Exoplanetary Atmospheres Analysis Through the Transit Spectroscopy Technique

Home , AB Aurigae, Primary atmosphere

UNIVERSITÀ 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

Exoplanetary atmospheres analysis through the transit spectroscopy technique

Relatori: Candidato: Prof. Giovanni Covone Gallo Francesco Dott. Elisa Quintana Matr. N85/652

Anno Accademico 2020/2021 Contents

1 Introduction to the science of exoplanets 5 1.1 Planetary system formation ...... 6 1.2 Detection methods ...... 7 1.2.1 Direct imaging ...... 7 1.2.2 Gravitational microlensing ...... 7 1.2.3 Radial velocity ...... 8 1.2.4 Transit ...... 8 1.2.5 The limb darkening ...... 10 1.3 Transiting Exoplanet Survey Satellite ...... 10 1.4 The Hubble Space Telescope ...... 11 1.4.1 Slitless spectroscopy ...... 11 1.4.2 G141 ...... 12 1.4.3 Wide Field Camera 3 ...... 13 1.4.4 IR Channel ...... 14 1.4.5 Spatial scan mode ...... 15 1.5 Earth-like exoplanets atmospheres: why? ...... 15

2 Atmospheres of exoplanets 18 2.1 Introduction ...... 18 2.2 Atmospheres in the Solar system ...... 19 2.3 Atmospheric general processes ...... 21 2.4 Composition of an exoplanetary atmosphere ...... 23 2.5 Transit Spectroscopy ...... 24 2.5.1 Transmission spectrum ...... 25 2.5.2 Limits of the transmission spectroscopy ...... 27

3 Data analysis 29 3.1 Iraclis pipeline ...... 29 3.2 Reduction steps ...... 30 3.2.1 Zero read and bias-level corrections ...... 30 3.2.2 Non-linearity correction ...... 30

1 3.2.3 Dark current subtraction ...... 31 3.2.4 Gain variations: ﬂat ﬁeld correction ...... 31 3.2.5 Sky background subtraction ...... 31 3.2.6 Bad pixels and cosmic-rays correction ...... 31 3.3 Spectrum extraction: geometric distortions and position shifts 32 3.4 Wavelength calibration ...... 33 3.5 Fitting the white light curve ...... 35 3.6 Fitting the spectral light curves ...... 35 3.7 Dataset ...... 36 3.7.1 HD 209458 b ...... 37 3.7.2 WASP-121 b ...... 38 3.7.3 WASP-62 b and WASP-79 b ...... 40 3.8 Transmission spectrum of L 98-59 b ...... 43 3.9 Conclusions ...... 45

Bibliography 46

2 Introduction

“Is our planet as unique as it seems? Are we alone in the universe?”. These are questions that humans have been carrying with them for centuries and to which scientists try to answer. The search of life is the ultimate goal of exoplanetary science, which is currently living an unprecedented devel- opment. In the past two decades scientists have discovered exoplanets of various kind, far exceeding the diversity seen in our Solar system. With over four thousand confirmed exoplanets, the research is shifting from discovery to characterisation of exoplanetary systems, thanks to spectroscopic observations. The study of exoplanetary atmospheres is the only way to infer if a planet is habitable or not. Encoded in the spectrum of a planetary atmosphere there are informations about its chemical and physical properties, as chemical compositions with relative abundances, T-P profiles, dynamic processes, clouds/hazes and insights about the formation and evolution of the planets. The first detection of an exoplanetary atmosphere was on HD 209458 b (Charbonneau, Brown, Noyes & Gilliland, 2002), an hot Jupiter orbiting a sun-like star with a a distance 8 times shorter than that between Mercury and the Sun. Observing the spectra of this planet it was possible to detect the presence of Sodium in his atmosphere, thanks to the characteristic absorption feature at 589nm and later observations showed that the oxygen and carbon found in its atmosphere are evaporating at an immense rate, due to the nearness of his parent star, that a new class of exoplanets has been proposed, the ‘chtonian planets’ or ‘dead’ rocky cores of completely evaporated gas giants. Nowadays, several tens of exoplanet spectra have been observed using the transit spectroscopy technique, with the bulk of these observations obtained with HST, Spitzer Space Telescope, and other ground based facil- ities. Thanks to recent space missions like KEPLER and TESS, we have discovered many Earth-like exoplanets in the habitable zone of the parent star. Today the challenge is to understand if the life is possible on these kind of planets, trough the study of their atmosphere, if they have one. This thesis aims to make a panorama on the science of exoplanetary atmospheres. Chap- ter 1 is an introduction to the detection methods, with more informations

3 on the photometric transit technique and the Hubble Space Telescope, which is the main instrument used for the transmission spectroscopy observations of exoplanetary atmospheres. Chapter 2 gives an overview on the atmospheric composition of the Solar system’s planets and introduces to transit spectroscopy technique. Chapter 3 contains a brief description about the pipeline we used to analyze our dataset, composed of four hot Jupiters and an Earth-like planet recently discovered (Kostov et al.,, 2019).

4 Chapter 1

Introduction to the science of exoplanets

The International Astronomical Union defines a planet as follow:" 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. Moreover, it is important to distinguish a planet from a brown dwarf, due to the discovery of many massive exoplanets. A brown dwarf is a star with a mass between 13MJ < Mbd < 72MJ , hence that burns some deuterium to produce small amount of energy and luminosity, but that never reaches stable nuclear-burning phase to self-stabilize. An exoplanet is a planet outside our Solar system, hence which orbits around a star different from the Sun. At date, more than four thousand exoplanets have been discovered, with a wide range of types, far different from the planets of our Solar system, that can be classified into different families, depending on the masses and radii:

• Eart-like, planets with masses similar to that of the Earth and a radii of 0.8 − 1.25REarth with a composition prevalently rocky

• Super Earths, planets with masses of 2 − 10MEarth and radii of 1.25 − 2REarth with a composition prevalently rocky • Mini-Neptunes, planets less massive than Neptune with a radii of 2 − 4REarth, with a rocky core and a thick layer of hydrogen and helium. • Gaseous giants, planets with masses and radii similar to Jupiter and that have a thick layer of hydrogen and helium. These family also contains some strange or "exotic" planets, but that are those discovered

5 more frequently, the hot Jupiters and warm Neptunes, planets that have migrated from their original orbits and that now are very close to their host stars.

1.1 Planetary system formation

The formation process, favored by many astronomers, is that planets grow in a process of accretion of smaller building blocks. After the formation of the protostar, the nebular disk’s temperature decreases, allowing the formation of small dust grains with icy mantles, that collide and stick together randomly. They grow in mass and dimension, beginning to gravitational influence other material in their areas, and forming the so-called planetesimals. The distance from the planetesimal where a particle can be gravitationally influenced is called Hill Radius, defined as the distance where the particle around the planetesimal has an orbital period equal to that the planetesimal around the star, for example for the Sun:

M 1/3 R = a (1.1) H M where M and a are respectively the mass of the Sun and the distance from it for a planetesimal with mass M. The accretion disk can be divided virtually in two regions: one closer to the star where the temperature is too high to let volatiles to condense and the other beyond the so-called "snow line". Gas and ice giants can form only beyond the snow line, were the limited action of the radiation pressure and the lower temperatures allow volatile materials to condense, in particular with the formation of water-ice. This kind of planets are made of a rocky core with the addiction of water-ice, which can reaches a mass of 10 − 15MEarth, surrounded by a thick atmosphere of hydrogen and helium swept away from the inner regions of the nebula, with the addiction of heavier elements for the ice giants, like methane-ice, ammonia,etc. In the inner region of the nebula, due to the higher temperatures, only heavier elements are present, and they can’t be swept away by the radiation pressure of the star. This region is full of CAI’s, silicates and other refractory elements that sticking together can form rocky planetesimals, like the four we see today in our Solar system. With the entry of the star in the T-Tauri phase, all the material of the disk that hadn’t yet collected into planetesimals, are swept away.

6 Figure 1.1: Protoplanetary disk around the young star AB Aurigae, obtained with the SPHERE VLT’s instrument. In the inner region of the disk we can see the ’twist’, in bright yellow, where probably a planet is forming. CREDITS: ESO/ (Boccaletti et al., 2020)

1.2 Detection methods

The ﬁrst discovered exoplanet orbiting a Sun-like star was 51 Pegasi b (Mayor & Queloz, 1995), trough the radial velocity method. At date, more than four thousand exoplanets have been found, with the bulk of the discoveries made by the NASA’s missions TESS and KEPLER with the transit method. Here is a brief description of the modern available detection methods.

1.2.1 Direct imaging Trough this method, a star is directly observed by a telescope, trying to obtain a direct image of a planet orbiting around it. This detection, is very diﬃcult, in fact the starlight can totally obscure the faint reﬂected light coming from the planet. Trough this method it is easier to discover massive planets orbiting far from the host stars, and with IR observations and coronographs uses, it’s possible to obtain images of these kind of planets.

1.2.2 Gravitational microlensing The eﬀect of a gravitational lense is formed when a massive star deﬂects the light rays coming from another star and conveys them, just like a lense does, leading to an apparent increase of the light intensity (Covone, de Ritis,

7 Dominik & Marino, 2000). If the second star has a planet, it contributes to the ﬁnal measured intensity, with a smaller contribute, hence it is possible to see the characteristic "blip" in the ﬁnal intensity in function of the time.

1.2.3 Radial velocity This method uses the Doppler spectroscopy. Trough this method is possible to measure the radial velocity’s variation of a star, caused by a planet that gravitationally inﬂuence it and leading to periodic variations of the star’s radial velocity. From our point of view, there’s a change in the stellar spectrum according to the Doppler eﬀect, trough which is possible to measure the variation of the star’s radial velocity in function of time:

∆λ v sin(i) = ∗ (1.2) λ c where i is the orbit’s inclination. Calculating the semiamplitude K∗ = v∗sin(i), using the Kepler third low and momentum conservation, we can ﬁnally calculate: K M P M sin(i) = ∗ ∗ (1.3) p 2πa allowing us to put a superior limit on the mass of the planet Mp, due to the unknown orbit’s inclination i.

1.2.4 Transit The photometric technique of the transit is an indirect method that exploits the decrease in light of a star due to a transiting planet. This method has been used by the recent missions KEPLER and TESS, and it allows us to obtain the parameters a, i and Rp. The greater limit of this technique is that it works good only with the planets with i ∼ 90◦. To detect a planet they are usually requested three transits, with follow-up observations by radial velocity method.

Light curve When the planet passes in front of the host, this passage is called "transit" or "primary eclipse" and it produces a decrease of the star’s incoming ﬂux, while when the planet is behind the host star, it is in the "occultation" phase or "secondary eclipse", where the star now blocks some light rays coming from the dayside of the planet (Fig. 1.2). Trough a simple geometric model, we can derive some fundamental parameters (Seager & Mallen-Ornelas, 2003):

8 Figure 1.2: Graphic illustration of a transit and the eﬀect on luminous ﬂux coming from the star.

• δ, the depth of the light curve, deﬁned as:

F − F R 2 δ = noT ransit T ransit = p . (1.4) FnoT ransit R∗ • P, the orbital period, obtained as the distance between two consecutive minimus of the light curve

• b, the impact parameters, deﬁned as the distance bewteen the centers of the planet and the star

• a/R*, the major semiaxis to stellar radius ratio, calculated as : s √ a (1 + δ)2 − b2[1 − sin2( Ttπ )] = P (1.5) R 2 Ttπ ∗ sin ( P )

where Tt and Tf are respectively the total transit time, where the transit begin, and the ﬂat time, where the planet’s silhouette is all inside the stellar surface

• i, the orbital inclination, calculated as :

R i = cos−1 b ∗ (1.6) a

9 1.2.5 The limb darkening The limb darkening is an optic effect responsible to the non-flatness of the transit light curves. This effect is mainly caused by two factors: • The temperature of the stellar photosphere decrease with the distance from the star’s cente

• The optical path, changes with watching to the star’s centre to respect from the stellar edges Due to this eﬀect, the star’s centre appeares brighter than the edges, and when a planet reaches the mid point of the transit, i.e. it is transiting on the stellar centre, it blocks the brightest light rays, leading to a deeper transit curve in this point. According to the solution of the radiative transfer of the energy, for the absorption part, the optical depth τ is deﬁned as:

−τλ I(λ) = I0λe (1.7)

Z Z τλ = kλdl = σλ ρN dl (1.8) where kλ = σλρN is the total opacity, σλ is the absorption cross section and ρN is the number density of the particles, dl is the infinitesimal path along the view of sight. The star becomes opaque at τ = 1, i.e. only a fraction of 1/e electrons passed the medium, and this effect occurs first for the edges, because, respect to our line of sight, there’s a longer optical path. When fitting a light curve model, the limb darkening effect has to been taking into account. A non linear law is defined as follow (Claret, 2000):

I(µ) = 1 − a (1 − µ1/2) − a (1 − µ) − a (1 − µ3/2) − a (1 − µ2) (1.9) I(µ = 1) 1 2 3 4 where an are the limb darkening coeﬃcients that depend from the stellar model and µ = cosθ, where θ is the angle between the incoming starlight to respect our line of sight.

1.3 Transiting Exoplanet Survey Satellite

The “Transiting Exoplanet Survey Satellite” (TESS) is a mission leading by MIT and NASA to discover new exoplanets trough the transit technique. TESS focuses its attention on the M-dwarfs of our galaxy; in fact thanks to their dimness, their habitable zones are very close and it seems that they

10 host the most of the small period, small mass and rocky transiting exoplanets (Dressing & Charbonneau, 2015). Thanks to its particular orbit, TESS is far from the Earth’s Van Allen’s belts, avoiding damages from radiations and minimizing the thermal noise, and moreover it has been projected to cover ∼ 85% of the sky, monitoring about 2x105 stars in its ﬁrst two years of observations, compared to its predecessor, KEPLER, that has observed a small portion of the sky with fainter stars.

1.4 The Hubble Space Telescope

Named in honor of the astronomer Edwin Hubble, the Hubble Space Tele- scope (HST) is a large, space-based observatory, which has revolutionized astronomy since its launch in 1990. This space-based telescope can rely on two essential benefits: the angular resolution is limited only by the diffraction of the light (while in the atmosphere it’s influenced by the turbulence that makes the star pulse), and there’s no absorption by the atmosphere, so UV and IR observations are possible. The HST was launched on April 24 of 1990 and from that day several servicing missions have been completed, including the important SM1 in 1991, where new instruments were installed, such as WFPC2 and COSTAR, which countered the severe effects of the primary mirror’s flawed shape. HST is classified as a Cassegrain refractor telescope, with a Ritchey-Chrétien design, with an hyperbolic primary mirror of 2,4m and an angular resolution of ∼ 0.05arcsec. HST is 13.2 m long and 4.2 m wide at the back, where the scientific instruments are housed. The instruments are powered by two solar arrays and in the middle of the spacecraft, near its center of gravity, there are four 45 kg reaction wheels used to reorient the observatory. The telescope uses 6 high-precision gyroscopes (gyros) to detect its rate and direction of motion, in addition with three Fine Guidance Sensors (FGSs) that act within the spacecraft’s overall pointing and control system to keep the telescope virtually motionless while observing. HST can communicate with the Earth trough a network of satellites in geosynchronous orbit named TDRS, that serves as a relay for commands and data going to and from Hubble trough its high and low gain antennas.

1.4.1 Slitless spectroscopy The slitless spectroscopy is a spectroscopic technique used in astronomy to study the diffraction of the light coming from a region slightly populated by celestial objects. The filter, thanks to which the spectra are obtained, is called GRISM (Fig.1.3), literally an union between a diffraction grating and

11 a prism. The light coming from a star is diffracted by the grating and then is refracted by the prism into a straight path, so the image can form all into the camera behind the grism. The image of a galaxy through a normal filter looks undispersed, but the image made through the grism is a spread-out spectrum of the same galaxy (Fig.1.4). Slitless spectroscopy has the advantage that with a single exposure is possible to obtain spectra for many objects, but the main disadvantages are that the spectra sometimes overlap, and that the night sky light also falls on all of the detector. In fact, from the ground, the atmosphere emits bright infrared radiation that could mask the signal of a galaxy; this effect is annulled by using entrance slits in a spectrograph to block most of the night-sky light. In orbit, Hubble sees much less sky background, so it is possible to do slitless observations. Spectroscopy with grisms is useful to measure the redshift of a galaxy or to obtain the spectra of supernovae, stars and galaxies, through which is possible to identify the spectral features of the gases of which this celestial objects are composed of.

Figure 1.3: How a grism works: a combination between a diﬀraction grating to spread out the wavelengths of the light, and a prism to direct the rays back into the rest of the camera.

1.4.2 G141 The low-dispersion G141, with a dispersion of ∼ 4.65nm/pixel, is a grism used in the IR channel of the HST’s WFC3 for slitless spectroscopy observations. The useful spectral range is 1075 − 1700nm, limited in the red by the grism bandpass. Over most of the spectral range, more than 80% of the throughput is in the +1st-order spectrum, and it has a spectral resolving

12 power R = 130 at 1.4µm, so the observations made with this grism provide low-resolution infrared spectra.

Figure 1.4: On the left: An image of several galaxies obtained with the F140W ﬁlter. On the right: the same image obtained with the G141 ﬁlter. For each galaxy bright enough on the left, there’s a spectrum on the right, represented by a streak. Moreover, on some streak is possible to note bright spots, which are emission lines. (Credit: Benjamin Weiner)

1.4.3 Wide Field Camera 3 The Wide Field Camera 3 (WFC3) is a fourth-generation UVIS/IR imager aboard the Hubble Space Telescope. WFC3 was installed in May 2009 during HST servicing mission 4, and replaces the WFPC2. It has two independent channels: one sensitive to ultraviolet and optical wavelengths (UVIS channel), with a range of ∼ 200−1000nm, and the other sensitive to near-infrared wavelengths, approximately 800−1700nm (IR channel). A channel-selection mirror directs on-axis light from the HST optical telescope assembly (OTA) to the IR channel, or the mirror can be simply removed to allow the light to enter the UVIS channel. This means that simultaneous observations with the UVIS and IR detectors are not possible. The light coming from the OTA passes trough several optical elements before reaching the channels, including those that correct the spherical aberration of the primary mirror. WFC3 images are subject to significant geometric distortions that result primarily from the tilt of the focal plane of the detectors relative to the optical axis, which leads to an elongation of the field of view in both channels. For this reason the UVIS field projected onto the sky is shaped like a rhombus, while the IR channel field onto the sky is rectangular, the same thing occurs for the single pixels, thus the UVIS pixels are rhomboidal, measuring 0.0395 arcsec on each side, while the IR pixels are rectangular, measuring 0.135X0.121 arcsec.

13 Figure 1.5: Coordinate systems on the CCD: the blue region is the area imaged by the UVIS detector, the red is for the IR. The fixed and optimum fiducial points are illustrated and also the concentric subarrays aperture, with their origins at the aperture’s fiducial point.

1.4.4 IR Channel The infrared channel of WFC3 employs a low-noise, high-QE, 1024x1024 pixel HgCdTe array. Active cooling by a six-stage thermo-electric cooler keeps the detector at a nominal operating temperature of 145K. The area sensitive to the light is 1014x1014 pixels, while the other pixels, called "reference pixels", are used to track and correct the bias drift effect that affects the CCD detectors. The IR focal plane is tilted by ∼ 22◦ with respect to the incoming beam; the geometric distortion due to this tilt results in a rectangular shape of the detector projected onto the sky. The detector is divided into four quadrants of 512x512 pixels, each of which is read out independently from its outer cor- ner. Unlike common CCDs, the IR detector allows the accumulated signal in each pixel to be measured non-destructively multiple times, for example in the SPARS mode, where evenly spaced time intervals between reads are used. The capability to sample the signal multiple times during the integra- tion can be exploited to reduce the effective read-out noise significantly and isolate and remove cosmic-ray events. IR exposures are called “ramps” due to this capability to sequentially read the detector as signal accumulates. A full frame exposure results in one raw 1024X1024 pixel image for each read- out, but is also possible to read-out smaller portions on the detector, called subarrays, which have 4 sizes: 64x64,128x128,256x256 and 512x512 pixels, referred only to the active pixels, hence subtracting the 5x5 reference pixels area located at the subarrays corners. All the subarrays are concentrics with an equal number of pixels in each quadrant, using each of the 4 detector am-

14 pliﬁers to read the subarray pixels contained in its quadrant. The coordinate systems used in the IR detector are the following: • Data image-based system (Axis1,Axis2; pixels)

• Proposal POS TARG system (X Pos, Y Pos; arcsec)

• HST-based system (V2,V3 or U2,U3; arcsec) The image-based coordinate system is a generic system used when an image is displayed on a computer screen, and coordinates are expressed in pixel units. The POS Targ reference frame, in units of arcsec, can be used to specify the placement of a target at an offset location within field of view, and it has the origin on the center of the chosen IR aperture, called "fiducial point". The HST-based system is an orthogonal reference frame tied to the telescope and is used operationally for alignment, pointing, and slewing purposes. The chosen aperture defines two quantities: the active region on the detector to be read-out and the fiducial point and the default procedure is to center the target at the fiducial point (Fig. 1.5).

1.4.5 Spatial scan mode The spatial scan mode is a technique trough which with many exoplanets have been studied and many atmosphere have been detected. It consists to trail the star target on the detector in the direction perpendicular to the dispersion of the spectrum (Fig.1.6). Exoplanet’s host stars are often bright, and the spatial scan allows the longest practical exposures for bright stars without saturating the detector. As a results, the total number of photons collected is much larger, increasing the signal-to-noise ratio (S/N). The main disadvantage is that astronomical sources will overlap more often than with staring-mode observations. The scan rate can be any real number between 0.0 and 7.84arcsecs−1. When the scan is in the increasing-row direction we refer to this scan with "forward scan", while in the opposite direction, with "reverse scan".

1.5 Earth-like exoplanets atmospheres: why?

At date, about 4284 exoplanets have been discovered, with a wide range of types. Most of them are Jupiter or Neptune like, thanks to the greater ease of being discovered: in fact thanks to their greater masses, they cause a greater gravitational inﬂuence on the host star, which will move faster and

15 Figure 1.6: Left panel: "Imaging"; each observed object shows up on the detector at its corresponding position on the sky. Middle Panel: "Staring Mode"; when a grism is inserted, the light from each object is spread-out according to its wavelengths, producing a spectrum. Right Panel: "Spatial Scan Mode"; the detector is slightly moved during exposure, spreading the spectra perpendicularly to the wavelength direction. being more detectable by radial velocity method, and thanks to their greater radius, they give rise to deeper transits. The discovered Earth-like planets are 162 and the first Earth-like exoplanet discovered, orbiting around a G star’s type and inside the so-called "habitable zone", was Kepler-186f (Quin- tana et al.,, 2014). From that moment hundred of Earth-like exoplanets have been confirmed, with the first detection of an atmosphere surrounding a super Earth, 55 Cancri e, probably constituted by hydrogen, helium and hydrogen cyanide (Tsiaras et al.,, 2016a). M-dwarfs are a type of stars that are present in large number in our galaxy, and it seems that this type of stars hosts the most large number of small and low-mass rocky bodies (Dressing & Charbonneau, 2015). These stars are particularly interesting for the potentially habitable planets that they host: in fact due to the dimness of this type of stars, their habitable zones are located at shorter orbital periods, which are much more accessible to observational study (in fact TESS mission focuses its attention on this type of stars). Transiting multiplanetary systems are so important in exoplanetary observations, in fact they provide ideal laboratories for comparative planetary studies. Planets that form around the same stars, hence in the same primordial nebula, share some features, as host star’s mass, composition, activity level, etc., so they are ideal candidates for atmospheric studies, to provide a better knowledge on planetary formation and evolution history.

16 The only small planets with transmission spectroscopy measurements, and no signiﬁcant atmosphere detection, are those in the TRAPPIST-1 system (de Wit et al.,, 2016) and the single-planet GJ 1132 b (Southworth, Mancini, Madhusudhan, Mollière, Ciceri & Henning, 2017). For the ﬁrst, a probably could/haze free H2O-dominated atmosphere was inferred, while successive studies have inferred an hazy H2O-dominated atmosphere (Moran, Hörst, Batalha, Lewis & Wakeford, 2018), while for the second a H2O/CH4. The lack of atmospheric observations of Earth-like planets is principally due to their small dimensions and great distances and the faintness of their host stars. We are moving to an era of exoplanetary characterization: in fact encoded in the spectrum of a planet there are the chemical composition of an atmosphere, and moreover, informations about history and evolution of the planet and about atmospheric dynamic processes, temperature and pressure, cloud/hazes presence. Hence, the only way to infer if a planet is habitable or not is studying his atmosphere. Future missions will provide clearer observations of this kind of planets. Thanks to its enhanced features than HST, the James Webb Space Telescope (JWST) will provide higher signals in exoplanetary spectroscopic observations, leading to a greater atmospheric detectability around Earth-like planets.

17 Chapter 2

Atmospheres of exoplanets

2.1 Introduction

An atmosphere is a layer, or a set of layers of gases surrounding a planet, that is held in place by its gravity. The evolution of a planetary atmosphere is a complex process that depends on the temperature of the primordial nebula together with the planet’s temperature, gravity and local chemistry during the planet’s formation. The temperature of a planet can be estimated assuming an equilibrium model where the star and the planet are considered as perfect black bodies, where a part of the radiation coming from the star is reﬂected by the planet into the outer space, known as albedo α, and the other part is all absorbed and then riemitted; assuming a circular orbit at a distance D from the star and a spherical geometry for the celestial bodies, the equilibrium temperature is: r R T = T (1 − α)1/4 s (2.1) p s 2D where Ts and RS are the temperature and radius of the host star, respectively. The gases in a planet’s atmosphere suﬀer a continuous dispersion toward the outer space, favored by high equilibrium temperatures (high kinetic energy of the particles) and star’s irradiation, and prevented by the planet’s gravity: for this, gas giants, that form in the outermost region of the primordial nebula, can preserve more easily their primordial atmospheres; inner planets, more often present secondary atmospheres formed by volcanic events. In some atmospheres is possible to detect the so-called biotraces, gases that can be produced only in biological processes. A biotrace is for example the oxygen; high presence of free oxygen in the atmosphere is an unique prerogative of the Earth: an atmosphere with an high presence of oxygen is not in a chemical

18 equilibrium, thanks to its high capacity to react and recombine with other elements or with the rocks on the surface, oxidizing them. The presence of an high concentration of oxygen into the Earth atmosphere is the consequence of the biological activity of plants due to photosinthesis process, for this reason oxygen is considered like a life indicator. Once the equilibrium temperature of the planet is known, we can test the stability of its atmosphere by comparing its escape velocity to the thermal velocity of different molecules (Tinetti, Encrenaz & Coustenis, 2013). The escape velocity Vesc, defined as the minimum velocity that a particle need to escape from the gravitational influence of a planet, is: 1/2 2GMp Vesc = (2.2) Rp where G is the universal universal gravity constant: MP and RP are the planet’s mass and radius. The thermal velocity (defined as the root mean square of the total velocity, in three dimensions), can be found from the equation for the average kinetic energy according the kinetic theory of the gases: 3K T N 1/2 V = b th A (2.3) rms µ where Kb is Boltzmann’s constant, Tth is the thermospheric temperature NA is the Avogadro number and µ is the molar mass of the molecule. As a rough estimate, an atmosphere will lost a particle if

Vrms > 0.2Vesc. (2.4)

We can deﬁne a critical molar mass µc, considered to be a lower limit because the thermospheric temperature is plausibly much higher than temperature equilibrium of the planet, where Vrms = 0.2Vesc, and the escape process begin:

3KbTthNA µc = 2 . (2.5) 0.04Vesc A rapid calculation for Jupiter (Tinetti et al., 2013), with an escape velocity of a 59.5 km/s and a thermospheric temperature of 1000K, shows a critical mass of µc = 0.17, that is the reason why the atomic hydrogen on Jupiter is stable over the timescale of the Solar system.

2.2 Atmospheres in the Solar system

Atmospheres surrounding planets in our solar system have been known and studied from the 19th century. In the early observations was noted that satel-

19 lites and stars gradually disappeared, not instantaneously, when occulted by the planet, and other features on the planets that didn’t change on a regular cycle, as would surface features on rotating object; in this way was proved the existence of atmospheres. The first spectroscopic observations on Solar system’s planets revealed, with the surprise of many, a chemical composition totally different from the Earth. Nowadays we know that Venus atmosphere is mostly composed of carbon dioxyde, responsible of a strong greenhouse effect, that raise the surface temperature on the planet to around 470◦. The last study on this planet have detected phosphine in its atmosphere, a biotrace gas that can form only trough biological processes, opening the hypothesis of biological life in the upper atmosphere of Venus (Greaves et al.,, 2020). Not all the planets have an atmosphere in the strictest sense of the word: Mercury, with a gravity equal to about ∼ 38% of that of the Earth, has an atmosphere that is estimated to be a trillion times thinner than Earth’s. Particles from the solar wind, coupled with the vaporization of surface rock as a result of meteor impacts, are probably the largest contributors to Mer- cury’s atmosphere. Earth’s atmosphere is mainly composed by nitrogen (78.09%) and oxygen (20.95%), with traces of other elements like argon (0.93%), carbon dioxyde (0.04%), and small amount of other gases. Earth’s atmosphere can be divided in five different layers, starting from the bottom:

• Troposphere: the lowest layer that extends from the surface to about 9km at the geographic poles to 17km at the equator, where occur all the meteorological phenomena and where is a temperature that decrease with the altitude until the −55◦ of the tropopause

• Stratosphere: it extends until 50-60 km from the surface and contains the ozonosphere, a region with an high concentration of ozone molecules, that absorb UV radiations, and are responsible of a thermal inversion, where the temperature rise with the altitude until 0◦.

• Mesosphere: it extends until 90km from the surface and here the gases starts to thin out, the temperature lowers down to −70◦-−140◦ and in this layer meteors impact with the gas particle producing the so called "falling stars".

• Thermosphere: it extends until ∼ 700km and here’s a new thermal inversion. At a distance ∼ 100km there’s the so called "Karman’s line", an imaginary line which marks the boundary between the earth’s atmosphere and the outer space. Inside this layer there’s also the iono- sphere, which extends from 60km to 1000km, therefore it belong either

20 to mesosphere and thermosphere. It presents gases strongly ionized, due the exposition to Sun’s radiation, and it is exploited mostly for telecommunications, because it can reﬂects radio waves.

• Esosphere: it’s the outermost region of the Earth’s atmosphere, where occurs most of the particles escape.

The atmosphere of Mars is much like Venus, composed primarily of carbon dioxide (CO2), even if it’s signiﬁcantly thinner, and as a consequence the surface temperature of Mars reaches a maximum of 35◦C. Jupiter, the biggest planet in the Solar system, has an atmosphere composed mostly of hydrogen (75%) and helium (24%). Like the other gas giants, there’s no clear boundary where atmosphere stops and the liquid interior begins, where pressure allow the hydrogen to exists in metallic liquid form. Jupiter’s banded clouds are composed of ammonia, water and other sulfur compounds. Like Jupiter, Saturn is composed mostly of hydrogen(93.2%) and helium (6.7%) and it’s upper clouds are composed by ammonia ice, water and sulfur, that give to the planet a pale yellow color. Uranus is composed mostly of hydrogen (83%), helium (15%), methane (2%) and traces of acetylene. The high presence of methane in the upper region of the atmosphere, causes greater absorption of red light from the Sun, in turn causing the planet to appear a blue-cyan colour. Uranus has the coldest atmosphere in the Solar system, at approximately −224◦C, and its atmosphere contains much more water ice than Jupiter and Saturn as a consequence of this. As with Uranus, the blue colouration of Neptune is partially a consequence of the presence of methane, even if, with more gaseous hydrocarbons than Uranus, its temperature is marginally higher. Neptune is also home to the strongest winds in the Solar system, with their speeds potentially as high as 600 m/s.

2.3 Atmospheric general processes

By observing an exoplanetary atmosphere at various spectral range, is possible to probe diﬀerent regions of the atmosphere, inside each of them there’s a diﬀerent process (Madhusudhan, 2019). These atmospheric processes can be understood as a function of the pressure P (Fig.2.1). Deep in the atmosphere (P ≥ 1bar), the pressure and temperature, and hence density and opacity, are high enough that thermochemical equilibrium and riadiative-convective

21 Figure 2.1: Different processes in an exoplanetary atmosphere and how they are probed by different parts of the electromagnetic spectrum. On the right: typical penetration depths of UV, optical and IR radiation, indicating which processes can be probed by observations in each wavelength range and different chemical species that can be detected. On the left: three types of temperature-pressure profiles, which can result out thanks to different atmospheric processes;a highly irradiated planet with a thermal inversion (red line), an irradiated planet without a thermal inversion (cyan line), and a poorly irradiated planet (gray dashed line). Credits: Madhusudhan, 2019. equilibrium prevail. The first occurs when the Gibbs free energy of the system, defined as G = H − TS, (2.6) where H and S are the enthalpy and the entropy of the system respectively, has a minimum. Radiative-Convective equilibrium (RCE) is a balance between the cooling of an atmosphere by radiation and the heating through latent heat release (when a phase transition occurs) and surface heat fluxes. Higher up in the atmosphere, between ∼ 1mbar and 1bar, there are preva- lent processes like atmospheric dynamic, cloud/hazes and thermal inversions; these processes occur due to an interaction between the incident radiation field, chemical composition and other planetary properties. These processes strongly influence, and are influenced by, the atmospheric chemical composition and temperature structure, both of which can be out of equilibrium. Further up in the atmosphere (P ∼ 10−6 −10−3bar), the low density and high radiation field cause photochemical processes to govern the atmospheric com-

22 position through photodissociation of molecules into their constituent atomic species and formation of new ones. Finally, in the upper part of the atmosphere, at very low pressures, atmospheric escape of atomic species leads to mass loss from the atmosphere. At the same time, different chemical species and different regions of the atmosphere are accessible to different parts of the electromagnetic spectrum. Molecular species as H2O, CO, CO2, CH4, etc., absorb primarily in the IR due to rovibrational transitions, with the ex- ception of some heavy metal species (T iO, VO, etc.), which also have strong visible absorption. By contrast, atomic species absorb primarily in the optical and UV, with electronic transitions. Therefore, while UV observations probe the uppermost regions of the atmosphere, where the composition is entirely atomic, the IR observations probe lower regions of the atmosphere, where the composition is primarily molecular, with optical spectra probing intermediate regions.

2.4 Composition of an exoplanetary atmosphere

At date, most of the observations have been done on gas giants, like hot Jupiters and warm Neptunes, thanks to the ease to detect spectral features due their great dimensions. An hot-Jupiter is a planet with a composition similar to Jupiter, hence dominated by hydrogen and helium, that has formed beyond the snow line and then migrated through processes of gravitational interaction with the stellar nebula. These planets have very short orbital periods (i.e., are so close to their parent star), so they are continuously blasted by radiations. Hot-Jupiters can be considered "hot and dark", in fact they emit principally in the infrared and eﬃciently absorb visible light, so they are poor reﬂectively (Seager & Deming, 2010). A planet heated upward 1000K, like an hot-Jupiters, and that have a planetary atmosphere with an elemental composition close to solar is expected to be dominated by H2, H2O, and, depending on the temperature and metallicity, CO, and/or CH4. An initial estimate on the composition of a planet atmosphere can be inferred assuming thermochemical equilibrium and cosmic abundances within the primordial stellar nebula (Tinetti et al., 2013). The form in which carbon and methane can be found depends upon the following gas phase equilibrium reactions: CO + 3H2 ↔ CH4 + H2O (2.7)

N2 + 3H2 ↔ 2NH3 (2.8) These reactions evolve toward the righ-hand side at low temperature and high pressure, and toward the left-hand side under the opposite conditions.

23 In the Solar system, the gas giants in the outermost region, are dominated by hydrogen with the presence of CH4 and NH3, while rocky planets atmospheres, like Mars and Venus, where temperature are higher, the atmospheres are predominantly made of CO, CO2 and N2, as hydrogen escaped due to the relatively lower gravity ﬁeld of these kind of planets. H2O is the most active gas. At date, with many transmission and emission spectra available for hot gas giants, it is known that H2O is a common constituent of the atmosphere of these planets, thanks to the characteristic spectral feature that water presents around 1.4µm (Iyer, Swain, Zellem, Line, Roudier, Rocha & Livingston, 2016). Other atomic and molecular species identiﬁed in the hot-Jupiter’s atmospheres, are atomic sodium (Na) (Charbonneau et al., 2002), potassium (K), methane (CH4) with a typical feature at around 2.2µm (Swain, Vasisht & Tinetti, 2008), carbon monoxyde (CO), carbon dioxyde (CO2) and heavier elements like T iO (Haynes, Mandell, Madhusud- han, Deming & Knutson, 2015) and VO.

2.5 Transit Spectroscopy

Exoplanetary atmospheres can be studied trough diﬀerent methods, for example the high-resolution Doppler spectroscopy or direct imaging, but the most successfully method is the transit spectroscopy, thanks to the simple geometry of the problem and the wide class of exoplanets that can be studied trough this method (Fig.2.2). The transit method can be divided into

Figure 2.2: Masses versus radii of transiting exoplanets whose atmospheres have been observed (Madhusudhan, 2019).

24 three categories: transmission spectrum, where the planet is observed during the transit, i.e. primary eclipse, that provides constraints primarly on the chemical composition of the atmosphere at the day-night terminator region, together with the mean molecular weight and temperature as function of altitude; emission spectrum, where the planet is observed when is behind the star, i.e. the secondary eclipse, and that can prove the temperature structure of the day-side atmosphere of the planet together with its chemical composition; the phase-curve, as the planets orbits between the primary and secondary eclipse, that provides complementary constraints on the atmospheric properties.

2.5.1 Transmission spectrum A transmission spectrum is the spectrum observed during the primary eclipse of a transiting exoplanet (Madhusudhan, 2019). It provides evidences on the presence of an atmosphere surrounding an exoplanet and it’s essentially the measure of its thickness (Fig.2.3). When the light coming from the star, passes trough the atmosphere of the planet, it causes energetic transitions of atoms and molecules which are present in the atmosphere by an absorption process, producing spectral features in the resultant spectrum. In fact the

Figure 2.3: Schematic illustration of a planet transiting in front of his star: if that planet has an atmosphere, the measured transit depth will vary as a function of the wavelength, due to the absorption of the atomic and molecules species present in the atmosphere.

25 energetic transitions occur at specific wavelengths, i.e. at specific energies of the incident light, and by observing the resulting light, that is deprived of specific components, it is possible to provide the chemical composition of the atmosphere. As a result of the absorption processes, the atmosphere become opaque at specific wavelengths increasing the measured transit depths (i.e. the radius of the planet increases at specific wavelengths). The absorbing annulus of the planet is a function of the atmospheric scale height H, defined as the change in altitude over which the pressure drops by a factor of e: K T H = b eq (2.9) µg where Kb is the Boltzmann constant, Teq is the equilibrium temperature of the the planet, µ is the mean molecular mass and g is the surface gravity. The increase on the transit depth, due to the atmospheric presence, can be calculated as follows (Kreidberg, 2017):

2 2 (Rp + nH) Rp 2nHRp δλ = 2 − 2 ≈ 2 (2.10) Rs Rs Rs where nH is the number of the crossed scale heights at a wavelength where the atmosphere becomes opaque (typically around two for cloud-free atmospheres at low spectral resolution).

Figure 2.4: Molecular signatures in the 1-10 µm range at the spectral resolving power of R = 100 (Rocchetto, 2017).

26 2.5.2 Limits of the transmission spectroscopy According to the eq. 2.10, it follows that the ideal candidates for transmission spectroscopy observations have high equilibrium temperatures (low albedo and small semi-major axis), small host stars, low surface gravity and low mean molecular mass composition (hydrogen-dominated), thanks to the greater signals that these candidates can provide. For a typical hot Jupiter, the increase in the transit depth is about δλ ∼ 0.1%, while for Earth-like planets the expected transit depth’s variation is two to three magnitude or- ders smaller, for this reason an hot Jupiter’s atmosphere is easier to detect, while to date, there are no appreciable observations of Earth-like exoplanetary atmospheres.

Figure 2.5: HST/Spitzer transmission spectra of ten hot-Jupiter (Sing et al., 2016). Planets with clear atmospheres are located at the top, while cloudy- hazy planets at the bottom, with the solid colored lines showing atmospheric models. Atmospheres with no clouds/hazes show strong alkali (Na, K) and H2O absorption features. Cloudy/hazy atmospheres exhibit no alkali absorption features, weak or no H2O absorption features and strong optical scattering slope.

27 Despite the success and the ease of this technique, a limit is represented by the wavelength coverage of the current instruments (Rocchetto, 2017). Most of the transit spectroscopy observations have been obtained with the IR channel of the WFC3 on HST, with a wavelength coverage of ∼ 1.1−1.7µm, where molecules like H2O or HCN have strong features, but it is at longer wavelengths that most of the molecules have rotovibrational transitions (Fig.2.4). Furthermore, the presence of high-altitude clouds/hazes can yield to scattering phenomena for the incoming light that diverge from a model of Rayleigh scattering for gaseous particles, imprinting distinct features on the optical transmission spectra. Moreover, the presence of clouds/hazes can weaken or mute the spectral features and reduce the observable region of the atmosphere (Madhusudhan, 2019). An example is given by the recent observation of tens of hot-Jupiters, where the amplitude of H2O features are less than expected (Fig.2.5). Every single planet has an amplitude that is below two scale heights, while the expected signal should be about ∼ 5−10 scale heights. The recent study (Sing et al., 2016), trough observations with wide wavelength range from optical to near-infrared, reported the possibility of clouds presence, that can introduces slopes in the optical spectra, and mute or weaken some spectral features, discarding the hypothesis of a water depletion at the planet’s formation.

28 Chapter 3

Data analysis

In this Chapter we describe the pipeline used for the data analysis, called Iraclis. Then we propose the analysis of ﬁve planets, four of which are hot Jupiters and one is an Earth-like, with a comparison of the transmission spectra obtained in this thesis with Iraclis and those available in literature, except for L 98-59 b, since it is the ﬁrst time that the this planet has been studied with transit spectroscopy observations.

3.1 Iraclis pipeline

Iraclis is a public tool, developed by A. Tsiaras (Tsiaras, Waldmann, Roc- chetto, Varley, Morello, Damiano & Tinetti, 2016b), allowing to reduce and analyze data produced by WFC3 in the spatial scanning mode. The code is written in python language, and it simply uses a parameters ﬁle to work, with all the stellar and planet informations, set by the user. The pipeline need the data in raw format, downloaded from the MAST archive, plus an undispersed image of the target, obtained with one of the ﬁlter on the IR channel, for calibration purposes. The main advantages of this pipeline can be resumed as follow:

• It’s completely free and public and it’s simple to download and to use, indeed it needs only a parameters ﬁle where you set the stellar and planet parameters

• It has the "pylightcurve" tool inside, that can be used for ﬁtting the white light curve of a transiting exoplanet

• The reduction and calibration steps are completely automatic

29 • It takes into account geometric distortions, caused by the tilt of the detector of about ∼ 22◦ respect the optical axis and by the inclination of the 1D spectrum of G141 used of about ∼ 0.5◦ respect the detector’s rows • Compared to the standard reduction pipeline CalWF3, it contains a sky background correction

3.2 Reduction steps

Iraclis need data in the raw format to work, then it performs some reduction steps to improve these data and cancel diﬀerent sources of noise, some of which are default steps for a CCD detector, others depend on the nature of WFC3’s IR detector.

3.2.1 Zero read and bias-level corrections The WFC3 lacks a shutter, for this reason it starts to collect photons before the exposure starts. The first non-destructive read is a reference for the successive ones, and the recorded flux in this first read, the zero-read flux, is indicated by fz. fz is obtained subtracting the super-zero read, contained in a calibration file, from the first non-destructive read. After the calculation of the zero-flux, the value of reference pixels, that are non sensitive to light, are subtracted from each non-destructive read, eliminating the 1/f photon noise between the reads (the so called read-out read-out noise, in fact a CCD exhibits in output a noise that is proportional to 1/f, where f is the frequency of reading). Finally, the zero-read, is subtracted from all the consecutive non- destructive reads, as it is the reference level.

3.2.2 Non-linearity correction WFC3’s IR detector performs non-linearity with the flux, according to the equation: 2 3 Fc(f) = (1 + c1 + c2f + c3f + c4f )f (3.1) where Fc is the collected flux, f is the recorded flux, cn are the non-linearity coefficients provided in a calibration file. The absolute flux collected by a pixel contains also the zero-read flux, so it has to taken into account. The zero read flux fz is first added to each non destructive reads fr, then is corrected according to the eq. 3.1, and finally is subtracted:

Ffinal = Fc(fr + fz) − Fc(fz) (3.2)

30 3.2.3 Dark current subtraction Dark current in a CCD is a little electric current, mostly dependents from the temperature, when no photons enter in the detector. Dark current in the WFC3/IR is non-linear with time and also depends on the selected sub-array and sampling process. The correction is made subtracting the dark current frames, contained in the calibration ﬁles, on each nondestructive reads.

3.2.4 Gain variations: flat field correction At this step the data number (DN) in output are converted to electrons number. The conversion gain is defined as the number of electrons per DN. Not all the pixels perform in same way (not identical construction , impurity in the optical path, etc.), so all the non-destructive reads are divided by the flat-field frame included in a calibration file, and then multiplied by the mean gain of the four amplifiers on each quadrant (mean gain= 2.35e−/DN).

3.2.5 Sky background subtraction The sky background subtraction is made scaling the master-sky frame included in the calibration ﬁles, and subsequently subtracting it from the images. The scaling factor is obtained diving the least illuminated area by the master-sky frame.

3.2.6 Bad pixels and cosmic-rays correction Bad pixels are those that don’t work in the right way. Examples of bad pixels are the hot pixels, those who expone an excess of charge, with more than 100 times the average dark current, or the dead pixels, those that don’t response to the incoming light. Bad pixels have been identified during several missions and are stored in the calibration files. Cosmic rays are positioned randomly on the detector, and have to been identified in each image, a process that is possible thanks to the nature of multiple non-destructive reading the detector in the IR channel (see chapter 1, section 1.6.4). A cosmic ray is identified by calculating two flags for each pixels: the difference from the average of the four horizontally neighboring pixels (x-flag), and the same from the average of the four verticals (y-flag). If a pixel’s x-flag is 5σ larger than the other pixels in the column and its y-flag 5σ larger than the other pixels in the row, it is identified as a cosmic ray. The pipeline corrects the bad pixels and cosmic rays by excluding and

31 8

) 6 6

4 ×10 (× − e

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 λ[μm]

Figure 3.1: 1D spectrum of HD 209458 obtained from our analysis. replacing them with a 2D interpolation of the scientiﬁc images, based on the surrounding pixels values.

3.3 Spectrum extraction: geometric distortions and position shifts

To produce a 1D spectrum from a 2D spatially scanned spectrum on the detector, the pipeline sums the value of each pixel over the columns of the detector (Fig. 3.1). Due to the geometric distortions, caused by the tilt of the detector of about ∼ 22◦ from the optical axis, a photon trajectory isn’t a straight line along the y axis of the detector, but it suffers some dispersions, which are taken into account by the pipeline (section 3.4). Due to these dispersions, the wavelength associated to a detector column increase toward the upper edge of the column, creating a wavelength difference between the two edges of the column. Moreover, the G141 grism produces a spatially scanned spectrum that is inclined of about 0.5◦ with respect to the detector’s rows, affecting the wavelength calibration. When HST points a target, the FSG system is capable to maintain that target practically motionless; but after a spatial scan observation, it fail to reset the target in the exactly position it was before the scan. This effect produces horizontal and vertical shifts of the target on the detector, and it can introduce variations and systematics into the final spectrum. Iraclis is

32 250

200

150

100 o (pix) row

0 0 50 100 150 200 250 column (pix)

Figure 3.2: The dispersed spectrum on the detector and the photometric aperture where the 1D spectra are extracted, taken from our analysis of HD 209458 b capable to track this shifts, comparing the ﬁrst spatially scanned spectrum to the consecutive ones, calculating the shifts for each image, both horizontal and vertical. To calculate the scan length li the pipeline ﬁt a Gaussian function on the sum over the rows of the last non-destructive read.

3.4 Wavelength calibration

Due to the geometric distortions, the trajectory of a photon is dispersed along the y axis while the star is guided along the detector. The pipeline is able to monitoring this trajectory through a wavelength calibration process. First of all the position of the star (x∗, y∗) is determined; y∗ changes during a scan, so it has to be calculate in each images, while x∗, that can be considered constant in each images, can be calculated from the undispersed image, trough the formula: ∗ x = x0 + (507 − 0.5L) + ∆xoff + ∆xref (3.3) where x0 is the results by fitting a 2D Gaussian function to the undispersed image, 507-0.5L gives the absolute position on the full detector array (in fact 507 is the center of the full detector array, subtracted the reference pixels), ∆xoff is the difference in the centroid offsets between the filter used for direct image and the F140W filter (all the calibration coefficients have been calculated relative to the direct images taken with the F140W), ∆xref

33 is the diﬀerence in the chip reference pixels, the origin of the target system coordinates, between the WFC3 aperture used for the direct image and the aperture used for the dispersed image. For any subsequent scan after the ﬁrst, the horizontal position of the star is:

∗ ∗ xi = x1 + ∆xi. (3.4)

In the staring mode, the trace of a spectrum on the detector is:

∗ ∗ y − y = at(x − x ) + bt. (3.5)

In the spatial scanning mode, the star is trailed across the vertical axis of the detector, and due the geometric distortions the photon is dispersed; so the positions of the dispersed photons (xλ, yλ along the main trace of the spectrum, are calculated through the formulas:

∗ atbt λ − bw −1 xλ = x − 2 + cos[tan (at)] (3.6) 1 + at aw

∗ ∗ yλ = at(xλ − x ) + bt + y (3.7) where at, bt, aw, bw are calibration coefficients (for details on these formulas see Tsiaras et al. (2016b)). Assuming x∗ to be constant, y∗ varying uniformly on the vertical scan, λ varying on the sensitive curve of the G141 filter (1 − 1.8Å), a grid points with (λ, xλ, yλ) values, is created trough the eq. 3.6-3.7. Finally, a dispersed photon trajectory function is fitted to this grid:

c1 s1 yλ = ( + c3) + ( + s3)xλ (3.8) c2 + λ s2 + λ that represent the straight line on the detector on which the dispersed photon move during the scan. The trajectories of the dispersed photons are used to extract 1D spectra: in fact each spectra is extracted from apertures of quadrangular shapes, calculated for each wavelength bin (λ1 − λ2). The left and right edges of the apertures are taken from the eq. 3.8 for λ = λ1 and λ = λ2, while the ∗ upper and lower edges are given from the eq. 3.7 for y = y1 + ∆yi and ∗ y = Y1 +∆yi +li +y2, where y1 and y2 correspond usually to 20 pixels above and below the spatially scanned spectrum, and the value of the pixels inside each quadrangular aperture is summed to produce 1D spectrum.

34 3.5 Fitting the white light curve

After the extraction of the 1D spectra from all frames, the pipeline started to produce the white light curve. The pipeline ﬁt a transit model F (t), dividing the raw light curve by a normalisation factor nw and by a function for the instrumental systematics R(t). In fact, IR detector of WFC3 produce two type of instrumental systematics dependent from the time: a "short-term ramp", for each HST orbit, that has an exponential behavior, and a "long- term ramp", on each visit, that has a linear one:

rb2(t−t0) R(t) = (1 − ra(t − T0))(1 − rb1e ) (3.9) where t is the time, T0 is the mid-transit time, t0 is the time when each orbit starts, ra is the slope of the linear, long-term ramp and (rb1, rb2), are the coeﬃcients of the exponential short-term ramp. The transit model F (t) is calculated taken into account the orbital parameters and the limb-darkening coeﬃcients an, that can be calculated automatically from the pipeline in a linear, quadratic, square-root, or non-linear model. The non-linear method is based on the Claret formula (Claret, 2000) :

n=4 X 2 n/4 I(an, r) = 1 − an(1 − (1 − r ) ). (3.10) n=1 3.6 Fitting the spectral light curves

The wavelength bins (channels), that define the photometric apertures (section 3.4), are chosen in way that the total flux is equally distributed in each channel, maintaining a constant S/N ratio, and avoid to splitting the spectrum where the stellar spectrum has strong variations. Also here is possible to calculate automatically the limb darkening coefficients for each spectral light curves (i.e., for each wavelength bin). Each spectral light curves is fitted in a way similar to the white one, dividing a wavelength dependent normalisation factor nλ and a wavelength dependent instrumental systematics function R(t, λ) to the raw fluxes and fitting for a wavelength dependent transit model F (t, λ). Finally, the depths calculated from each fitted spectral light curves are plotted together in function of the mean wavelength of the bins, to produce the transmission spectrum of the planet.

35 Figure 3.3: Artistic concept of L 98-59 planetary system with comparison to Earth and Mars. CREDIT: www.nasa.gov.

3.7 Dataset

The first goal is to use the pipeline described above to replicate some of the studies known from the literature and then to obtain the transmission spectrum for an Earth-like planet, that hasn’t studied before in transit spectroscopy observations. Our dataset contains four hot Jupiters, where a comparison with the literature is possible, and an Earth-like planet, that has never studied before. The first hot Jupiter is HD 209458 b, a gas giant also nicknamed ’Osiris’. Osiris is orbiting the star HD 209458, a Sun-like star, with a semi-major axis of only 0.047 AU; for this reason, this planet belongs to the category of ’chtonian planets’, because it is losing its atmosphere due to the proxim- ity to its star. According to the literature, in the transmission spectrum of this planet there’s the characteristic feature of the water around 1.4µm with some flatness caused by a probably high altitude clouds deck (Tsiaras et al., 2016b). The second hot-Jupiter is WASP-121 b, an ultra-hot gas giant orbiting the star WASP-121, with a Teq ∼ 2400K, a mass of ∼ 1.183MJ and radius of ∼ 1.865RJ . According to the literature, the transmission spectrum of this planet has the characteristic water feature at 1.4µm, many absorption features around 1.1 − 1.3µm for the presence of F eH and the probable presence of T iO/V O (Evans et al.,, 2016). The third and fourth hot Jupiters are WASP-62 b and WASP-79 b, two gas giants orbiting the stars WASP-62 and WASP-79, respectively. They have, respectively, masses of ∼ 0.58MJ and ∼ 0.85MJ , and radii of ∼ 1.34RJ and ∼ 1.53RJ . According to the literature, both transmission spectra present the water feature at 1.4µm and absorption features of F eH around 1.3µm (Skaf et al.,, 2020).

36 The last planet is L 98-58 b, an Earth-like planet orbiting the star L 98-59. The planet b is the smallest and the inner planet of the system, where the host star L 98-59, is a nearby (10.6pc), bright (H = 7.4) and quite M3 dwarf. This planetary system, discovered in 2019 (Kostov et al., 2019), contains three Earth-like planets, L 98-59 b-c-d, with radii of 0.80, 1.35, 1.57REarth, a period of 2.25, 3.69, 7.45days and masses of < 1.01, 2.42, 2.31MEarth (Cloutier et al.,, 2019), respectively. With insolation values spanning from 4-21 times that of Earth, all the planets are placed in the Venus-zone of the host star, making them not habitable. Due to the nearness to the host star and low surface gravity, the inner planet L 98-59 b probably didn’t retain an H2 dominated primary atmosphere. For this reason, a H2O dominated atmosphere has been proposed, due to the higher mean molecular weight that provides a much more resilient atmosphere against to the escaping process, with an expected signal for H2O of 88ppm (ID: 15856, PI: Barclay Thomas).

3.7.1 HD 209458 b The analysis started with downloading the spatially scanned spectroscopic images of the target (Proposal ID:12181, PI:Drake Deming) from the MAST Archive, all in the RAW format, except one, the undispersed image taken with the F139N ﬁlter, in the ﬂt format, which the pipeline needs for the calibration purposes. The images are obtained with a single visit of the

Figure 3.4: HD 209458 b: The normalized raw white light curve (top), white light curve divided by the best ﬁt model for the systematics R(t) (middle) and the Residuals from the ﬁtted white light curve (bottom).

37 target, containing six HST orbit, using the IR channel of the WFC3, the G141 grism for the dispersed images and a scan rate of 0.9arcsecs−1/7.44 pixs−1. The first HST orbit was discarded, a common process in transmission spectrum data analysis, due to the high systematics that effects it. Each image consists of five non destructive reads with a size of 256x256pixels in the SPARS10 mode with a total scan length li ∼ 170pixels. The parameters file has been set with the values in the table 3.1 and the limb darkening coefficients to default-Claret mode. Finally, we obtained the white light curve (Fig.3.4) and the transmission spectrum (Fig.3.5), compared to those obtained by the author of the pipeline and the principal investigator of the observation (Deming et al.,, 2013); the photometric aperture is also indicated in fig.3.2.

Figure 3.5: Transmission spectrum of HD209458 b, with comparison to which obtained by Tsiaras et al. (2016b) and Deming et al. (2013).

3.7.2 WASP-121 b The analysis started with downloading the spatially scanned spectroscopic images in the raw format from the MAST archive (ID: 14468, PI: Evans), obtained with the G141 grism, and the undispersed image in the flt format obtained with the F130N filter. A single visit of the target contains 5 HST orbits, and also here the first of them was discarded due to the high systematics that affect it. Each images consists of fifteen non-destructive reads with a size of 256X256 pixels, in the SPARS10 mode, with a total exposure

38 Figure 3.6: WASP-121 b: The normalized raw white light curve (top), white light curve divided by the best fit model for the systematics R(t) (middle) and the Residuals from the fitted white light curve (bottom). time of about ∼ 103s, a scan rate of 0.12arcsecs−1/0.88pixs−1 and a total scan length li ∼ 100pixels. The parameters file was set with the values on table 3.1 and the limb darkening coefficients to default-Claret mode. Finally we obtained the white light curve (figure 3.6) and the transmission spectrum (figure 3.7), with comparison to which obtained by Evans et al. (2016).

Figure 3.7: Transmission spectrum of WASP- 121 b with comparison to which obtained by Evans et al. (2016).

39 HD 209458 b WASP-121 b Stellar Parameters

Teff (K) 6065 ± 50 6460 ± 140 [F e/H] 0.00 ± 0.05 4.242 ± 0.09 +0.080 M∗(M ) 1.119 ± 0.033 1.353−0.079 R∗(R ) 1.155 ± 0.016 1.458 ± 0.030 +0.011 log(g) 4.361 ± 0.008 4.242−0.012 Planetary Parameters

Teq(K) 1449 ± 12 2358 ± 52 +0.064 Mp(MJ ) 0.685 ± 0.015 1.183−0.062 RP (RJ ) 1.359 ± 0.019 1.865 ± 0.044 +0.00049 a(AU) 0.04707 ± 0.00047 0.02544+0.00050 Transit Parameters

T0(HJD) 2452826.628521 ± 0.000087 2456635.70832 ± 0.00011 P eriod(days) 3.52474859 ± 0.00000038 1.27492550 ± 0.00000023 Ttransit(minute) 183.9 ± 1.1 173.22 ± 0.42 Rp 0.12086 ± 0.00010 0.12109+0.00047 R∗ −0.00048 a 8.76 ± 0.04 3.754+0.023 R∗ −0.028 i(deg) 86.71 ± 0.05 86.6 ± 0.6

Table 3.1: HD 209458 b and WASP-121 b systems informations. The values for HD 209458 b are taken from Tsiaras et al. (2016a) and those for WASP- 121 b from Evans et al. (2016) and Nasa’s exoplanet archive.

3.7.3 WASP-62 b and WASP-79 b The analysis started with downloading the spatially spectroscopic images of the target in the raw format from the MAST archive (ID: 14676, PI: David Sing), obtained with the G141 grism of the IR Channel of WFC3, and the undispersed image obtained with the F139N filter in the flt format. Each image consists of eight non-destructive reads, with a size of 512x512 pixels, a total scan length li ∼ 150pixels and a total exposure time of ∼ 138s. The parameters file was set with the stellar-planet parameters of table 3.2 and the limb-darkening coefficients to default-Claret mode. Finally we obtained the white light curves (figures 3.8 - 3.9 ) and the transmission spectra with comparison to that obtained by Skaf et al. (2020) (figures 3.10 - 3.11).

40 Figure 3.8: WASP- 62 b: The normalized raw white light curve (top), normalized raw white light curve divided by the best ﬁt model for the systematics R(t) (middle) and the Residuals from the ﬁtted white light curve (bottom)

Figure 3.9: WASP- 79 b: The normalized raw white light curve (top), normalized raw white light curve divided by the best ﬁt model for the systematics R(t) (middle) and the Residuals from the ﬁtted white light curve (bottom)

41 Figure 3.10: Transmission spectrum of WASP-62 b with comparison to which obtained by Skaf et al. (2020).

Figure 3.11: Transmission spectrum of WASP-79 b with comparison to which obtained by Skaf et al. (2020).

42 WASP-62 b WASP-79 b Stellar Parameters

Teff (K) 6230 ± 80 6600 ± 100 [F e/H] 0.04 0.03 M∗(M ) 1.11 ± 0.25 1.43 ± 0.43 R∗(R ) 1.23 ± 0.08 1.60 ± 0.14 log(g) 4.45 ± 0.10 4.20 ± 0.15 Planetary Parameters

Teq(K) 1475.3 1716.2 Mp(MJ ) 0.52 ± 0.008 0.85 ± 0.18 RP (RJ ) 1.32 ± 0.008 1.67 ± 0.15 a(AU) 0.0571 ± 0.0005 0.0519 ± 0.0008 Transit Parameters

T0(HJD) 2455767.1533 ± 0.0005 2456215.4556 ± 0.0005 P eriod(days) 4.411950 ± 0.000003 3.662380 ± 0.000005 Ttransit(hours) 0.866 ± 0.005 1.02 ± 0.00 Rp 0.1091+0.0038 0.09609+0.0023 R∗ −0.0023 −0.0027 a 9.5253 6.069 R∗ +0.4 i(deg) 88.5−0.7 86.1 ± 0.2

Table 3.2: WASP-62 b and WASP-79 b systems informations. All the values are taken from Skaf et al. (2020) and Nasa’s exoplanet archive.

3.8 Transmission spectrum of L 98-59 b

The analysis started with downloading the spatially scanned images in the raw format, obtained with the G141 grism of the IR channel of the WFC3, from the MAST archive (ID:15856, PI: Barclay Thomas), with the undispersed image in the flt format, obtained with the F130N filter. Each image consists of five non-destructive reads with a size of 512x512pixels, a total exposure time of about ∼ 69.61676s, a total scan length li ∼ 290pixels and a scan rate of about ∼ 4, 2pixels−1/0.56arcsecs−1. Both direction scans, forward (black points) and reverse (red points), have been used. The parameters file was set with the values in table 3.3 and the limb darkening coefficients were set to the default-Claret mode. Finally, we obtained the fitted white light curve (figure 3.12) and the transmission spectrum (Fig.3.13). An up- down stream correction has been set in the parameters file on the light curves fitting, due to the effect of coupling equal or different scan/reading direction

43 (Tsiaras et al., 2016a).

Figure 3.12: L 98-59 b: The normalized raw white light curve (top), normalized raw white light curve divided by the best ﬁt model for the systematics R(t) (middle) and the Residuals from the ﬁtted white light curve (bottom).

Figure 3.13: L 98-59 b transmission spectrum

44 L 98-59 b Stellar Parameters

Teff (K) 3412 ± 49 [F e/H] −0.5 ± 0.5 M∗(M ) 0.313 ± 0.014 R∗(R ) 0.312 ± 0.014 log(g) 4.94 ± 0.06 Planetary Parameters

Teq(K) 610 ± 13 Mp(ME) < 1.01 RP (RE) 0.80 ± 0.05 a(AU) 0.0233 ± 0.0017 Transit Parameters +0.0006 T0(HJD) 2458366.1701−0.0007 P eriod(days) 2.25314 ± 0.00002 +10.2 Ttransit(minute) 61.2−7.8 Rp 0.0234+0.0009 R∗ −0.0008 a 16.2+0.08 R∗ −0.1 i(deg) 88.7+0.8−0.7

Table 3.3: L 98-59 b System information. All the values are taken from Kostov et al. (2019) and Nasa’s Exoplanet Archive.

3.9 Conclusions

We have analyzed a small sample of planets, constituted by four hot Jupiters and an Earth-like planets. According to the obtained transmission spectra of the hot Jupiters, is evident that this class of planets is dominated by H2O rich atmosphere, due to the presence of the strong feature on the spectrum around 1.4µm. Some of them present flatness in their spectra, for example HD 209458 b around 1.2 − 1.3µm, whose reason may be the presence of high altitude clouds-hazes. For WASP- 121 b we can see the features around 1.2−1.3µm due to the probable presence of F eH, T iO and V iO. For WASP- 62 b and WASP- 79 b we can see a feature around 1.3µm due the presence of F eH, even if the wavelength transit depth obtained in this thesis are slightly different from the author of the observations, maybe for a different fitted model for the spectral light curves, that provides different transit depths. The spectra of the four hot Jupiters obtained in this thesis are consistent

45 with those available in literature. By the presented analysis, the difference between obtaining the transmission spectrum from a gas giant planet to respect of an Earth-like planet is evident. In the case of HD 209458b , we found a signal (i.e. the difference between the depth of the white light curve and the depth of the spectral light curve) of ∼ 130pm around 1.4µm, that represents ∼ 0.8% of the original transit depth and in the case of WASP-121b of ∼ 110pm at the same wavelength. Similar results were obtained for WASP-62 b and WASP-79 b. In the case of L 98-59 b, it can’t be appreciate significant differences between the depth of the white light curve and the spectral one, furthermore on the latter there are big uncertainty bars, that in the worst case reach a value of ∼ 90ppm on the fourth bin, with a relative uncertainty of ∼ 16%. For this reason we found a transmission spectrum almost flat. The reasons why we found a flat spectrum on L 98-59b could be:

• The S/N ratio is too small. In fact, because of the diﬃculty for HST for the observations of Earth-like planets, for their small dimensions and their great distances (section 1.5), the signal is too low compared to noise. This eﬀect is also probed by the big uncertainties in the data point, mainly due to photon noise present in the intrinsic features of the CCD detector.

• The planet has no atmosphere. As described in Chapter 2, due to the low expected mass of ∼ 0.3MEarth and hence low surface gravity of this planet, coupled with the activity of the near host star, L 98-59 b wasn’t able to retain an atmosphere, just like Mercury in our Solar system.

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48 Ringraziamenti

Vorrei dedicare questo spazio alle diverse persone che hanno contribuito, chi in un modo, chi nell’altro, allo sviluppo del mio lavoro di tesi, senza di voi non sarebbe nemmeno esistito. I miei ringraziamenti vanno: alla Dr. Elisa Quintana, per avermi accolto nella crescente collaborazione fra il GSFC della NASA ed il team di esopianeti dell’Università di Napoli Fed- erico II ed al prof. G. Covone, per gli indispensabili consigli e le conoscenze trasmesse durante tutto il percorso di stesura della tesi, ma soprattutto per la possibilità datami di confrontarmi con scienziati di fama internazionale; al mio collega ed amico Luca, per la tua instancabile pazienza, la tua reperi- bilità H/24 ogni volta che avevo un dubbio o un problema, sei stato una grande fonte di ispirazione per me; ai miei ex colleghi ed amici alle Poste, grazie ai quali sono diventato più responsabile, ai miei amici "musici" Andrea e Roberta, siete stati come dei secondi genitori per me, ed al mio amico Pasquale, per le ore passate insieme in musica, che hanno aiutato a calmare i miei momenti di stress, sei davvero una brava persona; a tutti i miei amici per le grandi serate passate insieme, senza di voi avrei sicuramente concluso prima il mio percorso di studi, siete un ottima scusa per giustiﬁcare il mio fuori corso! ; a mia sorella Roberta, senza di te non sarei nemmeno sopravvissuto in casa da solo nel periodo di lockdown, sei stata come una migliore amica per me, ed a mio padre, che attraverso la gentilezza che ti contraddistingue, da dietro le quinte sei stato capace di non farmi mancare mai nulla, sei un uomo di altri tempi; alla mia ragazza Luisa, in poche parole mi sento di dirti quanto sei speciale: sei stata la persona che più di tutte mi ha dovuto sopportare nei momenti di sclero e di nervosismo, ma nonostante ciò sei stata sempre presente nel risoll- evarmi con la dolcezza che ti caratterizza. Mi hai sempre spronato a non mollare mai e a dare il meglio di me, soprattutto perchè non vedevo l’ora di raccontarti ciò che di nuovo imparavo per vedere gli occhietti curiosi che fai quando ti parlo di astronomia. Con il tuo incredibile essere ambiziosa, hai saputo indirizzarmi e guidarmi in modo sapiente, come un faro durante una tempesta: è raro avere una persona come te vicino, ti amo, non cambiare mai. Mamma, che dire, senza di te non esisterei nemmeno. Non dimenticherò mai la tua faccia commossa nell’avermi visto dopo tre mesi di assenza, ti ho sentita vicino anche se non eri a casa e questo mi ha dato ancora di più la forza di andare avanti per darti una piccola soddisfazione. Questa tesi è completamente dedicata a te, grazie di esistere.