ﬁltering the 470 million point sources in the TIC by magnitude, proper motion, and lack of computed parameters(Teff , radius, and contamination ratio). The resulting list is ranked by priority; a function of sky position, stellar radius, brightness, and contamination,

28 3.6 The ground network

Given the ambiguities on the objects that the satellite is aiming to, one can determine the their types (transit,eclipsing binary etc.) using tools such as the Tess Exoplanet Vetter (TEV) developed by the Tess Science Office (TSO) for the research of Tess Objects of Interest (TOI) (Guerrero, Glidden, Fausnaugh & TESS Team, 2018). TSO is a late stage in Tess object science. The ground- based network (Martel et al.,, 2010) begins with NASA’s Space Network (SN) and JPL’s Deep Space Network (DSN) which are the first connection for Tess to download gathered data. SN and DSN are also used by the Mission Operation Center (MOC) and Goddard Space Flight Center (GSFC) to communicate with the space observatory for commanding. On the other hand the Science Oper- ations Center (SOC) is the beating heart of Tess’ science. It comprehends the Payload Observation Center (POC), which runs the first studies on the DSN gathered data, and the Science Processing and Operation Center (SPOC) which further analyzes data to produce light curves and transit signatures. This final data are then sent to the Mikulski Archive for Space Telescopes (MAST) and TSO.

Figure 3.7: TESS’ mission ground network [tess.mit.edu].

29 3.7 TESS data products

Diﬀerent types of data ﬁles are to be released on the Mikulski Archive for Space Telescopes (MAST) archive: FFIs, TPFs, light curves.

3.7.1 Target Pixel Files A target pixel file contains the raw and calibrated fluxes for the pixels downloaded at a cadence shorter than the full frame images. Nominally, these are at a two-minute cadence. It also contains information about the aperture, including which pixels were used to calculate the total flux, which pixels were used to estimate the background flux. The TESS target pixel files contain a primary Header Data Unit with metadata stored in the header. The first extension HDU contains more metadata in the header and stores arrays of data in a binary FITS table, which include the timestamps, fluxes, and background fluxes for each cadence of the pixels read out and downloaded by the spacecraft. The second extension HDU contains an image that stores the pixels that were read out, and records information such as which pixels were used in the optimal photometric aperture to create the flux data. TPF analysis is fundamental to isolate light curves and perform different apertures photometry which we will discuss in the last chapter.

Figure 3.8: A TESS typical Target Pixel File.

30 3.7.2 Full Frame Images A Full Frame Image (FFI) is a collection of actual target data and so-called collateral pixels. FFIs are taken every 30 minutes. There are 16 CCDs on the spacecraft, each of which is supported by 4 output channels so that the FFIs result image of the data release are alike the ones in following ﬁgure. TESS FFI ﬁles are in FITS format.

Figure 3.9: The four CCDs point at diﬀerent regions of the sky and then are sorted as the ﬁgure shows to form a FFI.

31 3.7.3 Light curves Light curve files are stored as FITS binary tables and images containing flux and time data and are produced for each target using simple aperture photometry and allow us to easily visualize transits, eclipsing binaries (EB), variable stars (VAR) phenomena. A single light curve file contains the data for one target for on observing sector. Light curve files consist of various parts: an header, the light curve binary table, the aperture mask image. The aperture mask image provided with each light curve is the same as that provided with the corresponding target TPF file.

Figure 3.10: TESS light curve images of EB, VAR and transit extracted from FITS tables.

32 Chapter 4

A candidate exo-system: TESS Object of Interest 175

In this Chapter we introduce the main target of our study (a candidate planetary system), the Python packages and the other tools used to complete the analysis, and our data analysis.

4.1 Target star: L98-59

As presented in Chapter 3, section 3.4, TESS target stars are enumerated in two catalogs. The star we aimed to study during this thesis project is contained in the TIC and it is identiﬁed by the code TIC 307210830 or Tess Object of Interest 175, TOI 175 from now on. This star is also known as L 98-59. According to Gaia Data Release 2, these are the main features of the target star: • Spectral type: M3 ± 1. It lays in the lower right part of the HR diagram. • Distance: 10.6 parsec. • Equatorial Coordinates: RA 08:18:07.6, Dec -68:18:48.6. So, it shines in the southern sky.

• Teff = 3455 ± 222K

• Radius = 0.315 ± 0.028 R

• Mass = 0.313 ± 0.020 M • Absolute K-band magnitude of 7.1, thus very bright for a dwarf star (which is good for follow up). After TESS SPOC first analysis the star is classified as hosting three planets, namely TOI 175b1, TOI 175c and TOI 175d. It is observed by TESS in Sectors 1The International Astrophysical Union set an official way to name exoplanets. The nearest to the parent star is indexed with a “b”, the further with a “c” and so on.

33 1, 2, 5, 8, 9, 10, 11, 12. Simbad (Wenger et al.,, 2000) and Aladin (Boch & Fernique, 2014) softwares have been used to study the region of sky where the target is set in.

Figure 4.1: Aladin software TOI 175 image highlighted with a purple pointer. Credits: Digitized Sky Survey

4.2 The software tools lightkurve and exoplanet

One of the first Python tools I used to work on TESS data is lightkurve2. This package offers a user-friendly way to analyze astronomical flux time series data, in particular the pixels and light curves obtained by NASA’s Kepler, K2, and TESS missions. It provides some powerful methods to be applied on TPFs and Light Curve Files.

4.2.1 A first display of LCs from TPFs I wrote some basic codes to retrieve these files from MAST archive and manip- ulate them to show the wanted results. Once downloaded, I plotted the TPF data, which appears as a grid of pixels where flux is represented as number of electrons per second in the CCD. One can change the aperture of the TPF to comprehend less or more pixels then the default aperture does. We can also access data tables using lightkurve methods. We can use the tolightcurve() method to turn our Target Pixel File into a light curve. This method considers the default aperture on the target, and compute flux as the mean on all the pixels inside the aperture. Occasional long-term trends can be removed using .flatten() method. Every light curve presents a noisy region around BJD 1’350, probably due to thrust maneuvers with the TESS spacecraft. We can remove this by masking the light curve.

2https://github.com/KeplerGO/lightkurve

34 Figure 4.2: First TPF retrieved of TOI 175 with lightkurve.

Figure 4.3: Long-term trend rough light curve obtained with tpf .tolightcurve() in lightkurve

Figure 4.4: Flattened light curve with lightkurve.

35 4.2.2 Periodograms Once we have extracted the light curves, we wish to find any periodic, transit- like signal into it. We can accomplish this using periodograms. The basic idea of this type of statistical analysis is to plot the data on a frequency-domain rather then on a time one, fig. 4.5. A frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A given function or signal can be converted between the time and frequency domains with a Fourier transform. It converts a time function into a sum of sine waves of different frequencies, each of which represents a frequency component. The ”spectrum” of frequency components is the frequency-domain representation of the signal. What we aim to do here is to check the periodicities in the data set.

Figure 4.5: Time to frequency domain transformation. The red signal (left) is divided in its sine components. Each of these components is represented by a peak in the periodogram (right)

In practice, a sequential approach is usually adopted (Baluev, 2013) to detect the periods in the data: plot a single-frequency periodogram, find a candidate period, ensure that it is significant, remove the relevant variation from the data and repeat. Spurious peaks in the spectrum can appear, giving the illusion of strong periodic behavior [(Feigelson & Babu, 2009)]. The possible presence of spurious peaks can be tested with permutations and simulations of the dataset, but a definitive conclusion requires new observations to test predictions.

4.2.3 Period analysis with exoplanet I performed this type of analysis with another useful tool: exoplanet [Foreman- Mackey (2018)]. The results show highlighted portions of the total periodogram extracted from the selected aperture which represent the frequency of periodic transits. A period is also shown on the upper-left side of the plot. Periods are found for the three planets:

36 Figure 4.6: The periodogram plotted via exoplanet. The orange stripe marks the probable time-set variations where one of the transits occur, namely 175b.

• TOI 175b: 2.25 days • TOI 175c: 3.68 days • TOI 175d: 7.45 days

4.2.4 Aperture Photometry & Difference Imaging Field Of View (FOV) is a fundamental parameter when studying faraway stars: even a portion of few tens of arcseconds could contain hundreds of stars. Graph- ing a single light curve over an entire frame would not be effective as one could not differentiate the wanted source from other ones. he simplest technique, known as aperture photometry, consists of summing the pixel counts within an aperture centered on the object and subtracting the product of the nearby average sky count per pixel and the number of pixels within the aperture: this will result in the values of the target object. Besides, even eclipsing binaries (EB) and variable stars (VAR) have to be taken care of, otherwise their variable signals could be registered as false positives. One technique, known as difference imaging, enables us to find out these unwanted signals by subtracting two images of the same sector taken in different times. The non-variable bodies vanish (only noise and systematics survive) while EB or VAR leave detectable signals. When wanted apertures are successfully achieved next step is to encode the data in a so-called Target Pixel File (TPF). This is a pixels grid indexed by row and column on which a color legend specifies the light intensity. The said light curves can be displayed starting from these TPFs using various tools (Vin´ıcius,Barentsen, Hedges, Gully-Santiago & Cody, 2018).

37 Figure 4.7: The image shows different circles (apertures) on top and the re- spective flux coming from them. The inner circle gathers the most of the light being centered on the target star. Significative noise is gathered by surrounding bodies.

Figure 4.8: Diﬀerence imaging on a TESS frame. The central image is obtained subtracting two diﬀerent images of the same region. Apart from the background noise, the only source that survives is a variable one [Oelkers & Stassun (2018)].

4.3 TOI 175 transits

I have previously displayed a simple TPF of our target, I will now display the same one highlighting the aperture used for the photometry. Actually, diﬀerent apertures are performed in order to achieve the best transit shape possible. Next thing we wish to do is identify and make a close up of the transits. We can use lightkurve .fold() method to achieve this zooming into the single transit event. Another improvement of the transit curve is obtained using the .bin() method. From the analysis of the TPFs, using the methods I quoted, we are able to

38 (a) TPF with default green aperture, see. (b) The same TPF with a diﬀerent aperture Fig. 4.2. displayed on it.

Figure 4.9: Diﬀerent apertures are used to achieve best possible curves (lightkurve). obtain the three transit curves.

Figure 4.10: TOI 175b transit.

39 Figure 4.11: TOI 175c transit.

Figure 4.12: TOI 175d transit.

Planets 175b and 175c transits are quite clear and recognizable. Planet 175d, instead, shows a shallower dip in the light curve, it certainly requires further analysis which could be performed on next TESS data release about this object.

4.4 Background signal analysis

Even though these are pretty much surely transits, we are willing to analyze the background in order to exclude that transit-like signals come from other sources in the nearby sky. I created GIF ﬁles with MAST Target Pixel Files via k2flix tool (Barentsen, 2015). These GIFs display succeeding frames of the selected region. I found a peculiar behaviour: the pixels seem to gather much more light around 500th and 1100th cadence. We did run this test on diﬀerent but near to TOI 175 regions of the sky.

40 (a) Random region of sky at frame 888. (b) The same region at frame 1164

Figure 4.13: Random region of sky one degree away from TOI 175 Eastwards. Around 500th and 1100th cadence a general brightening occurs

(a) Random region of sky at frame 132 (b) The same region at frame 552

Figure 4.14: Random region of sky one degree away from TOI 175 Westwards. Around 500th and 1100th cadence a general brightening occurs.

What about our target? Does it behave the same? What’s the general trend of this background feature? Due to the predominance of our bright target, the background variation is less visible using frames as I have done previously so I managed to highlight the same behaviour plotting it. I extracted from the FITS ﬁle the “F LUXBKG” column, which contains data from background light, and plotted it against time. The resulting plot shows the same peaks we are able to see in the previous examples on the frames. What is the eﬀect of these peaks on our data? First of all, considering only the portion before the peak we can see that no transit shaped event occur, this means no false positive signal is detected on background. The two spikes nature is still not clear and further investigations are to be done in order to understand its source. Possibilities could be red noise

41 Figure 4.15: Background flux for TOI 175 region of the sky. or a lowering of sky transparency in that region. Anyway our transit signals for the three planets seem not to be triggered by background effects. I searched for the signals of the three planets by folding various combinations of background pixels, and did not find evidence for them.

Figure 4.16: Background signal before ﬁrst peak. No transit-like signal evidence.

4.5 Suspected Eclipsing Binary

According to Gaia DR2 an eclipsing binary stands at 50 arcseconds away North- West from our target. We pointed it out using the software SAOImage DS9 of the Smithsonian Astrophysical Observatory. Then we conducted an analysis to isolate and analyze the data from this EB. Being outside the aperture, no disturbing signal should be discovered.

42 Figure 4.17: Eclipsing binary region of the sky highlighted with circle area using SAOImage DS9. The Yellow box is the whole TPF region while the little green one is the default aperture for TOI 175.

Figure 4.18: Light curve of the suspected, purple-highlighted, pixels. It looks like the transit is not disturbed by the EB.

The analysis seems to be negative, isolating the suspected pixels of the TPF no transit shaped curve is obtained.

4.6 Planets parameters

Being the background and eclipsing binary signals excluded, I proceeded with the study of the planets’ light curves. I did it via ktransit (Barclay, Burke & Howell, 2013). This tool enables us to compute features of a transit using geometrical observables as explained in Chapter 2 (Mandel & Agol, 2002). First of all a calibration of the tool is needed. We ran a simulation of transit data to test the ﬁtting abilities of the code. Five diﬀerent transit situations have

43 been simulated, one of the results is shown as example. Once the instrument is

Figure 4.19: ktransit simulation of a transit with radii ratio Rp/R*=0.04, orbital period P=4days. Residuals shown in down ﬁgure. thought to work as it should, the ﬁt on the interested planets can be performed.

• TOI 175b: Rp = 0.018 R∗ • TOI 175c: Rp = 0.044 R∗ • TOI 175d: Rp = 0.041 R∗ We can now compute the sizes in terms of Earth radii of these planets. Given that the star is ∼ 0.3R , the planets result to be more or less Earth-sized. Respectively, 0.8R⊕, 1.3R⊕ and 1.4R⊕.

44 Figure 4.20: Planet 175b ﬁtted light curved.

Figure 4.21: Planet 175c ﬁtted light curve

Figure 4.22: Planet 175d ﬁtted light curve.

45 4.7 Conclusions about the exo-system

In the field of the exoplanets discovery, the fraction of known multi-planet systems is close to 20%, with about 1.3 planets per system in average [(Baluev, 2013)]. The exo-system we are studying is an exciting three Earth-sized planet system orbiting an M dwarf star. This kind of system is probably the most common in the sky as M dwarf come with a 75% (Guinan, 2014) frequency. It is really different from our Solar System for several reasons, the most striking of which is its extension. The shortest period of a planet in our System is Mer- cury’s, with its 88 days, whilst the nearest planet to L98-59 only takes ∼ 2 days to orbit its parent star. The other two planets “years” also last within one week of ours. Being that close, these bodies are most certainly rocky ones but as previously stated, the habitability of the planets is a complicated matter where more variables have to be checked. When a planet orbits a red dwarf with a period of about six days is probably in its HZ (Guinan, 2014) but its atmosphere and the temperature of the star could make the planet not habitable. Stellar variability, flares and tidal locking give some concerns about this matter too. All of these questions need further studies both with TESS new data releases and with radial velocity and atmospheric characterization follow-ups. We certainly learnt that TESS photometric analysis is a non-trivial one: each CCD covers a very wide area, 21” squared, so that background noise is relevant because contamination from nearby stars cannot be easily removed from even a small photometric aperture Oelkers & Stassun (2018). Planet 175d is an example of these problems with its shallow dip and low signal-to-noise ratio. Its transit signal should probably be object of further studies and confirmations.

Figure 4.23: Artistic impression of a three planets system as TOI 175 one could be.

46 Chapter 5

Conclusions

The seek for exoplanets is one of the most active fields in astrophysics nowadays. TESS mission is just at the beginning of its lifetime and will go on for at least two years. Therefore, about 1’200 two-minute cadence plus 3’000 thirty-minutes cadence candidate exoplanets are going to be detected, requiring a large effort for their analysis and later follow-ups. So much more analysis is going to be performed on TIC candidates, and in particular for small radii planets: these are the ones we aim to for TESS mission to be declared as successful [Barclay, Pepper & Quintana (2018)]. According to Barclay et al. (2018) even though TESS will provide N ∼ 2000 candidates with radius inferior to 4 Earth radii, these will probably be too close to their stars, making follow-ups challenging or impossible. Ground based follow-ups will be possible for planets with this kind of radius if their star has a magnitude V=12 or fainter. In these cases, we will be able to confirm their nature unifying measurements of radius via transit and masses via radial velocity follow-ups giving us information about the densities of said planets. No later then 2025, the ESO Extremely Large Telescope will be a ground breaking instrument to analyze these planetary systems and their formation environments. Before that, James Webb Space Telescope, expected to operate in 2021, will be the perfect telescope to study the atmosphere of planets with particular priority to the ones which lays in the habitable zones of their stars. If we have any chance to find greenhouse atmospheric gases or just pre-biotic traces in proto-planetary disks, which ring the bell for extraterrestrial life, the Webb Telescope will be one of our best shots at it.

47 Bibliography

Baluev R. V., 2013, , 436, 807

Barclay T., Burke C. J., Howell 2013, Barclay T., Pepper J., Quintana E. V., 2018, , 239, 2 Barentsen G., 2015, K2ﬂix: Kepler pixel data visualizer, Astrophysics Source Code Library (ascl:1503.001), doi:10.5281/zenodo.15576, http://dx.doi. org/10.5281/zenodo.15576 Boch T., Fernique P., 2014, in Manset N., Forshay P., eds, Astronomical So- ciety of the Paciﬁc Conference Series Vol. 485, Astronomical Data Analysis Software and Systems XXIII. p. 277

Bolmont E., Raymond S. N., von Paris P., Selsis F., Hersant F., Quintana E. V., Barclay T., 2014, , 793, 3 Carroll B. W., Ostlie D. A., 1996, An Introduction to Modern Astrophysics Christ C. N., Montet B. T., Fabrycky D. C., 2018, preprint, (arXiv:1810.02826) Ciardi D. R., Pepper J., Colon K., Kane S. R., Astrophysical Community W. I. f. t., 2018, preprint, (arXiv:1810.08689) Farihi J., Becklin E. E., Zuckerman B., 2001, in American Astronomical Society Meeting Abstracts. p. 1397

Feigelson E., Babu G., 2009, Modern Statistical Methods for Astronomy: With R Applications, pp 1–484 Foreman-Mackey D., 2018, exoplanet v0.1.0, doi:10.5281/zenodo.1998448, https://doi.org/10.5281/zenodo.1998448 Guerrero N., Glidden A., Fausnaugh M., TESS Team 2018, in American Astro- nomical Society Meeting Abstracts #231. p. 439.11

48 Guinan E., 2014, in Habitable Worlds Across Time and Space, proceedings of a conference held April 28-May 1 2014 at the Space Telescope Science Institute. Online at ¡A href=“http://www.stsci.edu/institute/conference/habitable- worlds”¿http://www.stsci.edu/institute/conference/habitable-worlds¡/A¿, id.P16. p. P16

Kempton E. M.-R., et al., 2018, , 130, 114401 Mandel K., Agol E., 2002, , 580, L171 Martel F., et al., 2010, in American Astronomical Society Meeting Abstracts #215. p. 458

Mayor M., Queloz D., 1995, , 378, 355 Oelkers R. J., Stassun K. G., 2018, , 156, 132 Ricker G. R., et al., 2014, in Space Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave. p. 914320 (arXiv:1406.0151), doi:10.1117/12.2063489 Seager S., Mall´en-OrnelasG., 2003, , 585, 1038 Stassun K. G., et al., 2018, , 156, 102 Vin´ıciusZ., Barentsen G., Hedges C., Gully-Santiago M., Cody A. M., 2018, Ke- plerGO/lightkurve, doi:10.5281/zenodo.1181928, http://doi.org/10.5281/ zenodo.1181928 Wei J., 2018, preprint, (arXiv:1805.02771) Wenger M., et al., 2000, , 143, 9

Wolszczan A., Frail D. A., 1992, Zuckerman B., Becklin E. E., 1987, , 330, 138 nasa.gov, nasa.gov, https://www.nasa.gov/feature/jpl/ overlooked-treasure-the-first-evidence-of-exoplanets/